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University of Southern California Dissertations and Theses
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The role of the environment around the chromophore in controlling the photophysics of fluorescent proteins
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The role of the environment around the chromophore in controlling the photophysics of fluorescent proteins
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THE ROLE OF THE ENVIRONMENT AROUND THE CHROMOPHORE IN CONTROLLING THE PHOTOPHYSICS OF FLUORESCENT PROTEINS by Tirthendu Sen A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) August 2021 Copyright 2021 Tirthendu Sen Acknowledgements Graduate school of USC has been a quite learning experience for me since Fall 2016. This will remain as the most defining and fulfilling chapter of my career and life. I was lucky to have Professor Anna Krylov as my advisor. Her invaluable advice and encouragement helped me to understand and appreciate theoretical and computational chemistry. During the lab rota- tion, she exposed me to various directions that were pursued at the iOpenShell lab at that time. After considering different options I choose to work on excited-state properties of fluorescent proteins. Prof. Krylov is not only a great scientist but also an inspiration for novices like me at the beginning of their scientific research careers. She encouraged me to read, test, and discuss extensively, however crazy idea it might have been. One of her best qualities is the way she gradually integrates her students into the scientific community. I have attended 9 conferences and 1 workshop during my PhD, which allowed me to showcase my work as well as learn from others. All helped me to grow professionally. I cannot appreciate her contributions enough for gradually shaping both my scientific thinking and computational skills, which will stay with me for rest of my life. ii I feel lucky to be a part of the Department of Chemistry of USC because of the great sci- entific environment it provides. I would like to thank Prof. Chi Mak, Prof. Sri Narayan, Prof. Moh El-Naggar, and Prof. Jahan Dawlaty for being on the committee. I appreciate Prof. Chi Mak’s encouragement to to dig deep into problems. I also thank Prof. Oleg Prezdo and Prof. Alex Benderskii for teaching us concepts in statistical mechanics and spectroscopy. I would like to thank all my collaborators, Profs. Alexey Bogdanov, Konstantin Lukyanov, Alexander Nemukhin, Bella Grigorenko, Igor Polyakov, and Mikhail Baranov, as well as Prof. Yingying Ma, who worked with us for a brief period of time and returned to her university in China to continue her independent scientific career. I have learned a lot from senior group members in Prof. Krylov’s lab. Dr. Samer Gozem, Dr. Kaushik Nanda, Dr. Alexandre Barrozo, Dr. Wojciech Skomorowski welcomed me and made me feel comfortable in the group. I cannot thank enough Dr. Atanu Acharya who explained to me and taught me the basics of the project, which we started to work on during my first semester at USC. I would also like to thank all our current group members — Dr. Sven Kaehler, Dr. Maristella Alessio, Dr. Yongbin Kim, Madhubani Mukherjee, Goran Gludetti, Saikiran Kotaru, Ronit Sarangi, Pawel Wojcik, Sourav Dey, and Nayanthara Jayadev. Special thanks to Sahil Gulania for all wonderful shared memories and friendship that will endure in time to come. I am also deeply grateful to Dr. Dibyendu Mondal for his help when I first arrived to the United States. I treasure the time I spent with my roommates and friends with whom I was fortunate to share so many happy memories. Starting from Michael to Sayan, Tushar, Avik, Diganta, Prakarsh, iii we built new families with diverse backgrounds. I have to leave this place in the course of time with many precious memories. I would like to take this opportunity to acknowledge the support and encouragement that my parents showed over the years. Being a school teacher, my father encouraged me to make my own choices in pursuit of happiness. My mother shares the biggest credit to whatever I have achieved in life so far. Without their support, struggle, sacrifice I would not be able to do what I always wanted to do. List would not be complete without thanking my teachers from whom I have had the privilege to learn: Profs. Ananta Ghosh and Sukriti Samanta, my first chemistry teachers in undergraduate days, Prof. Naresh Patwari, my master’s advisor, Prof. Sourav Pal, who taught us the basics of electronic structure theory, and Prof. Sandip Kar who was source of constant encouragement at any stage when in doubt. iv Table of contents Acknowledgements ii List of tables ix List of figures xiv Abstract xxv Chapter 1: Introduction and overview 1 1.1 Green fluorescent proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fluorescent protein photocycle . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Excited-state lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Photoswitches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Chapter 1 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter 2: Methodology 17 2.1 Radiative lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 MD simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Protein structures and protonation states . . . . . . . . . . . . . . . . . . . . . 24 2.4 QM/MM optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 QM/MM protocols for excitation energy . . . . . . . . . . . . . . . . . . . . . 27 2.6 Nonradiative lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7 Free energies of different protonation states . . . . . . . . . . . . . . . . . . . 32 2.8 Chapter 2 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Chapter 3: Pyridinium Analogues of Green Fluorescent Protein Chromophore: Flu- orogenic Dyes with Large Solvent-Dependent Stokes Shift 38 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 Appendix A: Experimental details . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4.1 Appendix A1: Materials and methods . . . . . . . . . . . . . . . . . . 49 3.4.2 Appendix A2: Fluorescent imaging in cells . . . . . . . . . . . . . . . 51 v 3.5 Appendix B: Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 53 3.5.1 Appendix B1: Solvatochromic properties of compounds 1-3 . . . . . . 53 3.5.2 Appendix B2: Solvatochromic analysis of absorption and emission spec- tra of compounds 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . 53 3.5.3 Appendix B3: pH-titration of compound 2 . . . . . . . . . . . . . . . . 55 3.5.4 Appendix B4: 1 H and 13 C NMR spectra . . . . . . . . . . . . . . . . . 56 3.6 Appendix C: Theoretical methods and computational details . . . . . . . . . . 62 3.7 Appendix D: Computational results . . . . . . . . . . . . . . . . . . . . . . . . 63 3.7.1 Appendix D1: Excitation energies of 1, 2, and 3c in gas phase . . . . . 63 3.7.2 Appendix D2: Solvatochromic properties of molecule 1 . . . . . . . . . 65 3.7.3 Appendix D3: Solvatochromic properties of molecule 2 . . . . . . . . . 71 3.7.4 Appendix D4: Solvatochromic properties of molecule 3 . . . . . . . . . 74 3.7.5 Appendix D5: Analysis of ground- and excited-state structures of 1, 2, and 3c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.7.6 Appendix D6: Photoacidity/photobasicity of 1, 2, and 3c . . . . . . . . 77 3.7.7 Appendix D7: 2PA cross sections of 1 and 2 . . . . . . . . . . . . . . . 77 3.8 Chapter 3 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Chapter 4: Influence of the first chromophore-forming residue on photobleaching and oxidative photoconversion of EGFP and EYFP 83 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.1 Mutants general description (spectral characteristics) . . . . . . . . . . 86 4.2.2 Photostability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.3 Redding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2.4 Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2.5 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.4 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.4.1 Spectroscopy and fluorescence brightness evaluation . . . . . . . . . . 108 4.4.2 Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.4.3 Protein Expression and Purification . . . . . . . . . . . . . . . . . . . 109 4.4.4 Site-Directed Mutagenesis . . . . . . . . . . . . . . . . . . . . . . . . 110 4.4.5 Fluorescence lifetime imaging microscopy of the purified proteins upon single-photon excitation. . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.4.6 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.6 Appendix A: Absorbance and fluorescence data normalization . . . . . . . . . 114 4.7 Appendix B: Force field parameters for excited-state classical molecular dynam- ics simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.8 Appendix C: Excitation energies . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.9 Chapter 4 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 vi Chapter 5: Interplay between Locally Excited and Charge Transfer States Governs the Photoswitching Mechanism in the Fluorescent Protein Dreiklang 125 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2 Computational methods and protocols . . . . . . . . . . . . . . . . . . . . . . 130 5.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.3.1 Protonation states for the ON-state . . . . . . . . . . . . . . . . . . . . 134 5.3.2 Excited-state analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.3.3 Implications of the CT state and possible mechanism for photo-reaction 149 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.5 Appendix A: Definitions of protonation states . . . . . . . . . . . . . . . . . . 156 5.6 Appendix B: Computational details . . . . . . . . . . . . . . . . . . . . . . . . 158 5.7 Appendix C: Forcefield parameters for the neutral hydrated chromophore . . . 158 5.8 Appendix D: Structures of model systems . . . . . . . . . . . . . . . . . . . . 162 5.9 Appendix E: Analysis of excited states . . . . . . . . . . . . . . . . . . . . . . 170 5.10 Appenidx F: Structures of possible intermediates . . . . . . . . . . . . . . . . 180 5.11 Appendix G: Optimization and AIMD simulations: Additional results . . . . . 181 5.12 Chapter 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Chapter 6: BrUSLEE and his shadow: Two persistent excited-state populations within a GFP mutant 191 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 6.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.1 Structure analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.2 Time-resolved fluorescence . . . . . . . . . . . . . . . . . . . . . . . . 199 6.2.3 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.4 Appendix A: Computational details . . . . . . . . . . . . . . . . . . . . . . . . 209 6.4.1 Appendix A1: Model structures and ground-state dynamics . . . . . . . 209 6.4.2 Appendix A2: QM/MM setup for excited-state calculations . . . . . . . 211 6.4.3 Appendix A3: Molecular dynamics simulations on the excited-state sur- faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 6.4.4 Appendix A4: Ab initio molecular dynamics (AIMD) . . . . . . . . . . 215 6.4.5 Appendix A5: Calculation of free-energy difference between different protonation states of His148 . . . . . . . . . . . . . . . . . . . . . . . 215 6.4.6 Appendix A6: Calculation of radiative lifetimes and extinction coefficients218 6.5 Appendix B: Analysis of structures from equilibrium MD simulations . . . . . 219 6.6 Appendix C: F¨ orster energy transfer between tryptophane and chromophore . . 222 6.6.1 Appendix C1: Calculations of the dipole orientation factor from equi- librium MD simulations . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.7 Appendix D: Free-energy differences between different protonation states . . . 228 6.7.1 Appendix E: AIMD results . . . . . . . . . . . . . . . . . . . . . . . . 236 6.8 Appendix F: Calculations of radiative and radiationless lifetimes . . . . . . . . 238 vii 6.9 Chapter 6 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Chapter 7: Future Work 248 7.1 Understanding the photostability in EGFP mutants . . . . . . . . . . . . . . . . 248 7.2 Exploring the role of a triplet state in oxidative photochemistry in EGFP . . . . 250 7.3 Chapter 7 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 viii List of tables 3.1 Optical properties of 1, 2, and 3c in various solvents. . . . . . . . . . . . . . . 42 3.2 Kamlet-Taft’s parameters and absorption/emission maxima (in nm) and fluores- cence quantum yields (in %) of 1 and 2 in various solvents. . . . . . . . . . . . 55 3.3 Solvatochromic spectral parameters (in 10 3 /cm 1 ) of 1 and 2. . . . . . . . . . 55 3.4 Excitation energies of 1, 2, and 3c in gas phase. All energies are in eV; oscillator strength is given in parenthesis. aug-cc-pVDZ basis set. . . . . . . . . . . . . 65 3.5 Excitation energies of methylated analogues of 1, 2, and 3c in gas phase. All energies are in eV; oscillator strength is given in parenthesis.!B97X-D/aug-cc- pVDZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.6 Electronic properties of 1 in various solvents. Energies are in eV; dipole moments in debye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.7 Mulliken charges on nitrogen atoms in 1 (see Fig. 3.16 for atom numbering). . 67 3.8 Electronic properties of 2 in various solvents. Energies are in in eV , dipole moments in debye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.9 Mulliken charges on nitrogen atoms in 2 (see Fig. 3.16 for atom numbering). . 71 3.10 Electronic properties of 3c in various solvents. Energies are in in eV , dipole moments in debye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.11 Mulliken charges on nitrogen atoms in 3c (see Fig. 3.16 for atom numbering). 74 3.12 Key structural parameters of 1, 2, and 3c in S 0 and S 1 and changes in bondlengths (BL). All bondlength are in ˚ A. . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.13 Excitation energies, oscillator strength (f f ), and 2PA cross-section for degener- ate resonant photons ( 1 = 2 = 2~=! ex ), aug-cc-pVDZ. . . . . . . . . . . . 77 4.1 Fluorescent properties of EGFP, EYFP, and their mutants, EGFP-T65G and EYFP-G65T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2 Average number of hydrogen bonds (and standard deviation) formed within 6 ˚ Aaround the chromophore computed along the equilibrium trajectories. Dis- tance and angle cut off were set to 3.2 ˚ Aand 20 , respectively). Deviation of the chromophore from planarity (, in degrees) is also shown. . . . . . . . . . . . 99 ix 4.3 Theoretical estimates of radiative lifetime for different mutants. Computed excitation energies and oscillator strengths are also shown. QM/MM absorp- tion energies and oscillator strengths are averaged over 21 snapshots taken from ground-state equilibrium molecular dynamics simulations. fl ,rel values are rel- ative lifetimes calculated with respect to fl in EGFP. . . . . . . . . . . . . . . 100 4.4 Computed radiative and radiationless lifetimes of EGFP, EGFP-T65G, EYFP, EYFP-G65T, and EYFP+Cl (in parenthesis, the values relative to EGFP are shown) and estimated photophysical parameters. . . . . . . . . . . . . . . . . 107 4.5 Partial charges in Charmm27, and in the ground and excited states of the EGFP chromophore (!B97X-D/aug-cc-pVDZ). The last column shows adjusted par- tial charges used in excited-state molecular dynamics (see fig. 4.10). . . . . . . 117 4.6 Bond lengths in Charmm27 forcefield and computed with !B97X-D/aug-cc- pVDZ. The last column shows adjusted partial charges used in excited-state molecular dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.7 Bond angles in Charmm27 forcefield and computed with !B97X-D/aug-cc- pVDZ. The last column shows adjusted partial charges used in excited-state molecular dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.8 Parameterized force constant and periodicity (n) for torsional potentials for angles and. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.9 Computed excitation energy (eV), oscillator strength, and transition dipole moment (TDM, a.u.) at the ground-state optimized geometry of the isolated TYG and GYG chromophores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1 Excitation energies (eV) of the isolated chromophores (ON- and OFF-states, A and B forms) computed at the optimized geometries (!B97X-D/aug-cc-pVDZ). Oscillator strengths are shown in parenthesis a . . . . . . . . . . . . . . . . . . 141 5.2 Partial charges in the OFF-state. . . . . . . . . . . . . . . . . . . . . . . . . . 160 5.3 Optimized bond lengths (in ˚ A) involving key atoms. . . . . . . . . . . . . . . 160 5.4 Parameterization of the force constantk for bond lengths in kcal/mol/ ˚ A 2 . . . . 161 5.5 Optimized bond angles (in degrees) involving key atoms. . . . . . . . . . . . . 161 5.6 Parameterization of the force constantk for bond angles in kcal/mol/rad 2 . . . 161 5.7 Parameterization of the force constantk for dihedral angles; in degrees,k in kcal/mol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 5.8 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). The chromophore is neutral (A-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . 162 x 5.9 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). The chromophore is neutral (A-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . 163 5.10 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). Chromophore is anionic (B-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . 164 5.11 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). Chromophore is anionic (B-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . 165 5.12 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST3 (OFF-state). Chromophore is neutral. ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 166 5.13 Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST3 (OFF-state). Chromophore is neutral. ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. ?, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 167 5.14 Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the neutral chromophore in the ON-state. All energies are in eV; large QM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5.15 Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the anionic chromophore in the ON-state. All energies are in eV; large QM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 5.16 Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the OFF-form (neutral chromophore). All energies are in eV; large QM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 5.17 TD-DFT excitation energies (eV) of the two lowest states of protein-bound neu- tral chromophore in the ON-state with different basis sets and different size of QM region; oscillator strength is shown in parentheses. . . . . . . . . . . . . . 175 5.18 TD-DFT excitation energies (eV) of the two lowest states of protein-bound anionic chromophore in the ON-state; oscillator strength is shown in paren- theses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 xi 5.19 TD-DFT excitation energies (eV) of the two lowest states of protein-bound neu- tral chromophore in the OFF-state; oscillator strength is shown in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.20 Excitation energies (eV) of the two lowest states of protein-bound neutral chro- mophore in the ON-state; oscillator strength is shown in parentheses. Extended QM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 5.21 Excitation energies of the protein-bound anionic chromophore in the ON-state; oscillator strength is shown in parentheses. Extended QM. . . . . . . . . . . . 177 5.22 Excitation energies of the protein-bound neutral chromophore in the OFF-state; oscillator strength is shown in parentheses. Extended QM. . . . . . . . . . . . 178 5.23 Average excitation energies (eV) of the two lowest states of protein-bound neu- tral chromophore in the ON-state computed using structures from 21 MD snap- shots; oscillator strength is shown in parentheses. Large QM. . . . . . . . . . . 184 5.24 Average excitation energies (eV) of the two lowest states of protein-bound anionic chromophore in the ON-state computed using structures from 21 MD snapshots; oscillator strength is shown in parentheses. Large QM. . . . . . . . . . . . . . 184 5.25 Average excitation energies (eV) of the two lowest states of protein-bound hydrated chromophore in the OFF-state computed using structures from 21 MD snap- shots; oscillator strength is shown in parentheses. Large QM. . . . . . . . . . . 185 6.1 Lifetime distributions of EGFP and the mutants at 510 nm (2.43 eV). . . . . . 200 6.2 Activation energies (kcal/mol) for internal conversion of EGFP and its mutants. 201 6.3 Chromophore planarity and the number of hydrogen bonds around the chro- mophore. (Averaged over 400 snapshots from MD at 298 K, standard deviation is in parenthesis). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.4 Computed values of average lifetime (in ns), percentage population of each pro- tonation states, and fluorescent quantum yield. Experimental values are given in parenthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.5 Parameterized force constant and periodicity (n) for torsional potentials for angles and. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.6 EGFP. Comparison of the key distances in the crystal structure and in MD sim- ulations (T=298 K) considering 3 different protonation states for His148. . . . 219 6.7 T65G. Comparison of the key distances in the crystal structure and in MD sim- ulations (T=298 K) considering 3 different protonation states for His148. . . . 219 6.8 Duo. Comparison of the key distances in the crystal structure and in MD simu- lations (T=298 K) considering 3 different protonation states for His148. . . . . 221 6.9 BrUSLEE (Trio). Comparison of the key distances in the crystal structure and in MD simulations (T=298 K) considering 3 different protonation states for His148. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.10 Summary of the FRET experiments. . . . . . . . . . . . . . . . . . . . . . . . 224 6.11 Computed average distance (standard deviation in parenthesis), angle between average transition dipoles, and 2 . His148 is in the HSD state. . . . . . . . . . 226 xii 6.12 Gibbs free-energy differences (in eV) and relative populations of different pro- tonation states at room temperature (298 K) and at 100 K (numbers in parenthe- sis). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 6.13 Free-energy differences (in eV) between different protonation states at room temperature (298 K) and at 100 K (numbers in parenthesis), difference in enthalpy (H in eV) and entropy (S in eVK 1 ). . . . . . . . . . . . . . . . . . . . . 231 6.14 AIMD simulation in 1st excited state for 3 ns showing the twist around in 11 snapshots for EGFP and BrUSLEE. Time of the twist of the same snapshot in excited-state MD is shown in parenthesis (in ns). . . . . . . . . . . . . . . . . 236 6.15 Theoretical estimates of radiative lifetime for different mutants. Computed exci- tation energies and oscillator strengths are also shown. QM/MM absorption energies and oscillator strengths are averaged over 400 snapshots taken from ground-state equilibrium MD simulations. r ,rel values are relative lifetimes calculated with respect to r in EGFP-HSD. . . . . . . . . . . . . . . . . . . . 239 6.16 Computed non-radiative decay times (ns), populations of different protonation state of His148, and % of non-planar chromophores at the end of the excited- state simulation (3 ns). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 6.17 Computed values of average lifetime (in ns), percentage population of each pro- tonation states, and fluorescent quantum yield. Experimental values are given in parenthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 6.18 Computed and experimental values of photophysical parameters EGFP, T65G, Duo, and Trio (in parenthesis, the experimental values are shown). . . . . . . . 243 7.1 Computed and experimental values of relative photobleaching rate (relative to EGFP). Experimental values are in PBS+Ox. (Reproduced from Chapter 4). . . 249 xiii List of figures 1.1 Color tuning in fluorescent proteins: Different chemical structures of the chro- mophore lead to different colors. Main types of chromophore structures are shown together with corresponding excitation (upper bar) and emission (bot- tom bar) wavelengths designated by arrows. The size of-conjugated system is particularly important for determining the color: more extensive conjuga- tion leads to red-shifted absorption (compare, for example, blue, green, and red chromophores). Changes in protonation states of the chromophore also affect the energy gap between the ground and the excited states. Excited-state deprotonation of the chromophore is one of the mechanisms of achieving large Stokes shifts. Absorption/emission can be red shifted by-stacking of the chro- mophore with other aromatic groups (e.g., tyrosine), as in YFP (not shown). Specific interactions with nearby residues also affect the hue (for example, addi- tional red shift in mPlum fluorescence is attributed to a hydrogen bond formed by acylimines oxygen). [Reproduced from Ref. 7]. . . . . . . . . . . . . . . . 2 1.2 Left: A typical structure of a fluorescent protein represented by EGFP. Right: The chromophores in EGFP/GFP-S65T and EYFP/EGFP-T65G (HBDI). Repro- duced from Refs. 7 and 40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Excited-state processes in fluorescent proteins. The main relaxation channel is fluorescence. Radiationless relaxation, a process in which the chromophore relaxes to the ground state by dissipating electronic energy into heat, reduces quantum yield of fluorescence. Other competing processes, such as transition to a triplet state via inter-system crossing (not shown), excited-state chemistry and electron transfer, alter the chemical identity of the chromophore thus lead- ing to temporary or permanent loss of fluorescence (blinking and bleaching) or changing its color (photoconversion). Reproduced from Ref. 7. . . . . . . . . 7 1.4 Structural analysis of EGFP showing electron density overlaid on the chro- mophore and the neighbouring residues. The tridentate density around Glu222 clearly indicates alternate conformations of the side chain represented in orange and cyan. hydrogen bonds for each conformation are correspondingly shown in orange or cyan. Glu222 is either hydrogen bonded to Ser205 or to Thr65, but not to both residues at the same time. Reproduced from Ref. 30. . . . . . . . . 8 xiv 1.5 Left: The anionic GFP chromophore model p-hydroxybenzylidene-imidazolinone (HBI) in three different geometries: the planar fluorescent state (FS) minimum ( = = 0 ), the TwP geometry twisted 90 around the phenol bridge bond and the TwI geometry twisted 90 around the imidazolinone bridge bond. Right: Bridge bond torsions ( and) from an excited-state MD simulation of the sol- vated GFP with the anionic chromophore. The inset zooms on the time window where the twist occurs. Reproduced from Ref. 48. . . . . . . . . . . . . . . 10 2.1 Residues included in the extended QM part in the excited-state calculations of ON state of Dreiklang. TYR203 is Y203, GLUP222 is E222, ARG96 is R96. Only the chromophore was kept in small QM region. In the medium QM region ARG96, CRO, HIS145, SER205. TYR203, GLUP222, W were included in the QM region. In extended QM region LEU64, and V AL68 were added. Repro- duced from Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2 Definition of the two torsional angles and describing chromophore twisting. describes twist around the single bond (phenolate flip) and describes twist around the double bond (imidozalinone flip). Reproduced from Chapter 6. . . . 29 2.3 Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Chapter 4. . . . . . . . 31 2.4 The quantum mechanical thermodynamic cycle perturbation (QTCP) method employing a thermodynamic cycle to calculate QM/MM free-energy changes ? . 33 3.1 HBDI (core of the GFP chromophore) and analogous pyridine chromophores 1-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Optical properties of compounds 1, 2, and 3c. Top: Absorption and emission spectra in EtOAc. Bottom: FQY in various solvents. . . . . . . . . . . . . . . 41 3.3 NTOs for the two lowest excited states of 1 in gas phase. . . . . . . . . . . . . 43 3.4 Computed Stokes shifts versus the change in permanent dipole moment ( = (S 1 )(S 0 )). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.5 Confocal microscopy of the Hela-Kyoto and NIH 3T3 cells labeled with ER- Tracker Red (0.5 mkM) and 2 (5.0 mkM). 559 nm excitation and TRIC for ER-tracker Red and 405 nm excitation and 450-550 nm emission window for 2 with 60X magnification were used. Top: Labeled alive cells; scale 10 mkM. Bottom: Stained cells fixed with formaldehyde right after the fixation (A, B) and after the addition of an extra portion of compound 2 (C); scale 15 mkM. . . 45 xv 3.6 Bleaching behavior of Hela-Kyoto cells labeled with 2 and with ER-localized BFP-KDEL protein. Top: Fluorescence intensity of alive (A) and fixed (B) cells in a time-lapse fluorescence microscopy. Bottom: Fluorescent images of alive HeLa cells during the photobleaching. . . . . . . . . . . . . . . . . . . . . . . 47 3.7 Structures and properties of compounds 1-3. . . . . . . . . . . . . . . . . . . 49 3.8 Synthesis of compounds 1-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.9 From top to bottom: Fluorescence and absorption spectra of 1-3 in water, ethanol, acetonitrile, actetate, and dioxane. . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10 Left: pH-titration of compound 2. Right: Absorption spectra of 2 at different pH values. Neutral: abs =368 nm; Cation: abs =395 nm; pKa(Abs)=3.6. . . . . 56 3.11 Compound 1: 1 H NMR (800 MHz, DMSO-d 6 )=8.64 (d, J=5.9 Hz, 2 H, Ar), 8.08 (d, J=6.11 Hz, 2 H, Ar), 6.93 (s, 1 H, Ar-CH), 3.11 (s, 3 H, CH 3 ), 2.39 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 ) = 15.5, 26.3, 121.0, 124.9, 140.82, 142.3, 150.0, 167.1, 169.5; HRMS (m/z) calc-d. C 11 H 12 N 3 O for [M +H] + 202.0975, found 202.0978. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.12 Compound 2: 1 H NMR (700 MHz, DMSO-d 6 )=8.68 (d, J=6.2 Hz, 2 H, Ar), 8.17 (d, J=5.9 Hz, 2 H, Ar), 7.98 (d, J=6.9 Hz, 2 H, Ar), 7.69 (t, J=7.3 Hz,1 H, Ar), 7.63 (t, J=7.5 Hz, 2 H, Ar), 7.15 (s, 1 H, Ar-CH), 3.29 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 ) = 28.8, 123.1, 125.1, 128.5, 128.8, 128.9, 132.0, 140.8, 142.2, 150.1, 165.1, 170.4; HRMS (m/z) calc-d. C 16 H 14 N 3 O for [M +H] + 264.1131, found 264.1135. . . . . . . . . . . . . . . . . . . . . . . 58 3.13 Compound 3a: 1 H NMR (300 MHz, DMSO-d 6 )=8.87 (d, J=6.6 Hz, 2 H, Ar), 8.73 (d, J=6.5 Hz, 2 H, Ar), 8.29 (d, J=15.8 Hz, 1 H, CH=CH), 7.89 - 7.96 (m, 2 H, Ar), 7.50 - 7.55 (m, 3 H, Ar), 7.36 (d, J=15.7 Hz, 1 H, CH=CH), 7.13 (s, 1 H, Ar-CH), 3.33 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 ) = 26.5, 113.7, 120.9, 125.1, 128.6, 128.9, 130.5, 134.8, 141.2, 142.0, 142.9, 150.0, 162.9, 169.8; HRMS (m/z) calc-d. C 18 H 16 N 3 O for [M +H] + 290.1288, found 290.1292. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.14 Compound 3b: 1 H NMR (300 MHz, DMSO-d 6 ) = 8.87 (d, J=6.8 Hz, 2 H, Ar), 8.78 (d, J=6.7 Hz, 2 H, Ar), 8.29 (d, J=15.5 Hz, 1 H, CH=CH), 7.91 (d, J=8.8 Hz, 2 H, Ar), 7.21 (d, J=15.6 Hz, 1 H, CH=CH), 7.07 - 7.11 (m, 3 H, Ar, Ar-CH), 3.86 (s, 3 H, CH 3 ), 3.32 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO- d 6 )=26.5, 55.4, 110.8, 114.5, 119.9, 125.0, 127.6, 130.6, 141.3, 142.1, 143.1, 150.0, 161.4, 163.2, 169.9; HRMS (m/z) calc-d. C 19 H 18 N 3 O 2 for [M +H] + 320.1394, found 320.1397. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.15 Compound 3c: 1 H NMR (700 MHz, DMSO-d 6 )=8.66 - 8.71 (m, 4 H, Ar), 8.20 (d, J=5.9 Hz, 2 H, Ar), 8.09 (d, J=15.8 Hz, 1 H, CH=CH), 7.86 (d, J=5.9 Hz, 2 H, Ar), 7.54 (d, J=15.8 Hz, 1 H, CH=CH), 7.07 (s, 1 H, Ar-CH), 3.31 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 )=26.4, 118.3, 121.9, 122.2, 124.9, 138.9, 140.8, 141.7, 142.5, 149.9, 150.2, 162.2, 169.5; HRMS (m/z) calc-d. C 17 H 15 N 4 O for [M +H] + 291.1240, found 291.1244. . . . . . . . . . . . . . . 61 3.16 Model systems representing compounds 1, 2, and 3c. . . . . . . . . . . . . . . 62 xvi 3.17 Excited states and NTOs for 1 in (a) gas phase and (b) water. Left and right panels show the states at the S 0 and S 1 optimized geometries, respectively. . . 64 3.18 NTOs for the S 0 !S 1 transition in 2 (left) and 3c (right) in the gas phase. . . . 65 3.19 Ground- and excited-state structures of 1 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.20 Variation in absorption (top) and emission (middle) energies and Stokes shifts (bottom) of 1 in different solvents (left) and correlation between theory and experiment (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.21 Top: Absorption (left) and emission energies (right) in different solvents versus transition dipole moment for 1. Bottom: Stokes shift (left) and FQY (right) in different solvents versus transition dipole moment. . . . . . . . . . . . . . . . 70 3.22 Ground- and excited-state structures of 2 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.23 Variations in absorption (top) and emission (middle) energies and Stokes shifts (bottom) of 2 in different solvents (left) and correlation between theory and experiment (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.24 Top: Absorption (left) and emission energies (right) in different solvents versus transition dipole moment for 2. Bottom: Stokes shift (left) and FQY (right) in different solvents versus transition dipole moment. . . . . . . . . . . . . . . . 73 3.25 Ground- and excited-state structures of 3 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1 Absorption (A) and fluorescence (B) spectra of EGFP, EYFP, and mutants. In the fluorescence graph, dashed lines show fluorescence excitation, solid lines fluorescence emission. PB denotes phosphate buffer and PBS denotes phos- phate buffered saline containing sodium chloride (see text). . . . . . . . . . . . 87 4.2 Bleaching kinetics in the immobilized proteins EGFP, EYFP, and their mutants in vitro. (A) Photoconversion of EGFP and EGFP-T65G in PBS; (B) Photo- conversion of EGFP and EGFP-T65G in PBS in the presence of 0.2 mM potas- sium ferricyanide; (C) Photoconversion of EYFP and EYFP-G65T in PB and PBS (PBS contains potassium chloride); (D) Photoconversion of EYFP and EYFP-G65T in PB and PBS in the presence of 0.2 mM potassium ferricyanide. Green/yellow fluorescence intensities were background-subtracted and normal- ized to the maximum values. Standard deviation values (n = 1520 measurements in a representative experiment out of five independent experiments) are shown. 92 xvii 4.3 Redding kinetics in the EGFP, EYFP, and their mutants. (A) Appearance of red fluorescence in EGFP and EGFP-T65G. Non-normalized data for several mea- surements are shown. (B) Appearance of red fluorescence in EYFP and EYFP- G65T in PB and PBS (PBS contains potassium chloride). Averaged curves are shown. Red fluorescence intensities were background-subtracted and normal- ized to the maximum values. Standard deviation values (n = 1520 measurements in a representative experiment out of five independent experiments) are shown. (C) Appearance of red fluorescence in EYFP-G65T in PB and PBS (PBS con- tains potassium chloride). Non-normalized data for several measurements are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 Hydrogen-bond network around the chromophore (CRO) in EGFP (left) and EYFP (right). The network includes CRO:O-water314-SER205-GLU222-CRO:O (Thr65, in EGFP). Glu222 is protonated and His148 is neutral in EGFP (pro- tonated at deltaN atom). Also shown is -stacking of the chromophore and Tyr203 in EYFP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.5 Top: Structures of the model TYG (EGFP, YFP-G65T) (left) and GYG (YFP, EGFP-T65G) (right) chromophores. Torsional angles and are defined as CD-CG-CB-CA and CG-CB-CA-N, respectively. The difference between the two angles =- quantifies whether the chromophore is planar (=0) or not. Bottom: the QM/MM partitioning for EGFP (left) and EYFP (right). Blue color denotes the QM region and the black dotted lines denote the QM-MM boundary. Charges of red and green atoms were set to zero in the MM region. In EGFP- T65G, the chromophore is GYG and the neighboring residues are the same as in EGFP. Likewise, in EYFP-G65T, the chromophore is TYG and the neighboring residues are the same as in EYFP. . . . . . . . . . . . . . . . . . . . . . . . . 98 4.6 Oscillator strength for the S 0 -S 1 transition in the isolated TYG, GYG, and fluo- rinated GYG (GYG-F in which one -CH3 is replaced with -CF3) chromophores along torsional angle (all other degrees of freedom are relaxed) computed with !B97X-D/aug-cc-pVDZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.7 PES scans (relative energies) for the isolated GYG chromophore along the dihe- dral angles (left) and (right) in the ground (black) and electronically excited (red) states. All other degrees of freedom are frozen. The dots represent ab initio calculations (!B97X-D/aug-cc-pvDZ) and the solid lines are fits to the force- field torsional potential used in molecular dynamics simulations (see Chapter 2). In contrast to the isolated chromophores, the protein-bound excited chro- mophores can only undergo phenolate flip ( twist) because the imidozalinone ring is covalently bound to the protein backbone. . . . . . . . . . . . . . . . . 102 4.8 Left: Evolution of planar (A) population in excited-state molecular dynamics simulations of EGFP, EGFP-T65G, EYFP, EYFP-G65T, and EYFP+Cl . Right: Linear fit for ln[A]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.9 Correlation between theoretical and experimental apparent fluorescence life- times (left), FQY (middle), and the rate of bleaching (right). . . . . . . . . . . 107 xviii 4.10 EGFP chromophore with atom types consistent with CHARMM 27 forcefield notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.11 Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Ref. ?. . . . . . . . . . 118 4.12 Excited-state torsional potentials for (left) and (right) of the bare HBDI chromophore. Red curves: fit toabinitio calculations (from which the parame- ters were extracted). Pink and black curves: torsional potentials computed with the modified forcefield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.13 Distribution of oscillator strengths (!B97x-D/aug-cc-pVDZ) computed for 21 QM/MM snapshots from the ground-state molecular dynamics. . . . . . . . . 120 4.14 Distribution of excitation energ (!B97x-D/aug-cc-pVDZ) computed for 21 QM/MM snapshots from the ground-state molecular dynamics. . . . . . . . . . . . . . . 120 5.1 On-off photoconversion in Dreiklang is activated by photoexcitation of the neu- tral form of the chromophore in ON-state. The OFF-form can be turned on by photoexcitation at higher energy. . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2 Steady-state absorption spectra of the ON-state (black) and following irradiation (red) at 3.02 eV (410 nm) at pH 7.5. The spectra are from Ref. ?. The band maxima are at 3.01 eV and 2.43 eV in the ON-state and at 3.65 eV in the OFF- state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.3 Superimposed representations of the hydrogen-bond network around Dreiklang’s chromophore in the ON- and OFF-states. Color scheme: ON-state carbons, magenta; OFF-state carbons, gray; oxygen, red; nitrogen, blue. Important water molecules are shown as magenta (ON-state) and gray (OFF-state) spheres. Inset: hydrogen-bond network in EGFP.ReproducedfromRef. ?. . . . . . . . 128 5.4 Revised Dreiklang’s photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. After releasing the electron back to Tyr203, intermediate X undergoes nucleophilic attack by nearby water, forming the hydrated chromophore. . . . . . . . . . . . . . . . . . . . . . . . 130 xix 5.5 Defition of the QM subsystem. The residues numbering corresponds to the crystal structures (3ST3 and 3ST4). Left: Residues included in large QM in the QM/MM calculations of ON- (top) and OFF-states (bottom). Right: Residues included in extended QM in the excited-state calculations of ON- (top) and OFF-states (bottom). Small QM contains only the chromophore and medium QM contains the chromophore and Tyr203. The total charge of the small and medium QM is zero for the A-form (neutral chromophore) and -1 for the B-form (anionic chromophore). For large and extended QM, the total charge of the QM is +1 for the on-A (HSD-GLUP, HSE-GLUP, HSP-GLU), 0 for the on-A (HSD- GLU, HSE-GLU), 0 for the on-B (HSD-GLUP, HSE-GLUP, HSP-GLU), -1 for the on-B (HSD-GLU, HSE-GLU), +1 for the off-A (HSD-GLUP, HSE-GLUP, HSP-GLU), 0 for the off-B (HSD-GLU, HSE-GLU). See Fig. 5.16 in the SI for the definition of the protonation states. For on-A (HSE-GLUP) structure, large and extended QM comprised 113 and 118 atoms, respectively. . . . . . . . . . 135 5.6 Definitions of selected distances used to compare various structures for the ON-form: d1 = CRO:OH-HIS145:CE1, d2 = CRO:N2-GLU222:OE1, d3 = CRO:O2-ARG96:NH2, d4 = CRO:CE2-SER205:OG, d5 = CRO:OH-ASP146:O, d6 = CRO66:CG2-TYR203:CZ, d7 = CRO66:OH-TIP354:OH2, d8= CRO:N2- TIP242:O,d9= TYR203:OH-TIP242:OH2, d10= GLU222:OE2-TIP242:OH2, d11 = SER205:OG-TIP354:OH2, d12 = HIS145:ND1-TIP354:OH2, d13 = ASP146:O- TIP354:OH2, d14= GLU222:OE1-SER205:OG. . . . . . . . . . . . . . . . . 136 5.7 Definitions of selected distances used to compare various structures for the OFF-form: d1 = CRO:OH-HIS145:CE1, d2 = CRO:O1-GLU222:OE1, d3 = CRO:N2-GLU222:OE2, d4 = CRO:O2-ARG96:NH2, d5 = CRO:CE2-SER205:OG, d6 = CRO:OH-ASP146:O, d7 = CRO66:CG2-TYR203:CZ, d8 = CRO66:OH- TIP245:OH2, d9 = SER205:OG-TIP245:OH2, d10 = HIS145:ND1-TIP245:OH2, d11 = ASP146:O-TIP245:OH2, d12= GLU222:OE2-TIP287:OH2, d13= SER205:OG- TIP287:OH2, d14= GLU222:OE1-SER205:OG. . . . . . . . . . . . . . . . . 137 5.8 Key distances for ON-states: Comparison between crystal structure, average MD values, and QM/MM optimization. See Fig. 5.6 for definitions. . . . . . . 138 5.9 Key distances for OFF-states: Comparison between crystal structure, average MD values, and QM/MM optimizations. See Fig. 5.7 for definitions. Note that some MD values for d8, d9, and d14 are off the chart. . . . . . . . . . . . . . . 139 5.10 NTOs for the lowest bright states of the bare chromophores. Top left: neutral ON-state; top right: anionic ON-state; bottom left: neutral OFF-state; bottom right: anionic OFF-state.!B97X-D/aug-cc-pVDZ. . . . . . . . . . . . . . . . 140 5.11 NTOs for the two lowest excited states of the protein-bond chromophore (on-A form, HSE-GLUP protonation state). QM/MM/!B97X-D/aug-cc-pVDZ. . . . 143 5.12 Excitation energies for different model systems shown against the experimen- tal values. Top: TD-DFT/aug-cc-pVDZ; middle: SOS-CIS(D)/aug-cc-pVDZ; bottom: XMCQDPT2/aug-cc-pVDZ/cc-pVDZ. Extended QM + correction. . . 148 xx 5.13 Proposed reaction initiated by the population of the CT state. Solid orange arrows show proton transfer and dashed blue arrows show electron transfer. AIMD and excited-state optimization reveal that the steps leading to the forma- tion of X6-2/X7 are nearly barrierless and proceed on the scale of100-200 fs. The last two steps (shown by dashed arrows), back electron transfer from Chro to Tyr203, nucleophilic addition of OH to Chro, and reprotonation of Tyr203, are hypothesized. The structures of the possible intermediates are defined in Fig. 5.24 in the Appendix G. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.14 Left: Energies of the Kohn-Sham reference state (S 0 ) and the CT state along the AIMD trajectory on the CT potential energy surface. Right: Charges on the chromophore and Tyr203 in the Kohn-Sham reference state and the CT state (lowest TDDFT state). Labels X5, X6, and X7 denote points along the trajec- tories when structures resembling these intermediates are formed (see Fig. 5.24 in the Appendix F; X6-1 refers to HSE-GLU; X6-2 refers to HSE-GLUP2). . . 151 5.15 Definition of chromophore states. . . . . . . . . . . . . . . . . . . . . . . . . 156 5.16 Definition of protonation states of Glu222 and His145 in Dreiklang. GLUP can exist in two conformations: As shown or protonated on the other oxygen (GLUP2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.17 From left to right: proline, chromophore in off-state, threonine. . . . . . . . . 159 5.18 Key distances for ON-states: Comparison between crystal structure and QM/MM optimization. OPT1 and OPT2 denote two different protocols (see text). See Fig. 5 in the main text for definitions. . . . . . . . . . . . . . . . . . . . . . . 168 5.19 Key distances for OFF-states: Comparison between crystal structure, average MD values, and QM/MM optimizations. See Fig. 6 of the main text for defini- tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.20 Energy ordering (eV) of QM/MM (ONIOM) optimized structures (boxes mark the structures with the same number of atoms in QM). . . . . . . . . . . . . . 169 5.21 NTOs of the lowest excited states of the neutral form and different protonation states of His145 and Glu222; TD-DFT, extended QM. Left: CT state; right: LE state; top-to-bottom: HSD-GLU, HSD-GLUP, HSE-GLU, HSE-GLUP, HSP- GLU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 5.22 NTOs of the lowest excited states of the anionic form and different protonation states of His145 and Glu222; TD-DFT, extended QM. Left: LE state; right: CT state; top-to-bottom: HSD-GLU, HSD-GLUP, HSE-GLU, HSE-GLUP, HSP- GLUP. CT state is pushed to much higher energies and disappears in QM/MM calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 5.23 Excitation energies for different model systems shown against the experimen- tal values. Top: TD-DFT/aug-cc-pVDZ; middle: SOS-CIS(D)/aug-cc-pVDZ; bottom: XMCQDPT2/aug-cc-pVDZ/cc-pVDZ. Extended QM. . . . . . . . . . 179 xxi 5.24 Two possible initial steps for Dreiklang photoconversion. Ref. ? proposed that the photoconversion begins by ESPT (left), forming anionic chromophore, which undergoes further transformation. Following this route, one can consider structures X1-X4 as possible candidates for reaction intermediate X. We pro- pose an alternative mechanism via CT state (right). Following this route, one can consider structures X5-X8 as possible candidates for reaction intermediate X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 5.25 Energies of the Kohn-Sham reference state (S 0 ) and CT state along optimization path (on-A-HSE-GLUP structure). . . . . . . . . . . . . . . . . . . . . . . . . 181 5.26 Ground and excited state during the first two steps of the reaction in CT state (on-A-HSE-GLUP structure). Left: 1st step — proton abstraction by chro- mophore’s N from protonated Glu222. Right: 2nd step — proton transfer from Tyr203 to deprotonated Glu222. . . . . . . . . . . . . . . . . . . . . . . . . . 182 5.27 Analysis of the AIMD trajectory on the CT state (on-A-HSE-GLUP structure). 183 5.28 Energies of the Kohn-Sham reference state (S 0 ) and the LE state (2nd TD-DFT state) along the AIMD trajectory on the LE potential energy surface. . . . . . . 183 5.29 Relaxed energy profile on the ground state surface (starting from X7 interme- diate) along hydration reaction coordinate defined as W242:O-CRO:C1 dis- tance. Zero energy corresponds to the energy of the reference state of the structure at t=248 fs, roughly corresponding to X7. ONIOM, !B97X-D/aug- cc-pVDZ/CHARMM27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.1 Fluorescence quantum yield versus fluorescence lifetime for selected FPs. . . . 191 6.2 Structure of the chromophore in EGFP (left) and the 3 mutants studied in this Chapter (right). In EGFP, the chromophore is formed by the threonine-tyrosine- glycine (TYG) triad whereas in T65G mutants the chromophore is formed by the glycine-tyrosine-glycine (GYG) triad. The conjugated core of both chro- mophores is the same, but the TYG chromophore has additional electron-donating group. The twisting motion is described by dihedral angles (phenolate flip around the single bond) and (imidozalinone flip around the double bond); see Fig. 6.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 6.3 Superimposed crystal structures of EGFP (green) and BrUSLEE (orange), with the chromophore’s center of mass set at the origin. . . . . . . . . . . . . . . . 198 6.4 Top: Hydrogen-bond network around the chromophore in EGFP and Bottom: BrUSLEE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.5 Temperature dependence of fluorescence lifetimes in EGFP and the mutants. Fluorescence decay was measured at 510 nm under 470 nm excitation by 50 ps FWHM laser pulses. Color represents the logarithm of the amplitude of the corresponding component (Data courtsey to Bogdanovetal. . . . . . . . . . . 200 xxii 6.6 Definition of the key distances in EGFP. d1 = CRO66:CE1-PHE165:CE2; d2= CRO66:CD1-PHE165:CZ; d3 = CRO66:OH-TYR145:OH; d4 = CRO66:OH- HSD148:ND1; d5 = CRO66:OH-W84:OH2; d6 = CRO66:O2-ARG96:NH2; d7 = CRO66:N2-GLUP222:OE2; d8 = CRO66:OH-THR203:OG; d9 = CRO66- CE2-SER205:OG; d10 = SER205:OG-W84:OH2; d11 = SER205:OG-GLUP222:OE2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 6.7 Relative populations (at 298 K and 100 K) of different protonation states of His148 in EGFP (top left), T65G (top right), Duo (bottom left), and BrUSLEE (Trio) (bottom right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 6.8 Evolution of planar population in excited-state molecular dynamics simulations of EGFP, T65G, Duo, and BrUSLEE (Trio). The numbers indicate the surviving population of the planar chromophore after 3 ns of dynamics. . . . . . . . . . 207 6.9 Excited-state dynamics: Decay of planar population in EGFP, T65G, Duo, and BrUSLEE. Lifetimes are obtained as linear fit for ln[A]. . . . . . . . . . . . . 208 6.10 Different protonation states of histidine: HSD (left), HSP (middle), and HSE (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.11 Top: Residues involved in QM/MM calculations of EGFP, Bottom: BrUSLEE. Chromophore, water, residues 145, 148, 165, 96, 203, 205, 222 were included in the QM region in calculations of spectra and electronic properties. . . . . . 212 6.12 Definition of the two torsional angles and describing chromophore twisting. describes twist around the single bond (phenolate flip) and describes twist around the double bond (imidozalinone flip). . . . . . . . . . . . . . . . . . . 213 6.13 Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Ref. ?. . . . . . . . . . 214 6.14 Excited-state torsional potentials for (left) and (right) of the bare HBDI chromophore. Red curves: fit toabinitio calculations (from which the parame- ters were extracted). Pink and black curves: torsional potentials computed with the modified forcefield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.15 The quantum mechanical thermodynamic cycle perturbation (QTCP) method employing a thermodynamic cycle to calculate QM/MM free-energy changes ? . 216 6.16 Key distances in EGFP (top left), T65G (top right), Duo (bottom left), and BrUSLEE (Trio, bottom right). . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.17 Left: Two rotamers of Glu222and the definition of the key distance affected y the rotamers. Right: Equilibrium MD trajectories starting from the two rotameric forms in GLUP222 (T=298 K). The structure of the second rotamer is unstable: it flips after 0.25 ns into the main form and never comes back. . . . . . . . . . 220 6.18 Temperature dependence of Trp lifetimes in selected mutants. . . . . . . . . . 223 xxiii 6.19 Correlation plot of theoretical and experimental dipole orientation factor. Top: Computed using average dipoles. Bottom: Computed by averaging 2 at each snapshot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6.20 Plots of H versus -TS in different protonation states of mutants. . . . . . . 233 6.21 Extrapolation of G with respect to temperature in mutants. . . . . . . . . . . 234 6.22 Extrapolation of population of different protonation state with respect to tem- perature in mutants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 6.23 Correlation plot of twisting time for MD and AIMD excited-state trajectories initiated from 11 snapshots for each protonation state of His148 of EGFP and BrUSLEE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 6.24 Correlation between the average number of hydrogen bonds in the ground state and computed non-radiative lifetime (top) and the % of surviving planar confor- mation after 3 ns of excited-state dynamics (bottom). . . . . . . . . . . . . . . 242 6.25 Correlation plots in RB, FQY , extinction coefficient, RPS, lifetimes. . . . . . . 243 7.1 Summary of the mechanism of primed conversion: 488 nm excitation or priming of the anionic cis chromophore, C . populates the S 1 (C ) state. De-population of the S 1 (C ) state may occur via (i) fluorescence emission or (ii) low-yield intersystem crossing to the lowest triplet state, T 1 . Excitation of T 1 with the red conversion beam causes a T 1 T n transition. The ensuing relaxation process to the singlet ground state involves reverse intersystem crossing (RISC) and excited state chemical transformation generating the red species. (Reproduced from Ref. 10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 xxiv Abstract Fluorescent proteins from the family of Green Fluorescent Protein (GFP) are unique in that they are the only fluorescent probes of natural origin. Their photoproperties make them suitable for a wide variety of applications. Fluorescent proteins are useful devices for studying the mech- anistic details of various processes in cells, both in vitro and in cellulo. Excited-state lifetime is of the fundamental importance, as it limits the time-scales of competing relaxation channels of the excited chromophore. Structural changes in an excited state can cause temporary and permanent loss of fluorescence. For example, cis-trans photoisomerization often proceeds via a transient dark state, whereas a stable twisted geometry in excited state leads to a long-living dark state with a loss of fluorescence. This thesis covers studies of different fluorescent pro- teins and provides a mechanistic/operational insights into phenomena such as photoswitching in Dreiklang and loss of fluorescent quantum yield upon specific mutations in enhanced green fluorescent protein (EGFP). Chapter 1 presents an overview of GFP-like proteins. Chapter 2 presents the theoretical methods for computing radiative and nonradiative life- times and discusses requisite computational tools. An equation for radiative lifetime can be derived from first principles with classical harmonic oscillator, which allows us to estimate radiative lifetime with a help of electronic structure calculations. The dominant channel respon- sible for nonradiative decay is discussed in Chapter 1. To capture the essential physics and xxv to quantify nonradiative lifetime, we performed dynamics simulations of excited-state chro- mophores. Towards this end, we re-parameterised the ground-state forcefield parameters of the chromophore to describe excited-state potential energy surface (PES) with ab initio cal- culations. We then use excited-state lifetime to estimate fluorescent quantum yield in model systems. We then discuss multiple decay channels operational in proteins like EGFP and how the protonation states of the key residues affect excited-state dynamics. We utilize thermo- dynamic cycles to estimate free-energy changes upon changing the key protonation states to compute relative populations of different protonation states. In Chapter 3 fluorogenic dyes based on the GFP chromophore are discussed. The com- pounds contain a pyridinium ring instead of phenolate and feature large Stokes shifts and solvent-dependent variations in the fluorescence quantum yield, which facilitates their use for imaging the membrane structure of endoplasmic reticulum. Electronic structure calculations explain the trends in their solvatochromic behavior. Chapter 4 focuses on EGFP — one of the most popular genetically encoded fluorescent probes, which carries the threonine-tyrosine-glycine (TYG) chromophore, undergoes efficient green-to-red oxidative photoconversion (redding) with electron acceptors. In contrast, enhanced yellow fluorescent protein (EYFP), a close EGFP homologue (5 amino acid substitutions), with glycine-tyrosine-glycine (GYG) chromophore, is much less susceptible to redding and requires halide ions in addition to the oxidants. We clarified the role of the first chromophore- forming amino acid in photoinduced behavior of these fluorescent proteins. To that end, we compared photobleaching and redding kinetics of EGFP, EYFP, and their mutants with recipro- cally substituted chromophore residues, EGFP-T65G and EYFP-G65T. Experimental measure- ments showed that T65G mutation significantly increases EGFP photostability and inhibits its xxvi excited-state oxidation. Remarkably, while EYFP-G65T demonstrated highly increased spec- tral sensitivity to chloride, it is also able to undergo redding independent of chloride. Atom- istic calculations revealed that the GYG chromophore has an increased flexibility, which facil- itates radiationless relaxation leading to the reduced fluorescence quantum yield in the T65G mutant. The GYG chromophore also has larger oscillator strength relative to TYG, which leads to a shorter radiative lifetime (i.e., a faster rate of fluorescence). The faster fluorescence rate partially compensates for the loss of quantum efficiency due to radiationless relaxation. The shorter excited-state lifetime of the GYG chromophore is responsible for its increased photo- stability and resistance to redding. In EYFP and EYFP-G65T, the chromophore is stabilized by -stacking with Tyr203, which suppresses its twisting motions relative to EGFP. Chapter 5 presents the results of high-level electronic structure and dynamics simulations of the photoactive protein Dreiklang. With the goal of understanding the details of Dreik- lang’s photocycle, we carefully characterized the excited states of the ON- and OFF-forms of Dreiklang. The key finding of our study is the existence of a low-lying excited state of a charge- transfer character in the neutral ON form and that population of this state, which is nearly isoenergetic with the locally excited bright state, initiates a series of steps that ultimately lead to the formation of the hydrated dark chromophore (OFF state). These results allowed us to refine the mechanistic picture of Dreiklang’s photocycle and photoactivation. Chapter 6 introduces BrUSLEE—BRight Ultimately Shorttime Enhanced Emitter— a new fluorescent protein derived from the enhanced green fluorescent protein (EGFP) by 3 muta- tions: T65G/Y145M/F165Y . BrUSLEE shows an unusual combination of high fluorescence brightness and short fluorescence lifetime. To explain the peculiarities of its photobehavior, we investigated fine structural determinants of the fluorescence lifetime in connection with xxvii brightness by combination of time-resolved fluorescence measurements and atomistic simu- lations. High-resolution fluorescence measurements revealed 2 distinct subpopulations co- existing in a wide temperature range (4-300 K). The fluorescence lifetimes of these emissive states change considerably with temperature, converging to low temperature (intrinsic) life- times that are vastly different from each other and from that of the parental EGFP. The crystal structure and 15N-NMR spectroscopy of BrUSLEE show no obvious structural heterogeneity. Atomistic simulations suggest that the heterogeneity arises due to co-existing populations of different protonation states of chromophore-adjacent titratable residues. Different protonation states of His148 alter the hydrogen-bond network around the chromophore, which significantly affects its twisting flexibility in the excited state. Changes in the hydrogen-bond network also explain the variations in photo-physical properties among EGFP and the T65G, T65G/Y145M, and T65G/Y145M/F165Y (BrUSLEE) mutants. The result of the research presented in this thesis were summarized in the following publi- cations: 1. Y . G. Ermakova, T. Sen, Y . A. Bogdanova, A. Y . Smirnov, N. S. Nadezha, A. I. Krylov, M. S. Baranov, Pyridinium analogues of green fluorescent protein chromophore: fluorogenic dyes with large solvent-dependent Stokes shift, J. Phys. Chem. lett. 9, 1958 (2018). (Chapter 3). 2. T. Sen, A. V . Mamontova, A. V . Titelmayer, A. M. Shakhov, A. A. Astafiev, A. Acharya, K. A. Lukyanov, A. I. Krylov, and A. M. Bogdanov, Influence of the first chromophore- forming residue on photobleaching and oxidative photoconversion of EGFP and EYFP, Int. J. Mol. Sci. 20, 5229 (2019). (Chapter 4). xxviii 3. T. Sen, Y . Ma, I. V . Polyakov, B. L. Grigorenko, A. V . Nemukin, A. I. Krylov, Interplay between Locally Excited and Charge Transfer States Governs the Photoswitching Mech- anism in the Fluorescent Protein Dreiklang, J. Phys. Chem. B. 125, 757 (2021). (Chapter 5). 4. E. G. Maksimov, T. Sen, D. V . Zlenko, G. V . Tsoraev, N. V . Pletneva, V . Z. Pletnev, S. A. Goncharuk, K. S. Mineev, A. V . Mamontova, T. R. Simonyan, K. A. Lukyanov, A. M. Bogdanov, A. I. Krylov, BrUSLEE and his shadow: Two persistent excited-state populations within a GFP mutant, in-preparation. (Chapter 6). xxix Chapter 1: Introduction and overview 1.1 Green fluorescent proteins Capabilities in biological imaging changed dramatically since the first application of GFP to make green-glowing sensory neurons in C. elegans in 1994. A genetically encoded fluorescent label forinvivo imaging was immediately recognized as a major breakthrough in the domain of cell biology and bioimaging 1 . The unique properties such as low toxicity, ease of use, and the ability to tune its properties by genetic engineering made fluorescent proteins (FPs) powerful tools for in vivo observation of protein localization, and interactions, and intracellular pH measurements 2, 3 . Two Nobel Prizes in Chemistry (2008 and 2014) emphasize the importance of photophysical properties of FPs. GFP was first discovered in Pacific Northwest jellyfish Aequoria Victoria in 1962 4 . It took more than 30 years to decode GFP gene and to demonstrate that functional GFP can be expressed in various model organisms, 1, 5 which opened an era of applications of GFP as a fluorescent label. So far, GFP-like proteins have been found only in multicellular animal species (Metazoa kingdom), specifically in hydroid jellyfishes and coral polyps (phylum Cnidaria), combjellies (Ctenophora), crustaceans (Arthropoda), and lancelets (Chordata) 6 . Natural GFP-like proteins demonstrate a broad spectral diversity including cyan, green, yellow, orange, and red FPs as well as a colorful palette of non-fluorescent chromoproteins 6 (see Fig. 1 1.1). Sinus BFP GFP TagBFP CFP Keima WasCFP EGFP IaRFP zFP538 mOrange Kaede DsRed PS-mOrange 350 400 450 500 550 600 650 700 350 400 450 500 550 600 650 700 Figure 1.1: Color tuning in fluorescent proteins: Different chemical structures of the chromophore lead to different colors. Main types of chromophore structures are shown together with corresponding excitation (upper bar) and emission (bottom bar) wave- lengths designated by arrows. The size of -conjugated system is particularly impor- tant for determining the color: more extensive conjugation leads to red-shifted absorp- tion (compare, for example, blue, green, and red chromophores). Changes in protona- tion states of the chromophore also affect the energy gap between the ground and the excited states. Excited-state deprotonation of the chromophore is one of the mechanisms of achieving large Stokes shifts. Absorption/emission can be red shifted by -stacking of the chromophore with other aromatic groups (e.g., tyrosine), as in YFP (not shown). Specific interactions with nearby residues also affect the hue (for example, additional red shift in mPlum fluorescence is attributed to a hydrogen bond formed by acylimines oxy- gen). [Reproduced from Ref. 7]. As illustrated in Figure 1.1, color is the key aspect of FP’s application to bioimaging. Color tuning is achieved by varying the length of the extended -conjugated system, change in protonation state of the chromophore, and interactions with nearby residues. Another key aspect is brightness, which is highly desirable for labeling. Bright FPs possess large extinction coefficients (EC), and high fluorescent quantum yields (FQY). Properties like phototoxicity and photostability are also important. Due to a wide variety of applications, there is no single 2 best FP. Depending on the applications, different combinations of properties are desirable. Consider, for example, photostability. In many applications, bleaching, a gradual loss of optical output upon repeated irradiation, is undesirable. Consequently, protein engineering often aims at more photostable fluorescent proteins. On the other hand, bleaching is exploited in super-resolution imaging 2, 24–27 . Methods based on fluorescence loss and recovery are used to trace protein dynamics; photoconversions and photoswitching enable optical highlighting and timing of biochemical processes 23, 28 In a similar vein, phototoxicity, which is undesirable for in vivo imaging applications, can be exploited in photodynamic therapies and targeted protein/cell inactivation 29 . The photophysics of fluorescent proteins has inspired numerous experimental and theoreti- cal studies 15–23 . However, the details of the photocycle and chromophore formation, the effect of mutations, and the role of the chromophore’s surroundings are not fully understood due to the complexity of the system. Molecular-level understanding of these processes provides a crucial advantage in the design of new FPs with properties suitable for particular applications. Knowledge of structure-function relationship and detailed molecular-level mechanistic under- standing of the photocycle are essential prerequisites for controlling properties of FPs. To investigate these properties two strategies have been followed in the last two decades. In the first approach, a particular property is studied across a wide range of FPs and the variations of the property are then rationalized in terms of crystal structures, conjugation in chromophore, local environment, protonation state etc. The second approach focuses on one protein and a series of point mutations are introduced to understand the operational mechanisms and properties. For example, scientists have worked on GFP and built several variants of it with 3 tuned photoproperties. Mutations, leading to different variants may also cause critical structural changes in Fps. The crystal structure of the wild type GFP (PDB ID: 1W7S) 10 was reported in 1996. It contains 238 amino acids with 11-stranded -barrel around a single helix. The approximate molar weight of is 25 to 30 kDa. The diameter of the barrel is approximately 24 ˚ A and its height is 42 ˚ A 8, 9 . The chromophore resides inside a relatively tight- barrel. The chromophore is formed by an autocatalytic cyclization of the polypeptide backbone between residue Ser65 and Gly67 and an oxidation of the- bond of Tyr66 (SYG) upon protein folding 7 . EYFP, on the other hand, possesses Gly65 instead of Ser65 making the chromophore GYG (see Fig. 1.2). - EGFP/TYG HBDI/GYG - Figure 1.2: Left: A typical structure of a fluorescent protein represented by EGFP. Right: The chromophores in EGFP/GFP-S65T and EYFP/EGFP-T65G (HBDI). Reproduced from Refs. 7 and 40. 4 In wt-GFP, the chromophore exists in two protonation states, which are in equilibrium with each other: neutral form (A) and anionic form (B). Crystal structure of the GFP-S65T variant (PDB ID: 1EMA) 7 was published almost simultaneously, with resolution of approximately 1.9 ˚ A. The S65T mutation shifts the protonation equilibrium to nearly 100% B-form. This was the first step towards understanding the role of the nearby residues around the chromophore in controlling GFP’s photophysical properties. In 2011, another crystal structure (2Y0G) 30 of a GFP variant was reported with enhanced fluorescent intensity. The enhanced variant, named EGFP, differs from GFP-S65T by the F64L mutation. Being directly connected to the chromophore, residue 64 can be an important element of the local structure. The F64L mutation involves a less bulky side chain, increases van der Waals interaction energy, and results in a tighter packing of the helix during protein folding 30 . A crystal structure (6j6i) 32 of the same variant was published in 2019, with ultrahigh resolution. The paper not only reported an accurate structure, but also analyzed the protonation states of key residues around the chromophore. It is important to understand how these structural changes due to the mutations are related to photoproperties, of FPs. 1.2 Fluorescent protein photocycle GFP, EGFP, EYFP, Dreiklang, and many other FPs contain a hydroxy benzylidene imi- dazolone (HBDI) 33, 34 type chromophore. HBDI belongs to a class of cyanine dyes, owing to the following structural features: a phenol and imidazolinone moieties connected via a methylene bridge (See Fig. 1.2). This highly conjugated molecule may exist in various protonation states and various resonance structures, depending on the chemical environment around it. The photophysics of the isolated or solvated chromophore is very different from that 5 of the protein-bound chromophore. The chromophore is nonfluorescent in solution because of reduced excited-state lifetime 35, 36 due to fast radiationless decay facilitated by a twisting motion. The rigid protein environment restricts the chromophore’s motions in the excited state and limits the accessibility of solvent and other species (oxidants, reductants etc) to the chromophore. The ability of FP-chromophores to display different fluorescence in different environments can be utilized in developing fluorogenic and solvatochromic dyes. Fluorogenic dye changes fluorescent intensity upon binding with a target object (becomes fluorescent from nonfluorescent). Solvatochromic dyes, on the other hand, are dyes that change their fluorescent color depending on the solvent. Figure 1.3 outlines various excited-state processes in FPs. The photocycle is initiated by light absorption producing an electronically excited chromophore. The excited chromophore can decay via several competing relaxation channels from the electronically excited state(s). One of the dominant channels is fluorescence, which restores the ground-state chromophore. The color of emitted light often differs from the absorbed light. This color change, called Stokes shift, arises due to structural relaxation of the chromophore in the excited state, change in hydrogen-bonding network, or excited-state proton transfer (ESPT). For example, in mPlum, a far-red-shifted FPs (RFP), large Stokes shift arises because two different hydrogen-bonding networks around the chromophore in ground state collapse to one in the excited state 38 . ESPT is an established mechanism, operational in GFP, where change in protonation state of the chromophore causes large Stokes shift. In wt-GFP, the neutral chromophore is the dominant form whereas the anionic form becomes dominat in GFP-S65T 39 . Further investigation of the chromophore pocket reveals a hydrogen bonding network (tyrosylO-W-Ser205-Glu222- Ser/Thr66), as shown in Fig. 1.4, plays a key role in transferring the proton from neutral chromophore to the anionic glutamate (GLU), resulting in the anionic chromophore and neutral 6 Unoccupied (virtual) levels Oxidized chromophore h ν (light) Ground-state chromophore Fluorescence: Emit light and go back to ground state Radiationless relaxation: Go back to the ground state and dissipate energy into heat Atom rearrangement: Chemical transformation (photochemistry) Excited chromophore (chro*) occupied levels (molecular orbitals) Reduced chromophore -e +e Figure 1.3: Excited-state processes in fluorescent proteins. The main relaxation channel is fluorescence. Radiationless relaxation, a process in which the chromophore relaxes to the ground state by dissipating electronic energy into heat, reduces quantum yield of fluores- cence. Other competing processes, such as transition to a triplet state via inter-system crossing (not shown), excited-state chemistry and electron transfer, alter the chemical identity of the chromophore thus leading to temporary or permanent loss of fluorescence (blinking and bleaching) or changing its color (photoconversion). Reproduced from Ref. 7. glutamic acid (GLUP) via ESPT. 44 As the bonding pattern changes significantly in electronically excited FPs, the chromophore can readily undergo reactions like ET/CT, often resulting in permanent loss of fluorescence, especially in the presence of external agents. One such photoconversion is oxidative redding in 7 Tyr66 W84 W259 W85 W260 Ser205 Glu222 Gly67 Figure 1.4: Structural analysis of EGFP showing electron density overlaid on the chro- mophore and the neighbouring residues. The tridentate density around Glu222 clearly indicates alternate conformations of the side chain represented in orange and cyan. hydro- gen bonds for each conformation are correspondingly shown in orange or cyan. Glu222 is either hydrogen bonded to Ser205 or to Thr65, but not to both residues at the same time. Reproduced from Ref. 30. EGFP. Interestingly, in EYFP which differs from EGFP by three mutations T65G, T203Y , and H148L the redding is suppressed. Bogdanov et al. found that a-stacking between Y203 and the chromophore in EYFP increases the oxidation potential of the chromophore 40 . Other processes, which may be involved in the photocycle, are radiationless relaxation, photo-isomerization, and chemical transformations. In many FPs, fluorescence is the main channel, competing with radiationless relaxation. However, the yield of the processes such as bleaching, blinking, photostability, phototoxicity, photoswitching etc. are determined by the competition between the main relaxation channels (fluorescence versus radiationless relaxation) and various photoinduced transformations. The timescales of different channels 8 are key to accurate understanding of yields and branching ratios. These processes are limited by a finite excited-state lifetime, which varies between 1-10 ns in FPs. To play a role in FP photocycle, the excited-state process should have a lifetime comparable with the excited-state lifetime. Below we briefly discuss photoswitching phenomenon and excited-state lifetimes of FPs. 1.3 Excited-state lifetime The branching ratios of photoinduced processes are determined by excited-state lifetime (which varies between 1-10 ns). Excited-state lifetime determines FQY , relative brightness (RB), relative photostability (RP), etc. In the most basic case of a single emissive state, the population of excited fluorophores (Chro ) decays via two competing first-order processes 25 : Chro kr !Chro +h; (1.1) Chro knr !Chro; (1.2) wherek r is the radiative (intrinsic fluorescence) rate constant andk nr describes all quenching channels. The overall decay of the excited-state chromophore is also described by the first-order kinetics with k = k r +k nr and the corresponding apparent (measured) fluorescence lifetime = ln(2) k . It is well established that the dominant radiationless decay pathway is internal conversion (IC). The rate of IC was found to depend weakly on solvent viscosity. Separation of viscosity and thermal effects for HBDI (and a related model compound lacking the hydroxyl group) showed that IC is barrierless at room temperature, but exhibits an apparent activation barrier in rigid media. It was suggested that the coordinate promoting IC must displace only a small 9 FS TwP TwI τ φ τ = 90 0 φ = 90 0 Time (ns) Bridge bond torsions (deg) Time (ps) φ (deg) τ φ Figure 1.5: Left: The anionic GFP chromophore model p-hydroxybenzylidene- imidazolinone (HBI) in three different geometries: the planar fluorescent state (FS) min- imum ( = = 0 ), the TwP geometry twisted 90 around the phenol bridge bond and the TwI geometry twisted 90 around the imidazolinone bridge bond. Right: Bridge bond tor- sions ( and) from an excited-state MD simulation of the solvated GFP with the anionic chromophore. The inset zooms on the time window where the twist occurs. Reproduced from Ref. 48. solvent volume. One possibility is the concerted twist about the bridging C=C-C bonds (hula twist) proposed on the basis of quantum chemical calculations by Weberetal. 45 Martinezetal, performed high-level QM/MM calculations for the HBDI chromophore and concluded that the bare chromophore is nonfluorescent because of short lifeitme in the excited state in gas phase and in water. Upon excitation, the chromophore undergoes twist around the methylene bridge, relaxing back to ground state, resulting in the loss of fluorescence 35, 36 . In GFP-S65T, the radiationless relaxation of the chromophore is restricted due to rigid protein environment. Excited-state simulations revealed twisting around within a few nanoseconds (0.2-12.9 ns) in all simulations (see Fig. 1.5) , but showed no twisting around . This was attributed to the constrain created by the residues connected to the imidazolinone ring. 47, 48 . 10 However, the effect of the local environment on nonradiative relaxation is not fully understood. Similarly, the effect of the environment on intrinsic radiative lifetime is not understood. 1.4 Photoswitches Nonradiative relaxation, leading to long-living dark states, results in loss in fluorescence. The phenomenon enables molecular photoswitching behavior. Switching can be a result of cis-trans isomerization, which is one of the most important photoinduced transformations involved in photoresponse in biological systems (such as rhodopsin). In FPs, this process may lead to reversibly photoswitchable FPs (RS-FPs). The first efficient RS-FP, Dronpa 42, 43 , was discovered by Andoetal. Dronpa absorbs at 503 nm (2.46 eV) and emits at 518 nm (2.39 eV). It converts to the nonfluorescent form upon irradiation at 488 bm (2.54 eV) with poor QY . The reverse process occurs upon illumination with light of 405 bm (3.06 eV). Brakemann et al, who investigated the chemistry of photoswitching proposed that a primary factor determining the fluorescence ability of the chromophore in different conformations is its flexibility. The flexibility can be described in terms of tortional angle and around the methylene bridge. The cis-trans isomerization in Dronpa leads to blinking, a temporary loss of fluorescence. In this thesis, we investigated Dreiklang, a unique photoswitch. In contrast to other photo- switchable proteins, the mechanism in Dreiklang does not involve cis-trans isomerization. Instead, the chromophore undergoes a reversible hydration/dehydration reaction at the imidazolilone ring. Owing to this unique switching mechanism, the wavelengths used for photoswitching and for excitation inducing fluorescence are decoupled in Dreiklang, leading to important advantages for super-resolution microscopy. 11 Since the first application of FPs, many efforts we made to better understand the effect of mutations on its photophysical properties, such as lifetime and FQY . In collaboration with Bog- danov and his colleagues, we introduced BrUSLEE. It differs from EGFP in three mutations: T65G, Y145M, and F165Y . The BrUSLEE is unique in exhibiting short fluorescence lifetime (820 ps) and relatively high brightness (0.78) with FQY 0.3. This was a result of systamatic structural evolution in preparing and designing new variants in EGFP 51, 53 . However, the reason behind such drop in lifetime and FQY is not well understood. The key questions are how does radiative lifetime changes upon mutations, and what is the main channel in nonradiative relaxation. Why such channels are so dominant in BrUSLEE compared to EGFP? We made an effort to find answers to these questions in Chapters 4 and 6 of the thesis. We hope that our findings would be helpful in rational design of new FPs with desirable photoproperties. 12 1.5 Chapter 1 references 1 M. Chalfie, Y . Tu, G. Euskirchen, W.W. Ward, D.C. Prasher, Green fluorescent protein as a marker for gene expression, Science 263, 802 (1994). 2 K. Nienhaus and G.U. Nienhaus, Fluorescent proteins for live-cell imaging with super- resolution, Chem. Soc. Rev. 43, 1088 (2014). 3 H.C. Ishikawa-Ankerhold, R. Ankerhold, and G.P.C. Drummen, Advanced fluorescent microscopy techniques — FRAP, FLIP, FLAP, FRET and FLIM, Molecules 17, 4047 (2012). 4 F. H. Jhonson, O. Shimoura, Y . Saiga, L. C. Gershman, G. T. Reynolds, J. R. Waters. Quantum efficiency of Cypridina luminescence, with a note on that of Aequorea, J. Chem. Theory Comput. 60, 85 (1962). 5 D. C. Prasher, V . K. Eckenrode, W. W. Ward, F. G. 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Bogdanov, Bright GFP with subnanosecond fluorescence lifetime, Scientific reports 8, 1 (2018). 16 Chapter 2: Methodology This Chapter provides a brief overview of the theoretical background and computational protocols used in this thesis; full details can be found in the original papers listed in the Abstract. Here we discuss radiative lifetime and how it can be computed from electronic- structure calculations. The next few sections focus on molecular dynamics protocols and types of QM/MM calculations performed to evaluate properites. We also discuss re-parameterization of ground-state forcefield to describe excited states. Finally, we focus on the free energy calculations for different protonation states. 2.1 Radiative lifetime The process of radiative decay can be understood classically, by analyzing an oscillating charge model. The classical model is constructed by considering an atom of charge q, mass m in one-dimensional potential well described by Newton’s equation of motion: + _ +! 0 2 = 0; (2.1) 17 where,! 2 0 = k/m, is the damping rate, and is electric dipole defined as =qr. The mechanical energy of an oscillator is hW osc i cycle = 1 2 k (t) q 2 + 1 2 m _ (t) q 2 cycle =W 0 e t ; (2.2) where W 0 = 1 2 m! 2 0 q 2 0 : (2.3) The above equation means that the energy of the oscillator decays exponentially with time. Radiative lifetime is then defined as the inverse of the rate of damping rate ( = 1/ ). Power radiated by an oscillator is P rad = d dt hW osc i =W 0 e t ; (2.4) and average radiative power, according to classical electromagnetic theory is then: P rad = 0 ! 4 0 12 0 c 3 e t : (2.5) Comparing Eqs. (4) and (5), we obtain classical expression for radiative lifetime and radiative damping rate = 1 = 1 6 0 c 3 q 2 ! 2 0 m ;: (2.6) where, 0 is dielectric constant, c is the velocity of light in vacuum. In a medium of refractive index (n) classical radiative life time is = 1 = 6 0 c 03 m q 2 ! 2 0 ; (2.7) 18 where c 0 = c/n. The absorption cross-section is defined as abs = q 2 4mc 0 (!! 0 ) 2 + ( =2) 2 : (2.8) By defining a Lorentzian line shape function L(!! 0 ) = =2 (!! 0 ) 2 + ( =2) 2 ; (2.9) where L(!-! 0 ) has been normalized so that R 1 1 L(!-! 0 )d! = 1, Eq. (8) becomes abs (!) = q 2 2mc 0 L(!! 0 ): (2.10) Full width at half maxima (FWHM) is given by != . Another way of characterizing the interaction of the dipole with the driving field obtained by integrating the absorption cross section over frequency Z 1 1 (!)d! = q 2 2mc 0 : (2.11) The above equation eliminates the dependence on frequency. Z 1 1 (!)d! = q 2 2mc 0 = e 2 2m e c 0 f abs ; (2.12) wheref abs is the oscillator strength consisting of a single electron of massm e and chargee f abs = m e m q e 2 ; (2.13) 19 From Eq. (6) = 1 = e! 2 0 6m e 0 c 3 f abs : (2.14) This equation means that for the transitions at the same frequency, the intrinsic fluorescence lifetime should be inversely proportional tof abs . The absorption cross section becomes: abs = e 2 2m e c 0 L(!! 0 )f abs : (2.15) To develop QM treatment of absorption a quantum two-level system in presence of an external electric field, described by the following Hamiltonian: ^ H tot = ^ H atom + ^ H field + ^ H int ; (2.16) where ^ H int accounts for the interaction energy between an atom and the field: ^ H int =^ ^ E: (2.17) This leads to the following expression for radiative = 2 ~ j if u e j 2 f (~! if ); (2.18) where if is the transition dipole moment from statei to statef,u e is the direction of the polar- ization of the light, f is the density of the final states at the frequency of transition. 20 Starting from that, we arrive at the quantum analogues of the classsical relationships for absorp- tion cross-section and for the relationship between the oscillator strength and radiative lifetime. The absorption cross-section in quantum two level system is abs (!) = ! 0 j if j 2 3~c 0 L(!! 0 ): (2.19) Introducing the quantum oscillator strength in a direct analogy with Eq. (12) Z abs (!) = e 2 2m e c 0 f abs ; (2.20) where f abs = 2m e ! 0 j if j 2 3~e 2 : (2.21) This quantum oscillator strength is directly computed in quantum-chemical calculations. The classical treatment of light accounts for only absorption and stimulated emission (rate denoted asB if ). Spontaneous emission has be to treated quantum mechanically, which is incor- porated in the total rate equation as ad hoc (denoted as A fi ), i andf denotes initial and final states. The rate of absorption and stimulated emission are proportional to the energy density at transition frequency ! (! 0 ). Now we consider again a two-level system with two manifolds of degenerate states ofg i andg f . In thermodynamic equilibrium, the ratio of population in the two manifolds N f N i = g f g i e ~! 0 =kT : (2.22) Including the contribution from spontaneous emission, the total rate of change of the upper manifold’s population is N f = [N f B if N i B fi ] ! (! 0 )A fi N f : (2.23) 21 Using the relationB if =(g f /g i )B fi we obtain A fi B fi = ! (! 0 )e (~! 0 =kT1) : (2.24) Spectral density of the Plank radiation is given by ! (! 0 ) = ~! 3 0 2 c 3 1 e (~! 0 =kT1) : (2.25) Comparing Eqs. (24) and (25) we obtain A fi B fi = ~! 3 0 2 c 3 : (2.26) The Einstein cofficientB fl for absorption and stimulated emission are generalized as B fi = g i j if j 2 3~ 2 0 : (2.27) Comparing Eqn. (26) and (27) A fi = 1 = g i ! 3 0 j if j 2 g f 3~c 3 0 = g i ! 2 0 e 2 g f 2c 3 m e 0 f abs : (2.28) This is known as the Strickler-Berg equation 1 . In atomic units, these equations become rather simple. Including the effect of the dielectric environment and by redefining as r : 1 r = ! 2 0 f abs 2(c 0 ) 3 ; (2.29) 22 We use this equation to compute radiative lifetime. We take oscillator strength and excitation energies from electronic structure calculations. We follow two different strategies. The first one involves molecular dynamics (MD) simulation in ground state of model structure followed by QM/MM calculations and the results are averaged over snapshots. The other one involves QM/MM optimization of the model structure followed by computation of excitation energy. The second strategy is used when MD fails to predict the best possible model structure. 2.2 MD simulations In our computational studies, we always begin with MD simulations to carry out equilib- rium sampling. We also use MD to model excited-state dynamics. MD simulations employed the CHARMM27 4, 5 parameters for standard protein residues and the parameters derived by Reuteretal. for the anionic and neutral GFP chromophores 6 . Parameters for the off-state chromophore in Dreiklang were not available in literature. We obtained them by recognizing the similarity between parts of the chromophore and known amino acids. For example, in the off-state of the chromophore, the parts of the hydrated imidazolione ring can be viewed as combination of proline and threonine. The series of electronic structure calculations allowed us to reparameterize the forcefield for the off-state of the chromophore 7 . Chapter 5 provides the details of this parameterization. We used the TIP3P 8 water model to describe explicit solvent molecules around the protein. The protein was solvated in a box, producing a water buffer of about 15 ˚ A. The surface charges were neutralized with Na + and Cl ions at appropriate positions. This was the protocol followed consistently in different proteins that we studied and for different protonation states of the nearby residues. MD simulations were performed with NAMD 9 to generate equilibrated geometries (snapshots) that were used for the subsequent QM/MM calculations. Full details of 23 MD simulation are provided in Chapters 4, 5, and 6. 7, 10 2.3 Protein structures and protonation states Assigning the correct protonation states of the residues in proteins is challenging and com- plicated. Crystal structures provide only an indirect information about the protonation states, unless they are obtained with super-resolution crystallography. Experimental kinetics studies, especially isotope effects and the pH dependence of optical properties, are often used to eluci- date protonation states. Several computational methods can be used to evaluate correct proto- nation states. The most rigorous approach of identifying the most stable form 11, 12 is to compute Gibbs free energies of various protonation states. This approach requires extensive thermo- dynamic averaging. As a shortcut, one can use optimized geometries in different protonation states, assuming that the most stable structure represents the thermodynamically favorable one. This approach accounts for the stabilization provided by hydrogen-bonding 13, 14 , but ignores entropic effects. In EGFP, GLU222 and HIS148 are two residues near the chromophore that can exist in differ- ent protonation states. GLU can exist in two different protonation states: anionic (GLU) and neutral (GLUP). HIS can exist in three protonation states: neutral HSD (protonated at N), neutral HSE (protonated at N), positively charged HSP (protonated at both N). The structures of these residues are shown in Chapter 6. In Dreiklang, GLU222 and HIS145 are two residues near the chromophore that can exist in different protonation states. Note that the most favorable protonation state may not represent 100% population and different populations may coexist in the protein. This aspect is explored in detail in Chapter 6. We followed three different approaches to understand protonation state of HIS and GLU in 24 the FPs we studied (EGFP, EGFP-T65G, EGFP-T65G-Y145M (Duo), EGFP-T65G-Y145M- F165Y (BrUSLEE), EYFP, Dreiklang). 1. Protonation states for all proteins were first checked with Propka 15, 16 software and then the residues near the chromophore were checked manually. On the basis of pKa predicted by Propka, we concluded that GLU222 is in the neutral protonated GLUP form and HIS 148/145 is in the neutral HSD/HSE form ( HSD is the most favorable due to a strong hydrogen bond with the chromophore.) 2. We then prepared model systems with different combinations of protonation states and performed MD simulations. Averaged structural parameters can be compared with the crystal structure.The key distances around the chromophores are measured and compared with the crystal structure to figure out the best possible protonation state. The distance cut off was set to 0.5 ˚ A. This analysis is presented in detail in Chapters 4, 5, and 6. However, this analysis did not yield definitive conclusions due to the uncertainty of the forcefield parameters. 3. We used QM/MM optimization with mechanical embedding to optimize the geometry of a region around the chromophore and to compare the relative energies to identify the lowest-energy structure. Then the model structure with the lowest energy was concluded to represent the most probable protonation state. 25 Figure 2.1: Residues included in the extended QM part in the excited-state calculations of ON state of Dreiklang. TYR203 is Y203, GLUP222 is E222, ARG96 is R96. Only the chromophore was kept in small QM region. In the medium QM region ARG96, CRO, HIS145, SER205. TYR203, GLUP222, W were included in the QM region. In extended QM region LEU64, and V AL68 were added. Reproduced from Chapter 5. 2.4 QM/MM optimization Distance analysis from equilibrated MD trajectories is not always conclusive in determining protonation states of the key residues. Hence, we prepared model systems (as shown in Fig. 6.11) with different combinations of protonation states. QM/MM optimizations were carried out using ONIOM. ONIOM is a mechanical embedding scheme, which describes a model system in two parts X and Y , where X is treated classically and Y is treated quantum-mechanically. The total energy is defined as: E tot (X;Y ) =E MM (X) +E QM (Y ) +E(X;Y ): (2.30) whereE(X,Y) is intermolecular interaction energy 17–19 . If X and Y are connected via a covalent bond, a link atom (L) is introduced. E tot (XY ) =E MM (XY )E MM (YL) +E QM (YL); (2.31) 26 E MM (XY ) =E MM (X) +E MM (X;Y ) +E MM (Y ); (2.32) E MM (YL) =E MM (L) +E MM (Y;L) +E MM (Y ); (2.33) After simplifying: E tot (XY ) =E MM (X) +E MM (X;Y ) +E QM (YL) +E LINK : (2.34) whereE LINK denotes link atom correction term and this is given by: E LINK =E MM (L)E MM (Y;L): (2.35) In the course of optimization, all coordinates were allowed to relax, except for the positions of link atoms (C- carbons of the amino-acid residues shown in Fig. 6.11), which were pinned to the positions from the MM-relaxed structures. The QM part was described by !B97X- D/aug-cc-pVDZ. This functional 20, 21 belongs to the family of long-range corrected functionals in which the notorious self-interaction error is greatly reduced. The benchmarks illustrated excellent performance of !B97X-D for structures and energy differences of a broad range of compounds 20, 21 . Optimizations were performed with Q-Chem 22 . 2.5 QM/MM protocols for excitation energy Optimized geometries and equilibrium trajectories were used to compute excitation energy. In these calculations we used electrostatic embedding and described the MM part by point charges. One drawback of this approach is that it neglects the effect of polarization in the MM part. To prevent the overpolarization of the QM part, the charges on the boundary atoms were set to zero. Bonds before -CONH were cut and capped with hydrogen atoms and charge on 27 CONH was set to be zero; the excess charge was then redistributed over other atoms of the immediate residue to maintain the total charge of the amino acid. This is explained in detail in Chapters 5, and 6. In geometry optimizations, we used a finite cluster approach (see Chapter 5). To reduce the cost of calculations, a smaller model system was prepared (this does not affect geometry of the QM region in mechanical embedding scheme). We note that this smaller cluster is not sufficient for excitation-energy calculations because the electrostatic effect of the solvated ions and bulk solvent are not taken care of properly. We consider different size of the QM region (small, medium, large; as shown in Fig. 6.11) to check the convergence of electronic properties with respect to the size of the QM region. This approach is called a finite cluster approach. The effect of MM can be added by using an extrapolation scheme as follows: =hE ex (QM=MM)E ex (QM)i MD ; (2.36) E ex (QM=MMcorr) =E ex (QMopt) + ; (2.37) where (E ex (QM/MM-corr) is the extrapolated energy. Accurate computation of excitation energiess and oscillator strengths allow us to evaluate the spectroscopic properties as well as radiative lifetimes. We followed this approach to study the photoswitching mechanism in Dreik- lang, which is presented in Chapter 5. 2.6 Nonradiative lifetimes Excited-state PES of GFP-like chromophores was investigated in several studies by Mar- tinez et al., Jonasson et al., and many others. Electronically excited chromophore can decay via two competing first-order processes: radiative (intrinsic) and nonradiative. Nonradiative 28 decay can occur through many quenching channels. It is believed that twisting of the GFP- chromophore in the excited state is the dominant non-radiative decay channel. Jonasson et al. studied excited-state dynamics of GFP with high-level quantum-chemical calculations 24 . Energy of the S 1 excited state of the anionic chromophore (HBDI) at different geometries was computed to build two-dimensional torsional potential V(, ). This study suggested that a twisted structure is energetically favorable in the excited state. The twist around and (or) leads to energy lowering of an isolated chromophore. However, in the protein the twist around is restricted due to covalent bonding to nearby residues. We also optimized the geometry of the HBDI chromophore in first excited state with!B97X- - φ τ Figure 2.2: Definition of the two torsional angles and describing chromophore twisting. describes twist around the single bond (phenolate flip) and describes twist around the double bond (imidozalinone flip). Reproduced from Chapter 6. D/aug-cc-pVDZ and obtained geometries twisted around the methylene bridge (see Fig. 2.2) . This is consistent with previous studies 24, 25 . Using these structures, we reparameterized the forcefield parameters to describe PES in the excited-state 6 . First, we computed the NBO charges 26 of the HBDI chromophore in the ground and excited states. Partial charges, bond lengths, angles and dihedral angles were computed by performing electronic-structure calcula- tions in the ground and excited state of the bare HBDI chromophore. Details of the protocol is given in Chapter 4. 29 The force constants (k) are calibrated as: k excharmm = k excomputed k gscomputed k gscharmm : (2.38) The most important parameter is the torsional angle . The PES scans show that the chro- mophore is planar in the ground state and twisted in the excited state. We fitted the excited-state potential with a fitting potential with the calculated force constant, which enables the flip around . Partial charges and other force-field parameters are listed in Chapter4. Fitting the potential for excited-state PES (right) with respect to: E =k[1 +cos(n 180)];groundstate;n = 2; (2.39) E =k[1 +cos(n 180)];excitedstate;n = 4: (2.40) The major difference in the ground- and excited-state PES (other than force constants) is the change in periodicity (n) of the fitting potentials, with much lower value of force constant for the torsional angle (see Fig. 2.3). The quality of the reparameterized forcefield was examined by comparing with the AIMD calculations on several snapshots as discussed in Chapter 6. An excellent agreement validated our forcefield parameters. We analyzed the trajectories and the population of planar confor- mation is fitted to an exponent corresponding to first-order kinetics to evaluate nonradiative lifetime: A(t) =e kt ; (2.41) nr = ln2 k ; (2.42) where radiationless (non-radiative) half-life is nr . The protocol of the analysis is provided in detail in Chapter 4. 30 Figure 2.3: Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Chapter 4. Then we compute apparent excited-state lifetime for each form as: 1 = 1 r + 1 nr ; (2.43) = nr r r + nr ; (2.44) (2.45) and FQY as: FQY = nr r + nr : (2.46) We compute the macroscopic extinction coefficient using the following expression 27 : (~ !) = X i N a e 2 4m e c 2 0 ln 10 p f i exp " ~ ! ~ ! i 2 # ; (2.47) 31 where(~ !) is the molar extinction coefficient in Lmol 1 cm 1 ; ~ ! is the excitation wavelength, N a is the Avogadro number,e is the electron charge,m e is the electron mass,c is the speed of light in cm s 1 , 0 is the vacuum permittivity in F cm 1 ,f i is the oscillator strength of the state i, and is the broadening factor in cm 1 . We used wavenumbers, since the units are L mol 1 cm 1 and so is in cm 1 . The coefficient is: N a e 2 4m e c 2 0 ln 10 p = 1:277 10 8 L mol 1 cm 2 : (2.48) The choice of is the biggest uncertainty in the calculations, as we cannot compute it from first principles. In calculation we use = 0.3 eV . Brightness in given by: B =ECFQY (2.49) Using these expressions we are able to compute all properties that we are interested in EGFP and its mutants. 2.7 Free energies of different protonation states Although the fluorescence obeys first-order kinetics, in the presence of multiple distinct populations of the fluorophore, the observed decay becomes multi-exponential. In this case, the average lifetime is given by: hi = X i A i i : (2.50) Multi-exponential fluorescence decay (spectral heterogeneity) arises due to structural hetero- geneity, such as different conformations or protonation states of fluorophores, or different local 32 environments. Hence, calculation of free energy differences between different states is a crit- ical prerequisite in understanding the spectral heterogeneity. Various approaches have been proposed in the literature to compute accurate QM/MM free energies for chemical reactions in solutions 28–33 . In the quantum mechanical free energy (QM-FE) approach by Jorgensen and co-workers, 28, 29 a reaction pathway for atoms in QM region is calculated in a vacuum. Free energies for the interaction between the QM and MM atoms are then calculated along the reac- tion pathway by MM free energy perturbation (FEP) or thermodynamic integration, with elec- trostatic interactions between the QM and MM atoms are described by point charges. An alternative approach is the ab initio QM/MM apprach (QM(ai)/MM) by Warshel and co- workers. 31, 32 The phase space is sampled by MD simulations with a reference potential given by empirical valence bond (EVB) method. We used a quantum mechanical thermodynamic cycle perturbation (QTCP), a combination of QM-FE and Warshel’s approach, which employs a thermodynamic cycle (shown in Fig. 6.15) to estimate QM/MM free energy change 33 . A, QM/MM B, QM/MM A, MM B, MM ΔA qm/mm (A B) - ΔA mm qm/mm (A) ΔA mm qm/mm (B) ΔA mm (A B) Figure 2.4: The quantum mechanical thermodynamic cycle perturbation (QTCP) method employing a thermodynamic cycle to calculate QM/MM free-energy changes 33 . To compute free-energy differences, we employ the thermodynamic cycle shown in Fig. 6.15. This approach 33 , called QTCP, allows one to compute high-level QM/MM free energy changes between two states A and B based on classical (MM) sampling and a relatively modest amount of QM/MM calculations. In this approach, the free energy change between A and B 33 described by QM/MM is calculated as the sum of three terms: (1) free energy change between A described by MM and by QM/MM (-A mm!qm=mm (A)), (2) the free energy change between A and B, with both described by the MM potential (A mm (A!B)), and (3) the free energy change between B described by the MM potential and by QM/MM (A mm!qm=mm (B)). Hence, A qm=mm (A!B) =A mm!qm=mm (A) + A mm (A!B) + A mm!qm=mm (B);(2.51) A mm (A!B) =k B T lnhe [E tot mm (B)E tot mm (A)]=k B T i mm;A ;(2.52) A mm!qm=mm =k B T lnhe [E tot qm=mm (X)E tot mm (X)]=k B T i mm;X ;(2.53) Once free energies are computed, one can evaluate the populations of different forms by using the Maxwell-Boltzmann equation: P A P B =e A qm=mm (A!B) k b T : (2.54) We performed a series of QM/MM calculation with ONIOM to evaluate each terms of the equation above. Details of the protocol that we followed are described in Chapter 6. One of the drawbacks of such protocol is that we only sampled in the wells of two protonation states (A and B), but not along the reaction coordinate (as exercised in FEP). 34 2.8 Chapter 2 references 1 T. R. Gosnell, Fundamentals of Spectroscopy and Laser Physics, Camb. Univ. Press 3 (2002). 2 D. B. Hand, The refractivity of protein solutions, J. Biol. Chem. 108, 703 (1935). 3 T. L. MacMeekin, M. L. Merton, N. J. 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Chem. 99, 17516 (1995). 32 M. strajbl, G. Hong, A. Warshel, Ab initio QM/MM simulation with proper sampling:first principle calculations of the free energy of the autodissociation of water in aqueous solution, J. Phys. Chem. B. 106, 13333 (2002). 33 T. H. Rod, U. Ryde, Accurate QM/MM free energy calculations of enzyme reactions: methy- lation by catechol O-methyltransferase, J. Chem. Theory Comput. 1, 1240 (2005). 37 Chapter 3: Pyridinium Analogues of Green Fluorescent Protein Chromophore: Fluorogenic Dyes with Large Solvent-Dependent Stokes Shift 3.1 Introduction Fluorogenic dyes—compounds that are non-fluorescent in free state but show fluorescence enhancement upon binding with target objects—are very attractive in bioimaging 1 , because they can be used in fluorescence microscopy for staining various parts of living systems including proteins 2 , nucleic acids 3 , and other components 4–6 . Among numerous fluorogenic dyes partic- ularly interesting are structurally modified analogues of the chromophores of the fluorescent proteins from the GFP family 7–9 . These compounds, representing diverse benzylidene imida- zolones (BDI) 10–12 , have intense and multifarious colors, are small, highly soluble in water, and are easy to synthesize 13 . Despite being highly emissive inside intact proteins, the chromophores have an extremely low fluorescence quantum yield (FQY) in a free state 14 , which suggests their potential utility as fluorogens. The low FQY of free chromophores is attributed to the flexibility 38 of benzylidene moiety 7–9, 12 . Immobilizing the chromophores in a rigid matrix results in a sev- eral orders of magnitude increase in fluorescence 11, 12, 15–19 . The applicability of GFP-derived chromophores as fluorogenic labels in living systems has been illustrated, however, they were used to stain RNA 19–23 or proteins 24, 25 that were optimized for interaction with specific com- pounds. Their use for staining the cells’ components has been limited to staining all cell mem- branes indiscriminately 26 . Here we present synthesis, spectroscopic and computational char- acterization of novel highly fluorogenic pyridinium analogues of the GFP chromophore (Fig. 3.16) designed for measuring local polarity in cells. Their unique properties—large Stokes shifts and large environment-dependent variations of the FQY—enable their use for selective staining of endoplasmic reticulum (ER). ER plays a key role in cellular metabolism, protein synthesis, and transport of intermedi- ates and signaling molecules. Characterization of the ER structure in living cells is challenging due to a wide three-dimensional interconnected network of flattened, membrane-enclosed sacks or tube-like cisterns and tubules with different thicknesses. A number of fluorescent dyes for imaging ER structure have been reported 27 , including commercial dyes ER Tracker TM Red 28 , Green 29 , and Thermo Fisher Scientific (E34250, E34251, and E12353). However, most of these dyes mainly fill the ER cavities (ER-Tracker Red, Blue, and Green produced by Invitrogen), leaving its membrane structure unknown. Yet, membrane transport and changes in the compo- sition of membranes determine the most important ER functions. Figure 3.1: HBDI (core of the GFP chromophore) and analogous pyridine chromophores 1-3 39 Serendipitously, we found that one of the HBDI derivatives containing the pyridinic cycle, compound 1 in Fig. 3.16, shows dramatic solvent-dependent variations of FQY . Such behav- ior was only observed in 2,5-disubstituted BDIs 30–32 . Since the emission wavelength of 1 is too short for imaging applications, we synthesized several of its analogues featuring extended conjugated -system, compounds 2 and 3a-c (Fig. 3.16). All these molecules belong to the class of cyanine dyes owing to their common structural feature, a methyne bridge connecting conjugated aromatic moieties. In HBDI the two aromatic groups are imidozalinone and phenol, whereas in 1-3 the phenol ring is replaced by pyridinium. Compounds 1 and 2 were synthesized according to a standard procedure using corresponding carboxymidates 4–6, 10, 13, 33 . Compounds 3a-c containing an additional double bond were synthesized by condensation of 1 with a range of aromatic aldehydes 34 . The synthetic pathways, compounds properties and characterization are described in Appendix A and B. 3.2 Results and discussion An important feature of 1-3, which is essential to their use as fluorescent reporters of local polarity, is a strong dependence of their spectroscopic properties on solvent polarity. All synthe- sized compounds have extremely large Stokes shifts, which increase significantly in polar envi- ronment (Table 3.1). The increase in the Stokes shifts is accompanied by a marked decrease of the fluorescence intensity (Fig. 3.2). The absorption maxima in various solvents are very close and the increase in the Stokes shifts is due to bathochromic shifts in emission. As expected, the absorption and emission maxima of 2 and 3 are shifted to longer wavelengths relative to 1 (Figs. 3.2 and S3, Table 3.1). Unfortunately, the FQYs of 3 are low and nearly the same in all solvents, which precludes their use as fluorogenic dyes. In contrast, 2 has the largest variation of FQY: more than two orders of magnitude upon the transition from water to dioxane (Fig. 3.2). 40 Figure 3.2: Optical properties of compounds 1, 2, and 3c. Top: Absorption and emission spectra in EtOAc. Bottom: FQY in various solvents. The solvatochromic behavior of 1 and 2 can be described by the Kamlet-Taft model 35 , which correlates the spectral shift of the solute with the solvent parameters describing its acidic (), basic (), and polar ( ) solvating properties: (cm 1 ) = 0 +p +a +b: (3.1) The relative magnitude of solute’s parametersp, a, andb reflect the sensitivity of a particular property (e.g., absorption maxima) to solvent polarity, hydrogen-bond donating or accepting abilities, respectively. The results of the analysis are summarized in Appendix (Tables 3.2 and 3.3). An increase in parameter p upon excitation of both compounds suggests a signifi- cant increase in the dipole moment, which is typical for other BDIs 24, 30, 36 and is confirmed by electronic structure calculations. Also in both cases, we observe a change in the parametera, which indicates changes in proton-accepting properties upon excitation and suggests high pho- toacidity of the corresponding protonated form 37 , which is explained by calculations (Section 41 Table 3.1: Optical properties of 1, 2, and 3c in various solvents. Solvent Abs, nm Abs, eV Ext. coeff. Em, nm Em, eV QY SS, nm SS, eV max E ex (Mcm) 1 max E ex water 1 347 3.573 10500 464 2.672 0.65 117 0.901 2 368 3.369 16500 477 2.599 0.69 109 0.770 3a 408 3.039 11000 560 2.214 0.40 152 0.825 3b 425 2.197 13500 577 2.149 0.29 152 0.768 3c 402 3.084 14000 542 2.287 1.3 140 0.797 EtOH 1 351 3.532 11500 453 2.737 3.3 102 0.795 2 377 3.289 17500 477 2.599 7.3 100 0.690 3a 411 3.017 10500 550 2.254 9.9 139 0.763 3b 433 2.863 12000 570 2.175 0.27 137 0.688 3c 408 3.039 17000 545 2.275 2.8 137 0.764 CH 3 CN 1 356 3.483 10000 452 2.743 4.7 96 0.740 2 377 3.289 16000 475 2.610 4.8 98 0.679 3a 408 3.039 11000 550 2.254 1.1 142 0.785 3b 428 2.897 13000 574 2.160 0.26 146 0.737 3c 408 3.039 15000 541 2.292 3.3 133 0.747 EtOAc 1 353 3.512 11500 442 2.805 8.9 89 0.707 2 379 3.271 17500 472 2.627 18.6 93 0.644 3a 408 3.039 10500 544 2.279 1.7 136 0.760 3b 423 2.931 12000 566 2.191 0.3 143 0.740 3c 408 3.039 16000 535 2.317 4.1 127 0.722 dioxane 1 357 3.473 11000 439 2.824 16.5 82 0.648 2 379 3.271 17000 471 2.632 46.6 92 0.639 3a 411 3.017 10000 546 2.271 2.9 135 0.746 3b 422 2.938 12500 564 2.198 0.50 142 0.740 3c 408 3.039 16000 537 2.309 4.8 129 0.730 4.6 of Appendix B). Similar analysis of the FQYs reveals that the increase in the polarity and acidity/basicity of the solvent results in fluorescence quenching. This behavior is typical for many other fluorophores, including GFP chromophore derivatives 26, 30–32 and the compounds containing the pyridinium moiety 38 . A likely cause of reduced FQY in polar solvents is partial bond-order flipping associated with strong charge transfer character, which is stabilized in polar media. Changes in bond orders lead to reduced barriers for torsional motion in the excited state thus facilitating radiationless relaxation. However, the behavior of 1 and 2 is different, in partic- ular 1 has an extremely low FQY in hexane. This indicates possible changes in the nature of the excited state and/or in the quenching mechanism. The change in electronic state is confirmed by calculations. 42 S2 S1 Figure 3.3: NTOs for the two lowest excited states of 1 in gas phase. To understand the nature of the large Stokes shift and the effect of solvent polarity on the fluorescent properties of the chromophores, we carried out electronic structure calculations. As shown in Appendix, the computed excitation energies correlate reasonably well with the exper- imental peaks maxima: although the theoretical values of absorption and emission are system- atically blue-shifted relative to the experiment, the magnitude of the Stokes shifts is reproduced well by calculations. Fig. 3.17 shows natural transition orbitals (NTOs) corresponding to the two lowest excited states of 1 at the ground-state geometry (see also Fig. 3.17 and 3.18 in Appendix). Importantly, the lowest excited state of 1 is dark at the ground-state geometry; it can be described as ann! transition. The bright state corresponds to a! transition; the respective NTOs resemble those in HBDI 36, 39 . In all three model compounds, the NTOs of the bright state are localized on the methyne bridge and imidazolone ring (see Fig. 3.18), with only minor contributions from the pyridinium moiety. In compounds 2 and 3c, the bright state is always the lowest. To assess fluorescent properties of the chromophores, we optimized the structures of the lowest excited state. In isolated chromophore 1, the structural relaxation does not change the character of the state and S 1 remains dark, which, by virtue of Kasha’s rule, means low FQY . The calculations including solvent reveal that while solvent has a small effect on the energies of the excited states at the ground-state geometry (i.e., vertical excitation energies of the S 1 and S 2 states shift by0.12 eV), it profoundly affects structural relaxation, leading to the reversal of the state ordering in the polar solvents, such that 1, which has very low FQY in hexane, becomes fluorescent in polar solvents. This behavior can be explained by the change in the dipole moment in the excited state and by the trends in the transition dipole moments. ! electronic excitation results in a dipole moment increase by 2-3 D, which 43 further increases upon structural relaxation. The change in dipole moment is associated with the changes in bondlengths, i.e., in the excited state, formally double bonds elongate and formally single bond slightly contract (largest changes occur on the methyne bridge). These trends are well documented 39–41 in GFP-like chromophores and can be explained by the H¨ uckel model 36 . At the ground-state geometry, neither permanent nor transition dipole moments are affected by solvent polarity. However, structural relaxation in polar solvents leads to even higher charge separation in excited state, which results in noticeable solvent-induced variations of respective permanent and transition dipole moments. This explains large solvatochromic shifts in emis- sion that lead to solvent-induced variations in Stokes shifts. Fig. 3.4, which shows the computed Stokes shifts versus the difference of the permanent dipole moment () in S 1 and S 0 , illus- trates that the main factor responsible for large solvent-induced variations in the Stokes shift is the change of the dipole moment. The optimized excited-state structures (Figs. 3.19, 3.22, and 3.25 in Appendix) reveal that in polar solvents changes in bondlengths are more pronounced for all 3 model compounds. Significant solvent effect on the shape of excited-state potential energy surfaces has been observed in the HBDI chromophores 40 ; in this study 40 the calculations revealed that in the anionic form of HBDI, polar solvent increases changes in bond alternation upon photoexcitation, which is similar to the trends observed here. The changes in bondlengths are related to partial bond-order flipping, in particular, on the methyne bridge. The scans along torsional degrees of freedom in anionic HBDI have shown that the changes in bond alternation are accompanied by the reduced barriers to rotation, which is ultimately responsible for the enhanced radiationless relaxation in polar solvents. Given the similarity in the solvent-induced structural changes in chromophores 1-3 and HBDI 40 , a similar effect is likely to be operational here (see Appendix D6). Remarkable solvatochromism of the emission maxima and FQY of 2 suggests that it can be used for measurements of local polarity in living cells or as a fluorogenic dye for labeling cell 44 2 3 4 5 6 7 8 9 0.8 0.9 1.0 1.1 1.2 1.3 1, R 2 =0.82 2, R 2 =1.00 3c, R 2 =0.91 Stokes shift (eV) Δμ (Debye) Figure 3.4: Computed Stokes shifts versus the change in permanent dipole moment ( = (S 1 )(S 0 )). Figure 3.5: Confocal microscopy of the Hela-Kyoto and NIH 3T3 cells labeled with ER- Tracker Red (0.5 mkM) and 2 (5.0 mkM). 559 nm excitation and TRIC for ER-tracker Red and 405 nm excitation and 450-550 nm emission window for 2 with 60X magnification were used. Top: Labeled alive cells; scale 10 mkM. Bottom: Stained cells fixed with formaldehyde right after the fixation (A, B) and after the addition of an extra portion of compound 2 (C); scale 15 mkM. 45 organelles or lipids. Addition of 2 to cellular media leads to the instantaneous appearance of intense fluorescence inside the cells. This staining is much more selective than with other ana- logues of the GFP chromophore 26 and the main stained cellular part is ER. Various lipid droplets and the small vacuole-like structure were stained too, but the addition of 20% of Pluronic F-127 in DMSO stock of 2 decreases dramatically the percentage of the stained vacuoles and lipid drops. The addition of 3-20 mkM of 2 from x1000 DMSO-Pluronic stock to Hela-Kyoto and NIH 3T3 cells results in a selective staining of ER, as confirmed by colocalization with 0.5 mkM ER-tracker Red (Invitrogen) (Fig. 3.5, see Section Appendix A2. for more details). A slight difference in the staining was detected in NIH 3T3 fibroblasts, cells having lamelopodia at the head-part of the cell, for which 2 stains additional attached to ER structures or additional ER parts in the plasma membrane region (Fig. 3.5). We assume that these structures can be the thinnest or the most dense ER compartments into which the selected tube-filling ER-tracker penetrates poorly. The fixation of Hela-Kyoto cells stained with 0.5 mkM ER-tracker Red and 5 mkM of 2 using 4% formaldehyde leads to 2 elution, while ER-tracker Red is retained in ER (Fig. 3.5, bottom). However, upon adding another 10 mkM of 2, the staining of the ER mem- branes was again observed, but the proportion of non-segregated membranes of vacuole-like structures increased (Fig. 3.5, bottom). Furthermore, when 90% methanol or Triton X-100 was used for cell permeabilization, both dyes were washed out of the cells, presumably due to the destruction of the membranes and the integrity of the membrane cisterns. All this suggests that the observed staining is due to an increase of FQY and accumulation of 2 in the ER membranes. At the conditions of cell microscopy, 2 is remarkably photostable. We analyzed the per- formance of 2 in Hela-Kyoto cells compared to the ER-localized blue fluorescent protein BFP- KDEL. The fluorescence of BFP-KDEL was photobleached two-fold in 1.5-2.0 min of 14% 405 nm laser irradiation, while 2 showed no fluorescence decrease at all (Fig. 3.6). The apparent 46 Figure 3.6: Bleaching behavior of Hela-Kyoto cells labeled with 2 and with ER-localized BFP-KDEL protein. Top: Fluorescence intensity of alive (A) and fixed (B) cells in a time- lapse fluorescence microscopy. Bottom: Fluorescent images of alive HeLa cells during the photobleaching. interminable photostability of 2 suggests its high mobility in cell membranes, causing perma- nent exchange of bound and free dye molecules from the solution in the field of bleaching, as observed for other fluorogens 20, 26 . Note that during a more extended irradiation the fluores- cence intensity of 2 only increases (Fig. 3.6A). The effect can be explained by the photodamage of the membranes due to a high laser power and recruiting more dye molecules into damaged membranes from the surroundings. This effect disappears in fixed cells upon decreasing the laser power or exposure to irradiation (Fig. 3.6B). Such a rapid exchange probably indicates that the staining does not occur due to some chemical interactions of 2. Moreover, the staining is reversible — the replacement of the medium leads to a noticeable weakening of fluorescence, which can be reversed by adding a new portion of the dye. Also, the staining did not result in cells death, which were stable for 10-12 hours (at concentrations 20 mkM), while the test with trypan blue dye did not demonstrate any membrane damage (not shown). We also inves- tigated the pH dependence of optical properties of 2 (Fig. 3.10) and found that its imaging 47 utility should not be affected by pH-dependent transitions in cells. The pKa of 2 is 3.6, which lies far beyond the physiological range (the value and nature of the optical transition is typical for many other BDIs 42 ). Since one of the fluorogenic staining mechanics is the formation of fluorescent agglomerates, we tested 2 for possible aggregation-induced emission and showed that this compound demonstrates no visible emission in crystal solid or in freshly precipitated forms. Thus, we conclude that 2 stains ER membranes because of its unique combination of hydrophobic and fluorogenic properties. To assess a possibility of using these chromophores in the two-photon excitation regime, we computed 43 2PA (two-photon absorption) cross sections for several excited states for 1 and 2 and compared it with the prototype HBDI; the results are collected in Table 3.13. The cal- culations suggest that although 2 is less bright than HBDI in 2PA regime, the cross-sections are sufficiently large for it to be used in two-photon excitation imaging. In contrast, 1 has very bright 2PA transition at 458 nm. If the intensity of this band spills over to longer wavelengths due to inhomogeneous broadening and vibronic interactions (as observed, for example, in a recent study of stilbenes 44 ) 1 might actually be brighter than HBDI in two-photon excitation regime. 3.3 Conclusion We presented a novel group of fluorogenic dyes derived from the GFP chromophore. The compounds containing a pyridinium ring in the original chromophore’s core feature large solvent-dependent Stokes shifts and solvent-induced variations in the FQY . The calculations explain the observed trends in terms of the increase of the dipole moment upon excited-state relaxation in polar solvents, which is associated with the changes in bondlengths and partial bond-order flipping in the excited state. A unique combination of such optical characteristics and lipophilic properties enables using one of the new dyes for the ER staining. Owing to its 48 extremely high photostability (ensured by a dynamic exchange between the free and absorbed compound’s states) and selectivity (demonstrated by several examples), in combination with pH-independence in the physiological range, 2 is a promising label for this type of cellular organelles. 3.4 Appendix A: Experimental details 3.4.1 Appendix A1: Materials and methods Compound 1: (Z)-4-((Pyridin-4-yl)methylene)-1,2-dimethyl-1H-imidazol-5(4H)-one. Yel- low solid, 1.5 g (73%), mp = 175-178 C. Compound 2: (Z)-4-((Pyridin-4-yl)methylene)-1-methyl-2-phenyl-1H-imidazol-5(4H)-one. Yellow solid, 1.7 g (65%), mp = 190-192 C. Compound 3a: (Z)-4-((Pyridin-4-yl)methylene)-1-methyl-2-(E)-styryl-1H-imidazol-5(4H)- one.Yellow solid, 94 mg (33%), mp = 201-203 C. Compound 3b: (Z)-4-((Pyridin-4-yl)methylene)-1methyl-2-((E)-2-(4-methoxyphenyl)vinyl)- 1H-imidazol-5(4H)-one. Yellow solid, 67 mg (21%), mp = 223-225 C. Compound 3c: (Z)-4-((Pyridin-4-yl)methylene)-1-methyl-2-((E)-2-(pyridin-4-yl)vinyl)- 1H-imidazol-5(4H)-one. Yellow solid, 100 mg (35%), mp255 C with decomposition. Figure 3.7: Structures and properties of compounds 1-3. 49 Commercially available reagents were used without additional purification. E. Merck Kieselgel 60 was used for column chromatography. Thin layer chromatography (TLC) was performed on silica gel 60F 254 glass-backed plates (MERCK). Visualization was effected by UV light (254 or 312 nm) and staining with KMnO 4 . NMR spectra were recorded on a 700 MHz Bruker Advance III NMR at 293 K, 800 MHz Bruker Advance III NMR at 333 K, and Bruker Fourier 300. Chemical shifts are reported relative to the residue peaks of CDCl 3 (7.27 ppm for 1 H and 77.0 ppm for 13 C) or DMSO-d 6 (2.51 ppm for 1 H and 39.5 ppm for 13 C). Melting points were measured on an SMP 30 apparatus. High-resolution mass spectra (HRMS) spectra were recorded on AB Sciex TripleTOF 5600+ equipped with a DuoSpray (ESI) source. General method for the preparation of (Z)-4-((Pyridin-4-yl)methylene)-1-methyl-1H- imidazol-5(4H)-ons (1,2). The corresponding aromatic aldehyde (10 mmol) was dissolved in CHCl 3 (50 mL) and mixed with methylamine solution (40% aqueous, 2.5 mL) and anhydrous Na 2 SO 4 (10 g). The mixture was stirred for 48 h at room temperature, filtered, and dried over the additional Na 2 SO 4 . The solvent was evaporated, the ethyl((1-methoxy)amino)acetate or benzoate (20 mmol) was added and the mixture was stirred for 24 h at room temperature. The mixture was dried in vacuum and the product was purified by column chromatography (CHCl 3 /EtOH 100:1). General method for the preparation of (Z)-4-((Pyridin-4-yl)methylene)-1-methyl-2- aryl-1H-imidazol-5(4H)-ones (3). The product of previous stage 1 (1 mmol) was dissolved in dioxane (20 mL), ZnCl 2 (2 g) and the corresponding aldehyde (20 mmol) were added and the reaction mixture was heated to 80 C for 2-20 h. The mixture was cooled and dissolved with EtOAc (100 mL) washed by NaHPO 4 solution (5%, 250mL), EDTA solution (5%, 250 mL), water (250 mL), and brine (250 mL) and dried over Na 2 SO 4 . The solvent was 50 evaporated and product 2 was purified by column chromatography (CHCl 3 /EtOH 100:2). Figure 3.8: Synthesis of compounds 1-3. 3.4.2 Appendix A2: Fluorescent imaging in cells Fluorescent imaging of non-transfected cells HeLa-Kyoto and NIH 3T3 cells (the both from EMBL collection) were seeded into 35-mm glass bottom dishes (MatTek Corporation) and cultured in DMEM (Hela-Kyoto) or RPMI (NIH 3T3) media with 10% FBS, 20 mM potassium pyruvate at 37 C in a 5% CO 2 atmosphere. After the 24-48 hours cells were placed into an environmental chamber in 2 mL of Hank’s Balanced Salt Solution with calcium and magnesium (HBSS/Ca/Mg, Gibco cat.# 14025-092) supplemented with 20 mM HEPES (pH 7.2) and 20 mM glucose at 37 C. Afterwards cells were incubated with the 5.0M of compound 2 (added from 5 mM stock in 80% DMSO and 20% Pluronic F-127 (Thermo Fisher Scientific cat.# P3000MP)) and/or 0.5M ER-tracker TM Red (added from 1 mM stock Invitrogen cat. #E34250) for 30 min. Images were captured 51 using Olympus FluoView 1200 confocal Microscope at 559 nm excitation and TRIC for ER- tracker TM Red and 405 nm excitation and 450-550 nm emission window for compound 2 chan- nel using 60X magnification. Images were processed and analyzed for co-localization in Image J. Cells fixation and fixed-cells imaging HeLa-Kyoto cells were grown in 35-mm glass bottom dishes and stained by compound 2 and/or 0.5 M ER-tracker TM Red as described above. Afterwards cells were fixed with 4% formaldehyde, washed 3 times with 1 ml of PBS and imaged. Images were captured using Olympus FluoView 1200 confocal Microscope at 559 nm excitation and TRIC for ER- tracker TM Red and 405 nm excitation and 450-550 nm emission window for compound 2 using 60X magnification (Fig. 5 bottom, A and B). Afterwards 10 mkM of compound 2 was added to cell media, and new image of compound 2 staining was obtained (Fig. 5 bottom, C). Photobleaching analysis We conducted a bleaching analysis of compound 2 in Hela-Kyoto cells compared to the ER-localized blue fluorescent protein BFP-KDEL (Addgene #49150). HeLa-Kyoto cells were seeded into 35-mm glass bottom dishes (MatTek Corporation) and cultured in DMEM (Hela- Kyoto) or RPMI (NIH 3T3) media with 10% FBS, 20 mM potassium pyruvate at 37 C in a 5% CO 2 atmosphere. After 24-36 h, cells were transfected by a mixture of 1 ng DNA and 3 mkL FuGene HD transfection reagent in 100 mkL OptiMEM solution per one dish. After 14 h, cell medium was replaced by 2 mL fresh medium. For imaging 24-48 hours after transfection cells were placed into an environmental chamber in 2 mL of Hank’s Balanced Salt Solution with calcium and magnesium (HBSS/Ca/Mg, Gibco cat.# 14025-092) supplemented with 20 mM HEPES (pH 7.2) and 20 mM glucose at 37 C. After that cells were imaged using a Olimpus 52 FluoView 1200 confocal microscope equipped with a 60X oil objective using 405 nm excitation and 450-550 nm emission window. Images were processed and analyzed for co-localization in Image J. All graphs were processed in OriginPro8.1 (OriginLab). 3.5 Appendix B: Experimental results 3.5.1 Appendix B1: Solvatochromic properties of compounds 1-3 UV-VIS spectra were recorded with a Varian Cary 100 spectrophotometer. Fluorescence excitation and emission spectra were recorded with Agilent Cary Eclipse fluorescence spec- trophotometer. Table 1 of the paper shows optical properties of compounds 1-3 in various solvents. 3.5.2 Appendix B2: Solvatochromic analysis of absorption and emission spectra of compounds 1 and 2 Kamlet-Taft’s model 35 correlates the spectral shift of the solute with the solvent parameters that are responsible for the acidic (), basic (), and polar ( ) solvating properties: (cm 1 ) = 0 +p +a +b (3.2) Table 3.2 summarizes parameters , , and for various solvents 35 and absorption/emission maxima and fluorescence quantum yields of 1 and 2 in various solvents. Table 3.3 presents Kamlet-Taft-type linear regression analyses. 53 s Figure 3.9: From top to bottom: Fluorescence and absorption spectra of 1-3 in water, ethanol, acetonitrile, actetate, and dioxane. 54 Table 3.2: Kamlet-Taft’s parameters and absorption/emission maxima (in nm) and fluo- rescence quantum yields (in %) of 1 and 2 in various solvents. Solvent 1 2 abs em FQY abs em FQY Et 2 O 0.24 0.47 0 351 434 6.06 376 470 26.27 EtOH 0.54 0.77 0.83 351 453 3.27 377 477 7.27 EtOAc 0.45 0.45 0 353 442 8.90 379 472 18.64 MeOH 0.60 0.62 0.93 349 458 1.75 375 482 3.68 ACN 0.66 0.31 0.19 356 452 4.72 377 475 4.76 CH 2 Cl 2 0.73 0 0.3 355 438 8.50 378 472 16.76 DMF 0.88 0.69 0 361 455 4.32 382 481 6.83 DMSO 1.00 0.76 0 362 458 0.55 383 485 2.37 Water 1.09 0.4 1.17 347 464 0.65 366 477 0.69 Acetone 0.62 0.48 0.08 355 443 4.67 378 476 11.24 THF 0.55 0.55 0 359 445 6.47 381 476 43.35 Hexane 0 0 -0.04 353 416 0.008 374 458 54.27 Toluene 0.49 0.11 0 356 437 12.97 381 476 53.12 Dioxane 0.49 0.37 0 357 439 16.46 379 471 46.61 PY 0.87 0.64 0 360 454 5.00 378 483 23.58 Table 3.3: Solvatochromic spectral parameters (in 10 3 /cm 1 ) of 1 and 2. a b p 0 /FQY a 0 R 1 Abs 0.8 - 0.2 -0.6 28.5 0.92 Em -0.4 -1.0 -1.3 23.8 0.97 FQY b 0 -0.1 0 0.09 0.50 FQY c 0 -0.1 -0.1 0.16 0.80 2 Abs 0.6 -0.4 -0.1 26.6 0.80 Em 0.0 -0.5 -0.7 21.7 0.91 FQY b -0.2 -0.2 -0.3 0.53 0.79 a in cm 1 and FQY in %. For FQY the corresponding coefficients were calculated using multivariative linear regression analogously to Kamlet-Taft’s equation. b All solvents. c The data for hexane excluded. 3.5.3 Appendix B3: pH-titration of compound 2 pKa values of protonated forms of compound 2 were measured by titration of 15M solu- tion in water. Absorption spectra of 2 in water at various pH and its titration curves are shown in Fig. 3.10. 55 Figure 3.10: Left: pH-titration of compound 2. Right: Absorption spectra of 2 at different pH values. Neutral: abs =368 nm; Cation: abs =395 nm; pKa(Abs)=3.6. 3.5.4 Appendix B4: 1 H and 13 C NMR spectra 56 Figure 3.11: Compound 1: 1 H NMR (800 MHz, DMSO-d 6 )=8.64 (d, J=5.9 Hz, 2 H, Ar), 8.08 (d, J=6.11 Hz, 2 H, Ar), 6.93 (s, 1 H, Ar-CH), 3.11 (s, 3 H, CH 3 ), 2.39 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 ) = 15.5, 26.3, 121.0, 124.9, 140.82, 142.3, 150.0, 167.1, 169.5; HRMS (m/z) calc-d. C 11 H 12 N 3 O for [M +H] + 202.0975, found 202.0978. 57 Figure 3.12: Compound 2: 1 H NMR (700 MHz, DMSO-d 6 )=8.68 (d, J=6.2 Hz, 2 H, Ar), 8.17 (d, J=5.9 Hz, 2 H, Ar), 7.98 (d, J=6.9 Hz, 2 H, Ar), 7.69 (t, J=7.3 Hz,1 H, Ar), 7.63 (t, J=7.5 Hz, 2 H, Ar), 7.15 (s, 1 H, Ar-CH), 3.29 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO- d 6 ) = 28.8, 123.1, 125.1, 128.5, 128.8, 128.9, 132.0, 140.8, 142.2, 150.1, 165.1, 170.4; HRMS (m/z) calc-d. C 16 H 14 N 3 O for [M +H] + 264.1131, found 264.1135. 58 Figure 3.13: Compound 3a: 1 H NMR (300 MHz, DMSO-d 6 ) =8.87 (d, J=6.6 Hz, 2 H, Ar), 8.73 (d, J=6.5 Hz, 2 H, Ar), 8.29 (d, J=15.8 Hz, 1 H, CH=CH), 7.89 - 7.96 (m, 2 H, Ar), 7.50 - 7.55 (m, 3 H, Ar), 7.36 (d, J=15.7 Hz, 1 H, CH=CH), 7.13 (s, 1 H, Ar-CH), 3.33 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 ) = 26.5, 113.7, 120.9, 125.1, 128.6, 128.9, 130.5, 134.8, 141.2, 142.0, 142.9, 150.0, 162.9, 169.8; HRMS (m/z) calc-d. C 18 H 16 N 3 O for [M +H] + 290.1288, found 290.1292. 59 Figure 3.14: Compound 3b: 1 H NMR (300 MHz, DMSO-d 6 ) = 8.87 (d, J=6.8 Hz, 2 H, Ar), 8.78 (d, J=6.7 Hz, 2 H, Ar), 8.29 (d, J=15.5 Hz, 1 H, CH=CH), 7.91 (d, J=8.8 Hz, 2 H, Ar), 7.21 (d, J=15.6 Hz, 1 H, CH=CH), 7.07 - 7.11 (m, 3 H, Ar, Ar-CH), 3.86 (s, 3 H, CH 3 ), 3.32 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 )=26.5, 55.4, 110.8, 114.5, 119.9, 125.0, 127.6, 130.6, 141.3, 142.1, 143.1, 150.0, 161.4, 163.2, 169.9; HRMS (m/z) calc-d. C 19 H 18 N 3 O 2 for [M +H] + 320.1394, found 320.1397. 60 Figure 3.15: Compound 3c: 1 H NMR (700 MHz, DMSO-d 6 )=8.66 - 8.71 (m, 4 H, Ar), 8.20 (d, J=5.9 Hz, 2 H, Ar), 8.09 (d, J=15.8 Hz, 1 H, CH=CH), 7.86 (d, J=5.9 Hz, 2 H, Ar), 7.54 (d, J=15.8 Hz, 1 H, CH=CH), 7.07 (s, 1 H, Ar-CH), 3.31 (s, 3 H, CH 3 ); 13 C NMR (176 MHz, DMSO-d 6 )=26.4, 118.3, 121.9, 122.2, 124.9, 138.9, 140.8, 141.7, 142.5, 149.9, 150.2, 162.2, 169.5; HRMS (m/z) calc-d. C 17 H 15 N 4 O for [M +H] + 291.1240, found 291.1244. 61 3.6 Appendix C: Theoretical methods and computational details 1 2 3c Figure 3.16: Model systems representing compounds 1, 2, and 3c. We investigated electronic properties of the synthesized chromophores computationally. The calculations were carried out for model structures of 1, 2, and 3c in which the terminal methyl groups were replaced with hydrogens. Fig. 3.16 shows the model systems. Although terminal methyl groups can affect excited-state lifetimes in conjugated GFP-like dyes, their effect on the energetics of excited states or photoacidic properties is known to be small 37 . The comparison (shown below) of gas-phase excitation energies of methylated and unmethylated model structures of 1, 2, and 3c confirms that the computed excitation energies are not sensitive to substituting methyls by hydrogens. The structures of the gas-phase chromophores were optimized by DFT and TDDFT using long-range corrected functional, !B97X-D (Ref. 46) and the aug-cc-pVDZ basis set. The structures of the chromophores in solvents were optimized by DFT/TDDFT with !PBEPBE and aug-cc-pVDZ. All relevant Cartesian coordinates are given below. Absorption and emission energies were computed by TDDFT/!PBEPBE (Ref. 47) with aug-cc-pVDZ as vertical energy differences at the S 0 and S 1 optimized geometries, respectively. To validate TDDFT protocol, we carried out additional calculations using another long-range 62 corrected functional, !B97X-D as well as wave function methods, SOS-CIS(D) 48 and EOM- EE-CCSD 49 . To analyze excited-state wave functions, we computed natural transition orbitals (NTOs) using libwa module 50–52 . Cross sections for two-photon absorption (2PA) were com- puted at the EOM-CCSD level of theory 43 . To account for solvent effects, we used non-equilibrium polarizable continuum model (PCM) 53, 54 . We employed both linear response (LR) and state-specific (SS) approaches. We also included perturbative corrections, ptLR and ptSS 53, 54 . In excited-state calculations of solvated chromophores, we considered two different proto- cols: (i) single-point energy calculation using gas-phase optimized geometries of S 0 and S 1 and (ii) single-point energy calculation using the geometries of S 0 and S 1 optimized in a particu- lar solvent. We found that the results obtained with protocol (ii) agree much better with the experimental trends; thus, the results reported below follow protocol (ii). Interestingly, the two protocols yield significantly different results only for emission energies because the S 0 struc- tures are not sensitive to the solvent, in contrast to the S 1 structures. All calculations were carried out using Q-Chem 55, 56 . 3.7 Appendix D: Computational results 3.7.1 Appendix D1: Excitation energies of 1, 2, and 3c in gas phase Fig. 3.17 shows energy levels and NTOs corresponding to the two lowest excited states of 1 at the ground-state and relaxed excited-state geometries. Table 3.4 presents excitation energies at the S 0 and S 1 geometries and the corresponding Stokes shifts for 1, 2, and 3c in gas phase computed at different levels of theory; Table 3.5 shows excitation energies for methylated model structures. In agreement with the experimental findings 37 , methyl groups have negligible effect on the excitation energies. The results for the key electronic properties are consistent across 63 S 0 S 1 S 2 σ 2 =0.98 σ 2 =0.95 σ 2 =0.97 π- π * n- π * n- π * 3.953 (0.51) 3.688 (0.00) 3.00 (0.00) (a) S 0 S 1 S 2 σ 2 =0.97 σ 2 =0.95 σ 2 =0.98 π- π * n- π * π- π * (b) 3.86 (0.49) 3.75 (0.00) 2.62 (0.76) Figure 3.17: Excited states and NTOs for 1 in (a) gas phase and (b) water. Left and right panels show the states at the S 0 and S 1 optimized geometries, respectively. all methods. The results in Table 3.4 reveal important differences between 1, 2, and 3c. The lowest bright transition at the ground-state geometry in 1 corresponds to the S 0 !S 2 transition, whereas in 2 and 3c it corresponds to the S 0 -S 1 transition. In 1, the S 1 state is dark at the ground-state geometry. The oscillator strengths of S 1 and S 2 can be explained by NTOs, which correspond ton! and! type transitions, respectively. Because the emission usually happens from S 1 , by virtue of Kasha’s rule, 1 is non-fluorescent. In 2 and 3c, the NTOs for the S 0 !S 1 transition correspond to! excitation. Participation ratios for all transitions are close to one. 64 Table 3.4: Excitation energies of 1, 2, and 3c in gas phase. All energies are in eV; oscillator strength is given in parenthesis. aug-cc-pVDZ basis set. Method 1 2 3c E ex E ex Stokes E ex E ex Stokes E ex E ex Stokes (S 0 -S 2 ) (S 1 -S 0 ) shift (S 0 -S 1 ) (S 1 -S 0 ) shift (S 0 -S 1 ) (S 1 -S 0 ) shift !PBEPBE 3.953 3.003 0.95 3.660 2.935 0.725 3.512 2.881 0.631 (0.51) (0.00) (0.69) (0.60) (1.24) (1.25) !B97X-D 3.923 3.128 0.805 3.595 2.914 0.681 3.428 2.829 0.599 (0.53) (0.00) (0.69) (0.65) (1.24) (1.27) SOS-CIS(D) 4.238 3.152 1.086 3.170 2.331 0.839 3.382 2.639 0.743 (0.77) (0.00) (0.71) (0.69) (1.04) (1.08) EOM-CCSD 4.256 3.374 0.882 3.281 2.399 0.882 3.311 2.604 0.707 (0.55) (0.00) (0.80) (0.88) (1.09) (1.08) Using!B97X-D optimized geometries. Table 3.5: Excitation energies of methylated analogues of 1, 2, and 3c in gas phase. All energies are in eV; oscillator strength is given in parenthesis.!B97X-D/aug-cc-pVDZ. Molecule E abs ex (f l ) E em ex (f l ) Stokes shift 1 3.910 (0.51) 2.976 (0.12) 0.934 2 3.566 (0.57) 2.787 (0.48) 0.779 3c 3.367 (1.00) 2.737 (1.01) 0.630 S 0 -S 1 σ 2 =0.97 π- π * 3.66 (0.69) (a) S 0 -S 1 σ 2 =0.92 π- π * 3.51 (1.24) (b) Figure 3.18: NTOs for the S 0 !S 1 transition in 2 (left) and 3c (right) in the gas phase. 3.7.2 Appendix D2: Solvatochromic properties of molecule 1 Table 3.6 shows electronic properties of 1. Mulliken’s charges on nitrogens in the ground and excited states are shown in Table 3.7. Ground- and excited-state structures are optimized in each solvent, as described in Section 3.6. Fig. 3.19 shows the key bondlengths in S 0 - and S 1 -optimized structures of 1 in gas phase and in water (only bonds that show significant change 65 Figure 3.19: Ground- and excited-state structures of 1 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. Table 3.6: Electronic properties of 1 in various solvents. Energies are in eV; dipole moments in debye. Solvent E ex tr gs ex E ex tr ex gs E ss tr ge (S 0 -S 2 ) (S 0 -S 2 ) (S 0 ) (S 0 ) (S 1 -S 0 ) (S 1 -S 0 ) (S 1 ) (S 1 ) gas phase 3.95 2.30 4.03 5.88 3.00 0.05 6.66 4.08 0.95 2.25 2.63 water 3.86 2.26 5.78 8.04 2.62 3.39 8.69 6.22 1.24 1.13 2.91 acetonitrile 3.86 2.28 5.73 7.98 2.63 3.24 8.44 6.06 1.23 0.96 2.71 methanol 3.86 2.25 5.72 7.96 2.63 3.23 8.43 6.05 1.22 0.98 2.70 acetate 3.86 2.27 5.34 7.42 2.71 3.02 7.82 5.59 1.15 0.75 2.48 dioxane 3.87 2.31 4.75 6.57 2.86 2.37 7.12 4.92 1.02 0.06 2.37 hexane 3.88 2.32 4.62 6.38 2.98 0.07 7.16 4.85 0.90 2.31 3.54 upon excitation are shown). The theoretical values of excitation energies are systematically blue-shifted relative to the experiment. Tables 3.6 and 3.8 show that absorption energy is not affected by solvent polarity (see also Fig. 3.20). Because the variations in absorption energy are small (0.01-0.02 eV), the correlation between calculated and experimental values appears to be poor. Yet, theory and experiment are in qualitative agreement that absorption maximum is not very sensitive to the solvent polarity. The two protocols described in Section 3.6 yield very different results. When emission energies are computed without re-optimization of excited-state structures in each solvent, there 66 is no solvatochromic shift, which contradicts the experimental observation. However, upon re-optimization of excited-state structures in each solvent, we obtain solvent-dependent shifts which correlate well with the experimental values. This result illustrates the sensitivity of excited-state geometries to solvent polarity (Fig. 3.20). The analysis of the optimized struc- tures (Fig. 3.19) reveals that changes in bondlengths upon photoexcitation increase in polar solvent. Tables 3.6 and 3.8 show that emission energies decrease in polar solvents, giving rise to the increased Stokes shifts. Thus, in agreement with the experiment, the calculations con- firm that the variations in Stokes shifts in 1 and 2 are driven by the variations in emission energy. Although the computed excitation energies are blue-shifted relative to the experimental peak maxima, the differences appear to be systematic and the computed and theoretical Stokes shifts are in good agreement. Moreover, the computed and experimental solvatochromic trends correlate well, confirming that the blue shift of theoretical values relative to the experiment is systematic. Table 3.7: Mulliken charges on nitrogen atoms in 1 (see Fig. 3.16 for atom numbering). solvent N 1 (S 0 ) N 2 (S 0 ) N 3 (S 0 ) N 1 (S 2 ) N 2 (S 2 ) N 3 (S 2 ) N 1 (S 1 ) N 2 (S 1 ) N 3 (S 1 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 1 ) (S 1 ) (S 1 ) gas phase -0.09 -0.10 -0.44 -0.09 0.04 -0.44 -0.16 0.08 -0.45 water -0.24 -0.13 -0.47 -0.20 -0.08 -0.48 -0.21 -0.17 -0.52 acetonitrile -0.24 -0.13 -0.47 -0.20 -0.08 -0.48 -0.22 -0.36 -0.49 methanol -0.24 -0.13 -0.47 -0.20 -0.08 -0.48 -0.20 -0.31 -0.51 acetate -0.24 -0.12 -0.46 -0.20 -0.07 -0.47 -0.20 -0.31 -0.49 dioxane -0.23 -0.11 -0.45 -0.19 -0.07 -0.46 -0.22 -0.28 -0.46 hexane -0.23 -0.11 -0.45 -0.19 -0.07 -0.46 -0.29 0.00 -0.48 Solvent-dependent variations in excitation energy and Stokes shifts can be explained by comparing the trends in energies with transition and permanent dipole moments (Table 3.6 and Figs. 3.20 and 3.21). Electronic excitation leads to an increase of the dipole moment in the bright state, which is consistent with its character. Similarly to the excitation energies, ground-state dipole moment and transition dipole moment at the S 0 geometry are not strongly affected by variations in solvent polarity. In contrast, at the S 1 geometry both permanent and 67 transition dipole moments show large variations; both values increase in polar solvents. We observe good correlation in the trends in Stokes shifts with the transition dipole moment (Fig. 3.21) and the change in permanent dipole moment ( ge , Fig. 4 of main text). This correla- tion confirms that the solvatochromism of the Stokes shifts in these chromophores originates in increased charge separation in the state, which leads to significant and solvent-dependent structural relaxation of the excited state. Fig. 3.21 (bottom) compares the trend in FQY versus the transition dipole moment (in this figure, hexane is excluded because of the change in elec- tronic state character). Interestingly, there is a reasonable correlation between the two quantities — the FQY decreases with the increase of tr . 68 0 10 20 30 40 50 60 70 80 3.70 3.72 3.74 3.76 3.78 3.80 3.82 3.84 3.86 3.88 3.90 Theory Exp Dielectric constant E ex (eV) 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62 3.64 C 3.860 3.865 3.870 3.875 3.880 3.46 3.48 3.50 3.52 3.54 3.56 R 2 =-0.08 E ex ,Exp (eV) E ex ,Theory (eV) v 0 10 20 30 40 50 60 70 80 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 Theory Exp Dielectric constant E ex (eV) 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 C 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 R 2 =0.87 E ex ,Exp (eV) E ex ,Theory (eV) 0 10 20 30 40 50 60 70 80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 Theory Exp Dielectric constant Stokes shift (eV) 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 C 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 R 2 =0.82 Stokes shift,Exp (eV) Stokes shift,Theory (eV) Figure 3.20: Variation in absorption (top) and emission (middle) energies and Stokes shifts (bottom) of 1 in different solvents (left) and correlation between theory and experiment (right). 69 2.25 2.26 2.27 2.28 2.29 2.30 2.31 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.90 R 2 =0.77 E ex (eV) μ tr (S 0 -S 2 ) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 2.60 2.65 2.70 2.75 2.80 2.85 2.90 R 2 =0.98 E ex (eV) μ tr (S 1 -S 0 ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.00 1.05 1.10 1.15 1.20 1.25 R 2 =0.96 Stokes shift (eV) μ tr 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 R 2 =0.96 FQY μ tr Figure 3.21: Top: Absorption (left) and emission energies (right) in different solvents versus transition dipole moment for 1. Bottom: Stokes shift (left) and FQY (right) in different solvents versus transition dipole moment. 70 3.7.3 Appendix D3: Solvatochromic properties of molecule 2 Figure 3.22: Ground- and excited-state structures of 2 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. Table 3.8: Electronic properties of 2 in various solvents. Energies are in in eV , dipole moments in debye. Solvent E ex tr gs ex E ex tr ex gs E ss tr ge (S 0 -S 1 ) (S 0 -S 1 ) (S 0 ) (S 0 ) (S 1 -S 0 ) (S 1 -S 0 ) (S 1 ) (S 1 ) gas phase 3.66 2.77 5.31 5.91 2.93 2.88 6.09 5.84 0.73 0.11 0.78 water 3.57 2.76 7.33 9.44 2.47 3.94 10.79 8.71 1.11 1.19 3.46 acetonitrile 3.58 2.76 7.28 9.36 2.48 3.77 10.68 8.64 1.10 1.02 3.40 methanol 3.57 2.76 7.27 9.35 2.48 3.92 10.67 8.63 1.09 1.16 3.39 acetate 3.58 2.77 6.84 8.73 2.57 3.78 9.80 8.04 1.00 1.01 2.96 dioxane 3.59 2.77 6.17 7.69 2.75 3.51 8.39 7.09 0.84 0.78 2.22 hexane 3.59 2.77 6.02 7.44 2.79 3.44 8.06 6.87 0.81 0.67 2.05 Table 3.9: Mulliken charges on nitrogen atoms in 2 (see Fig. 3.16 for atom numbering). solvent N 1 (S 0 ) N 2 (S 0 ) N 3 (S 0 ) N 1 (S 1 ) N 2 (S 1 ) N 3 (S 1 ) N 1 (S 1 ) N 2 (S 1 ) N 3 (S 1 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 1 ) (S 1 ) (S 1 ) gas phase -0.29 -0.30 -0.47 -0.21 -0.13 -0.48 -0.23 -0.17 -0.49 water -0.34 -0.37 -0.52 -0.31 -0.34 -0.53 -0.33 -0.40 -0.55 acetonitrile -0.34 -0.37 -0.52 -0.31 -0.34 -0.53 -0.33 -0.40 -0.55 methanol -0.34 -0.37 -0.52 -0.31 -0.34 -0.53 -0.33 -0.40 -0.55 acetate -0.33 -0.35 -0.51 -0.30 -0.33 -0.52 -0.32 -0.40 -0.52 dioxane -0.31 -0.34 -0.50 -0.29 -0.32 -0.50 -0.31 -0.38 -0.52 hexane -0.31 -0.33 -0.49 -0.28 -0.31 -0.50 -0.30 -0.38 -0.52 71 0 10 20 30 40 50 60 70 80 3.50 3.52 3.54 3.56 3.58 3.60 3.62 3.64 Theory Exp Dielectric constant E ex (eV) 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.570 3.575 3.580 3.585 3.590 3.26 3.28 3.30 3.32 3.34 3.36 3.38 R 2 =0.24 E ex ,Exp (eV) E ex ,Theory (eV) 0 10 20 30 40 50 60 70 80 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 Theory Exp Dielectric constant E ex (eV) 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 R 2 =0.74 E ex ,Exp (eV) E ex ,Theory (eV) 0 10 20 30 40 50 60 70 80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 Theory Exp Dielectric constant Stokes shift (eV) 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 C 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 R 2 =0.63 Stokes shift,Exp (eV) Stokes shift,Theory (eV) Figure 3.23: Variations in absorption (top) and emission (middle) energies and Stokes shifts (bottom) of 2 in different solvents (left) and correlation between theory and experi- ment (right). 72 2.760 2.762 2.764 2.766 2.768 2.770 3.570 3.575 3.580 3.585 3.590 R 2 =0.81 E ex (eV) μ tr (S 0 -S 1 ) 3.4 3.5 3.6 3.7 3.8 3.9 4.0 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 R 2 =0.92 E ex (eV) μ tr (S 1 -S 0 ) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 R 2 =0.91 Stokes shift (eV) μ tr 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 R 2 =0.94 FQY μ tr Figure 3.24: Top: Absorption (left) and emission energies (right) in different solvents versus transition dipole moment for 2. Bottom: Stokes shift (left) and FQY (right) in different solvents versus transition dipole moment. 73 3.7.4 Appendix D4: Solvatochromic properties of molecule 3 Figure 3.25: Ground- and excited-state structures of 3 in the gas phase (left) and in water (right). Black and red numbers denote selected bondlengths in S 0 and S 1 , respectively. Table 3.10: Electronic properties of 3c in various solvents. Energies are in in eV , dipole moments in debye. Solvent E ex tr gs ex E ex tr ex gs E ss tr ge (S 0 -S 1 ) (S 0 -S 1 ) (S 0 ) (S 0 ) (S 1 -S 0 ) (S 1 -S 0 ) (S 1 ) (S 1 ) gas phase 3.51 3.79 7.63 9.61 2.88 4.21 9.39 8.81 0.63 0.42 1.76 water 3.37 3.86 10.50 14.99 2.26 5.39 19.25 14.28 1.11 1.53 8.75 acetonitrile 3.37 3.86 10.42 14.87 2.27 5.35 18.89 14.09 1.10 1.49 8.47 methanol 3.37 3.87 10.40 14.85 2.28 5.35 18.84 14.05 1.09 1.48 8.44 acetate 3.39 3.85 9.75 13.82 2.45 4.61 14.63 11.31 0.94 0.76 4.88 dioxane 3.42 3.82 8.76 12.02 2.44 4.67 12.60 11.08 0.98 0.85 3.84 hexane 3.43 3.82 8.54 11.60 2.56 4.31 10.97 10.01 0.87 0.49 2.43 Table 3.11: Mulliken charges on nitrogen atoms in 3c (see Fig. 3.16 for atom numbering). solvent N 1 (S 0 ) N 2 (S 0 ) N 3 (S 0 ) N 1 (S 1 ) N 2 (S 1 ) N 3 (S 1 ) N 1 (S 1 ) N 2 (S 1 ) N 3 (S 1 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 0 ) (S 1 ) (S 1 ) (S 1 ) gas phase -0.31 -0.19 -0.49 -0.27 -0.18 -0.50 -0.29 -0.33 -0.51 water -0.36 -0.28 -0.53 -0.34 -0.26 -0.54 -0.38 -0.42 -0.57 acetonitrile -0.36 -0.28 -0.53 -0.34 -0.26 -0.54 -0.37 -0.42 -0.57 methanol -0.36 -0.28 -0.53 -0.34 -0.26 -0.54 -0.37 -0.42 -0.57 acetate -0.35 -0.26 -0.52 -0.33 -0.24 -0.53 -0.37 -0.41 -0.56 dioxane -0.34 -0.24 -0.51 -0.32 -0.22 -0.51 -0.34 -0.38 -0.54 hexane -0.33 -0.24 -0.50 -0.31 -0.21 -0.51 -0.34 -0.37 -0.53 74 3.7.5 Appendix D5: Analysis of ground- and excited-state structures of 1, 2, and 3c Table 3.12: Key structural parameters of 1, 2, and 3c in S 0 and S 1 and changes in bondlengths (BL). All bondlength are in ˚ A. System Solvent State C 1 C 2 C 2 C 3 C 3 C 4 C 4 C 6 C 6 N 1 N 1 C 5 C 5 N 2 C 4 N 2 1 gas phase S 0 1.40 1.46 1.35 1.50 1.40 1.38 1.29 1.41 S 1 1.41 1.44 1.38 1.49 1.37 1.37 1.31 1.36 BL 0.01 -0.02 0.03 -0.01 -0.03 -0.01 0.02 -0.05 water S 0 1.40 1.46 1.35 1.50 1.42 1.38 1.29 1.41 S 1 1.43 1.41 1.43 1.47 1.40 1.33 1.36 1.35 BL 0.03 -0.05 0.08 -0.03 -0.02 -0.05 0.07 -0.06 2 gas phase S 0 1.40 1.46 1.35 1.50 1.40 1.39 1.30 1.39 S 1 1.42 1.41 1.45 1.47 1.39 1.36 1.36 1.33 BL 0.02 -0.05 0.10 -0.03 -0.01 -0.03 0.06 -0.06 water S 0 1.40 1.47 1.35 1.50 1.40 1.39 1.30 1.39 S 1 1.43 1.40 1.46 1.48 1.38 1.35 1.34 1.33 BL 0.03 -0.07 0.11 -0.02 -0.02 -0.04 0.04 -0.06 3 gas phase S 0 1.40 1.46 1.35 1.50 1.39 1.39 1.30 1.40 S 1 1.42 1.42 1.40 1.49 1.38 1.37 1.35 1.38 BL 0.02 -0.04 0.05 -0.01 -0.01 -0.02 0.05 -0.02 water S 0 1.40 1.47 1.35 1.50 1.38 1.39 1.31 1.40 S 1 1.42 1.42 1.41 1.49 1.37 1.37 1.38 1.34 BL 0.02 -0.05 0.06 -0.01 -0.01 -0.02 0.07 -0.06 Optimized ground- and excited-state structures of 1, 2, and 3c are shown in Figs. 3.19, 3.22, and 3.25 and summarized in Table 3.12. In agreement with previous studies of GFP- like chromophores 39–41 , photoexcitation results in significant changes in the bondlength pattern, which can be explained by the simple H¨ uckel model ?, ?, 36 . The most affected bonds are those of the methyne bridge (C 2 C 3 and C 3 C 4 ) and around N 2 (C 5 N 2 and C 4 N 2 ). Formally double bonds (C 3 C 4 and C 5 N 2 ) elongate and formally single bonds (C 2 C 3 and C 4 N 2 ) contract. The changes are consistently larger in polar solvents. The changes in bondlengths alternation reflect changes in relative weights of leading resonance structures and are, therefore, related to changes in charge redistribution (as discussed, for example, in Refs. 36, 41 ). Thus, they can be related to trends in dipole moments (i.e., larger change in bondlengths in S 1 corresponds to larger dipole 75 moment). The changes in bondlengths can also be related to the shape of the S 1 PES. As was shown in Ref. 40 , partial flipping of bond orders in excited state leads to a flatter (along torsional coordinate) PES, which increases the efficiency of internal conversion. Thus, the trend in equilibrium structures suggest a possible explanation of the observed anti-correlation between FQY and solvent polarity. 76 3.7.6 Appendix D6: Photoacidity/photobasicity of 1, 2, and 3c The NTO analysis reveals the origin of photobasicity — in all three compounds, electronic excitation results in the redistribution of electronic density on the imidazolone cycle. Tables 3.7, 3.9, and 3.11 show partial charges of the nitrogen atoms in the ground and excited states for 1, 2, and 3c. As one can see, the most significant charge redistribution occurs on N 2 , which becomes more negative (thus, more basic) in S 1 . The change in charge is large in 1 and 3c (about 0.2e) and is relatively small in 2. In all three molecules, the charge on N 2 shows the largest solvent-dependent variations. 3.7.7 Appendix D7: 2PA cross sections of 1 and 2 Table 3.13 shows excitation energies, oscillator strengths, and 2PA cross-sections (for paral- lel polarization) for HBDI and chromophores 1 and 2. 2PA excitation wavelengths correspond to E ex =2. We note that the computed excitation energies are systematically overestimated, meaning that the actual wavelength can be longer. As one can see, the 2PA cross-section in 2 is about 8-10 times smaller than in HBDI, which suggest that it still might be used in a two-photon excitation regime. The lowest transitions in 1 are also dim, but it also has a very bright 2PA transition at 458 nm. The intensity of this band can spill over to longer wavelengths 44 , so 1 might actually be brighter than HBDI. Table 3.13: Excitation energies, oscillator strength (f f ), and 2PA cross-section for degen- erate resonant photons ( 1 = 2 = 2~=! ex ), aug-cc-pVDZ. Compound State E ex , eV f l , nm 2PA (a.u.) (GM) HBDI 1A 0 3.97 0.77 625 977.762 5.64 1 2A 0 4.26 0.55 582 64.997 0.43 5A 0 5.42 0.20 458 4321.8 46.39 2 1A 0 3.28 0.80 756 137.18 0.54 2A 0 3.91 0.08 634 131.93 0.74 3A 0 4.09 0.02 606 98.7 0.60 77 3.8 Chapter 3 references 1 Klymchenko, A. S. Solvatochromic and Fluorogenic Dyes as Environment-Sensitive Probes: Design and Biological Applications.Acc.Chem.Res. 2017,50, 366–375. 2 Hori, Y .; Norinobu, T.; Sato, M.; Arita, K.; Shirakawa, M.; Kikuchi, K. Development of Fluorogenic Probes for Quick No-Wash Live-Cell Imaging of Intracellular Proteins. J. Am. Chem.Soc. 2013,135, 12360–12365. 3 Schoen, I.; Ries, J.; Klotzsch, E.; Ewers, H.; V ogel, V . Binding-Activated Localization Microscopy of DNA Structures.NanoLett. 2011,11, 4008–4011. 4 Collot, M.; Kreder, R.; Tatarets, A. L.; Patsenker, L.; Mely, Y .; Klymchenko, A. S. 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M.; Dreuw, A. Experimental benchmark data and systematic evaluation of two a posteriori, polarizable-continuum correc- tions for vertical excitation energies in solution.J.Phys.Chem.A. 2015,119,21, 5446-5464. 55 Shao, Y .; Gan, Z.; Epifanovsky, E.; Gilbert, A. TB.; Wormit, M.; Kussmann, J.; Lange, A. W.; Behn, A.; Deng, J.; Feng, X.; others. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package.Mol.Phys. 2015,113,2, 184-215. 56 Krylov, A. I.; Gill, P. MW. Q-Chem: an engine for innovation. Wiley Interdisciplinary Reviews: ComputationalMolecularScience 2013,3,3, 317-326. 82 Chapter 4: Influence of the first chromophore-forming residue on photobleaching and oxidative photoconversion of EGFP and EYFP 4.1 Introduction Fluorescent proteins (FPs) constitute a unique group of the genetically encoded fluorescence probes with the chromophore formed from their own amino acid residues. Genetic encodability and self-sufficient chromophore maturation determine the high value of FPs as the multipurpose imaging tools. Protein engineering has played an essential role in the development of the available FPs pallette, which currently includes dozens of spectral variants. Introduction of only two mutations (F64L and S65T) to the first described wild-type FP - avGFP - has resulted in EGFP 1 , as yet most popular fluorescent protein. In EGFP, the chromophore dwells almost exclusively in the bright anionic state (fluoresces at ex=490 nm/2.53 eV , em=510 nm/2.43 eV), whereas the wild-type avGFP chromophore exists mostly in the protonated form (abs=395 nm/3.14 eV) and is weakly fluorescent. One more representative of the classic FPs - EYFP, in which Ser65Gly/Thr203Tyr substitutions lead to 35 nm fluorescence excitation bathochromic shift relative to avGFP, was also derived from avGFP 2 . The bicyclic chromophore of avGFP and most of its derivatives (including EGFP and EYFP) is formed from the -X65-Tyr66-Gly67- tripeptide motif by autocatalytic post-translational modification that involves consecutive cyclization, dehydration, and oxidation 3, 4 . Tyr66 and 83 Gly66 are highly conservative in the native FPs. Despite the variability of the first residue in a chromophore triad (X), proteins with different amino acids in this position form very similar chromophores. Thus, a typical GFP-like chromophore can be found in avGFP with SYG triad, EGFP with TYG, and EYFP with GYG. Although amino acid at the first position only weakly affects the structure of the chromophore core, it is essential for the interaction of the chromophore with its protein environment which, in turn, dramatically influences properties of the fluorescent protein, in particular those relevant for applications, such as fluorescence brightness and lifetime, Stokes shifts, and photostability 5–7 . The importance of the 65th position can be illustrated by the fact that Ser65 substitution by Gly, Ala, Cys, Val, or Thr led suppresses the shortwave neutral chromophore absorbance peak (395 nm/3.14 eV) in favor of the anionic chromophores peak at 470-490 nm (2.64-2.53 eV) 2, 8, 9 . In EGFP, the S65T mutation causes a significant rearrangement of the hydrogen-bond network in the chromophore region 2, 10, 11 : the threonine residue forms a new hydrogen bond with Val61 10 . Also, Thr65 induces Glu222 protonation and accelerates chromophore maturation (maturation time constant is 0.45 h in GFP-S65T versus 2 h in wild-type avGFP) speeding up the rate-limiting oxidation reaction rate 8, 12 . In EYFP, S65G and V68L substitutions result in a 0.9 ˚ Ashift of the chromophore towards the barrel surface relative to its position in GFP-S65T and wild-type avGFP 13 . Both mutations also improve brightness of the cells expressing respective mutants relative to the avGFP-expressing cells, probably due to their effect on the protein folding or chromophore maturation 1 . Remarkably, the shift of the chromophore observed in EYFP (and connected particularly with the S65G substitution) leads to the appearance of the fluorescence sensitivity to halide and nitrate anions in this protein 14 . Mutational analysis of the first chromophore-forming amino acid position (Ser65 in avGFP) had been carried out in several studies and aimed primarily at determining the influence of this position on the maturation of the chromophore 10 and its basic spectral characteristics 2 . 84 However, a systematic analysis of the influence of this position on the less obvious physico- chemical characteristics of fluorescent proteins, such as photostability, fluorescence lifetime, blinking, excited-state reactions, mediated by the molecular interactions of the chromophore with the nearest protein environment, to the best of our knowledge, has not yet been carried out. Existing data indicate that the amino acid in the 65th position has a significant impact on the GFP photophysics. For example, the EGFP mutants carrying the T65G substitution show significantly reduced quantum yield, shorter fluorescence lifetime, and an increased extinction coefficient 15, 16 ; an increased photostability of such proteins was also reported 16 . At the same time, in EYFP carrying the same GYG chromophore, the quantum yield is even higher and the lifetime is longer than in the EGFP with the TYG chromophore. The effect of the 65th position on the ability of GFP-like proteins to undergo light-induced oxidative green-to-red photoconversion (called oxidative redding) is also of interest. Redding was described for green proteins of different taxonomic origin with Thr, Ser, Cys, Asn, Lys, and Gly in the first position of the chromophore, but the efficiency of the red spectral form appearance was maximal in EGFP (Thr65) 17 . As for EYFP, it is capable of redding only in the presence of halide anions, and even if they are present, it is much less effective than in EGFP 18 . The current mechanistic hypothesis 18 states that the redding is initiated by the electron transfer from the electronically excited chromophore to a nearby residue. Consequently, the effectiveness of this gateway step determines the ultimate yield of the red form. Under the same hypothesis, the yield of bleaching is also correlated with the effectiveness of the photoinduced electron transfer. The calculations of the energetics of one-electron oxidation and possible electron transfer pathways suggested that excited-state electron transfer proceeds through a hopping mechanism via Tyr145; the role of Tyr145 in redding has been confirmed by mutage- nesis 18 . In YFPs, the -stacking of the chromophore with Tyr203 reduces its electron-donating ability, which can be restored by halide binding, due to its effect on the -stacking 18 . However, a 85 possible role of Gly65 was not investigated. In this contribution, we examine the mutants of EGFP and EYFP proteins with reciprocal substitutions at the 65th position, EGFP-T65G and EYFP-G65T, focusing on their brightness, photostability, fluorescence lifetime, and redding ability compared to parental proteins. To rationalize the observed differences, we carried out quantum chemical and molecular dynamics simulations to estimate radiative and radiationless decay rates. On the basis of these calcu- lations, we developed a kinetic model of the photocycle, which provides a unified picture of how the chromophores structure affects the photophysical properties of fluorescent proteins. The simulations revealed that the main effect of the T65G mutation is the reduced excited-state lifetime of the GYG chromophore, resulting in its increased photostability. The effect of the residue in position 65 on the brightness and quantum yield is explained by an interplay between the radiative and radiationless relaxation channels. The effect of the mutation 65 in EYFP is modulated by the -stacking interactions between the chromophore and Tyr203. 4.2 Results 4.2.1 Mutants general description (spectral characteristics) EYFP-G65T and EGFP-T65G mutants generally showed spectral similarity to their parental proteins (Fig. 4.1). Like the original EGFP, EGFP-T65G has a single main absorption max- imum, peaking at approximately 488 nm (2.54 eV) and corresponding to the anionic chro- mophore with fluorescence emission maximum at 510 nm (2.43 eV). The neutral (protonated) state of the chromophore in EGFP-T65G (absorption maximum 395 nm/3.14 eV) is minor, although it is more expressed than in EGFP, which is consistent with literature data on the role of Thr65 in maintaining the neutral state of Glu222 and the hydrogen-bond network favoring 86 chromophores deprotonation. The absorption spectra of EYFP-G65T, which have two pro- nounced maxima 410 and 513 nm (3.02 and 2.42 eV , respectively), corresponding to the neutral and anionic chromophores, is distinctly different from both the parent protein (EYFP) and from EGFP-T65G. Figure 4.1: Absorption (A) and fluorescence (B) spectra of EGFP, EYFP, and mutants. In the fluorescence graph, dashed lines show fluorescence excitation, solid lines fluores- cence emission. PB denotes phosphate buffer and PBS denotes phosphate buffered saline containing sodium chloride (see text). A small (about 2 nm) blue shift in the anion and a significant (about 15 nm) red shift in the neutral chromophore absorption, which is unusual for proteins with the chromophore -stacked 87 with Tyr203 including EYFP 2 , are noteworthy in the spectral comparison of EYFP-G65T with EYFP. Even more remarkable, however, is the observed dramatic dependence of the relative amplitudes of the peaks at 410 and 513 nm (3.02 and 2.42 eV) on the composition of the external environment. For example, in the hydrophosphate-dihydrophosphate buffer (PB, pH 7.4) the amplitudes ratio is about 1:1, while in the PBS buffer (pH 7.4, app. 140 mM Cl ) the ratio becomes approximately 3:1 in favor of the neutral chromophore. Therefore, the protonation state of the EYFP-G65T chromophore seems to exhibit an enhanced sensitivity to the electrostatic interactions with the solvated ions. This property makes it a promising candidate for the sensitive core of the ratiometric halide ion sensor. Parental EYFP also shows spectral sensitivity to the buffer content. That is, having essentially no absorbance around 400 nm (3.10 eV) in PB, in PBS it absorbs at 395 nm (3.14 eV) (as the classic protonated GFP-chromophore), while decreasing its main absorbance at 515 nm (2.41 eV) peak by circa 6%. EYFPs halide sensitivity, which is attributed to the shift of chromophores pKa induced by electrostatic interactions, is well-known; and fluorescence intensity decrease by about 40% at pH 7.0 was reported for this protein 14 . However, the contrast of the optical response to halides addition in the case of G65T mutant appears to be significantly higher. 4.2.2 Photostability We measured the photostabilities of mutants versus parental proteins with and without electron acceptors in media, aiming to reveal the influence of the T65G/G65T substitutions on the primary excited-state electron transfer process that is believed to result in a permanent bleaching. Also, for EYFP/EYFP-G65T we introduced an additional variable - halide presence - to photostability measurements testing their possible role in the excited-state chemistry. The photostability is quantified by the bleaching half-times (the time it takes for the fluorescence to drop by a factor of two), i.e., longer half-times correspond to more photostable proteins. The 88 EGFP-T65G mutant (with enhanced photostability relative to EGFP in vitro and in cellulo 18 ) showed approximately twofold higher photostability (relative photostability is defined as the ratio of the photobleaching rates) in PBS and almost 20-fold higher in PBS with 200 M of potassium ferricyanide relative to those of EGFP (Fig. 4.2A, 4.2B, Table 4.1). 89 Table 4.1: Fluorescent properties of EGFP, EYFP, and their mutants, EGFP-T65G and EYFP-G65T. FP ex / em EC FQY RB, % FL FL PB, S PB, S PB, S PB, S Redding PB PBS PB PBS PB+Ox PBS+Ox PBS EGFP 489/509 55000 0.60 100 n/d 2.8 n/d 8010 n/d 52.5 strong T65G 488/508 70000 0.06 13 n/d 1.3 n/d 17025 n/d 8515 weak EYFP 514/526 67000 0.61 124 3.18 3.0 212 352 32 21 moderate G65T 510/525 n/d 0.78 n/d 3.7 3.5 258 1808 102 327 moderate 4.0 0.5 3.9 n/d = not determined.Relative brightness is calculated as a product of the molar extinction coefficient and the fluorescence quantum yield, and reported relative to the brightness of EGFP. For EGFP and EYFP, the absolute quantum yields are shown, for the mutants the quantum yields measured relative to the equally absorbing EGFP or EYFP are shown. For EYFP the single fluorescence lifetime value measured under 450 nm excitation is shown. For EYFP-G65T a pair of values measured under 400 and 490 nm excitation (value400/value490) is shown. In PBS, at 400 nm excitation EYFP-G65T showed fluorescence decay better fitted by bi-exponential function ( 1 =3.5 ns, 2 =0.5 ns). Photobleaching is reported as the bleaching haf-time for each fluorescent protein, i.e., larger values correspond to the slower photobleaching rate and higher photostability. 90 Taking into account that EGFP-T65G (EC=70000 M 1 cm 1 ; FQY=0.06) is 8 times dimmer than EGFP, one could explain the increase of photostability in PBS by its shorter excited-state lifetime (which is also responsible for its reduced emitter efficiency). However, the degree of the photostability increase in EGFP-T65G in the presence of oxidant does not match the degree of the proteins brightness decrease, and this probably indicates a less effective oxidative bleaching channel in this protein. The shapes of the bleaching curves with oxidant may favor this hypothesis: EGFP-T65G has a bimodal curve, but its fast component, probably related to excited-state electron transfer, is relatively short. EYFP and its mutant behavior seems more complex, in part due to the presence of an additional variable (presence or absence of the chloride anions in PBS or PB buffer, respectively) in the experimental conditions. In PB, EYFP-G65T photostability is close to that of the parental EYFP, while in PBS, the mutant shows circa 5-fold decreased photobleaching rate relative to EYFP under the same conditions and around 7-fold relative to itself in PB (Fig. 4.2C, Table 4.1). This observation is in accord with the absorption spectra behavior of two proteins (Fig. 4.1A): in the presence of 140 mM chloride only around 25% of EYFP G65T chromophore is in anion state and absorbs excitation light. In fact, EYFPs photostability also somewhat increases in the presence of chloride, probably for the same reason. Oxidant addition (200M potassium ferricyanide) has significantly accelerated bleaching in all cases (Fig. 4.2D, Table 4.1). EYFPs photostability in PB with oxidant is reduced 6-7- fold. However, as in the case of EGFP/EGFP-T65G, the effect of ferricyanide on EYFP-G65T and EYFP behavior varies under different conditions. For EYFP with oxidant, the rate of photobleaching in PB and PBS is almost the same. One can suppose that the bleaching channel, which is dominant when electron acceptor is added, is less sensitive to chromophores pKa than the one that functions under normal conditions. In PB+oxidant, EYFP-G65T shows a 91 Figure 4.2: Bleaching kinetics in the immobilized proteins EGFP, EYFP, and their mutants in vitro. (A) Photoconversion of EGFP and EGFP-T65G in PBS; (B) Photo- conversion of EGFP and EGFP-T65G in PBS in the presence of 0.2 mM potassium fer- ricyanide; (C) Photoconversion of EYFP and EYFP-G65T in PB and PBS (PBS contains potassium chloride); (D) Photoconversion of EYFP and EYFP-G65T in PB and PBS in the presence of 0.2 mM potassium ferricyanide. Green/yellow fluorescence intensities were background-subtracted and normalized to the maximum values. Standard deviation val- ues (n = 1520 measurements in a representative experiment out of five independent exper- iments) are shown. 3-fold decrease in the photobleaching rate relative to EYFP (whereas without oxidant the rates are almost equal). In PBS+oxidant, the mutant demonstrates a 10-fold photostability increase relative to EYFP (versus 5-fold increase without oxidant), and a 3-fold increase relative to itself in PB+oxidant (versus a 6-fold increase without ferricyanide). Taken together, these ratios suggest that the oxidant reduces the dependence of the bleaching efficiency on the chromophore protonation state (see G65T-PB-ox versus G65T-PBS-ox, which changes in the presence of chloride), while the replacement of G65T generally disfavors the oxidative bleaching channel (see G65T-PB-ox versus EYFP-PB-ox). 92 4.2.3 Redding We also tested redding efficiency among the mutants irradiated in presence of ferricyanide, our hypothesis being that the red form appearance rate should be inversely related to the pho- tostability. This appears to be true in a pair of EGFP/EGFP-T65G where the parental protein demonstrated 20-30-fold more efficient redding (and 20-fold lower photostability) (Fig. 4.3A). Figure 4.3: Redding kinetics in the EGFP, EYFP, and their mutants. (A) Appearance of red fluorescence in EGFP and EGFP-T65G. Non-normalized data for several measure- ments are shown. (B) Appearance of red fluorescence in EYFP and EYFP-G65T in PB and PBS (PBS contains potassium chloride). Averaged curves are shown. Red fluores- cence intensities were background-subtracted and normalized to the maximum values. Standard deviation values (n = 1520 measurements in a representative experiment out of five independent experiments) are shown. (C) Appearance of red fluorescence in EYFP- G65T in PB and PBS (PBS contains potassium chloride). Non-normalized data for several measurements are shown. As in the case of bleaching, the reduced rate of redding in EGFP-T65G cannot be explained only by the 8-fold lower relative brightness of this mutant, especially since it absorbs light even more effectively than the original protein (EC = 70000 versus 55000 in EGFP). When comparing the redding rates in different proteins, care should be taken to normalize the appear- ing red signal to the initial intensity of the green fluorescence. We suggest a normalization method adequate when studying redding of the same protein under slightly different conditions (for example, in cell culture). However, when comparing different proteins, this method can lead to artifacts because it does not take into account the chromophore’s ability to absorb light and its quantum efficiency. We evaluated redding in EYFP-G65T and EYFP in PB (without chloride) and PBS (140 mM Cl ), both supplemented with 200M of ferricyanide. 93 For EYFP in PB, we observed almost no detectable appearance of the red form (Fig. 4.3B). We do not consider the weak growth of the red signal visible on the graph to be reliable and attribute it to the imperfectness of the procedure of the subtraction of the red component of the main spectral form leaking through the RFP filter set (see Subtraction and normalization procedure in Supplementary materials). In PBS, we detected well-expressed (both in rate and absolute value) redding, in agreement with the observations reported earlier. EYFP-G65T undergoes redding both with and without chloride, demonstrating similar kinetics/rate but different yield (red signal plateau) under these two conditions (Fig. 3B). It is, however, possible that the seeming quantitative difference in the redding yields of EYFP-G65T in PB and PBS represents an artifact originating from an inadequate normalization procedure. To address this issue, we also compared non-normalized datasets for EYFP-G65T redding (Fig. 4.3C); this comparison did not confirm the trend exhibited by the normalized/averaged curves. Generally, the G65T mutation in EYFP enables the ability to undergo redding in the standard regime, i.e., independently on the halide binding. To compare quantitatively redding in PB and PBS, one should take into account an extreme sensitivity of the EYFP-G65T brightness to halide presence, which leads to a 2.5-3-fold difference in the green signal intensity at zero time. 4.2.4 Lifetime Fluorescence lifetime of EGFP was measured to be 2.8 ns 13 ; other studies estimated it in the range from 2.3 to 2.8 ns 16, 19–22 . The spread in the reported values reflects the sensitivity towards the instrument and measurement conditions 16, 19–22 . EGFP-T65G fluorescence lifetime (1.3 ns) is twice shorter than in EGFP 16 . For EYFP, fluorescence lifetime weakly depends on the halide presence (3.180.07 ns in PB (without Cl ) and 30.08 ns in PBS (with Cl )), which is in rough agreement with the relevant data reported for the near homologs of EYFP 23, 24 . Similarly to our observations 94 in the spectral domain, EYFP-G65T demonstrated a complex behavior in lifetime domain (Table 1). Thus, the mutant shows two clearly distinguishable lifetime values under 400 and 490 nm excitation wavelengths in the PB and PBS environment. In PB, both fluo- rescence decay kinetics can be fitted by the single-exponential functions with 400 =3.7 ns, 490 =4 ns. In PBS, excitation at 400 nm leads to a bi-exponential decay ( 1 =3.5 ns, 2 =0.5 ns), where the faster component might be attributed to excited-state proton transfer (ESPT), although the ESPT kinetics is usually much faster than hundreds of picoseconds 25 . Excitation of the anionic form does not significantly change its fluorescent lifetime compared to the PB value. 4.2.5 Computational results To rationalize observed differences in photophysical behavior of the four proteins due to the residue in position 65, we carried out the following quantum chemical and molecular dynamics calculations: Quantum-chemical calculations of the isolated model chromophores (structures, excita- tion energies, and oscillator strengths); Molecular dynamics simulations of the model proteins in the ground and electronically excited states; Hybrid QM/MM (quantum mechanics/molecular mechanics) calculations of the spectral properties of the model proteins (excitation energies and oscillator strengths for the structures taken from the ground-state molecular dynamics simulations). 95 The results from these calculations were used to estimate radiative and radiationless lifetimes, as described below. We considered four model systems, representing EGFP, EGFP-T65G, EYFP, and EYFP-G65T. For EYFP, we carried out calculations with and without chloride anions, as in Ref. 18. In all simulations, we considered only the deprotonated (anionic) chromophore. The protonation states of the protein residues were determined using Propka software 25–27 and verified by comparing the results of the molecular dynamics simulations with the available crystal structures (2Y0G for EGFP 9 , 1F0B for EYFP), following the same protocols as in our earlier work 17 . Specifically, we determined that Glu222 is protonated (neutral) and His148 is neutral (HSD form, protonated atN atom). The protonation state of Glu222 agrees with the conclusions of the experimental study. These protonation states give rise to a robust hydrogen-bond network around the chromophore, as shown in Fig. 4.4. The structures of the model chromophores and the definition of the QM/MM partitioning are shown in Fig. 4.5. Full details of the computational protocols are provided in Chapter 2. We begin with characterization of the bare model chromophores. Figure 4.5 shows the structures of the isolated model chromophores and defines important structural parameters; it also shows how the chromophores are connected to the protein backbone. As one can see, the conjugated core of the TYG and GYG chromophores is the same; it comprises the phenolate and imidazolinone rings connected via the methine bridge. However, whereas the GYG chromophore is directly attached to the protein backbone through the exocyclic imidozalinones carbon, the TYG chromophore has an additional -CH(OH)CH3 tail attached to it. The presence of this tail has a relatively small effect on the excitation energy (red shift of about 0.02 eV), but leads to a 4% decrease in the oscillator strength of the bare chromophore. The -CH3 and -CH(OH)CH3 groups differ by their electron-donating ability - the presence of electronegative OH makes the latter a less effective electron donor. Thus, we attribute 96 Figure 4.4: Hydrogen-bond network around the chromophore (CRO) in EGFP (left) and EYFP (right). The network includes CRO:O-water314-SER205-GLU222-CRO:O (Thr65, in EGFP). Glu222 is protonated and His148 is neutral in EGFP (protonated at deltaN atom). Also shown is-stacking of the chromophore and Tyr203 in EYFP. the larger oscillator strength in GYG relative to TYG to an increased electron density in the conjugated part of the chromophore due to stronger electron-donating ability of -CH3. To test this hypothesis, we carried out calculations for a fluorinated GYG chromophore in which one -CH3 group was replaced by -CF3. The fluorinated GYG chromophore shows significant reduction (7.3%) of the oscillator strength relative to the GYG chromophore, consistently with strong electron-withdrawing ability of fluorine (see Fig. 4.6). As discussed below, larger oscillator strength in GYG chromophore contributes to its increased brightness and reduced radiative lifetime (i.e., faster fluorescence). Importantly, the tail has a major effect on the hydrogen-bond network around the chromophore, its planarity and con- formational flexibility. Figure 4 shows the hydrogen-bond networks around the chromophore in EGFP and EYFP. As one can see, in both proteins there are 4 hydrogen bonds around the chromophore. However, the Ser205-Glu222 distance (Ser205:O - Glu222:OE1) is much larger 97 Figure 4.5: Top: Structures of the model TYG (EGFP, YFP-G65T) (left) and GYG (YFP, EGFP-T65G) (right) chromophores. Torsional angles and are defined as CD-CG- CB-CA and CG-CB-CA-N, respectively. The difference between the two angles =- quantifies whether the chromophore is planar (=0) or not. Bottom: the QM/MM parti- tioning for EGFP (left) and EYFP (right). Blue color denotes the QM region and the black dotted lines denote the QM-MM boundary. Charges of red and green atoms were set to zero in the MM region. In EGFP-T65G, the chromophore is GYG and the neighboring residues are the same as in EGFP. Likewise, in EYFP-G65T, the chromophore is TYG and the neighboring residues are the same as in EYFP. (3.74 ˚ Aand 4.27 ˚ Ain EGFP and EYFP, respectively) in EYFP. By allowing for larger thermal fluctuations causing transient breaking of the hydrogen bonds, a larger Ser205-Glu222 distance signifies a weaker hydrogen-bond network, which is illustrated by the results in Table 4.2. Table 4.2. summarizes the analysis of the hydrogen-bond pattern and deviations of the chro- mophore from planarity in the course of the ground-state equilibrium dynamics. The average number of hydrogen bonds is smaller for the GYG chromophores compared to the proteins with TYG chromophores. Interestingly, despite a smaller number of hydrogen bonds, the deviation from planarity is smaller for EGFP-T65G relative to EGFP, both in terms of the average values 98 Table 4.2: Average number of hydrogen bonds (and standard deviation) formed within 6 ˚ Aaround the chromophore computed along the equilibrium trajectories. Distance and angle cut off were set to 3.2 ˚ Aand 20 , respectively). Deviation of the chromophore from planarity (, in degrees) is also shown. Protein/Chro EGFP/TYG EGFP- EYFP/GYG EYFP- EYFP+Cl T65G/GYG G65T/TYG /GYG No. H-bond 2.81 2.31 1.34 1.93 1.45 STD(hbond) 1.12 1.03 0.83 1.06 0.87 7.40 6.44 4.41 5.50 7.02 STD () 16.7 8.2 7.8 8.0 7.29 of and in terms of standard deviation. The latter indicates a larger dynamic range of chro- mophore motions in EGFP. A reduced range of thermal torsional motions in EGFP-T65G and smaller deviations from planarity are probably due to the bulkier size of the TYG chromophore. The EYFP chromophore shows smaller deviations from planarity, because of the stabilizing effect of the-stacking with Tyr203 (this is consistent with the observations in Ref. 18). The average number of hydrogen bonds around the chromophore is larger in EYFP-G65T than in EYFP because the OH group of the threonine participates in the hydrogen-bond network. Torsional motions of the chromophore modulate the oscillator strength of the S 0 -S 1 transition, as illustrated in Fig. 4.6. In EGFP, the standard deviation for (which quantifies the twisting motion of the chromophore) is 17 degrees. In this range of motion, the oscillator strength can be reduced by several percent (Fig. 4.6 shows that the oscillator strength depends quadratically on). These results explain the variations in the average oscillator strengths for the S 0 -S 1 tran- sition for the four systems discussed below. On the basis of the QM/MM calculations of the transition energies and oscillator strengths, we estimate intrinsic fluorescence lifetime, fl . Intrinsic radiative lifetime is inversely propor- tional to the oscillator strength of the transition (f l ) and to the square of corresponding excitation energy (E ex ). In atomic units, intrinsic radiative lifetime fl 28 is: 1 r = ! 2 0 f abs 2(c 0 ) 3 ; (4.1) 99 Figure 4.6: Oscillator strength for the S 0 -S 1 transition in the isolated TYG, GYG, and fluorinated GYG (GYG-F in which one -CH3 is replaced with -CF3) chromophores along torsional angle (all other degrees of freedom are relaxed) computed with!B97X-D/aug- cc-pVDZ. wherec 0 is the speed of light in the medium (c 0 =c=n;c is the speed of light in vacuum andn is the index of refraction) and is the dielectric constant. For vacuum,=1 andc=137. Dielectric constant in proteins is small (i.e., 2-8). The index of refraction of water is 1.33; the refractivity of protein solutions is generally larger, around 1.6 29, 30 . Table 4.3: Theoretical estimates of radiative lifetime for different mutants. Computed excitation energies and oscillator strengths are also shown. QM/MM absorption energies and oscillator strengths are averaged over 21 snapshots taken from ground-state equilib- rium molecular dynamics simulations. fl ,rel values are relative lifetimes calculated with respect to fl in EGFP. Mutant E ex , eV (f l ) E ex ,eV (f l ) fl , ns fl , ns fl , ns fl rel, ns fl rel, ns (gas) (QM/MM) gas, QM/MM, QM/MM, gas QM/MM n=1 n=1 n=1.6 EGFP 3.101 (1.02) 3.081 (0.97) 29.50 31.24 7.63 1.00 1.00 EGFP-T65G 3.123 (1.05) 3.142 (1.04) 28.25 28.18 6.88 0.95 0.90 EYFP 3.123 (1.05) 3.097 (1.05) 28.25 28.71 7.02 0.95 0.92 EYFP-G65T 3.123 (1.05) 3.015 (0.98) 28.25 32.49 7.94 1.00 1.04 EYFP+Cl 3.123 (1.05) 3.077 (1.07) 28.25 28.57 6.97 0.95 0.91 Table 3 shows excitation energies of the isolated chromophores and average excitation ener- gies and oscillator strengths computed for 21 QM/MM snapshots taken from the ground-state equilibrium trajectories. These values are used to compute radiative lifetimes by Eq. (1) with 100 n=1 and=1. The absolute values of the computed lifetimes are almost 10 times longer than the experimentally observed fluorescence lifetimes, which is expected given the uncertainties in the computed values and the key constants (i.e.,n and). Using n=1.6 brings the computed values down, to the range of 7-8 ns. Moreover, we note that Eq. (1) provides only an upper bound of fl and does not account for other decay channels available to such complex polyatomic systems as fluorescent proteins. However, we expect that these calculations capture the essential trend of variations in the intrinsic fluorescence lifetime due to the variations in the oscillator strength induced by thermal motions and differences in the chromophores structure. To zoom into this trend, the last two columns of Table 4.3 show relative values of the computed fluorescence life- times with respect to that of EGFP. As one can see, the proteins with the GYG chromophore are expected to have intrinsic fluorescence lifetimes shorter by 8-12% than their counterparts with TYG. This difference is due to slight red shifts, dynamically reduced oscillator strengths in TYG, and the electronic effect of OH, all caused by the bulkier and more electronegative threonine group. In contrast to a relatively modest effect of the residue in position 65 on the chromophore struc- ture in the ground state, it has a dramatic effect on the excited-state potential energy surface indicates a significant effect on subsequent dynamics of the chromophore following photoexci- tation. The origin of this strong effect of hydrogen bonding is a much flatter torsional potential of the chromophore in the excited state 31, 32 . Fig. 4.7 shows the scans of potential energy sur- faces in the ground and the first excited state of the isolated GYG chromophore along the two torsional angles. As one can see, the chromophore in its ground state is rather rigid due to its -conjugated system: the barriers for the (phenolate flip) and (imidozalinone flip) rota- tions are about 31.61 and 34.47 kcal/mol, respectively. However, in the S 1 state (which has - character), the bond order is reduced, giving rise to rel4tively flat potential energy pro- files along the twisting coordinates (the computed barriers for the and rotations are 3.59 101 and 4.52 kcal/mol, respectively). These flat profiles are responsible for low FQY of isolated chromophores 31–34 . The hydrogen-bond network around protein-bound chromophores plays a crucial role by stabilizing the otherwise floppy structure in a planar configuration, thus prevent- ing the chromophores trapping in dark twisted states and suppressing the radiationless relax- ation via conical intersections 31–33 . That is why different hydrogen-bond patterns around GYG and TYG chromophores have a profound effect on their excited-state dynamics. Specifically, as illustrated by excited-state molecular dynamics simulations, GYG chromophores are much more likely to twist in the excited state than the TYG chromophores. Figure 4.7: PES scans (relative energies) for the isolated GYG chromophore along the dihedral angles (left) and (right) in the ground (black) and electronically excited (red) states. All other degrees of freedom are frozen. The dots represent ab initio calculations (!B97X-D/aug-cc-pvDZ) and the solid lines are fits to the force-field torsional potential used in molecular dynamics simulations (see Chapter 2). In contrast to the isolated chro- mophores, the protein-bound excited chromophores can only undergo phenolate flip ( twist) because the imidozalinone ring is covalently bound to the protein backbone. 102 To quantify excited-state evolution, we carried out molecular dynamics simulations using the modified force-field parameters (see Appendix B and Fig. 4.11, 4.12) designed for the S 1 state. Starting from 101 snapshots harvested from the ground-state trajectories for each protein, we propagated excited-state trajectories for 3 ns; the results were saved each 2.5 ps. To estimate the rate of radiationless relaxation, we monitored the dihedral angle along simulation trajectories and defined two populations: A (planar chromophore, defined as< 50 ) and B (twisted chromophore, > 50 ). The dihedral angle does not fluctuate significantly ( 20 ) in the course of dynamics, because of the covalent bond between the imidazolinone ring and the proteins backbone. Once the value of reached the critical value of 50 , we stopped the trajectory assuming that strongly twisted structures undergo fast and irreversible non-adiabatic transitions to the ground state. Fig. 9 shows the evolution of the two populations (A and B) in the studied proteins. As one can see, in the EGFP-T65G mutant all chromophores eventually undergo twisting in the course of excited-state dynamics. The twisting dynamics can be used to estimate the rate of the radiationless relaxation using 1st order kinetics fit of A(t): A(t) =e kt nr = ln2 k (4.2) where radiationless (non-radiative) half-life is nr . Fitting the decay of the planar population (shown in Fig. 4.8) by a first-order kinetics yields half-lives of 5.92 ns and 0.25 ns for EGFP and EGFP-T65G, respectively. In EYFP and EYFP- G65T the computed half-lives are 1.73 ns and 10.8 ns, respectively. These numbers roughly correspond to the excited-state decay via radiationless relaxation. As one can see, the T65G mutation in EGFP leads to a 23-fold drop in the non-radiative lifetime, which is in a semi- quantitative agreement with the 10-fold drop in FQY . The effect of the mutation of residue 65 in EYFP is slightly smaller, only 6-fold, which is qualitatively in agreement with 30% larger FQY in EYFP-G65T relative to EYFP. Addition of halide to EYFP leads to faster twisting by a 103 factor of three, because halide binding upsets -stacking of the chromophore with Tyr203. Figure 4.8: Left: Evolution of planar (A) population in excited-state molecular dynamics simulations of EGFP, EGFP-T65G, EYFP, EYFP-G65T, and EYFP+Cl . Right: Linear fit for ln[A]. 4.3 Discussion Photophysical properties of the fluorescent proteins are determined by an interplay between chromophores intrinsic electronic structure, its interactions with the surrounding residues, and several competing excited-state processes. We begin by outlining the connection between the macroscopic observables (extinction coefficients, brightness, and photostability) with the micro- scopic properties of the chromophores. The extinction coefficient is proportional to the intrinsic 104 brightness of the chromophore as characterized by the oscillator strength of the S 0 -S 1 transi- tion. Apparent excited-state lifetime () is a result of the intrinsic fluorescence lifetime, fl , and various non-radiative decay channels ( nr ): 1 = 1 r + 1 nr (4.3) (4.4) The non-radiative channels include radiationless relaxation and bleaching. However, given the small quantum yield of bleaching in typical fluorescent proteins (<10 5 ) 38 , the second term in Eq. (4) is dominated by the radiationless relaxation lifetime. FQY is determined by the ratio of the radiative and radiationless lifetimes: FQY = nr fl + nr (4.5) That is, for a given fl , FQY is larger when radiationless decay is slow (longer nr ). Conversely, for a fixed nr , FQY is larger for systems with shorter radiative lifetime. Intrinsic radiative lifetime is related to the chromophores excitation energy and oscillator strength by Eq. (1), i.e., larger oscillator strength leads to shorter radiative lifetimes (i.e., faster fluorescence rate). The photostability of the fluorophores depends on the ratio of excited-state lifetime and the rate of the bleaching process, i.e., within the first-order kinetics, the yield of bleaching Y bl can be estimated as: Y bl = bl (4.6) This means that for a given rate of the bleaching process (via photo-oxidation or other photochemical processes), the yield of bleached forms is smaller for systems with shorter apparent excited-state lifetimes. As photostability is inversely proportional to Y bl , the ratios of 1/Y bl can be interpreted as relative photostabilities. Of course, bleaching rates can vary significantly among different proteins, because electron-transfer pathways and the rates are 105 sensitive to mutations 17 . Because of the high cost of such calculations, the effects of mutations on the rates of electron transfer are not investigated in the present study. Our simulations suggest that the principal effect of the T65G mutation is two-fold: (i) it increases the oscillator strength, leading to shorter fluorescence lifetimes; and (ii) it increases chromophores flexibility in the excited state, leading to faster radiationless relaxation. These two trends qualitatively explain all results from Table 1: EGFP-T65G has a larger extinction coefficient than EGFP because of its larger oscillator strength; Because of the faster radiation- less relaxation, EGFP-T65G has lower FQY than EGFP; likewise, EYFP has lower FQY than EYFP-G65T; Having glycine in position 65 leads to faster radiationless relaxation (shorter half-life of A), thus suppressing the bleaching and leading to an increased photostability; Larger FQY in EYFP relative to EGFP-T65G arises due to the suppression of torsional motions by the-stacking interactions, which is reflected in longer radiationless half-life. To relate these calculations to the photophysical properties of the proteins, we collect the estimated half-lives due to radiationless relaxation and estimated radiative half-lives in Table 4. Fig. 9 shows the comparisons between theory and experiment graphically. We estimate FQY and the relative rates of bleaching using Eqns. (5) and (6). Although the computed FQY is not in quantitative agreement with the experimental values (which is not surprising, given that several there are several approximations in the model), the differences between the mutants are described rather well: compare, for example, the ratio of FQY in EGFP-T65G and EGFP: 0.09 (computed) versus 0.1 (experimental). Likewise, the computed ratio of FQY in EYFP and EYFP-G65T is 0.34, to be compared with the experimental ratio of 0.78. The trend in the apparent fluorescence lifetime () is also captured reasonably well: the computed relative lifetimes are 1:0.1:0.4:1.4, to be compared with the experimental ratios of 1:0.4:1.1:1.4 (estimated from the fluorescence lifetimes from Table 4.1). Finally, the estimated bleaching yield (assuming the same rate of bleaching process) ratios are 106 1:0.1:0.4:1.4. The relative photostabilities can be estimated as the ratios of the inverse of Y bl : 1:10:2.5:0.71. The experimental macroscopic bleaching half-lives, which are inversely propor- tional to the rate of bleaching and can, therefore, be interpreted as relative photostabilities, are 1:2.1:0.4:2.2 (see Table 1, PBS). As anticipated above, the agreement here is worse, because the present study does not account for the variations in electron-transfer rates due to the mutations. The rate of bleaching is expected to vary between different systems, because the rate of electron transfer is sensitive to structural variations, especially between EGFP and EYFP 17 . In EYFP, the rate of bleaching is strongly affected by the halide binding, for example, the calculated electron-transfer rate to Tyr145 are five orders of magnitude faster in EYFP+Cl (kEYFP+Cl : kEYFP = 13300 :1), which overshadows small variations in radiationless relaxation rates. Table 4.4: Computed radiative and radiationless lifetimes of EGFP, EGFP-T65G, EYFP, EYFP-G65T, and EYFP+Cl (in parenthesis, the values relative to EGFP are shown) and estimated photophysical parameters. Protein fl , ns ( fl;rel nr , ns nr;rel , ns ( rel ) FQY Y bl;rel EGFP 7.63 (1.00) 5.92 (1.00) 3.33 (1.0) 0.44 1.0 EGFP-T65G 6.88 (0.90) 0.25 (0.04) 0.24 (0.1) 0.04 0.1 EYFP 7.02 (0.92) 1.73 (0.29) 1.39 (0.4) 0.20 0.4 EYFP-G65T 7.94 (1.04) 10.8 (1.82) 4.58 (1.4) 0.58 1.4 EYFP+Cl 6.97 (0.91) 0.57 (0.10) 0.53 (0.2) 0.07 0.2 Figure 4.9: Correlation between theoretical and experimental apparent fluorescence life- times (left), FQY (middle), and the rate of bleaching (right). We conclude this section by considering the implications of the above findings for imaging applications. Faster radiationless relaxation of EGFP-T65G may result in the suppression of 107 not only the bleaching but also other excited-state processes. This might be valuable from the practical point of view, for example, in the context of live-cell imaging where fluorophores with the decreased photoreactivity would potentially demonstrate such advantages as the decreased phototoxicity and fewer artifacts due to the redox-photoreactions with the intracellular com- pounds. The high spectral sensitivity of EYFP-G65T to chloride (and probably to other anions of similar size) may open up new avenues for the design of FP-based molecular indicators, including those functioning in the lifetime domain. This is of special interest since EYFP and its circularly permuted variants have been utilized in several popular indicators 35–37 . 4.4 Materials and Methods The experimental measurements were carried out as follows. His-tagged proteins were expressed in Escherichia coli and purified by a metal-affinity resin. The resin beads with immobilized proteins were placed into phosphate buffer (PB, pH 7.4), or phosphate buffered saline (PBS, pH 7.4), or PB/PBS with 0.2 mM potassium ferricyanide as an oxidant and illuminated with strong blue light using a fluorescence microscope. Changes of fluorescence in green/yellow and red channels were monitored during illumination. 4.4.1 Spectroscopy and fluorescence brightness evaluation For absorbance and fluorescence excitation-emission spectra measurements, Cary 100 UV/VIS spectrophotometer and Cary Eclipse fluorescence spectrophotometer (Varian) were used. Fluorescence brightness was evaluated as a product of molar extinction coefficient by quantum yield multiplication. Measurements on all native proteins were carried out in 108 phosphate buffered saline (PBS, pH 7.4, Gibco). For molar extinction coefficient determination, we relied on measuring mature chromophore concentrationn 38 . EYFP and its mutants were alkali-denatured in 1 M NaOH. Under these conditions GFP-like chromophore is known to absorb at 447 nm with extinction coefficient of 44,000 M 1 cm 1 . Based on the absorption of the native and alkali-denatured proteins, molar extinction coefficients for the native states were calculated. For determination of the quantum yield, the areas under fluorescence emission spectra of the mutants were compared with equally absorbing EYFP (quantum yield 0.61) 38 and EGFP (quantum yield 0.60) 38 . 4.4.2 Microscopy For wide-field fluorescence microscopy, a Leica AF6000 LX imaging system with Pho- tometrics CoolSNAP HQ CCD camera was used. Green and red fluorescence images were acquired using 631.4NA oil-immersion objective and standard filter sets: GFP (excitation BP470/40, emission BP525/50) and TX2 (excitation BP560/40, emission BP645/75). Photo- bleaching and redding were monitored in time-lapse imaging in the green and red channels at low light intensity combined with exposures to blue light of maximum intensity (GFP filter set, light power density of 2-3 W/cm 2 ). Images were acquired and quantified using Leica LAS AF software. 4.4.3 Protein Expression and Purification EYFP and EGFP as well as EGFP-T65G and EYFP-G65T mutants were cloned into the pQE30 vector (Qiagen) with a 6His tag at the N terminus, expressed in E. coli XL1 Blue strain (Invitrogen) and purified using TALON metal-affinity resin (Clontech). 109 4.4.4 Site-Directed Mutagenesis The EGFP-T65G, and EYFP-G65T mutants were generated using overlap- extension PCR technique with the following oligonucleotide set containing the appropriate substitutions: forward 5-ATGCGGATCCATGGTGAGCAAGGGCGAG- 3, reverse 5-ATGCAAGCTTTTACTTGTACAGCTCGTC-3 and forward 5- ACCACCTTCACCTACGGCCTG-3 and reverse 5-CAGGCCGTAGGTGAAGGTGGT- 3 for EYFP G65T; forward 5-ATGCGGATCCATGGTGAGCAAGGGCGAG- 3, reverse 5-ATGCAAGCTTTTACTTGTACAGCTCGTC-3 and forward 5- ACCACCTTCGGCTACGGCCTG-3, reverse 5-CAGGCCGTAGCCGAAGGTGGT-3 for EGFP-T65G. For bacterial expression, a PCR-amplified BamHI/HindIII fragment encoding an FP variant was cloned into the pQE30 vector (Qiagen). 4.4.5 Fluorescence lifetime imaging microscopy of the purified proteins upon single-photon excitation. Femtosecond laser pulses (80 MHz repetition rate, up to 100 fs, up to 25 nJ per pulse) were generated by a Ti:Sapphire oscillator (Tsunami, Spectra-Physics) pumped by a green Nd:YVO4 CW laser (532 nm, Millennia Prime 6sJ, Spectra-Physics) and frequency doubled in an LBO nonlinear crystal (Spectra-Physics). Second harmonic laser beam was coupled to an inverted optical microscope Olympus IX71 by a Thorlabs FESH0750 dielectric filter mounted at 45 and then focused by objective lens (40 0.75NA, UPlanFLN, Olympus) on a sample, which was placed on a 3-axis stage. The samples were prepared as droplets of the purified fluorescent proteins dissolved in phosphate buffered saline (PBS, pH 7.4, GIBCO) applied onto a standard 24 24 mm cover glass (Heinz Herenz, Germany). The average laser power was tuned with a polarizing attenuator and further attenuated with a glass neutral filter. A 110 typical laser power coupled to the microscope was about 3W. The central wavelength of the fundamental harmonic pulses was either 800 or 980 nm, and of the second harmonic pulses 400 or 490 nm respectively. The SF10 prism compressor was used to compensate for the group velocity dispersion in the objective lens and other optical elements. Fluorescence was excited by one-photon absorption of femtosecond laser, passed back through the objective lens and laser coupling filter, was filtered by a long-pass dielectric filter (FELH0500, Thorlabs), and then was directed to the input of Acton SP300i monochromator with two separate outputs. PI-MAX 2 CCD camera (Princeton Instruments) at the first output was employed for the fluorescence spectra registration. Photomultiplier tube of the time-correlated single photon counting system SPC-730 (Becker and Hickl GmbH) at the second output detected the fluorescence decay kinetics in the 510 nm530 nm band. Fluorescence decay data were primarily acquired using SPCImage software (Becker and Hickl, Germany) and then exported in ASCII format and analyzed using Origin Pro 9 software (OriginLab, USA). 4.4.6 Computational details Protonation state and crystal structures. Structures of EGFP and EYFP were taken from the protein data bank (PDB) with ids: 2Y0G and 1F0B respectively. The protonation states of titratable residues were determined using PropKa software 25–27 . Particularly important are the protonation states of the residues around the chromophore: the Glu 222 and His 148. PropKa 25 predicts the glutamate to be neutral (GLUP 222) for both EGFP and EYFP. To validate this prediction, we carried out separate molecular dynamics simulations of EGFP and EYFP with protonated and deprotonated Glu222 and analyzed the key interatomic distances from the equilibrium trajectories. Direct comparison of these calculated distances with the crystal structures confirmed dominant population of the protonated Glu222 residue. This conclusion is also in accord with the prior experimental 111 findings. In EGFP, we visually inspected the local environment around the His148 residue and concluded that it exists in HSD (neutral, protonated at N atom) form because of hydrogen bonding with the phenolate oxygen of the chromophore. Additional confirmation of HSD protonation state was obtained from similar His148-chromophore distances from equilibrium molecular dynamics simulation and the crystal structure. The resulting hydrogen-bond patterns around the chromophore are shown in Fig. 4.4. Molecular dynamics setup. We used CHARMM27 force-field parameters for protein residues 39 and the ground-state anionic chromophores force-field parameters were obtained from an old work 40 . Charged amino acids on the surface were locally neutralized by adding counter ions close ( 4.5 ˚ A) to them. Charged residues that do not form a salt bridge inside the protein barrel were also neutralized by adding appropriate counter ions at the surface. This neutralization protocol resulted in the addition of 21 Na + and 14 Cl in the EGFP, and 20 Na + and 14 Cl in the EYFP. The proteins were solvated in water boxes producing a buffer of 15 ˚ Awith the box size of approximately 69 ˚ A 77 ˚ A 75 ˚ A. The TIP3P 41 water model was used to describe external waters. Molecular dynamics simulations were performed using these solvated neutralized model structures as follows: Minimization for 2000 steps with 2 fs time step. Equilibration of the solvent (keeping the protein frozen) for 500 ps with 1 fs time step. Equilibration of the system for 2 ns (with 1 fs time step) with periodic boundary condition (PBC) under the isobaric-isothermal NPT ensemble. 112 Production run for 2 ns with 1 fs time step in an NPT ensemble. Molecular dynamics simulations were performed with NAMD 42 in an NPT ensemble with Langevin dynamics. Pressure and temperature were kept at 1 atm and 298 K during the simulation. QM/MM setup. We computed electronic properties (vertical excitation energies, oscillator strengths) using snapshots generated along equilibrium trajectories (production runs of molecular dynamics sim- ulations) using a QM/MM scheme. The chromophore is included in the QM region and the rest of the system is treated as fixed MM point charges (see fig. 4.5) via electrostatic embedding. Hydrogen atoms were added at the QM/MM boundary to saturate the valencies. Point charges on the red and green atoms in Fig. 5 were set to zero and the excess charge was redistributed over the rest of the atoms of the respective residues to avoid over-polarization of the QM atoms at QM/MM boundary. Electronic structure calculations were performed at the!B97X-D/aug- cc-pVDZ 43, 44 level of theory. Benchmark results using different electronic structure methods are presented in the Appendix. All quantum chemistry and QM/MM calculations were carried out using the Q-Chem electronic structure package 45 . 4.5 Conclusions In this contribution, we investigated the effect of residue in position 65 on the photophysical properties of EGFP and EYFP, with an emphasis on photostability and oxidative redding. We compared bleaching and redding kinetics in EGFP, EYFP, and their mutants with reciprocally substituted chromophore residues, EGFP-T65G and EYFP-G65T. Measurements showed that T65G mutation significantly increases EGFP photostability and inhibits its excited-state oxidation efficiency. Remarkably, while EYFP-G65T demonstrated highly increased spectral sensitivity to chloride, it is also able to undergo redding in the absence of chloride. 113 To shed light on the origin of the observed differences in photophysical behavior of the two seemingly very similar chromophores, TYG (EGFP and EYFP-G65T) and GYG (EYFP and EGFP-T65G), we carried out atomistic simulations of the four model systems. The effect of the residue in position 65 can be explained by a simple kinetic model of the photocycle, which considers the competition between radiative and radiationless relaxation channels and photochemical bleaching. The atomistic simulations reveal that the main effect of the T65G mutation is the reduced excited-state lifetime of the GYG chromophore, resulting in its increased photostability. The effect of the residue in position 65 on the brightness and quantum yield is explained by an interplay between the radiative and radiationless relaxation channels. Directed simulation- and structure-guided tuning of a relative significance of the radia- tive/radiationless processes can be a basis for the development of the new fluorescent proteins with pre-determined photostability and fluorescence lifetime optimized for application in the next-generation imaging techniques. 4.6 Appendix A: Absorbance and fluorescence data normal- ization Absorption and fluorescence excitation/emission spectra (fig. 4.1) were normalized to the maximum mean value. Photobleaching curves (fig. 4.2) were background-subtracted and nor- malized to the maximum values. EGFP and EGFP-T65G redding kinetics are shown as non- normalized and non-averaged background-subtracted curves (fig. 4.3A). In the case of EYFP and EYFP-G65T redding representation, we had to take into account the fact that fluorescence of the yellow (non-converted) spectral form, routinely detected in GFP channel, has a spectral crosstalk with the red (RFP) channel, thus complicating correct red form appearance regis- tration. Namely, redding-specific signal was masked by the background yellow fluorescence. 114 To address this issue, we subtracted the background signal acquired in RFP channel consider- ing its kinetics strictly proportional to that observed in GFP channel (according to the follow- ing equation RFPcorrected=RFPraw-(GFPraw*RFPzero/GFPzero), where raw is unprocessed value, zero initial value). The products of subtraction described above are represented either as maximum yellow signal-normalized and averaged curves (fig. 4.3B) or as non-normalized single measurements (fig. 4.3C). 4.7 Appendix B: Force field parameters for excited-state classical molecular dynamics simulations To perform excited-state molecular dynamics, we reparameterized partial charges, key bond lengths, angles, and torsional angles, as well as the corresponding force constants. First, we optimized the structure of the isolated chromophore with B97x-D/aug-cc-pVDZ in its ground and the first excited state. We then computed the NBO charges with the same functional/basis set and used the differences between ground- and excited-state charges to calculate the partial charges in the excited state force-field by using the following equations: q excharmm =q gscharmm + q NBO(exgs) ; (4.7) where, q NBO(exgs) =q NBO(ex) q NBO(gs) : (4.8) Bond lengths, angles, and dihedral angles were computed with the equations E =k(bb 0 ) 2 ; (4.9) E =k(AA 0 ) 2 : (4.10) 115 WhereB 0 is equilibrium bond length andA 0 is equilibrium bond angle. E =k[1 +cos(n)]: (4.11) wheren is periodicity, is phase and is dihedral angle. The force constants were computed by tweaking the parameters from the equilibrium value in ground and excited states by constructing the PES. The second derivative of the parabolic fit gives the force constant. We took the ratio of the computed force constant and multiplied that with those in ground state force constants: k excharmm = k excomputed k gscomputed k gscharmm : (4.12) Figure 4.10: EGFP chromophore with atom types consistent with CHARMM 27 forcefield notations. NOTE: Largest changes in partial charge happen on the methine bridge (marked by red). The most important parameter was the torsional angle . The PES scans show that the chromophore is planar in the ground state and twisted in the excited state. We fitted the excited- state potential with a fitting potential with the calculated force constant, which enables the flip around. Partial charges and other force field parameters are listed at forcefield section. Fitting the potential for excited state PES (right) with respect to: E =k[1 +cos(n 180)];groundstate;n = 2; (4.13) 116 Table 4.5: Partial charges in Charmm27, and in the ground and excited states of the EGFP chromophore (!B97X-D/aug-cc-pVDZ). The last column shows adjusted partial charges used in excited-state molecular dynamics (see fig. 4.10). Atom Charmm27(gs) NBO (gs) NBO (ex) q NBO(exgs) Charmm 27(ex) C1 0.50 0.43 0.41 -0.02 0.48 N2 -0.60 -0.56 -0.64 -0.08 -0.68 N3 -0.57 -0.54 -0.54 0.00 -0.57 C2 0.57 0.66 0.61 -0.05 0.52 O2 -0.57 -0.75 -0.68 0.07 -0.50 CA2 0.10 -0.08 0.17 0.25 0.35 CB2 -0.14 -0.09 -0.47 -0.38 -0.52 HB2 0.21 0.25 0.25 0.00 0.21 CG2 -0.09 -0.21 0.06 0.27 0.18 CD1 -0.08 -0.17 -0.25 -0.08 -0.16 HD11 0.14 0.21 0.21 0.00 0.14 CD2 -0.08 -0.17 -0.25 -0.08 -0.16 HD21 0.14 0.24 0.24 0.00 0.14 CE1 -0.28 -0.31 -0.22 0.09 -0.19 HE11 0.10 0.21 0.21 0.00 0.10 CE2 -0.28 -0.31 -0.22 0.09 -0.19 HE21 0.10 0.23 0.23 0.00 0.10 CZ 0.45 0.46 0.39 -0.07 0.38 OH -0.62 -0.72 -0.67 0.05 -0.57 CA3 -0.18 -0.41 -0.41 0.00 -0.18 HA31 0.09 0.26 0.26 0.00 0.09 HA32 0.09 0.20 0.20 0.00 0.09 C 0.51 (H) 0.21 (H)0.21 0.00 0.51 O -0.51 — — – -0.51 N -0.47 (H)0.24 (H)0.24 -0.00 -0.47 HN 0.31 — — – 0.31 CA 0.07 -0.51 -0.51 0.00 0.07 HA 0.09 0.24 0.24 0.00 0.09 CB1 0.14 0.09 0.10 0.01 0.15 HB1 0.09 0.20 0.20 0.00 0.09 OG1 -0.66 -0.77 -0.82 -0.05 -0.71 HG1 0.43 0.50 0.52 0.02 0.41 CG1 -0.27 -0.65 -0.65 0.00 -0.27 HG11 0.09 0.21 0.21 0.00 0.09 HG12 0.09 0.20 0.20 0.00 0.09 HG13 0.09 0.23 0.23 0.00 0.09 Table 4.6: Bond lengths in Charmm27 forcefield and computed with !B97X-D/aug-cc- pVDZ. The last column shows adjusted partial charges used in excited-state molecular dynamics. Bond k gs;charmm b 0(gs;charmm) b 0(computed) b 0(ex;charmm) k gs;computed k ex;computed k ex;charmm CG2Q- 437 1.410 0.035 1.445 564.301 327.936 253.96 CB2Q CB2Q- 500 1.390 0.000 1.390 623.96 430.6 345.05 CA2Q 117 Table 4.7: Bond angles in Charmm27 forcefield and computed with !B97X-D/aug-cc- pVDZ. The last column shows adjusted partial charges used in excited-state molecular dynamics. Bond k gs;charmm A 0(gs;charmm) A 0(computed) A 0(ex;charmm) k gs;computed k ex;computed k ex;charmm CG2Q- 130.0 133.2 -5.50 127.7 201.96 195.058 123.1 CB2Q- CA2Q E =k[1 +cos(n 180)];excitedstate;n = 4: (4.14) The major difference in the ground and excited state PES other than force constants is the change in periodicity (n) of the fitting potentials with much lower value of force constant for the torsional angle. Figure 4.11: Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Ref. 10. Table 4.8: Parameterized force constant and periodicity (n) for torsional potentials for angles and. Dihedral k gs;charmm n (gs) n (ex) k gs;qm k ex;qm k ex;charmm 2.7 2 4 15.05 3.79 0.68 3.9 2 4 14.99 4.90 1.27 118 -877.510 -877.505 -877.500 -877.495 -877.490 -877.485 -225 -180 -135 -90 -45 0 45 90 135 180 225 Energy (hartree) dihedral angle f fitting potential Torsional angle φ Electronic energy (a.u.) -200 -150 -100 -50 0 50 100 150 200 -877.51 -877.50 -877.49 -877.48 -877.47 -877.46 Energy (hartree) dihedral angle t Torsional angle τ Electronic energy (a.u.) Figure 4.12: Excited-state torsional potentials for (left) and (right) of the bare HBDI chromophore. Red curves: fit to ab initio calculations (from which the parameters were extracted). Pink and black curves: torsional potentials computed with the modified force- field. As one can see, our fit reproduces the barriers for twisting reasonably well, but does not reproduce the depth of the well of the twisted structures (the fitted potential is too shallow). Hence, to prevent the trajectories from re-crossing, in the excited-state MD simulations we simply stop the trajectories once they twist by more than a specified threshold value (50 ). 4.8 Appendix C: Excitation energies Table 4.9: Computed excitation energy (eV), oscillator strength, and transition dipole moment (TDM, a.u.) at the ground-state optimized geometry of the isolated TYG and GYG chromophores. Method TYG TYG TYG GYG GYG GYG E ex f l TDM (a.u.) E ex f l TDM (a.u.) !B97X-D/aug- 3.367 (S 0 -S 1 ) 1.425 4.156 3.387 (S 0 -S 1 ) 1.467 4.204 cc-pVDZ (TDA) !B97X-D/aug- 3.101 (S 0 -S 1 ) 1.016 3.657 3.123 (S 0 -S 1 ) 1.052 3.708 cc-pVDZ (RPA) !B97X-D/aug- 3.363 (S 0 -S 1 ) 1.420 4.151 3.382 (S 0 -S 1 ) 1.460 4.198 cc-pVTZ (TDA) !B97X-D/aug- 3.097 (S 0 -S 1 ) 1.014 3.657 3.119 (S 0 -S 1 ) 1.052 3.710 cc-pVTZ (RPA) EOM-CCSD/ 2.947 (S 0 -S 1 ) 1.153 3.785 2.965 (S 0 -S 2 ) 1.188 3.839 aug-cc-pVDZ 119 Figure 4.13: Distribution of oscillator strengths (!B97x-D/aug-cc-pVDZ) computed for 21 QM/MM snapshots from the ground-state molecular dynamics. Figure 4.14: Distribution of excitation energ (!B97x-D/aug-cc-pVDZ) computed for 21 QM/MM snapshots from the ground-state molecular dynamics. 120 4.9 Chapter 4 references 1 B. P. Cormack, R. H. Valdivia, S. Falkow, FACS-optimized mutants of the green fluorescent protein (GFP), Gene 173, 33 (1996). 2 M. Orm¨ o, A.B. Cubitt, K. Kallio, L.A. Gross, R.Y . Tsien, and S.J. 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Phys. 113, 184 (2015). 124 Chapter 5: Interplay between Locally Excited and Charge Transfer States Governs the Photoswitching Mechanism in the Fluorescent Protein Dreiklang 5.1 Introduction Many fluorescent proteins (FPs) undergo reversible photoswitching upon photoexcitation, which is instrumental in several imaging modalities 1 , including super-resolution techniques 2, 3 . The most common mechanism is cis-trans photoisomerization of the chromophore, sometimes coupled with changes in its protonation state; notable examples include Dronpa 4 , Padron 5 , and KFP 6 . However, an entirely different mechanism is operating in Dreiklang 7 , where the switch- ing is based on reversible photoinduced hydration/dehydration of the imidazolinone ring of the chromophore (Fig. 5.1). 3.06 eV (405 nm) 3.40 eV (365 nm) On state Off state H H Figure 5.1: On-off photoconversion in Dreiklang is activated by photoexcitation of the neutral form of the chromophore in ON-state. The OFF-form can be turned on by pho- toexcitation at higher energy. Dreiklang 7 was derived by random mutagenesis from Citrine, a close relative of EYFP 8 . It has the same chromophore, formed by the glycine-tyrosine-glycine (GYG) tripeptyde-stacked 125 with a nearby tyrosine residue (Tyr203). The chromophore’s conjugated core (Fig. 5.1) is the same as in EGFP 9 , but due to the T65G mutation the connection to the peptide backbone via imidazolinone’s carbon is slightly different. - Wavelength (nm) 1.0 1.0 0.8 0.6 0.4 0.2 0.0 350 400 450 500 550 Absorbance (a.u.) Off-A On-A On-B - - - - - - - - - - H H Figure 5.2: Steady-state absorption spectra of the ON-state (black) and following irradia- tion (red) at 3.02 eV (410 nm) at pH 7.5. The spectra are from Ref. 10. The band maxima are at 3.01 eV and 2.43 eV in the ON-state and at 3.65 eV in the OFF-state. Fig. 5.2 shows absorption spectra of the ON- and OFF- forms of Dreiklang 7, 10 . The absorp- tion spectrum of the ON-form features two bands: one at 3.01 eV (411-413 nm) and a twice- more intense one at 2.43 eV (511 nm), with a shoulder at 2.58 eV (480 nm). These bands are assigned to the neutral and anionic forms of the chromophore, traditionally called form A and form B 11, 12 . In many other GFP-like proteins 11 , excitation of either band leads to the identi- cal fluorescence spectra with the maximum around 2.3 eV (green or yellow), ascribed to form B. This is explained by ultrafast (picoseconds or shorter) excited-state proton-transfer (ESPT) from the chromophore to a proton acceptor via a proton wire 11, 13, 14 . In wt-GFP, ESPT proceeds as a sequential proton transfer from the excited neutral chromophore to the Glu222 carboxy- late through a water molecule and the hydroxyl group of Ser205 12, 15–18 . This pathway can be disrupted by mutations. In Dreiklang, excitation of peak B leads to fluorescence at 2.34 eV (529 nm), with a quan- tum yield of 0.41. However, in contrast to many other FPs, the excitation of peak A leads to very 126 weak (albeit non-negligible 10 ) fluorescence. This weak steady-state fluorescence is identical 10 to the fluorescence produced by excitation of peak B. These observations suggest that ESPT in Dreiklang is strongly suppressed and happens with a very small quantum yield. Reduced effectiveness of ESPT is consistent with the observation 7 that the essential difference between the parent system (Citrine) and Dreiklang is the upshift of the pKa of the ON-state of the chro- mophore (7.2 versus 5.7). The distinguishing feature of Dreiklang is that irradiation of peak A results in photoconver- sion to the dark form (OFF-state) 7 . Thus, in imaging applications, the fluorescence of Dreiklang can be excited by using 2.43 eV light, recorded at 2.34 eV , and turned off by 3.01 eV light. This decoupling of the fluorescence excitation from photoswitching makes Dreiklang very attractive and is responsible for its name (Dreiklang is the German word for a three-note chord in music). The OFF-state spontaneously returns to the ON-state in the course of minutes. Alternatively, the dark state can be switched back by irradiation at 3.65 eV (340 nm). The X-ray structures 7 of the ON- and OFF-states (PDB IDs: 3ST2/3ST4 and 3ST3, respec- tively) show that the ON-state is indeed similar to EGFP/EYFP, whereas the OFF-state has a hydrated chromophore, similar to an intermediate form of the immature chromophore 19 but with a methyne double bond. The exact details of the photoswitching mechanism remain unknown. Espagne and co- workers 10 investigated the mechanism using transient absorption and concluded that formation of photoproducts occurs on a nanosecond time scale or slower. They reported spectroscopic evidence of the formation of excited-state (on a ps timescale) and ground-state (picosecond to nanosecond timescale) intermediates and proposed a tentative mechanism; however, the pro- posed structures of the intermediates have not been validated by theoretical modeling of their spectral properties. On the theoretical side, we investigated 20 thermal (ground-state) recov- ery of the ON-state. The calculations predicted a reaction barrier of about 27 kcal/mol on the 127 ground-state potential energy surface and identified Glu222 as the key residue involved in the recovery reaction, while the scan of the excited-state surface suggested a barrierless OFF!ON photoreaction. This work also presented a cursory analysis of the structures of the ON- and OFF-states, including tentative assignment of the protonation states of the key residues around the chromophore, and computed their spectral properties. 944 VOLUME 29 NUMBER 10 OCTOBER 2011 NATURE BIOTECHNOLOGY ARTICLES After the off-state diffraction data was recorded at 100 K, we warmed the very same crystal of Dreiklang back to 295 K, switched it by irra- diation with 365 nm light until the fluorescence reached a maximum and recorded the on-state diffraction data at 100 K. In addition, we solved the X-ray structure of Dreiklang in the fluorescent equilib- rium-state to a resolution of 1.9 Å (Fig. 2). Notably, the kinetics of the thermal equilibration of the fluorescence signal after switch- ing off was comparable for Dreiklang in solution and in the crystal (Supplementary Fig. 8), indicating that the crystal lattice did not have major effects on the switching behavior. The overall structure of Dreiklang resembles that of GFP and related proteins (Fig. 2b). The chromophore, autocatalytically formed from the Gly65-Tyr66-Gly67 tripeptide, resides in an alpha-helical seg- ment, enclosed by an 11-stranded beta-barrel. As expected from the similar spectroscopic properties, the on-state structure was practically superimposable on the fluorescent equilibrium-state structure. The on-state chromophore consists of an imidazolinone-ring, connected by a methine bridge to a p-hydroxyphenyl ring. The two rings of the chromophoric systems were largely co-planar, facilitating a conju- gated pi-electron system and hence supporting fluorescence. In the off-state, the p-hydroxyphenyl ring lies largely in plane with the C 66 -C 66 bond, as well as with the C 66 -C 66 and the C 66 -N 66 bonds, indicating that the methine bridge connecting the two rings is maintained. However, in the off-state structure, the planarity of the five-membered ring was markedly distorted with the chromophoric C 65 exhibiting a tetrahedral geometry indicative of an sp 3 hybridi- zation. A clear signal in the electron density map indicates a new hydroxyl group at the C 65 atom, suggesting that the imidazolinone ring was converted into a 2-hydroxyimidazolidinone ring (Fig. 2a and Supplementary Fig. 9). We propose that the hydration of the imidazolinone ring shortens the chromophoric pi-electron system, resulting in the new absorption band at 340 nm and the simultaneous disappearance of the absorption bands at 412 and 511 nm (Fig. 1e). To further confirm this light-induced chemical modification, we carried out electrospray ionization mass spectrometry (ESI-MS). To this end, switching of Dreiklang in solution (pH 6.9; 295 K) was monitored by measuring the fluorescence signal; the proteins in the respective states were immediately analyzed by ESI-MS under native conditions (in 18% acetonitrile). We found a mass difference of 18 0.3 Da between the nonfluorescent state and the light-induced on- state or the equilibrium state, respectively (Fig. 2a and Supplementary Figs. 10 and 11). This strongly indicates the reversible covalent addi- tion of a water molecule that occurred parallel to changes in the fluo- rescence signal. Hence, the ESI-MS data are in full agreement with the X-ray data, supporting the view of a reversible light-induced covalent chemical modification, that is, a hydration-dehydration reaction of the chromophoric five-membered ring as the underlying molecular mechanism of switching in Dreiklang. A similar reversible hydration reaction was postulated, although controversially discussed, to occur during the chromophore forma- tion of GFP 27–29 . This might suggest that the light-induced reversible switching of Dreiklang is based on a molecular reaction that is pos- sibly occurring during chromophore maturation of some fluorescent proteins. Hence, we propose that Dreiklang may be used as a scaffold for further engineering and that this switching mechanism may be transferred to other fluorescent proteins. Our mutagenesis studies showed that the amino acid residues Y203 and E222 as well as the chromophore building G65 are crucial for the unusual switching characteristics of Dreiklang. The amino acids G65 and Y203 facilitate the positioning of the side chain of E222 close to the imidazolinone ring (Fig. 2c). In the fluorescent-state, Y203 and E222 form hydrogen bonds to a water molecule (Wat a ) and thereby stabilize it in close vicinity to the C 65 of the chromophore (Fig. 2d), a situation that is different in the nonswitchable GFP (avGFP-S65T) 25 (Fig. 2d, inset). In GFP , a water molecule corresponding to Wat a is stabilized by water-mediated H-bonds only. We propose that Wat a is Figure 2 Molecular basis of Dreiklang photoswitching. (a) Dreiklang in the fluorescent equilibrium-state (top), the nonfluorescent off-state (middle) and the fluorescent on-state (bottom). Left, top: representative Dreiklang protein crystal. Left, bottom: proposed chemical structure of the chromophore. Central: details of the X-ray structures (PDB IDs: 3ST2, 3ST3, 3ST4, respectively, top to bottom). Shown is the chromophore (carbon, magenta/gray; oxygen, red; nitrogen, blue). In the equilibrium-state and the on-state, water Wat a (magenta sphere) is additionally displayed. Final 2F o –F c electron densities are contoured at the 1 level. The off-state and the on-state structures have been successively recorded on the same protein crystal. Right: representative deconvoluted ESI-MS spectra of Dreiklang photoswitched in solution and measured under native conditions. (b) Overall Dreiklang ribbon structure displayed in two orthogonal views. (c) Chromophore and immediate surrounding of on-state Dreiklang (magenta) and GFP (PDB: 1EMA 25 ) (cyan). The Van-der-Waals’ radii of important atoms are indicated by spheres to highlight structural restraints. The chromophores are depicted as ball and stick whereas the surrounding amino acid residues are shown in the stick representation. (d) Superimposed representations of the Dreiklang hydrogen bond network in the (fluorescent) equilibrium- and the off-states. Equilibrium-state carbons, magenta; off-state carbons, gray; oxygen, red; nitrogen, blue. Important water molecules are shown as magenta (equilibrium-state) and gray (off-state) spheres. Inset: hydrogen bond network in GFP. a b d c 17.0 28,510.4 Da hv 405 nm T203 GFP E222 GFP GYG off Wat c Wat b Wat a GYG eq H145 Y203 S205 E222 H148 T203 TYG Q69 S205 E222 GFP TYG GFP Y203 Drei E222 Drei GYG Drei hv 365 nm 14.0 10.0 Intensity (a.u.) Intensity (a.u.) 6.9 3.5 85 68 51 34 17 0 28,400 28,500 28,600 28,400 28,500 Mass (Da) Mass (Da) 28,528.2 Da Intensity (a.u.) 7.8 6.3 4.7 3.1 1.6 0 28,400 28,500 28,600 Mass (Da) 28,510.5 Da 28,600 0 Equilibrium Off-state On-state © 2011 Nature America, Inc. All rights reserved. Figure 5.3: Superimposed representations of the hydrogen-bond network around Dreik- lang’s chromophore in the ON- and OFF-states. Color scheme: ON-state carbons, magenta; OFF-state carbons, gray; oxygen, red; nitrogen, blue. Important water molecules are shown as magenta (ON-state) and gray (OFF-state) spheres. Inset: hydrogen-bond network in EGFP.ReproducedfromRef. 7. Given the importance of proton wires in the photocycle of FPs, here we revisit the ques- tion of protonation states using more advanced computational protocols and assess the effect of different protonation states on the excited states of the chromophore. Dreiklang operates in a wide range of pH (6-9). Figure 6.3 shows superimposed crystal structures 7 of the ON-state (equilibrium structure, PDB ID 3ST2) and OFF-state (PDB ID 3ST3), indicating the hydrogen- bond network around the chromophore. It also compares the network around the Dreiklang chromophore with that in EGFP (PDB ID 1EMA) 9 . Dreiklang’s structure clearly shows partici- pation of His145, Glu222, and Ser205, as well as several water molecules. In contrast, in EGFP 128 the chromophore forms hydrogen bonds with His148 (position 145 is occupied by Tyr145 in EGFP), Thr203, and Glu222. The two critical residues near the chromophore binding site in Dreiklang are Glu222 and His145. A tentative mechanism proposed in Ref. 10 assumed that both Glu222 and His145 are in the neutral form, at least, in the ON-state. In our study of the thermal recovery reaction 20 , we considered Glu222 to be deprotonated and pointed out that the change in its protonation state along the reaction profile plays an essential role. Given the significant differences in the hydrogen-bond network in Dreiklang relative to EGFP, protonation states of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the quantum part), we also consider total energies of the optimized structures. After obtaining model structures for different forms of the chromophore and for different protonation states of His145 and Glu222, we compute excitation energies and analyze the effect of the protein environment. The key finding is that in the neutral form of the chromophore there is a low-lying state of charge-transfer (CT) character (Tyr203!Chro), corresponding to elec- tron transfer from Tyr203 to the chromophore. This state is only present in the neutral form and is located within 0.25 eV of the bright locally excited (LE) state of character. We further investigate implications of the CT state by dynamical simulations and geometry optimizations. Our results indicate that population of the CT state plays the key role in Dreiklang’s photo- switching. On the basis of our calculations, we propose a refined picture of the photoconversion mechanism, summarized in Fig. 5.4. As discussed below, this mechanism is consistent with all available experimental findings 7, 10 . 129 The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using different protocols. We first consider differ- ent protonation states and the excited states of the chromophore. We then discuss excited-state dynamics of the chromophore and the role of the CT state in the photoconversion. We conclude by discussing the implications of the revised photocycle. 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . H H + FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . H H + FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We ON-A ON-B OFF LE CT ESPT X 3.01 2.76 3.65 2.43 2.34 (+H + ) (-H + ) (+OH - ) (-e) (-e) 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . - FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . H H FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . H FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We . 5 of the key residues should be carefully re-evaluated. We use the structure as the primary gauge and compare the distances between the selected residues and the chromophore. In some cases (e.g., for structures that have exactly the same atoms in the QM part), we also consider total energies of the optimized structures. After obtaining model structures for di↵ erent forms of the chromophore and for di↵ erent protonation states of His145 and Glu222, we computed excitation energies and analyzed the e↵ ect of the protein environment. The key finding is that in the neutral form of the chromophore there is low-lying state of charge-transfer (CT) character (Tyr203!Chro), cor- responding to electron transfer from Tyr203 to the chromophore. This state is only present in the neutral form. We further investigate an implications of this states by dynamical sim- ulations and geometry optimizations. Our results indicate that population of the CT state, which is located within⇠ 0.25 eV ?? from the bright locally excited (LE) state of ⇡⇡ ⇤ character, plays the key role in Dreklang’s photoswitching. On the basis of our calculations, we propose a refined picture of photoconversion mechanism, summarized in in Fig. 4. As discussed below, this mechanism is consistent with all available experimental findings 7,10 . H H FIG. 4: Revised Dreiklang photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then stabilized by proton transfer. AfterreleasingtheelectronbacktoTyr203,intermediateXundergoesnucleophilicattackbynearby water, forming hydrated chromophore. The structure of the paper is as follows. We begin by describing computational protocols. We then discuss the results of the simulations using di↵ erent computational protocols. We first consider di↵ erent protonation states and the excited states of the chromophore. We .- Figure 5.4: Revised Dreiklang’s photocycle. Excitation of form A can lead to ESPT and fluorescence, but this channel is suppressed in Dreiklang. Alternatively, the locally excited chromophore can undergo a non-adiabatic transition to the CT state, which is then sta- bilized by proton transfer. After releasing the electron back to Tyr203, intermediate X undergoes nucleophilic attack by nearby water, forming the hydrated chromophore. 5.2 Computational methods and protocols We begin with the crystal structure of the recovered ON-state (3ST4), which is nearly exactly superimposable on the equilibrium ON-structure (3ST2) 7 . The structure includes two water molecules: W354 near the phenolate end and W242 near the imidazolinone moiety. We note that in the previous study 20 we used 3ST2 as the starting point for the ON-state and the model structure also included an additional water molecule, which is present in 3ST3 structure (OFF-state) but not seen in 3ST2 and 3ST4. We consider the following protonation states: Chromophore is anionic or neutral in the ON- state and is neutral in the OFF-state. Depending on the local environment, His145 can have 3 130 different protonation states: HSD (protonated at N ), HSE (protonated at N ), and HSP (pro- tonated on both N, positively charged). Glu222 can be GLU (anionic) or GLUP (protonated). Figures 5.15 and 5.16 in the Appendix A summarize the names and definitions of different pro- tonation states. Propka 21 suggested a neutral state (HSD or HSE) for His145 (pKa 2.2) and GLUP state (pKa 9.2) for the Glu222. We built the model structures as follows. Starting from the PDB structure, hydrogen atoms were added using the VMD plugin and a modified (to include the chromophore) CHARMM27 topology file. Protonation states were initially assigned by Propka 21 and then manually set for the chromophore, His145, and Glu222. Charged amino acids on the surface were locally neutralized by adding counterions close (4.5 ˚ A) to them. Charged residues that do not form salt bridges inside the protein barrel were also neutralized by adding appropriate counter ions at the surface. For HSD-GLUP structures, this protocol resulted in the addition of 19 Na + and 12 Cl in the neutral forms (ON- and OFF-states), and 19 Na + and 11 Cl in the anionic forms. For other protonation states the number of counter ions was adjusted accordingly. The proteins were solvated in water boxes producing a solvation layer of 15 ˚ A. The TIP3P water model was used to describe water. Molecular dynamics (MD) simulations were performed using these solvated neutralized model structures as follows: 1. Minimization using steepest descent algorithm for 2000 steps (protein, crystal water, counterions). 2. Minimization using steepest descent algorithm for 2000 steps of the fully solvated struc- ture (keeping protein frozen), with the subsequent equilibration of the solvent (keeping the protein frozen) for 500 ps with 1 fs time step using the NPT (isobaric-isothermal) ensemble. 131 3. Full equilibration of the system for 2 ns (with 1 fs time step) with periodic boundary con- dition (PBC) using the NPT ensemble (Noose-Hoover barostat with Langevin dynamics). 4. Production run for 2 ns with 1 fs time step using the NPT ensemble. Pressure and tem- perature were kept at 1 atm and 298 K. The structures from production-run MD simulations were used to compute average struc- tural parameters. We also used 21 snapshots from MD simulations to compute QM/MM (quan- tum mechanics/molecular mechanics) excitation energies; in these calculations, the geometry of the QM part was not optimized. To obtain better structures for more accurate estimate of the excitation energies, we carried out QM/MM optimizations using a mechanical embedding scheme (ONIOM), starting from the final structures from Step 1. To reduce the system size, in these calculations we removed the counterions and pruned the solvation shell, only retaining waters within 4 ˚ A from the surface of the protein. In these calculations, the size of the system was5900 atoms and the charge was -7 (for the neutral ON form in HSE-GLUP state). In the MD and QM/MM simulations we used CHARMM27 parameters for standard protein residues 22 and the parameters derived by Reuteretal. for the anionic GFP chromophore 23 . The parameters for the hydrated form of the chromophore were derived from additional quantum mechanical calculations (optimized structures and natural bond orbital (NBO) charges 24 ), as described in the SI. QM/MM optimizations were carried out using ONIOM. The definitions of the QM part used in ONIOM are shown in Fig. 5.5 (large QM). All coordinates were allowed to relax, except for the positions of link atoms (C carbons of the amino-acid residues shown in Fig. 5.5), which were pinned to the positions from the MM-relaxed structures. The QM part was described by!B97X-D/aug-cc-pVDZ in the QM/MM optimizations and in the AIMD (ab initio MD) simulations. This functional 25, 26 belongs to the family of long- range corrected functionals in which the notorious self-interaction error is greatly reduced 27–30 ; 132 it also includes dispersion correction 31 . The benchmarks illustrated excellent performance of !B97X-D for structures and energy differences of a broad range of compounds 25, 26 . Using long- range corrected functionals is particularly important for charged systems and for describing CT states. Excitation energies were computed using a finite cluster approach with slightly larger QM system (extended QM, see Fig. 5.5), which also included Ile64 and Leu68 directly connected to the chromophore. Excitation energies were computed using several electronic structure meth- ods: TD-DFT with!B97X-D, SOS-CIS(D) 32 , EOM-CCSD 33 , and XMCQDPT2 34 . In these cal- culations we used the following basis sets: cc-pVDZ, aug-cc-pVDZ on all atoms, and a mixed basis set, aug-cc-pVDZ on the heavy atoms of the chromophore and Tyr203 and cc-pVDZ on the rest of the atoms. The charge of the the large QM and extended QM is +1 for the neu- tral forms of the chromophore (due to the positively charged arginine) and zero for the anionic forms for all protonation states of the His148 and Glu222 except HSD-GLU, HSE-GLU, and HSP-GLUP (see Fig. 5.16 in the Appendix A for the definition of protonation states). The XMCQDPT2 calculations were based on the CASSCF wave functions obtained by distributing 16 electrons over 12 orbitals and using density averaging. The active space included orbitals from the chromophore and Tyr203. In addition, we computed excitation energies using electrostatic embedding, as in our pre- vious studies 35–38 . To prevent the overpolarization of the QM part, the charges on the boundary atoms were redistributed as follows 37, 38 : bonds before -CONH were cut and capped with hydro- gen atoms and the charge on CONH was set to zero; the excess charge was then redistributed over other atoms of the residue to maintain the total charge of the amino acid. These calcula- tions were performed using 21 snapshots from the MD trajectories (step 4 above) and the large QM system with the aug-cc-pVDZ basis set. 133 Fig. 5.5 shows the QM parts used in the ONIOM optimizations (large QM) and in the cal- culations of excitation energies (large QM and extended QM). We also carried out calculations with minimal QM (chromophore), and with the medium QM (chromophore and Tyr203). Excited-state AIMD simulations were performed using the same protocol as the geometry optimization (ONIOM embedding, large QM, !B97X-D/aug-cc-pVDZ, CHARMM27 force- field), with constant energy (NVE) ensemble and using initial velocities corresponding to 298 K thermal distribution with 1 fs time step for 10 ps (10,000 steps). All electronic structure calculations were carried out with Q-Chem 39, 40 , except for XMC- QDPT2 calculations, which were carried out with Firefly 41 . MD simulations were performed with NAMD 42 .The excited-state analysis was carried out using the libwfa library 43 . In the Appendix D, we also present the results for the structures from Ref. 20, which were obtained with a different QM/MM protocol. 5.3 Results and discussion 5.3.1 Protonation states for the ON-state It is instructive to begin by revisiting the hydrogen-bonding network around the EGFP chro- mophore. As clearly seen in Fig. 6.3, the EGFP network comprises Glu222, Ser205, Thr203, and His148. In EGFP, position 145 is occupied by tyrosine (not shown in the figure), which does not form a hydrogen bond with the chromophore. The protonation states of the key residues in EGFP (in the anionic form) are well established: Glu222 is protonated (neutral) and His148 is neutral (HSD form, protonated at N ) 12, 37, 38 . In the neutral form, Glu222 is deprotonated 12 and the protonation state of His148 is the same as in the anionic form. We note that alternative pro- tonation states are thermodynamically accessible and can be populated, especially at different pH. A recent study reported a subatomic resolution X-ray structure of GFP in the neutral (T203I mutant) and anionic (S65T and E222Q mutants) forms 44 . For the neutral form, hydrogen atom 134 H145 H145 H145 H145 CRO CRO CRO CRO R96 R96 R96 R96 S205 S205 S205 S205 E222 E222 E222 E222 W W W W W W W W W W Y203 Y203 Y203 Y203 Figure 5.5: Defition of the QM subsystem. The residues numbering corresponds to the crystal structures (3ST3 and 3ST4). Left: Residues included in large QM in the QM/MM calculations of ON- (top) and OFF-states (bottom). Right: Residues included in extended QM in the excited-state calculations of ON- (top) and OFF-states (bottom). Small QM con- tains only the chromophore and medium QM contains the chromophore and Tyr203. The total charge of the small and medium QM is zero for the A-form (neutral chromophore) and -1 for the B-form (anionic chromophore). For large and extended QM, the total charge of the QM is +1 for the on-A (HSD-GLUP, HSE-GLUP, HSP-GLU), 0 for the on-A (HSD- GLU, HSE-GLU), 0 for the on-B (HSD-GLUP, HSE-GLUP, HSP-GLU), -1 for the on-B (HSD-GLU, HSE-GLU), +1 for the off-A (HSD-GLUP, HSE-GLUP, HSP-GLU), 0 for the off-B (HSD-GLU, HSE-GLU). See Fig. 5.16 in the SI for the definition of the protonation states. For on-A (HSE-GLUP) structure, large and extended QM comprised 113 and 118 atoms, respectively. densities show that the chromophore is in the neutral form, His148 is in HSD form, and Glu222 is in anionic form, which is consistent with our choices of protonation states in neutral GFP. For the anionic form, the maps confirm that Glu222 is in neutral form (in agreement with the 135 proton wire picture), but His148 is positively charged (HSP)—this suggests that in the ground state there is an additional proton involved in protonation equilibrium. In Dreiklang, Thr203 is replaced by tyrosine, which participates in -stacking instead of hydrogen bonding. This difference has a major effect on the distance between Glu222 and Ser205: compare 4.18 ˚ A in Dreiklang and 3.72 ˚ A in EGFP. Another important difference is that in Dreiklang position 145 is occupied by histidine, which coordinates the water molecule that forms a hydrogen bond with the phenolic oxygen atom of the chromophore. In EGFP, position 145 is occupied by tyrosine (which is not involved in the hydrogen bonding network around the chromophore) and His148 is much closer to the chromophore than in Dreiklang, forming a hydrogen bond. Furthermore, T65G substitution, which, as was shown recently 38 , significantly weakens the hydrogen-bonding network around the chromophore, increasing its flexibility in the excited state. HIS145 is not a part of that network. 2 Distanceanalysis(MD,QM/MMoptimization,andNe- mukin opt d1 d3 d5 d6 d8 d9 d12 d13 CRO HSD145 ASP146 ARG96 W354 TYR203 W242 CRO W354 SER205 GLUP222 W242 d2 d4 d7 d10 d11 d14 Figure2: Distancebetweenkeyresiduesinonstatechromophore. (topleft)MD/QMMM-OPT, (top right) MD/QMMM-OPT, (bottom) OPT-nemukin. d1 = CRO:OH-HIS145:CE1, d2 = CRO:N2-GLU222:OE1, d3 = CRO:O2-ARG96:NH2, d4 = CRO:CE2-SER205:OG, d5 = CRO:OH-ASP146:O, d6 = CRO66:CG2-TYR203:CZ, d7 = CRO66:OH-TIP354:OH2,d8=CRO:N2-TIP242:O,d9=TYR203:OH-TIP242:OH2,d10=GLU222:OE2- TIP242:OH2,d11=SER205:OG-TIP354:OH2,d12=HIS145:ND1-TIP354:OH2,d13=ASP146:O- TIP354:OH2, d14= GLU222:OE1-SER205:OG 2.1 On neutral (A) • As there are lots of distances listed in the Table 5 we focus on values. We conclude that HSE-GLUP is the best protonation state for on neutral chromophore. 3 Figure 5.6: Definitions of selected distances used to compare various structures for the ON-form: d1 = CRO:OH-HIS145:CE1, d2 = CRO:N2-GLU222:OE1, d3 = CRO:O2- ARG96:NH2, d4 = CRO:CE2-SER205:OG, d5 = CRO:OH-ASP146:O, d6 = CRO66:CG2- TYR203:CZ, d7 = CRO66:OH-TIP354:OH2, d8= CRO:N2-TIP242:O,d9= TYR203:OH- TIP242:OH2, d10= GLU222:OE2-TIP242:OH2, d11 = SER205:OG-TIP354:OH2, d12 = HIS145:ND1-TIP354:OH2, d13 = ASP146:O-TIP354:OH2, d14= GLU222:OE1- SER205:OG. Figures 5.6 and 5.7 show the definition of the key distances used to validate the structures of the ON- and OFF-states. Tables 5.8-5.13 in the Appendix D contain the average values com- puted along the MD trajectories, the values at the QM/MM optimized structures, and compare 136 • As there are lots of distances listed in the Table 5 we focus on values. We conclude that HSD-GLUP is the best protonation state for on anionic chromophore. • Nemukinsoptimization(QMMM)alsoconcludeHSP-GLUPtobethelowestenergystruc- ture in ground state. Distance analyis is not avilable. However, from our calculation we see some major disagreements on HSP-GLUP (d1, d4, d14). But on anionic is less im- portant right now as reaction does not occurs from this chromophore. We need further investigation to reach final conclusion. 2.3 O↵ neutral CRO HSD145 ASP146 ARG96 W354 TYR203 d1 d4 d6 d7 d11 d10 CRO W354 SER205 GLUP222 W287 d2 d3 d5 d8 d9 d12 d13 d14 Figure 3: (Distance between key residues in o↵ state chromophore. d1 = CRO:OH-HIS145:CE1, d2 = CRO:O1-GLU222:OE1, d3 = CRO:N2-GLU222:OE2, d4 = CRO:O2-ARG96:NH2, d5 = CRO:CE2-SER205:OG, d6 = CRO:OH-ASP146:O, d7 = CRO66:CG2-TYR203:CZ,d8=CRO66:OH-TIP245:OH2,d9=SER205:OG-TIP245:OH2,d10 =HIS145:ND1-TIP245:OH2,d11=ASP146:O-TIP245:OH2,d12=GLU222:OE2-TIP287:OH2, d13= SER205:OG-TIP287:OH2, d14= GLU222:OE1-SER205:OG. 6 Figure 5.7: Definitions of selected distances used to compare various structures for the OFF-form: d1 = CRO:OH-HIS145:CE1, d2 = CRO:O1-GLU222:OE1, d3 = CRO:N2-GLU222:OE2, d4 = CRO:O2-ARG96:NH2, d5 = CRO:CE2-SER205:OG, d6 = CRO:OH-ASP146:O, d7 = CRO66:CG2-TYR203:CZ, d8 = CRO66:OH-TIP245:OH2, d9 = SER205:OG-TIP245:OH2, d10 = HIS145:ND1-TIP245:OH2, d11 = ASP146:O- TIP245:OH2, d12= GLU222:OE2-TIP287:OH2, d13= SER205:OG-TIP287:OH2, d14= GLU222:OE1-SER205:OG. them with the respective values from the crystal structures. These values are presented graphi- cally in Figs. 5.8 and 5.9. Fig. 5.20 in the Appendix D shows relative energies of the optimized structures for the model systems where the QM parts contains the same set of atoms, such that the total energies are comparable. We note that the comparison with crystal structure is complicated by the equilibrium between the anionic and neutral chromophores. The averaged distances from the MD simu- lations generally agree well with the values from QM/MM optimization, which provides vali- dation of the force-field parameters; the largest differences are observed for d7 and d11 (water position). For the ON-state with the neutral chromophore, we observe the best agreement (as judged from the smallest standard deviations of the QM/MM optimized structures from the X-ray structure) for the HSE-GLUP state (this is in agreement with Ref. 20). The largest varia- tions between different protonation states are observed for d2 (Glu222-imidozalinone) and d14 (Ser205-Glu222). For the latter, the crystal structure value is 4.18 ˚ A and the HSE-GLUP value is 4.72 ˚ A, whereas other protonation states yield shorter distances — e.g., in the structures with GLU d142.5 ˚ A. In Ref. 20, d18=4.87 ˚ A for HSE-GLUP (neutral ON-state), which is close 137 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (A) On-A (MD) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU d d d6 d7 d11 d14 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (A) On-A (QM/MM-opt) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU d d d6 d7 d11 d14 0 1 2 3 4 5 6 On-A (QM/MM-opt2) Distance (A) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSP-GLU d1 d2 d6 d7 d11 d14 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (Å) On-B (MD) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLUP d d d6 d7 d11 d14 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (Å) On-B (QM/MM-opt) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLUP d6 d7 d11 d14 d d 0 1 2 3 4 5 6 On-B (QM/MM-opt2) 3ST4 HSE-GLUP HSD-GLUP HSP-GLUP d1 d2 d6 d7 d11 d14 Figure 5.8: Key distances for ON-states: Comparison between crystal structure, average MD values, and QM/MM optimization. See Fig. 5.6 for definitions. to the present value. Further comparison between the present model structures and those from Ref. 20 is given in the Appendix D (Tables 5.8 and 5.9 and Figure 5.18). In terms of the total electronic energies, HSE-GLUP is 0.33 eV below HSD-GLUP, which is 0.42 eV lower than HSP-GLU; this energetics are consistent with the HSE-GLUP state being 138 the most favorable for the ON-state with the neutral chromophore. The gap between HSD-GLU and HSE-GLUP is 1.05 eV . For the anionic chromophore, we observe the best agreement for HSD-GLUP. Here again d2 and d14 show the largest variations between different protonation states. The HSE-GLUP state is also a viable candidate. In contrast, in Ref. 20 HSP-GLUP was used to describe the anionic ON-state. In terms of the structures, the largest difference between HSD-GLUP and HSP-GLUP is in d14: compare 4.18 ˚ A (X-ray) with 4.59 ˚ A (HSD-GLUP) and 5.79 ˚ A (HSP- GLUP). For HSE-GLUP, the largest differences are observed for d11 (Wat-Asp146) and for Chro-Tyr203: compare 5.14 ˚ A (in HSE-GLUP) versus 2.59 (HSD-GLUP). Here again, MD simulations and QM/MM optimizations are in qualitative agreement. In terms of the total electronic energies, HSD-GLUP is only 0.35 eV below HSE-GLUP. HSD-GLU and HSE-GLU are nearly isoenergetic (the latter is 0.1 eV lower). Hence, on the basis of structures and energetics, HSD-GLUP appears to be the best match, but other states cannot be ruled out. 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (Å) Off-A (md) 3ST3 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU HSE-GLUP2 HSD-GLUP2 d1 d3 d7 d8 d9 d14 1 2 3 4 5 6 0 1 2 3 4 5 6 7 Distance (Å) Off-A (QM/MM-opt) 3ST3 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU HSE-GLUP2 HSD-GLUP2 d3 d7 d8 d9 d14 d Figure 5.9: Key distances for OFF-states: Comparison between crystal structure, average MD values, and QM/MM optimizations. See Fig. 5.7 for definitions. Note that some MD values for d8, d9, and d14 are off the chart. Fig. 5.9 shows the key distances for the OFF-state. Here the differences between the MD values and QM/MM optimizations are much larger (some values are off the chart), highlighting 139 the advantage of using rigorous QM potentials. For the OFF-state, we observe the best agree- ment in terms of structures for the HSE-GLUP2, HSD-GLU, and HSP-GLU, but the differences are not that large. Comparisons of the total energies favor HSD-GLUP-OE2 (among HSD- GLUP-OE2, HSP-GLU, HSE-GLUP-OE2, HSE-GLUP, and HSD-GLUP series) and HSD- GLU (relative to HSE-GLU); HSP-GLU is slightly more stable compared to HSE-GLUP-OE2 (0.09 eV). In Ref. 20, HSE-GLUP and HSP-GLU were chosen as the best candidates. Thus, we conclude that HSE-GLUP is the most likely protonation state in the neutral ON state. For the anionic form and for the OFF state, several choices appear to be possible. In the next section, we discuss the effect of the different protonation states on the excited states of the chromophore. 5.3.2 Excited-state analysis On-A On-B Off-A S 1 /2.88/0.06 S 2 /3.39/0.73 On-A (HSE-GLUP) Off-B Figure 5.10: NTOs for the lowest bright states of the bare chromophores. Top left: neutral ON-state; top right: anionic ON-state; bottom left: neutral OFF-state; bottom right: anionic OFF-state.!B97X-D/aug-cc-pVDZ. We begin by analyzing excited states of the isolated chromophores computed at their equi- librium geometries (see the SI). Table 5.1 shows computed excitation energies and oscillator strengths of the isolated chromophores in ON- and OFF-states and Fig. 5.10 shows the respec- tive natural transition orbitals (NTOs) 43, 45 . The excited state of a GFP-like chromophore cor- responds to the ! transition, with the main action happening on the methyne bridge 46 . Consistently with previous studies 47, 48 , we observe that lower-level methods (TD-DFT) overes- timate the excitation energies. EOM-CCSD energies are 0.06-0.28 eV below the TD-DFT ones. 140 Table 5.1: Excitation energies (eV) of the isolated chromophores (ON- and OFF-states, A and B forms) computed at the optimized geometries (!B97X-D/aug-cc-pVDZ). Oscillator strengths are shown in parenthesis a . System TDDFT SOS-CIS(D) EOM-CCSD XMCQDPT2 XMCQDPT2 aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ cc-pVDZ aug-cc-pVDZ-mod b on-A 3.75 (0.72) 3.88 (1.04) 3.69 (0.98) 3.54 (0.50) 3.26 (0.49) 331 nm 320 nm 336 nm 350 nm 380 nm on-B 3.10 (1.00) 2.75 (1.07) 2.95 (1.14) 2.58 (1.11) 2.40 (1.02) 400 nm 451 nm 420 nm 481 nm 517 off-A 4.29 (0.60) 4.62 (0.71) 4.01 (0.88) 4.47 (0.68) c 4.04 (0.42) 289 nm 268 nm 309 nm 277 nm 307 nm off-B 3.39 (0.91) 3.07 (1.07) d 3.23 (1.11) 3.02 (0.90) 2.82 (0.78) 366 nm 404 nm 384 nm 411 nm 440 nm a The lowest excited state is the bright state in all cases except when marked otherwise. b aug-cc-pVDZ on heavy atoms and cc-pVDZ on hydrogens. c The lowest bright state corresponds to the S 0 -S 2 transition. d The lowest bright state corresponds to the S 0 -S 2 transition. XMCQDPT2 energies are below the EOM-CCSD energies by 0.4-0.5 eV for on-A and on-B, but are nearly he same for off-A. We note a generally good agreement between SOS-CIS(D) and XMCQDPT2 for all four cases: the differences are less than 0.4 eV and XMCQDPT2 val- ues are below SOS-CIS(D). Importantly, all methods capture (qualitatively) the large red shift (0.6 eV) between the neutral and anionic chromophores (we note that SOS-CIS(D) overes- timates the shift by almost a factor of 2). The shift can be explained in the framework of the H¨ uckel model 46 and is due to the increased delocalization on the methyne bridge in the anionic form. The oscillator strength for the anionic form is higher than that for the neutral, but the values depend on the method, i.e., the ratio is 1.2 for EOM-CCSD, 1.4 for TD-DFT, and 2.2 for XMCQDPT2. As expected, the excitation energies in the hydrated chromophore (OFF-state) are blue- shifted relative to the ON-state by roughly 0.6 eV due to disrupted conjugation. Here again all methods are in qualitative agreement, although SOS-CIS(D) yields much higher values than TD-DFT, EOM-CCSD, and XMCQDPT2. 141 As the next step, we consider the effect of the environment on excitation energies. The protein environment is important for quantitative comparison of the theoretical values with experiments 12, 35–37 . Here we primarily rely on a finite cluster approach and compute excitation energies using the extended QM system (Fig. 5.5). To assess the effect of the protein beyond the extended QM, we also include the results of the QM/MM calculations using electrostatic embedding computed for 21 snapshots taken from the MD simulations. The protein environment affects excitation energies through the electrostatic interactions that are sensitive to different charge distributions in the ground and excited states. In addition, protein environment may change the characters of the excited states and even lead to the emer- gence of new types of states. Orbital analysis 43, 49, 50 of the transitions provides a clear picture of such qualitative changes. Fig. 5.11 shows NTOs for the two lowest excited states of of the on-A form (HSE-GLUP protonation state; TD-DFT/aug-cc-pVDZ/extended QM). As one can clearly see, the character of the second excited state is the same as in the bare chromophore (Fig. 5.10)—both the hole and particle NTOs are localized on the chromophore and their shapes are not affected by the protein. This state also has a large oscillator strength, consistent with the character of the transition. In contrast, the lower state (which only appears in the protein environment) shows a clear charge-transfer character—the hole NTO is a-type orbital residing on Tyr203 and the particle orbital is the orbital of the chromophore; this state has much lower (but non-negligible) oscillator strength. Below we refer to these two states as locally excited (LE) and charge-transfer (CT) states. The NTOs for all protonation forms of the neutral and anionic forms are shown in the Appendix E (Figures 5.21 and 5.22). As one can see, the two lowest states in the on-A form correspond to the CT state (Tyr203!Chro) and bright LE state ( ) in all protonation states of His145 and Glu222. 142 In the on-B form, the lowest excited state has the same character as in the bare chro- mophore. In QM-only calculations (extended QM), the second excited state is of CT character (0.3-0.8 eV above), but this state disappears when the rest of the protein is included. The protonation states of His145 and Glu222 affect the excitation energies, but not the characters of the states. Importantly, the low-lying CT state appears in all protonation forms of on-A. On-A On-B Off-A S 1 /2.88/0.06 S 2 /3.39/0.73 On-A (HSE-GLUP) Off-B Figure 5.11: NTOs for the two lowest excited states of the protein-bond chromophore (on-A form, HSE-GLUP protonation state). QM/MM/!B97X-D/aug-cc-pVDZ. Table 5.17 in the Appendix E shows TD-DFT excitation energies computed for large and extended QM with different basis sets for the on-A form. As one can see by comparing the extended QM with the bare chromophore, the protein environment leads to a red shift of the excitation energy of the LE state by 0.2-0.4 eV . We observe the lowest excitation energy in HSE- GLUP (the most likely protonation state) and the highest in HSP-GLU. The differences between large and extended QM are less than 0.1 eV . The effect of the basis set is small — for all forms, changing the basis from the cc-pVDZ to a mixed basis (aug-cc-pVDZ on the chromophore and Tyr203 and cc-pVDZ on the rest) and to the full aug-cc-pVDZ basis leads to small red shifts for all protonation states; the largest magnitude was 0.06 eV . To estimate the effect of the rest of the protein (beyond extended QM), we compare the results of the QM and QM/MM calculations 143 using MD snapshots (Table 5.14 in the Appendix E): as one can see, including the rest of the protein leads to a small blue shift of about 0.1 eV for the LE state. The results for the CT state show somewhat stronger dependence on the computational protocol. At the TD-DFT level, the CT state appears 0.3-0.5 eV below the LE state in finite-cluster calculations. Increasing the basis set can blue-shift its energy by up to 0.03 eV . Interestingly, including the effect of the rest of protein (Table 5.14) leads to a larger blue-shift of the CT state than for the LE state (0.3 versus0.1). The results suggest that the position of the CT state in the QM-only calculations is slightly underestimated. We attribute this effect to the overstabilization of the CT state by the positively charged arginine in finite-cluster calculations; including the rest of the protein and the counterions leads to the partial screening of the arginine field and, therefore, increases the energy of the CT state. We also note that the position of the CT state is sensitive to the counterions and varies among the snapshots; this is similar to the observations reported in Refs. 35 and 51. Importantly, even including this additional correction, the CT state appears below the LE state at TD-DFT level in the neutral chromophore in all protonation states of His145 and Glu222. To further refine the positions of the LE and CT states, we computed excitation ener- gies using XMCQDPT2; these results are collected in Table 5.20. Similar to the isolated chro- mophore, the XMCQDPT2 excitation energies of the state are red-shifted relative to TD- DFT. The inclusion of the protein environment has the same effect as in TD-DFT — overall red shift relative to the isolated chromophore. In the finite-cluster calculations, the XMCQDPT2 excitation energies of the LE state appear to be red-shifted relative to the experiment by 0.4 eV in HSD-GLUP and by 0.2 in HSE-GLUP protonation states; including the effect of the rest of the protein is expected to reduce this discrepancy. Importantly, XMCQDPT2 calculations confirm the presence of the CT state. At this level of theory, the gap between the LE and CT states is smaller than at the TD-DFT level, which is consistent with the tendency of TD-DFT 144 to overestimate the positions of valence excited states and to underestimate the position of CT states. In the HSE-GLUP form, our best candidate for the neutral ON-form, the CT state is 0.3 eV below LE state at the XMCQDPT2 level in finite-cluster calculations. Extrapolating to the full protein, we expect this gap to shrink to about 0.15 eV . These comparisons provide a measure of the uncertainty of the calculations due to the basis set, QM size, and the correlation treatment; they also quantify the variations due to different pro- tonation states. Importantly, although we cannot pinpoint the exact location of the CT state, our results indicate that it is energetically close to the LE state. Taking into account the variations in energies due to different protonation states and uncertainties of computational protocols, we estimate that the CT state is within 0.25 eV of the LE state in the neutral ON-state. We also observe that its position is very sensitive to the hydrogen bond pattern and positions of counter- ions. Hence, its energy can fluctuate in the course of thermal motions, bringing it in resonance with the LE state. Hence, the CT state can be accessed either via direct excitation (since it has non-zero oscillator strength) or via non-adiabatic transition from the LE state. Since CT states are known to be involved in bleaching and some photochonversions 37, 51–53 , the appearance of this state in Dreiklang is highly suggestive of its role in photoconversion. Below we further investigate this question. Tables 5.18, 5.15, and 5.21 show the results for the anionic chromophore (on-B form). In this case, all methods (TD-DFT, SOS-CIS(D), and XMCQDPT2, both finite-cluster and QM/MM calculations) agree that the lowest state is LE of character. In finite-cluster calcu- lations, TD-DFT shows the CT state about 0.3-0.6 eV above the LE state, but when the rest of the protein is included, this state disappears. The effect of the protein leads to a small shift of the LE state (-0.2/+0.02 eV). The effect of the protein environment beyond the extended QM is of similar magnitude as for the LE state in ON-state (-0.03/+0.1 eV). The differences between 145 the cc-pVDZ and aug-cc-pVDZ bases do not exceed 0.1 eV . Better treatment of electron cor- relation leads to substantial red-shift, up to 0.6 eV . Comparing to the experimental value (2.43 eV), the XMCQDPT2 values are within 0.1-0.2 eV , depending on the protonation state. At the XMCQDPT2 level, the best agreement is observed for HSE-GLUP and HSD-GLU structures. The results for the OFF-state (shown in Tables 5.19, 5.16, and ?? in the SI) reveal similar trends. Regardless of the protonation state, there are no low-lying CT states. In this case, the protein environment leads to larger red shifts of 0.4-0.8 eV , depending on the protonation state. As for the LE states in the ON-states, the effect of the protein beyond the extended QM is small (0.01-0.2 eV). At the XMCQDPT2 level, the best agreement with experiment is observed for HSE-GLUP and HSE-GLUP2 structures (and the largest deviation—for HSE-GLU and HSD- GLUP2). We note that the results of the SOS-CIS(D) calculations show rather non-systematic behav- ior. Whereas TD-DFT systematically overestimates excitation energies of the LE state relatively to XMCQDPT2 in all forms and protonation states, the SOS-CIS(D) results are in between TD-DFT and XMCQDPT2 for the neutral and anionic forms of the ON-state, but not in the OFF-state, where they are above TDDFT for some protonation states. Likewise, SOS-CIS(D) results for the CT state show large discrepancy relative to the XMCQDPT2, which can be traced to the systematic overestimation of the CT states by the CIS method. These type of errors are expected for a low-level method relying on perturbative account of the correlation on top of the CIS wave functions. To graphically summarize these results, we show the computed excitation energies (with extrapolation correction) versus the experimental band maxima in Fig. 5.12 (raw QM/MM energies are plotted in Fig. 5.23). Whereas the absorption bands corresponding to the LE states are unambiguous, the position of the CT state is not known. In Fig. 5.12, we show the CT excitation energy against the shoulder of the main peak (2.58 eV , see Fig. 5.2), in order to see if 146 there is a correlation between the computed position of the CT state and the shoulder that might suggest that the shoulder is due the absorption to the CT state. The extrapolated excitation energies for our best candidates (selected on the basis of the structural analysis) are as follows: on-A/HSE-GLUP — TD-DFT is 3.46 eV and XMCQDPT2 is 2.93 eV , to be compared with the 3.01 experimental value; on-B/HSD-GLUP — TD-DFT is 2.88 eV and XMCQDPT2 is 2.09 eV , to be compared with 2.43 eV experimental value; on-B/HSE-GLUP — TD-DFT is 3.01 eV and XMCQDPT2 is 2.36 eV , to be compared with 2.43 eV experimental value; and for the off-A/HSE-GLUP2 form — 3.90 eV/3.62 eV; HSD- GLU: 3.78/3.44 eV , HSP-GLU: 3.89/3.50 eV; all these numbers are reasonably close to the experimental value of 3.65 eV . Based on these results, the excitation energies in different protonation states are close and cannot be used to confidently rule out some protonation states (in contrast to other cases 36 ). Moreover, given the small energy differences between the respective optimized structures, dif- ferent protonation states can be populated simultaneously. Overall, the extrapolated XMC- QDPT2 results suggest that the least likely protonantion states are HSD-GLUP for the ON-state (both neutral and anionic) and HSE-GLU and HSD-GLUP2 for the OFF-state. The results also suggest that the shoulder at 2.58 eV in the absorption spectrum of the ON- state (Fig. 5.2) may be due to either the presence of another major protonation state or the CT state of the neutral chromophore; a vibronic nature of the shoulder cannot be ruled out. One way to experimentally pinpoint the location of the CT state and to assess whether the shoulder is due to the CT state would be to measure the dependence of the quantum yield of the photoconversion as a function of the excitation wavelength. One of the implications of the revised mechanism is that direct excitation of the CT state would lead to increased yield of the OFF-form. 147 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), TDDFT Experiment (eV) ON-B CT ON-A OFF-A 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), SOS-CIS(D) Experiment (eV) ON-B CT ON-A OFF-A 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), XMCQDPT2 Experiment (eV) ON-B CT ON-A OFF-A Figure 5.12: Excitation energies for different model systems shown against the experi- mental values. Top: TD-DFT/aug-cc-pVDZ; middle: SOS-CIS(D)/aug-cc-pVDZ; bottom: XMCQDPT2/aug-cc-pVDZ/cc-pVDZ. Extended QM + correction. 148 5.3.3 Implications of the CT state and possible mechanism for photo- reaction .- .+ - .+ . . . + - PT OFF-A X7 E222 Y203 W242 CRO 66 ON-A/CT X6-1 X6-2 PT ET Figure 5.13: Proposed reaction initiated by the population of the CT state. Solid orange arrows show proton transfer and dashed blue arrows show electron transfer. AIMD and excited-state optimization reveal that the steps leading to the formation of X6-2/X7 are nearly barrierless and proceed on the scale of100-200 fs. The last two steps (shown by dashed arrows), back electron transfer from Chro to Tyr203, nucleophilic addition of OH to Chro, and reprotonation of Tyr203, are hypothesized. The structures of the possible intermediates are defined in Fig. 5.24 in the Appendix G. Fig. 5.4 shows the essential steps of Dreiklang’s photocycle and outlines the revised pho- toconversion mechanism via the CT state. The CT state can be populated either via direct excitation or by non-adiabatic transition from the LE state. This is followed by a rapid pro- ton transfer from a nearby residue. The protonated neutral radical chromophore loses the extra electron and undergoes nucleophilic addition of OH from the nearby water; this is the slowest, rate-determining step. Below we describe the computational support for the proposed mecha- nism. 149 To investigate possible excited-state pathways, we carried out geometry optimization and AIMD simulations for the CT and LE states (for the on-A-HSE-GLUP structure). Fig. 5.13 shows the structural transformation along the AIMD/optimization trajectories. Fig. 5.14 shows additional details of the AIMD simulations: energy profiles of the two lowest electronic states (Kohn-Sham reference state and the lowest TD-DFT state) and the charges of the key residues (chromophore and Tyr203) in these two states. The abrupt changes in the charges clearly indi- cate the instances of proton transfer. In the CT state, both the optimization and AIMD simulations show rapid (on the scale of 100-250 fs) and barrierless proton-transfer steps leading to the formation of the protonated chromophore; this can be rationalized by an increased basisity of the imidozalinone nitrogen caused by the electron attachment. First, the proton is transferred from Glu222 to the imidozali- none nitrogen (this happens within 50 fs). Then Glu222 is reprotonated via proton transfer from Tyr203 (acidified as a result of the electron transfer to the chromophore) via a water-mediated pathway. This process is completed in 200-250 fs. At this point, the CT state is energeti- cally nearly degenerate with the reference Kohn-Sham state (S 0 ); or, in other words, the Chro- Tyr203 radical pair (neutral protonated radical chromophore and neutral deprotonated Tyr203 radical, X6-2 structure) is nearly isoenergetic with the closed-shell ion-pair state (in which the chromophore is protonated and positively charged and Tyr203 is deprotonated and negatively charged, X7 structure). Hence, one can assume effective back-electron transfer resulting in the formation of the ground-state X7 intermediate. Based on these observations, X6-2 (Chro : -Tyr203 : radical pair) or X7 (Chro + -Tyr203 ion pair) are our candidates for the intermediate X observed spectroscopically in the time-resolved study 10 . Experimentally 10 , strong transient absorption was observed at 2.67-2.88 eV (with 100 fs kinetics). At the nanosecond scale, the formation of the intermediate X adsorbing at 2.76 150 X5 X6-1 X6-2 X7 0 50 100 150 200 250 0 1 2 3 4 5 S 0 CT Relative energies (eV) Time (fs) 0 50 100 150 200 250 -1.5 -1.0 -0.5 0.0 0.5 1.0 CRO (S 0 ) CRO (CT) TYR (S 0 ) TYR (CT) NBO charges Time (fs) Figure 5.14: Left: Energies of the Kohn-Sham reference state (S 0 ) and the CT state along the AIMD trajectory on the CT potential energy surface. Right: Charges on the chro- mophore and Tyr203 in the Kohn-Sham reference state and the CT state (lowest TDDFT state). Labels X5, X6, and X7 denote points along the trajectories when structures resem- bling these intermediates are formed (see Fig. 5.24 in the Appendix F; X6-1 refers to HSE-GLU; X6-2 refers to HSE-GLUP2). eV was observed. Hence, both short-time transient absorption and longer time-scale absorption occurs at about 2.8 eV , which is 0.2 eV red-shifted relative to the absorption of the A form. At the geometry taken from AIMD trajectory at time248 fs, the excitation energy of the ion pair X7 (computed as the lowest bright transition from the Kohn-Sham reference state) is 3.56 eV (oscillator strength 0.40), which is too high compared to the experimental absorption 151 of X. On the other hand, the excitation energy of the radical pair X6-2 (computed as the lowest bright transition from the lowest TDDFT state) is 2.93 eV (oscillator strength 0.22), which is close to the experimental value. The large difference in the excitation energies of the two struc- tures can be easily rationalized: protonation of the closed-shell neutral chromophore should lead to a blue-shift relative to the parent on-A form, whereas the absorption of the radical anion (chromophore with the additional electron) or protonated neutral radical is expected to be red- shifted relative to the respective closed-shell parent species. Hence, X6-2 appears to be a good candidate for the hot I intermediate formed on the femtosecond timescale 10 . Further changes in its excitation energy (leading to a small blue shift in the absorption of X relative to I ) are anticipated as the result of the structural relaxation of the protein. A back electron-transfer step (Chro!Tyr203) would result in the formation of X7 in which the chromophore is positively charged and, therefore, appears to be a good candidate for nucle- ophilic attack by the nearby water, leading to the formation of the hydrated chromophore and reprotonation of Tyr203. Our preliminary calculations indicate that this step would need to over- come a barrier—the scan along the water-imidozalinone distance (Fig. 5.29 in the Appendix G) yields a barrier of25 kcal/mol, which is very similar to the barrier of the thermal recovery reaction. This is a relatively crude estimate, which should be regarded as an upper bound on the barrier; more accurate estimates will be a subject of future studies. The delayed appearance of the hydrated chromophore is consistent with such a barrier. We note that, in contrast to the ther- mal recovery reaction, the reaction may still be rather fast, because of the high excess energy available to the system (see left panel in Fig. 5.14). We validated (by AIMD simulations) that once the system reaches this transition state, the dynamics swiftly proceeds downhill, leading to the formation of the hydrated chromophore and reprotonated Tyr203. The AIMD simulations also show that the reverse reaction, from X7 back to the neutral chromophore and reprotonated Tyr203, is very efficient and can compete with the final step of the nucleophilic addition. This 152 competition between the (slow) nucleophilic addition step and the (fast) reverse reaction, along with other possible channels, is likely to be responsible for a small quantum yield of the photo- transformation, despite the fast and barrierless initial steps. In contrast to the CT state, geometry optimization and AIMD simulation (1 ps long trajec- tory) on the LE potential energy surface do not show any significant structural changes, i.e., no evidence of the ultrafast ESPT from the chromophore (Fig. 5.28) posited in Ref. 10. In summary, the following picture of Dreiklang’s photocycle emerges from the results of our theoretical modeling: 1. Excitation of the anionic form (peak B in the ON-state) leads to fluorescence. 2. Excitation of the neutral form (peak A in the ON-state) leads to non-adiabatic transition to the CT state, from which photochemical transformation ensues. It can also lead to ESPT and fluorescence from the anionic state (as in the main photocycle of wt-GFP), but this channel is strongly suppressed. This picture differs from the mechanism outlined in Ref. 10, where it was proposed that pho- tochemistry unravels in the anionic state, formed by ESPT of photoexcited form A. We note that the ESPT mechanism does not explain why there is no photoconversion upon the direct excitation of the anionic form. In contrast, our proposed mechanism via the CT state, which can only be populated by the excitation of the neutral form, explains the essential trait of Dreik- lang: the decoupling of the fluorescence excitation (produced via the anionic form) from the photoconversion (produced by excitation of the neutral form). Ref. 10 invoked ESPT because of the observed isotope effect. But this effect can be explained by concerted proton transfer to the chromophore in CT state. Ref. 10 invoked ESPT to explain the observed short-time dynamics (510 fs) and commented that this process is an order of magnitude faster than ESPT in GFP (2 ps). This is inconsistent with the lack of strong 153 fluorescence following the excitation of peak A and increased pKa of the chromophore, which greatly reduces the thermodynamic drive for proton transfer in the excited state. Our AIMD simulations on the LE PES show no evidence of the ultrafast ESPT. The authors of Ref. 10 also commented that the putative ESPT in Dreiklang is significantly less sensitive to H/D exchange than ESPT in GFP, deuterium slowing the observed kinetics by a factor of 1.5 instead of 5. Our simulations strongly suggest that what is seen on the femtosecond time scale is formation of the radical pair Chro : -Tyr203 : in which the chromophore is protonated on imidozalinone’s nitrogen and Tyr203 is deprotonated. Our dynamics show 250 fs time for proton transfers, but one needs also to include time for non-adiabatic transition from the LE state populating the CT state. Sub-picosecond timescales are very likely and there should be some isotope effect. In addition, our revised photocycle is consistent with the following observations. As pointed out in Ref. 7, the essential difference between the parent system (Citrine) and Dreiklang is the upshift of the pKa of the ON-state of the chromophore (7.2 versus 5.7), which increased the effectiveness of photoconversion. Larger pKa suggests that the ESPT from the neutral form is suppressed, making the population of the CT state more competitive. Note that the fluorescence excitation spectrum (Fig. 1B from Ref. 7) shows that very little fluorescence is produced by excitation of the peak A. We note that the photoconversion is achieved by continuous irradiation in the course of5 s, which suggests that the quantum yield for this process is relatively small. Ref. 7 emphasized that Tyr203 and Glu222 (and Gly65) are crucial for Dreiklang func- tion. The authors also comment that in the fluorescent-state, Tyr203 and Glu222 form hydrogen bonds to a water molecule and thereby stabilize it in close vicinity to the C65 of the chro- mophore, a situation that is different in the nonswitchable GFP (avGFP-S65T). This strengthens the argument that the reaction may proceed by concerted proton transfer from water-to-Glu222- to-Chro. 154 We conclude by noting that neither the ET step (population of the CT state) nor the sub- sequent barrierless proton-transfer steps should be affected by temperature, meaning that these steps would not be suppressed at cryogenic temperatures. We also note that previous studies indicate that the photoinduced recovery of the ON-state is likely to be barierrless 20 . These observations suggest that Dreiklang could be a good starting point for developing photoswitch- able fluorescent proteins that can operate at low temperatures, as desired for cryogenic super- resolution imaging applications 54, 55 . 5.4 Conclusion In this contribution, we investigated properties of the fluorescent protein Dreiklang using high-level electronic structure methods combined with QM/MM and dynamics simulations. The results allowed us to quantify the spectral consequences of possible protonation states of the key residues around the chromophore and to refine the properties of the low-lying excited states. The key finding is that the neutral (protonated) ON-state of Dreiklang features a low-lying state of CT character (Tyr203!Chro), which is energetically close to the LE and is strongly affected by hydrogen bonding and thermal motions. Once this state is populated (either by direct photoexcitation or via non-adiabatic transition), the system undergoes a cascade of proton transfer steps leading to the protonation of the chromophore (on imidozalinone’s nitrogen) and formation of the neutral Chro-Tyr203 radical pair, nearly iso-energetic with the ion-pair state (in which Tyr203 is in deprotonated anionic state and the chromophore is positively charged). This structure appears to be a good candidate for nucleophilic addiction of hydroxide to the chromophore, coupled with reprotonation of Tyr203. This mechanism is consistent with the available experimental data. The disrupted hydrogen- bonding network around the chromophore and its reduced acidity explain why the canonical ESPT route is strongly suppressed, making the CT channel competitive. The key role of the CT 155 state, which is only accessible by photoexcitation of the on-A form, explains the unique feature of Dreiklang, the decoupling of fluorescence from photoswitching. 5.5 Appendix A: Definitions of protonation states On state Off state Form A Form B - - H H Figure 5.15: Definition of chromophore states. 156 + δ ϵ δ ϵ δ ϵ Charge HSD/HID 0 HSE/HIE 0 HSP/HIP +1 GLU -1 - GLUP 0 - Figure 5.16: Definition of protonation states of Glu222 and His145 in Dreiklang. GLUP can exist in two conformations: As shown or protonated on the other oxygen (GLUP2). 157 5.6 Appendix B: Computational details In addition to the structures obtained by the computational protocol described in the main manuscript, we also consider the structures from our previous study 20 in which we started with 3ST2 structure and used QM/MM optimization with electrostatic embedding, as implemented in NWChem. The QM part was described by M06-L/cc-pVDZ and the MM part was described by the AMBER forcefield. In these calculations 20 , QM included the chromophore, side chains of Gln94, Arg96, His145, Tyr203, Ser205, and Glu222, and seven water molecules. This defini- tion is similar to our extended QM. We note that these model structures also included additional water molecule, which is present in 3ST3 structure (OFF-state) but not seen in 3ST2 and 3ST4. The comparisons between the two protocols quantify the effect of the level of theoretical treat- ment. The key structural parameters two sets of structures are compared in Tables 5.8-5.13 below and graphically in Figs. 5.18 and 5.19. 5.7 Appendix C: Forcefield parameters for the neutral hydrated chromophore To derive missing forcefield parameters (for the OFF-form of the chromophore) we followed a protocol described in our previous work 37, 38 . The key equations and the values of the forcefield parameters are given below. q (on;charmmqm) =q on;charmm q NBO(on;qm) (5.1) q (off;charmm) =q NBO(off;qm) + q (on;charmmqm) (5.2) E =k(bb 0 ) 2 (5.3) 158 Figure 5.17: From left to right: proline, chromophore in off-state, threonine. k off;param = k off;theory k on;theory k oncharmm (5.4) b 0 is the equilibrium bond length. E =k(AA 0 ) 2 (5.5) k off;param = k off;theory k on;theory k oncharmm (5.6) A 0 is the equilibrium bond angle. E =k[1 +cos(n)] (5.7) wheren is the phase, is the optimized dihedral angle. k off;param = k off;theory k on;theory k oncharmm (5.8) 159 Table 5.2: Partial charges in the OFF-state. Atom, off on, charmm on, qm q (on;charmmqm) q adjusted off, qm off, charmm C1(threonine) 0.10 0.15 -0.05 -0.02 0.67 0.69 N2 (proline) -0.74 -0.28 -0.46 -0.43 -0.68 -0.25 N3 -0.64 -0.52 -0.12 -0.09 -0.56 -0.47 C2 0.8 0.74 0.06 0.09 0.74 0.65 O2 -0.61 -0.60 -0.01 0.02 -0.63 -0.65 CA2 0.24 0.05 0.19 0.22 0.12 -0.10 CB2 -0.10 -0.09 -0.01 0.02 -0.24 -0.26 HB2 0.1 0.28 -0.18 -0.15 0.27 0.42 CG2 0.00 -0.11 0.11 0.14 -0.09 -0.23 CD1 -0.115 -0.14 0.025 0.06 -0.185 -0.245 HD11 0.115 0.27 -0.155 -0.12 0.25 0.37 CD2 -0.115 -0.14 0.025 0.06 -0.185 -0.245 HD21 0.115 0.27 -0.155 -0.12 0.25 0.37 CE1 -0.115 -0.27 0.155 0.19 -0.275 -0.465 HE11 0.115 0.27 -0.155 -0.12 0.25 0.37 CE2 -0.115 -0.27 0.155 0.19 -0.275 -0.465 HE21 0.115 0.27 -0.155 -0.12 0.25 0.37 CZ 0.11 0.38 -0.27 -0.24 0.34 0.58 OH -0.54 -0.68 0.14 0.17 -0.70 -0.87 OHH 0.43 0.52 -0.09 -0.06 0.50 0.56 OT (threonine) -0.78 -0.65 -0.13 -0.10 -0.75 -0.65 HT(threonine) 0.50 0.44 0.06 0.09 0.50 0.41 HH (proline) 0.41 0.11 0.30 0.33 0.44 0.11 CA3 -0.18 -0.18 HA31 0.09 0.09 HA32 0.09 0.09 C 0.51 – – – 0.51 O -0.51 – – – – -0.51 N -0.47 – – – – -0.47 HN 0.31 – – – – 0.31 CA -0.02 -0.02 HA1 0.09 0.09 HA2 0.09 0.09 Table 5.3: Optimized bond lengths (in ˚ A) involving key atoms. Bonds B on;charmm B on;opt B off;opt C1-N2 (proline) 1.434 1.46 1.45 N2-CA2 1.40 1.41 1.39 N2-HH (proline) 0.997 1.02 1.01 C1-OT (threonine) 1.42 1.40 1.41 C1-CA 1.49 1.49 1.53 C1-N3 1.39 1.38 1.45 160 Table 5.4: Parameterization of the force constantk for bond lengths in kcal/mol/ ˚ A 2 . Bonds k on;charmm k on;theory k off;theory k off;theory /k on;theory k off;param C1-N2 (proline) 320 1156.50 1226.15 1.06 339.27 N2-CA2 400 940.00 1257.53 1.34 535.12 N2-HH (proline) 440 976.40 1044.80 1.07 470.82 C1-OT (threonine) 428 847.14 744.22 0.88 376.00 C1-CA 354 562.25 542.79 0.965 341.75 C1-N3 320 1156.50 1226.15 1.06 339.27 Table 5.5: Optimized bond angles (in degrees) involving key atoms. Angles A on;charmm A on;opt A off;opt N2-C1-N3 114.0 113.99 102.31 C1-N2-CA2 106.0 106.18 111.21 HH-N2-C1 (proline) 117.0 111.44 115.90 HH-N2-CA2 117.0 111.44 117.8 OT-C1-CA (threonine) 110.1 112.6 110.31 OT-C1-N2 (threonine) 110.1 112.6 107.90 OT-C1-N3 (threonine) 110.1 112.6 111.39 N2-CA2-CB2 129.5 129.58 130.17 N2-CA2-C2 108.3 108.73 106.54 C1-N3-C2 107.9 113.47 108.26 CA-C1-N3 (threonine) 113.5 111.6 112.01 Table 5.6: Parameterization of the force constantk for bond angles in kcal/mol/rad 2 . Angles k on;charmm k on;theory k off;theory k off;theory /k on;theory k off;param N2-C1-N3 130.0 444.28 347.33 0.78 101.6 C1-N2-CA2 130.0 438.63 259.98 0.59 77.05 HH-N2-C1 (proline) 35.0 89.73 79.69 0.89 31.08 HH-N2-CA2 35.0 89.73 79.69 0.89 31.08 OT-C1-CA (threonine) 75.7 232.18 259.37 1.12 84.56 OT-C1-N2(N3) (threonine) 75.7 232.18 259.37 112 84.56 N2-CA2-CB2 45.8 151.23 169.42 1.12 51.3 N2-CA2-C2 130.0 472.5 376.50 0.797 103.6 C1-N3-C2 130.0 498.24 305.6 0.61 79.7 CA-C1-N3 (threonine) 70.0 180.72 179.47 0.99 69.5 Table 5.7: Parameterization of the force constantk for dihedral angles; in degrees,k in kcal/mol. Angles k on;charmm n k off;theory /k on;theory k off;param OT-C1-N2-HH 0.16 3 180 0.263 0.053 OT-C1-N2-CA2 0.20 3 0 13.83 2.213 CA-C1-N2-HH 0.16 3 180 0.263 0.053 HH-N2-CA2-CB2 0.16 3 0 0.263 0.053 HH-N2-CA2-C2 0.20 3 180 13.83 2.213 HH-N2-C1-N3 0.20 3 180 13.83 2.213 CA-C1-N3-CA3 0.16 3 0 0.263 0.053 OT-C1-N3-CA3 0.16 3 0 0.263 0.053 CA-C1-N3-C2 0.20 3 180 13.83 2.213 161 5.8 Appendix D: Structures of model systems Table 5.8: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). The chromophore is neutral (A-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST4 HSE- HSE- HSD- HSD- HSP- GLU GLUP GLU GLUP GLU d1 md 3.52 3.42(0.3) 3.96(0.8) 3.74(0.4) 3.63(0.4) 4.68(1.0) opt – 3.31 3.92 3.53 4.2 3.78 opt2 – 3.45 3.50 3.49 3.46 d2 md 2.97 3.94(0.3) 3.44(0.3) 3.92(0.3) 3.54(0.4) 4.00(0.3) opt – 3.99 2.78 4.06 2.86 4.00 opt2 – 3.46 3.09 3.44 3.49 d3 md 2.73 3.42(0.3) 2.77(0.1) 2.74(0.1) 2.77(0.1) 2.74(0.1) opt – 2.58 2.62 2.6 2.67 2.61 opt2 – 2.77 2.85 2.80 2.81 d4 md 3.81 3.60(0.2) 4.82(0.8) 3.62(0.2) 3.91(0.3) 4.02(0.7) opt – 3.53 3.67 3.52 3.77 3.38 opt2 – 3.96 3.92 3.96 4.16 d5 md 4.04 4.38(0.4) 4.08(0.3) 4.05(0.4) 3.86(0.3) 4.67(0.4) opt – — — — — —- opt2 – — – — — — d6 md 3.64 3.85(0.2) 3.82(0.2) 3.88(0.2) 3.87(0.2) 3.82(0.2) opt – 3.69 3.52 3.63 3.6 3.59 opt2 – 3.85 3.63 3.68 3.67 d7 md 2.63 V .L 2.69(0.1) 2.71(0.1) 2.74(0.1) 3.19(0.8) opt – 2.97 2.59 2.63 2.63 3.59 opt2 – 2.59 2.66 2.66 2.67 d8 md 3.41 3.18(0.2) 3.43(0.2) 3.49(0.3) 3.43(0.2) 3.6(0.3) opt – 3.25 3.22 3.71 3.27 3.59 opt2 – 3.05 3.26 3.02 3.01 d9 md 2.89 2.92(0.2) 2.99(0.3) 2.88(0.2) 2.99(0.3) 2.96(0.2) opt – 2.64 2.68 2.78 2.67 2.79 opt2 – 2.82 2.81 2.79 2.81 d10 md 2.69 2.63(0.1) 2.81(0.2) 2.63(0.1) 2.78(0.2) 2.66(0.1) opt – 2.58 2.7 2.8 2.72 2.73 opt2 – 2.67 2.75 2.67 2.67 162 Table 5.9: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). The chromophore is neutral (A-form). ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST4 HSE- HSE- HSD- HSD- HSP- GLU GLUP GLU GLUP GLU d11 md 2.73 V .L 3.76(0.8) 2.9(0.2) 3.02(0.3) 2.93(0.3) opt – 3.01 2.7 2.52 2.59 2.89 opt2 – 2.72 2.69 2.67 2.63 d12 md 3.05 V .L 3.06(0.3) 3.53(0.4) 3.42(0.4) 3.89(0.4) opt – 3.33 2.58 2.83 2.95 3.23 opt2 – 3.53 2.70 3.10 2.74 d13 md 2.89 V .L 2.84(0.3) 3.4(0.4) 3.41(0.6) 3.87(0.4) opt – – – – – – opt2 – — – — — — d14 md 4.18 2.67(0.1) 4.28(0.5) 2.66(0.1) 3.48(0.4) 2.68(0.1) opt – 2.7 4.72 2.56 4.32 2.5 opt2 – 5.06 4.38 5.02 5.03 163 Table 5.10: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). Chromophore is anionic (B-form). ’md’ denotes struc- tures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST4 HSE- HSE- HSD- HSD- HSP- GLU GLUP GLU GLUP GLUP d1 md 3.52 3.90(0.3) 3.19(0.2) 3.57(0.4) 3.32(0.3) 3.05(0.3) opt – 3.66 3.39 3.39 3.47 2.88 opt2 – 3.30 3.24 3.10 d2 md 2.97 3.98(0.3) 3.17(0.3) 4.62(0.4) 3.13(0.2) 3.07(0.2) opt – 4.02 2.74 4.11 2.9 2.79 opt2 – 3.47 3.49 3.08 d3 md 2.73 2.72(0.1) 2.75(0.1) 2.74(0.1) 2.72(0.1) 2.73(0.1) opt – 2.52 2.57 2.51 2.57 2.64 opt2 – 2.74 2.76 2.81 d4 md 3.81 3.78(0.3) 4.83(0.8) 3.73(0.3) 3.97(0.3) 4.42(0.4) opt – 3.93 3.84 3.33 4.06 4.51 opt2 – 4.01 4.01 3.99 d5 md 4.04 4.22(0.2) 4.74(0.3) 4.15(0.3) 3.82(0.2) 4.14(0.3) opt – — — — — — opt2 – – – – – — d6 md 3.64 3.96(0.2) 3.78(0.2) 4.00(0.3) 3.84(0.2) 3.94(0.2) opt – 3.84 3.64 3.97 3.67 3.64 opt2 – 3.68 3.83 3.68 d7 md 2.63 2.79(0.2) 5.24(1.0) 2.8(0.2) 2.75(0.2) 2.79(0.2) opt – 2.86 5.14 2.87 2.59 2.54 opt2 – 2.74 2.68 2.63 d8 md 3.41 3.00(0.1) 3.86(0.5) 3.01(0.1) 3.72(0.4) 3.88(0.4) opt – 3.19 3.29 3.47 3.23 3.51 opt2 – 3.34 3.02 3.27 d9 md 2.89 2.83(0.1) 2.86(0.2) 2.84(0.1) 2.84(0.1) 2.85(0.2) opt – 2.71 2.88 2.58 2.77 2.77 opt2 – 2.87 2.86 2.80 d10 md 2.69 2.66(0.1) 2.8(0.2) 2.64(0.1) 2.78(0.2) 2.78(0.2) opt – 2.46 2.64 2.89 2.77 2.81 opt2 – 2.91 2.89 2.75 164 Table 5.11: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST4 (ON-state). Chromophore is anionic (B-form). ’md’ denotes struc- tures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM optimized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST4 HSE- HSE- HSD- HSD- HSP- GLU GLUP GLU GLUP GLUP d11 md 2.73 3.67(0.7) 4.54(0.8) 2.9(0.2) 2.9(0.2) 2.97(0.4) opt – 3.95 4.11 2.66 2.74 2.76 opt2 – 2.62 2.63 2.70 d12 md 3.05 5.41(0.3) 3.07(0.4) 3.43(0.4) 3.25(0.3) 3.33(0.3) opt – 3.31 2.89 3.76 2.85 2.65 opt2 – 3.37 3.31 2.76 d13 md 2.89 3.38(0.6) 4.73(0.5) 3.25(0.3) 2.81(0.2) 3.24(0.5) opt – – – – – — opt2 – — — – – – d14 md 4.18 2.68(0.1) 4.33(0.5) 2.65(0.1) 4.1(0.4) 5.24(0.4) opt – 2.65 4.27 2.55 4.59 5.79 opt2 – 4.90 4.99 4.53 165 Table 5.12: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST3 (OFF-state). Chromophore is neutral. ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM opti- mized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST3 HSE HSD HSE HSD HSE HSD HSP GLU GLU GLU GLU GLU GLU GLU P P P2 P2 d1 md 3.35 3.37 3.75 3.71 3.68 3.63 3.53 2.97 (0.3) (0.5) (0.6) (0.2) (0.5) (0.4) (0.2) opt – 4.1 2.96 3.17 4.2 4.29 3.48 3.38 opt2 – 3.58 3.27 3.44 3.47 3.46 d2 md 2.46 3.25 3.28 4.21 4.53 3.20 3.23 3.13 (0.2) (0.2) (0.4) (0.4) (0.2) (0.2) (0.1) opt – 2.8 2.85 2.76 2.67 2.66 2.67 2.78 opt2 – 2.82 2.86 2.62 2.63 2.63 d3 md 2.85 4.23 4.32 3.56 3.49 3.91 3.67 3.51 (0.6) (0.4) (0.3) (0.3) (0.4) (0.5) (0.3) opt – 3.5 3.45 3.13 3.09 2.96 3.03 3.0 opt2 – 3.17 3.17 2.96 2.96 2.98 d4 md 3.01 2.69 2.7 2.71 2.67 2.68 2.68 2.67 (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) opt – 2.66 2.68 2.66 2.67 2.6 2.62 2.61 opt2 – 2.82 2.79 2.80 2.82 2.82 d5 md 3.82 4.13 4.93 4.84 5.51 5.66 3.81 4.69 (0.3) (0.4) (0.6) (0.7) (0.5) (0.3) (0.4) opt – 3.6 4.12 3.96 4.05 3.85 3.79 3.78 opt2 – 4.16 3.95 4.02 4.04 4.15 d6 md 3.98 3.91 4.96 4.62 4.14 4.50 3.98 4.44 (0.3) (0.4) (0.4) (0.3) (0.4) (0.3) (0.4) opt – – – – – – – – opt2 – – – – – — – – d7 md 3.91 3.98 3.78 3.80 3.94 3.99 4.05 4.21 (0.3) (0.2) (0.2) (0.3) (0.3) (0.3) (0.3) opt – 3.68 3.67 3.66 3.74 3.95 3.7 3.67 opt2 – 3.70 3.73 3.72 3.69 3.67 166 Table 5.13: Comparison of the distances (in ˚ A) from MD and QM/MM simulations with crystal structure 3ST3 (OFF-state). Chromophore is neutral. ’md’ denotes structures averaged over equilibrium MD trajectories. ’opt’ and ’opt2’ denote the QM/MM opti- mized structures obtained with present protocol and with the protocol from Ref. 20, respectively. D 3ST3 HSE HSD HSE HSD HSE HSD HSP GLU GLU GLU GLU GLU GLU GLU P P P2 P2 d8 md 2.59 L.V 3.86 10.4 2.87 L.V 2.64 L.V (1.1) (7.9) (0.4) opt – 2.7 2.71 2.96 2.61 2.71 2.83 2.67 opt2 – 2.7 2.67 2.63 2.66 2.68 d9 md 2.64 L.V 7.28 7.38 3.97 L.V 2.80 L.V (0.7) (8.2) (0.6) opt – 2.71 4.36 2.62 2.53 2.6 2.62 2.51 opt2 – 2.65 2.62 2.75 2.67 2.63 d10 md 3.17 L.V 4.79 9.60 5.40 L.V 3.37 L.V (0.7) (8.3) (0.3) (0.4) opt – 4.5 3.8 2.62 2.83 4.03 2.87 2.54 opt2 – 2.68 3.55 3.44 3.13 2.75 d11 md 2.80 L.V 3.95 7.37 2.82 L.V 3.21 L.V (1.4) (8.6) (0.2) (0.4) opt – – – – – – – – opt2 – – – – – – – – d12 md 2.67 4.29 4.38 4.72 4.64 2.79 3.04 2.62 (0.9) (0.8) (0.1) (0.5) (0.3) (0.6) (0.1) opt – 3.53 3.6 2.73 2.71 2.68 2.58 2.53 opt2 – 2.55 2.54 2.68 2.65 2.65 d13 md 2.47 L.V 3.03 2.78 2.89 4.70 4.22 2.81 (0.4) (0.1) (0.2) (1.8) (1.7) (0.1) opt – 2.64 2.69 2.6 2.56 3.16 2.56 2.5 opt2 – 2.65 2.66 2.60 2.58 2.56 d14 md 4.88 3.74 5.18 6.56 6.36 4.52 3.69 4.59 (1.2) (0.9) (0.4) (0.5) (0.6) (1.0) (0.4) opt – 6.02 5.95 4.91 5.04 5.27 4.76 4.82 opt2 – 4.79 4.91 5.01 4.95 4.93 167 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (A) On-A (QM/MM-opt) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU d d d6 d7 d11 d14 0 1 2 3 4 5 6 On-A (QM/MM-opt2) Distance (A) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSP-GLU d1 d2 d6 d7 d11 d14 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance (Å) On-B (QM/MM-opt) 3ST4 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLUP d6 d7 d11 d14 d d 0 1 2 3 4 5 6 On-B (QM/MM-opt2) 3ST4 HSE-GLUP HSD-GLUP HSP-GLUP d1 d2 d6 d7 d11 d14 Figure 5.18: Key distances for ON-states: Comparison between crystal structure and QM/MM optimization. OPT1 and OPT2 denote two different protocols (see text). See Fig. 5 in the main text for definitions. 168 1 2 3 4 5 6 0 1 2 3 4 5 6 7 Distance (Å) Off-A (QM/MM-opt) 3ST3 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU HSE-GLUP2 HSD-GLUP2 d3 d7 d8 d9 d14 d 0 1 2 3 4 5 6 Distance (Å) Off-A (QM/MM-opt2) 3ST3 HSE-GLU HSE-GLUP HSD-GLU HSD-GLUP HSP-GLU d1 d3 d7 d8 d9 d14 Figure 5.19: Key distances for OFF-states: Comparison between crystal structure, aver- age MD values, and QM/MM optimizations. See Fig. 6 of the main text for definitions. HSP GLU HSD GLUP HSE GLUP HSD GLU HSE GLU ON-A 0.32 0.42 1.05 HSP GLUP HSD GLUP HSE GLUP HSD GLU HSE GLU ON-B 0.35 0.09 HSP GLU HSD GLUP HSE GLUP HSD GLU HSD GLUP2 OFF-A 0.61 0.17 0.22 HSE GLUP2 0.26 0.60 HSE GLU Figure 5.20: Energy ordering (eV) of QM/MM (ONIOM) optimized structures (boxes mark the structures with the same number of atoms in QM). 169 5.9 Appendix E: Analysis of excited states S 1 /3.10/0.13 S 2 /3.41/0.66 S 1 /2.94/0.22 S 2 /3.39/0.63 S 1 /2.81/0.04 S 2 /3.37/0.77 S 1 /2.76/0.05 S 2 /3.32/0.82 S 1 /3.26/0.14 S 2 /3.56/0.59 Figure 5.21: NTOs of the lowest excited states of the neutral form and different protona- tion states of His145 and Glu222; TD-DFT, extended QM. Left: CT state; right: LE state; top-to-bottom: HSD-GLU, HSD-GLUP, HSE-GLU, HSE-GLUP, HSP-GLU. 170 S 1 /3.12/0.88 S 2 /3.45/0.18 S 1 /2.95/0.86 S 2 /3.56/0.14 S 1 /2.90/0.54 S 2 /3.22/0.55 S 1 /3.04/0.97 S 2 /3.74/0.06 S 1 /2.94/0.64 S 2 /3.28/0.39 Figure 5.22: NTOs of the lowest excited states of the anionic form and different protona- tion states of His145 and Glu222; TD-DFT, extended QM. Left: LE state; right: CT state; top-to-bottom: HSD-GLU, HSD-GLUP, HSE-GLU, HSE-GLUP, HSP-GLUP. CT state is pushed to much higher energies and disappears in QM/MM calculations. 171 Table 5.14: Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the neutral chromophore in the ON-state. All energies are in eV; large QM. System State TD-DFT TD-DFT TD-DFT TD-DFT TD-DFT aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ QM/MM (MD) QM only (MD) a QM only (opt) b QM/MM-corr c HSD-GLUP CT 4.01 (0.05) 3.76 (0.17) +0.25 3.07 (0.26) 3.32 (0.26) LE 3.49 (0.56) 3.42 (0.52) +0.07 3.49 (0.54) 3.56 (0.54) HSE-GLUP CT 3.96 (0.10) 3.70 (0.38) +0.26 2.88(0.06) 3.14 (0.06) LE 3.58 (0.52) 3.44 (0.30) +0.14 3.49 (0.73) 3.63 (0.73) HSD-GLU CT 3.84 (0.10) 3.58 (0.19) +0.26 3.10 (0.13) 3.36 (0.13) LE 3.39 (0.49) 3.30 (0.51) +0.09 3.41 (0.66) 3.50 (0.66) HSE-GLU CT 3.93 (0.08) 3.62 (0.11) +0.31 2.81 (0.04) 3.12 (0.04) LE 3.45 (0.56) 3.37 (0.60) +0.08 3.37 (0.77) 3.45 (0.77) HSP-GLU CT 3.88 (0.16) 3.71 (0.12) +0.17 3.26 (0.14) 3.43 (0.14) LE 3.56 (0.63) 3.53 (0.69) +0.03 3.56 (0.59) 3.59 (0.59) a is the difference in excitation energies in QM/MM and QM only calculation evaluated using structures from 21 MD snapshots. b QM only excitation energies computed using ONIOM optimized structures. c Extrapolated values: QM only excitation energies computed using ONIOM optimized structures plus correction. 172 Table 5.15: Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the anionic chromophore in the ON-state. All energies are in eV; large QM. System State TD-DFT TD-DFT TD-DFT TD-DFT TD-DFT aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ QM/MM (MD) QM only (MD) a QM only (opt) b QM/MM-corr c HSD-GLUP LE 2.89 (0.91) 2.96 (0.86) -0.07 3.01 (0.88) 2.94 (0.88) HSE-GLUP LE 2.99 (1.02) 3.02 (0.99) -0.03 3.09 (0.95) 3.06 (0.95) HSD-GLU LE 3.07 (0.96) 3.02 (0.90) +0.05 3.14 (0.98) 3.19 (0.98) HSE-GLU LE 3.03 (0.88) 2.92 (0.81) +0.11 3.04 (0.94) 3.15 (0.94) HSP-GLUP LE 3.14 (0.94) 3.22 (0.88) -0.08 3.05 (0.84) 2.97 (0.84) a is the difference in excitation energies in QM/MM and QM only calculation evaluated using structures from 21 MD snapshots. b QM only excitation energies computed using ONIOM optimized structures. c Extrapolated values: QM only excitation energies computed using ONIOM optimized structures plus correction. 173 Table 5.16: Effect of the protein environment beyond extended QM estimated from the 21 MD snapshots for the OFF- form (neutral chromophore). All energies are in eV; large QM. System State TD-DFT TD-DFT TD-DFT TD-DFT TD-DFT aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ QM/MM (MD) QM only (MD) a QM only (opt) b QM/MM-corr c HSD-GLUP LE 4.10 (0.44) 3.97 (0.39) +0.13 3.86 (0.41) 3.99 (0.41) HSE-GLUP LE 3.89 (0.51) 3.88 (0.48) +0.01 3.92 (0.33) 3.93 (0.33) HSD-GLU LE 4.12 (0.56) 4.03 (0.36) +0.09 3.69 (0.53) 3.78 (0.53) HSE-GLU LE 3.88 (0.40) 3.79 (0.41) +0.09 3.52 (0.57) 3.61 (0.57) HSP-GLU LE 3.89 (0.63) 3.85 (0.57) +0.04 3.85 (0.60) 3.89 (0.60) HSD-GLUP2 LE 3.79 (0.66) 3.63 (0.59) +0.16 3.52 (0.64) 3.68 (0.64) HSE-GLUP2 LE 3.77 (0.40) 3.74 (0.32) +0.03 3.87 (0.58) 3.90 (0.58) a is the difference in excitation energies in QM/MM and QM only calculation evaluated using structures from 21 MD snapshots. b QM only excitation energies computed using ONIOM optimized structures. c Extrapolated values: QM only excitation energies computed using ONIOM optimized structures plus correction. 174 Table 5.17: TD-DFT excitation energies (eV) of the two lowest states of protein-bound neutral chromophore in the ON-state with different basis sets and different size of QM region; oscillator strength is shown in parentheses. System State Extended QM Extended QM Extended QM Large QM cc-pVDZ mixed basis a aug-cc-pVDZ aug-cc-pVDZ QM only QM only QM only QM only HSD-GLUP LE 3.43 (0.72) 3.40 (0.61) 3.39 (0.63) 3.49 (0.54) CT 2.91 (0.16) 2.96 (0.24) 2.94 (0.22) 3.07 (0.26) HSE-GLUP LE 3.38 (0.87) 3.34 (0.82) 3.32 (0.82) 3.39 (0.73) CT 2.71 (0.03) 2.80 (0.05) 2.76 (0.05) 2.88 (0.06) HSD-GLU LE 3.46 (0.73) 3.41 (0.65) 3.41 (0.66) 3.44 (0.60) CT 3.09 (0.08) 3.12 (0.14) 3.10 (0.13) 3.16 (0.11) HSE-GLU LE 3.42 (0.80) 3.38 (0.75) 3.37 (0.77) 3.48 (0.67) CT 2.74 (0.03) 2.85 (0.05) 2.81 (0.04) 2.88 (0.02) HSP-GLU LE 3.62 (0.65) 3.57 (0.58) 3.56 (0.59) 3.58 (0.52) CT 3.26 (0.09) 3.28 (0.14) 3.26 (0.14) 3.32 (0.13) a mixed basis: aug-cc-pVDZ for the chromophore and tyrosine and cc-pVDZ for rest of QM. Table 5.18: TD-DFT excitation energies (eV) of the two lowest states of protein-bound anionic chromophore in the ON-state; oscillator strength is shown in parentheses. System State Extended QM Extended QM Large QM cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ QM only QM only QM only HSD-GLUP LE 3.03 (0.86) 2.95 (0.86) 3.01 (0.88) HSE-GLUP LE 3.12 (0.98) 3.04 (0.97) 3.09 (0.95) HSD-GLU LE 3.10 (0.79) 3.12 (0.88) 3.14 (0.98) HSE-GLU LE 2.89 (0.36) 2.90 (0.54) 3.04 (0.94) HSP-GLUP LE 2.96 (0.49) 2.94 (0.64) 3.05 (0.84) Table 5.19: TD-DFT excitation energies (eV) of the two lowest states of protein-bound neutral chromophore in the OFF-state; oscillator strength is shown in parentheses. System State Extended QM Extended QM Large QM cc-pVDZ aug-cc-pVDZ aug-cc-pVDZ QM only QM only QM only HSD-GLUP LE 4.03 (0.19) 3.86 (0.41) 3.80 (0.58) HSE-GLUP LE 3.97 (0.63) 3.92 (0.33) 3.93 (0.56) HSD-GLU LE 4.07 (0.11) 3.69 (0.53) 3.70 (0.49) HSE-GLU LE 3.57 (0.56) 3.52 (0.57) 3.58 (0.54) HSP-GLU LE 3.89 (0.58) 3.85 (0.60) 3.83 (0.52) HSD-GLUP2 LE 3.58 (0.64) 3.52 (0.64) 3.57 (0.60) HSE-GLUP2 LE 3.95 (0.56) 3.87 (0.58) 3.83 (0.52) 175 Table 5.20: Excitation energies (eV) of the two lowest states of protein-bound neutral chromophore in the ON-state; oscillator strength is shown in parentheses. Extended QM. System State TD-DFT SOS-CIS(D) XMCQDPT2 XMCQDPT2 a XMCQDPT2 aug-cc-pVDZ aug-cc-pVDZ cc-pVDZ cc-pVDZ aug-cc-pVDZ /cc-pVDZ QM only QM only QM only QM only QM only HSD-GLUP LE 3.39 (0.63) 2.87 (1.04) 2.62 (0.50) 2.59 (0.59) CT 2.94 (0.22) 3.40 (0.08) 2.98 (0.12) 3.04 (0.17) HSE-GLUP LE 3.32 (0.82) 2.87 (0.99) 2.64 (0.57) 2.88 (0.31) 2.79 (0.41) CT 2.76 (0.05) 3.17 (0.13) 2.89 (0.23) 3.09 (0.05) 2.51 (0.28) HSD-GLU LE 3.41 (0.66) 3.10 (0.97) 2.89 (0.72) 2.85 (0.40) 2.83 (0.24) CT 3.10 (0.13) 3.68 (0.04) 3.01 (0.03) 3.12 (0.03) 2.76 (0.28) HSE-GLU LE 3.37 (0.77) 2.98 (0.94) 2.70 (0.30) 2.74 (0.56) 2.87 (0.45) CT 2.81 (0.04) 3.21 (0.10) 2.98 (0.29) 3.08 (0.01) 2.59 (0.18) HSP-GLU LE 3.56 (0.59) 3.42 (0.93) 3.02 (0.14) 2.90 (0.16) 2.96 (0.26) CT 3.26 (0.14) 4.05 (0.04) 3.10 (0.15) 2.93 (0.02) 2.94 (0.11) a Using structures and QM definition from the old protocol 20 . 176 Table 5.21: Excitation energies of the protein-bound anionic chromophore in the ON-state; oscillator strength is shown in parentheses. Extended QM. System state TD-DFT SOS-CIS(D) XMCQDPT2 XMCQDPT2 a XMCQDPT2 aug-cc-pVDZ aug-cc-pVDZ cc-pVDZ cc-pVDZ aug-cc-pVDZ /cc-pVDZ QM only QM only QM only QM-only QM-only HSD-GLUP LE 2.95 (0.86) 2.41 (1.29) 2.30 (0.94) 2.39 (0.89) 2.16 (0.87) HSE-GLUP LE 3.04 (0.97) 2.68 (1.41) 2.58 (0.96) 2.37 (0.93) 2.39 (0.98) HSD-GLU LE 3.12 (0.88) 2.64 (1.34) 2.50 (0.93) 2.37 (0.92) HSE-GLU LE 2.90 (0.54) 2.41 (1.29) 2.41 (0.90) 2.29 (0.92) HSP-GLUP LE 2.94 (0.64) 2.43 (1.23) 2.39 (0.84) 2.41 (0.85) 2.27 (0.81) a Using structures and QM definition from the old protocol 20 . 177 Table 5.22: Excitation energies of the protein-bound neutral chromophore in the OFF- state; oscillator strength is shown in parentheses. Extended QM. System TDDFT SOS-CIS(D) XMCQDPT2 XMCQDPT2 a XMCQDPT2 aug-cc-pVDZ aug-cc-pVDZ cc-pVDZ cc-pVDZ aug-cc-pVDZ /cc-pVDZ QM only QM only QM only QM-only QM-only HSD-GLUP 3.86 (0.41) 3.98 (0.83) 4.06 (0.52) 3.79 (0.21) 3.50 (0.63) HSE-GLUP 3.92 (0.33) 4.17 (0.79) 4.11 (0.53) 4.00 (0.61) 3.67 (0.58) HSD-GLU 3.69 (0.53) 3.93 (0.76) 3.51 (0.58) 3.99 (0.66) 3.35 (0.55) HSE-GLU 3.52 (0.57) 3.62 (0.80) 3.30 (0.63) 3.97 (0.43) 3.05 (0.55) HSP-GLU 3.85 (0.60) 4.11 (0.72) 3.60 (0.55) 3.94 (0.60) 3.46 (0.60) HSD-GLUP2 3.52 (0.64) 3.53 (0.87) 3.34 (0.52) 3.14 (0.52) HSE-GLUP2 3.87 (0.58) 4.06 (0.78) 3.92 (0.21) 3.59 (0.54) a Using structures and QM definition from the old protocol 20 . 178 ON-B CT ON-A OFF-A 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), TDDFT Experiment (eV) 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), SOS-CIS(D) Experiment (eV) ON-B CT ON-A OFF-A ON-B CT ON-A OFF-A 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 HSD-GLUP HSE-GLUP HSD-GLU HSE-GLU HSP-GLU HSD-GLUP2 HSE-GLUP2 Theory (eV), XMCQDPT2 Experiment (eV) Figure 5.23: Excitation energies for different model systems shown against the experi- mental values. Top: TD-DFT/aug-cc-pVDZ; middle: SOS-CIS(D)/aug-cc-pVDZ; bottom: XMCQDPT2/aug-cc-pVDZ/cc-pVDZ. Extended QM. 179 5.10 Appenidx F: Structures of possible intermediates Photoswitching in Dreiklang:Intermediates July 3, 2020 1 Introduction Chromophore Deprotonation via LE HSE(/D)145 Chromophore TYR203 CT Figure 1: On to o↵ photoconversion starting from neutral form (A) of the chromophore. Table 1: Gas phase excitation energy for all intermediates. System TDDFT SOS-CIS(D) Exp. E ex (eV) x1 3.27 (0.69) 3.99 (0.61) 2.76 x2 3.46 (0.62) 3.92 (0.61) – x3 3.39 (0.91) 3.07 (1.17) – x4 3.05 (0.95) 2.66 (1.46) – x5 3.00 (0.49) S 0 -S 11 0.84 – x6 2.99 (0.21) S 0 -S 4 1.08 – 3.47 (0.34) S 0 -S 6 0.85 – x7 3.47 (0.79) S 0 -S 1 0.00 – x8 3.18 (0.38) S 0 -S 15 0.82 – 3.34 (0.13) S 0 -S 17 0.83 – 1 . X1 . X2 _ X3 _ + X4 Figure 2: On to o↵ photoconversion starting from neutral form (A) of the chromophore. 2 . - X5 . - + X6 + X7 . - X8 Figure 3: On to o↵ photoconversion starting from neutral form (A) of the chromophore. 3 Figure 5.24: Two possible initial steps for Dreiklang photoconversion. Ref. 10 proposed that the photoconversion begins by ESPT (left), forming anionic chromophore, which undergoes further transformation. Following this route, one can consider structures X1- X4 as possible candidates for reaction intermediate X. We propose an alternative mech- anism via CT state (right). Following this route, one can consider structures X5-X8 as possible candidates for reaction intermediate X. We considered several structures of the intermediates. Fig. 5.24 shows 2 possible scenarios for initiating photoconversion. Ref. 10 proposed that the photoconversion begins by ESPT, form- ing anionic chromophore, which undergoes further transformation. Following this route, one can consider structures X1-X4 as possible candidates for reaction intermediate X. As explained in the main text, there are several major objections to this mechanism. We propose an alternative mechanism via CT state. Following this route, one can consider structures X5-X8 as possible candidates for reaction intermediate X. Intermediate X5 corresponds to the chromophore in the CT state (Chro : ). Intermediate X5 is the result of proton transfer to Chro : , forming neutral radical. X7 is the result of the 180 protonated chromophore after back-transfer of the electron. X8 is the result of the hydrated chromophore which still has the extra electron. 5.11 Appendix G: Optimization and AIMD simulations: Additional results 0 20 40 60 80 100 0.0 0.5 1.0 1.5 2.0 2.5 3.0 S 0 CT Optimization cycles Relative energies (eV) Figure 5.25: Energies of the Kohn-Sham reference state (S 0 ) and CT state along optimiza- tion path (on-A-HSE-GLUP structure). 181 44 45 46 47 48 49 50 51 52 53 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Relative energies (eV) Time (fs) S 0 CT 98 100 102 104 106 108 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Relative energies (eV) Time (fs) S 0 CT Figure 5.26: Ground and excited state during the first two steps of the reaction in CT state (on-A-HSE-GLUP structure). Left: 1st step — proton abstraction by chromophore’s N from protonated Glu222. Right: 2nd step — proton transfer from Tyr203 to deprotonated Glu222. 182 h υ 48.76 fs 102.61 fs 103.62 fs X7-HSE- GLUP2 X6-HSE- GLUP2 (2) X6-HSE- GLU (1) ET PT PT PT *, CT *, CT *, TS * ON-A- HSE-GLUP X5-HSE- GLUP Figure 5.27: Analysis of the AIMD trajectory on the CT state (on-A-HSE-GLUP struc- ture). 0.00 0.20 0.40 0.60 0.80 1.00 0 1 2 3 4 5 6 S 0 LE Relative energy (eV) Time (ps) Figure 5.28: Energies of the Kohn-Sham reference state (S 0 ) and the LE state (2nd TD- DFT state) along the AIMD trajectory on the LE potential energy surface. 183 2.6 2.8 3.0 3.2 3.4 3.6 3.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Relative energy (eV) Distances (W242:O-CRO:C1) 1.06 eV Q Figure 5.29: Relaxed energy profile on the ground state surface (starting from X7 inter- mediate) along hydration reaction coordinate defined as W242:O-CRO:C1 distance. Zero energy corresponds to the energy of the reference state of the structure att=248 fs, roughly corresponding to X7. ONIOM,!B97X-D/aug-cc-pVDZ/CHARMM27. Table 5.23: Average excitation energies (eV) of the two lowest states of protein-bound neutral chromophore in the ON-state computed using structures from 21 MD snapshots; oscillator strength is shown in parentheses. Large QM. System State TDDFT aug-cc-pVDZ QM/MM (MD) HSD-GLUP LE 3.49 (0.56) CT 4.01 (0.05) HSE-GLUP LE 3.58 (0.52) CT 3.96 (0.10) HSD-GLU LE CT HSE-GLU LE CT HSP-GLU LE 3.52 (0.49) CT 3.72 (0.02) Table 5.24: Average excitation energies (eV) of the two lowest states of protein-bound anionic chromophore in the ON-state computed using structures from 21 MD snapshots; oscillator strength is shown in parentheses. Large QM. System State TDDFT aug-cc-pVDZ QM/MM (MD) HSD-GLUP LE 2.99 (0.85) HSE-GLUP LE HSD-GLU LE HSE-GLU LE HSP-GLUP LE 2.98 (0.86) 184 Table 5.25: Average excitation energies (eV) of the two lowest states of protein-bound hydrated chromophore in the OFF-state computed using structures from 21 MD snap- shots; oscillator strength is shown in parentheses. Large QM. 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Sci. 117, 13937 (2020). @articlecase2004amber, title=AMBER, ver. 8, author=Case, DA and Darden, TA and Cheatham III, TE and Simmerling, CL and Wang, J and Duke, RE and Luo, R and Merz, KM and Wang, B and Pearlman, DA and others, journal=University of California at San Francisco, San Francisco, CA, year=2004 190 Chapter 6: BrUSLEE and his shadow: Two persistent excited-state populations within a GFP mutant 6.1 Introduction into account. This work is devoted to the BrUSLEE protein, which is a descendant of the popular EGFP [26], and differs from it in the three mutations T65G/Y145M/F165Y. From Royant, 2011: We initially used EGFP crystals as a test case to validate our fluorescence lifetime measurement system (Royant et al., 2007) because EGFP exhibits a single lifetime in solution. We could verify that EGFP also exhibits a single lifetime in the crystalline state, either at cryo- or room temperature (Fig. 1a). У Glu222 в EGFP две конформации [Royant, 2011; Arpino, 2012]. Обе группы, опубликовавшие структуры EGFP удивляются, что fluorescence decay при этом моноэкспоненциальный, делают предположения, почему (не заряжен, малые подвижки). Наши данные по EGFP, видимо, свидетельствуют о том, что decay дивергирует, но видно это становится только при 37 С. AIK: Low barriers giving rise to sub-nanosecond interconversion would explain this R e s u l t s Time-resolved fluorescence Chromophore emission Figure 6.1: Fluorescence quantum yield versus fluorescence lifetime for selected FPs. In 1994, the green fluorescent protein (avGFP) fromAequoreaVictoria jellyfish was used to implement a genetically encoded fluorescent label forinvivo imaging 1 . The unique structure of 191 the chromophore formed by the protein’s own amino acid residues, the possibility of targeted labeling inside a living cell, low toxicity, relative ease of use, and the ability of tuning its proper- ties by genetic engineering have made fluorescent proteins (FPs) an essential molecular tool for biological imaging 2–4 . Biomedical research often requires to monitor multiple macromolecules or subcellular structures, and to record signal of the fluorescent indicators. The efficiency is lim- ited mainly by the spectral properties of fluorophores. Thus, hundreds of the probes of different origins described to date (including dozens of FP variants) can provide a reliable simultane- ous detection in 3-5 spectral channels only 5 . Namely, bright and photostable fluorophores are widespread in green-yellow range but are relatively rare in the blue and far-red parts of the spectrum 2, 6–8 . The design of FPs with properties matching particular applications requires understanding of how the structure of the protein relates to its photophysical and photochemical properties. Despite intense research efforts aiming to unravel fundamental aspects of the FP photocycle 9 , many questions remain unanswered, including structural determinants of fluorescence lifetime and quantum yield and the limits of their tunability. In the most basic case of a single emissive state, the population of excited fluorophores (Chro ) decays via two competing first-order processes 10, 11 : Chro kr !Chro +h; (6.1) Chro knr !Chro; (6.2) wherek r is the radiative (intrinsic fluorescence) rate constant andk nr describes all quenching channels. The overall decay of the excited-state chromophore is also described by the first- order kinetics with k = k r + k nr and the corresponding apparent (measured) fluorescence lifetime = ln(2) k . If non-radiative channels are much slower than the radiative rate (k nr k r ), then the apparent excited-state lifetime corresponds to the intrinsic fluorescence lifetime 192 ( r = ln(2) kr ). It is expected that at cryogenic conditions, when various quenching channels are suppressed, the apparent lifetime represents the intrinsic fluorescence lifetime. In contrast, if the radiationless decay is fast (k nr > k r ), then the apparent lifetime reflects the kinetics of the radiationless decay and is shorter than r . If several distinct populations of fluorophores are present, the fluorescence kinetics becomes multi-exponential and the above simple relationships between rate constants and lifetimes are no longer true. Multi-exponential fluorescence decay (spectral heterogeneity) arises due to structural heterogeneity, such as different conformations or protonation states of fluorophores, or different local environments. The fluorescence quantum yield (FQY) is determined by the competition between radiative and radionionless decay: FQY = k r k r +k nr = r = 1 1 + r nr ; (6.3) where r denotes the intrinsic fluorescence lifetime and nr = ln(2) knr represents a timescale asso- ciated with non-radiative decay. Thus, large FQY can be attained by either suppressing non- radiative decay rates (i.e., increasing nr ) or increasing the radiative decay rate (i.e., decreasing r ). The intrinsic radiative lifetime is inversely proportional 39 to the oscillator strength of the transition (f l ) and to the square of corresponding transition energy (E). In atomic units 1 r = E 2 f l 2(c 0 ) 3 (6.4) where c 0 is the speed of light in the medium and is the dielectric constant. The extinction coefficient (EC) is proportional to the oscillator strength of the transition. The radiationless decay constant represents the sum of all non-radiative excited-state decay channels. It can vary widely among different fluorophores and is strongly affected by fluo- rophore’s environment. In contrast, the radiative decay constant is an intrinsic property of the 193 fluorophore and, therefore, is expected to be the same for chemically identical chomophores. Conversely, for FPs with the same type of chromophores, the variations in FQY can be attributed to the variations in non-radiative decay rates, so that the correlation between the apparent fluo- rescence lifetime and FQY is expected. This conjecture can only be tested by direct measurements ofk r for hundreds of FPs. How- ever, experiments are usually carried out at room temperature and, therefore, reflect the apparent fluorescence lifetimes. FPs with self-maturing chromophores exhibit a broad range of the appar- ent fluorescence lifetimes—some members having much longer (3.9-5.1 ns) and some having much shorter (0.76-1.6 ns) lifetimes than the average 6 . Fig. 6.1 shows FQYs against fluo- rescence lifetimes for a variety of FPs. Some FPs exhibit a good correlation between and FQY , combining either a long lifetime with a high quantum yield or a short lifetime with a low- to-moderate quantum yield. The first group comprises mCerulean3 (=4.1 ns/FQY=0.87) 13 , Aquamarine (=4.1 ns/FQY=0.89) 14 , mTurquoise2 (=4.0 ns/FQY=0.93) 15 , mScarlet (=3.9 ns/FQY=0.7) 16 , and WasCFP (=5.1 ns/FQY 0.85) 17 . The second group contains mCherry (=1.4 ns/FQY=0.22), TagRFP675 (=0.9 ns/FQY=0.08) 18 , mGarnet (=0.8 ns/FQY=0.09) 19 , mGarnet2 (=0.76 ns/FQY=0.087) 20 . There is a also third group—deviants for which the cor- respondence between and FQY is less pronounced. For example, in the orange KO and mKO proteins, the impressive 4.1-4.2 ns lifetimes go together with moderate FQYs 21, 22 . Green BrUSLEE, a new FP introduced here, also belongs to this group, featuring short lifetime (=0.8 ns) and a moderate FQY of 0.12-0.3. Because the radiative lifetime is inversely proportional to the oscillator strength (as per Eq. (6.4)), it is expected that large EC (i.e, large oscillator strength) would result in the decrease of the r nr term in Eq. (6.3), giving rise to an increased FQY . This is generally the case – brighter FPs often have larger FQY . However, there are interesting exceptions. For example, some of the proteins listed above (for example, cyan mCerulean, Aquamarine, and mTurquoise2), feature 194 relatively low EC and high FQY/long , and in the pair of orange KO/mKO, an increase in FQY is accompanied by a decrease in EC. These exceptions can be rationalized by assuming that in these FPs changes in r are compensated by changes in nr . Hence, the process of tuning up optical properties of FPs requires simultaneous optimization of oscillator strength (which defines brightness and fluorescence lifetime) and non-radiative decay rates. Because the former is largely the property of the chromophore and the latter largely depends on the interactions of the chromophore with its immediate environment, it should be possible to tune them independently. Figure 6.2: Structure of the chromophore in EGFP (left) and the 3 mutants studied in this Chapter (right). In EGFP, the chromophore is formed by the threonine-tyrosine-glycine (TYG) triad whereas in T65G mutants the chromophore is formed by the glycine-tyrosine- glycine (GYG) triad. The conjugated core of both chromophores is the same, but the TYG chromophore has additional electron-donating group. The twisting motion is described by dihedral angles (phenolate flip around the single bond) and (imidozalinone flip around the double bond); see Fig. 6.12. Photophysical properties of the fluorescent proteins are determined by an interplay between chromophore’s intrinsic electronic structure, its interactions with the surrounding residues, and several competing excited-state processes 9, 23 . Oscillator strength, which is the key determinant of EC, depends on the transition dipole moment, and is affected by the size of the conjugated -system. Electron donating groups attached to the chromophore can lead to an increasedf l . Chromophore twisting disrupts conjugation and reduces f l ; hence, deviations from planarity 195 are expected to lead to dimmer FPs. One interesting feature of the GFP-type chromophore (shown in Fig. 6.2) is that it is rigid in the ground state (torsional barriers along and of around 30 kcal/mol), but becomes rather floppy in the excited state (torsional barrier drops to 3 kcal/mol). Because of this flexibility, the bare chromophore is non-fluorescent—twisting motion leads to an effective radiationless decay. Only when constrained by the protein environ- ment (or another matrix), which prevent it from twisting, the chromophore becomes fluorescent. Hence, hydrogen-bond network around the protein-bound chromophore has a major effect on its excited-state dynamics and fluorescent properties. Because the rigidity of the chromophore in the ground state, the changes in hydrogen-bond network due to mutations do not necessarily lead to prominent structural changes (i.e., the chromophore remains planar in the course of ther- mal motions), but can have a profound effect on the excited-state dynamics and, consequently, the non-radiative decay rate. In this Chapter we introduce the BrUSLEE protein and investigate mechanistic details of its photophysical properties. BrUSLEE is a descendant of the popular EGFP 24 and differs from it by 3 mutations: T65G/Y145M/F165Y . These mutations were inspired by the previ- ous study 25 , which identified the involvement of the respective residues in photoinduced elec- tron transfer ultimately leading to photobleaching. BrUSLEE—BRight Ultimately Shorttime Enhanced Emitter—demonstrates an unusual combination of high fluorescence brightness and short lifetime, which prompted us to investigate structural determinants of its photophysical properties by time-resolved fluorescence measurements and atomistic simulations. We also considered the T65G and T65G/Y145M mutants. Below we often refer to the double mutant (T65G/Y145M) as Duo and to the triple mutant (T65G/Y145M/F165Y; BrUSLEE) as Trio. In addition to an unusual FQY/ combination, BrUSLEE also shows multi-exponential fluo- rescence decay, revealing 2 distinct subpopulations, co-existing in a wide temperature range 196 (4-300 K). The fluorescence lifetimes of these emissive states change considerably with tem- perature, converging to low temperature limits that are vastly different from each other and from that of the parental EGFP. As discussed below, crystal structure and 15N-NMR spectroscopy of BrUSLEE show no obvious structural heterogeneity. Atomistic simulations suggested that the heterogeneity arises due to co-existing populations of different protonation states of the chromophore-adjacent titratable residues. In particular, different protonation states of His148 alter the hydrogen-bonding network around the chromophore, affecting significantly effect on its twisting flexibility in the excited state. Simulations also explain trends in and FQY by the changes in the electronic properties of the chromophore and hydrogen-bond network around it due to mutations. In particular, the T65G mutation 26 increases conformational flexibility of the chromophore in the excited state, leading to faster nr ; at the same time it increases the oscillator strength of the transition, leading to shorter r . Consequently, despite the reduction in excited-state lifetime, relatively large FQY is observed. 6.2 Results and discussion 6.2.1 Structure analysis Fig. 6.3 shows superimposed x-ray structures of EGFP and BrUSLEE 45, 46 and Fig. 6.4 compares hydrogen-bond network around the chromophore. MD simulations (discussed in the Appendix A1 and below) yield average structural parameters that agree well with the crystal structures and provide additional insight into the thermal range of motion of the chromophore and the key residues; the simulations also provide structural data for the T65G and Duo mutants. In addition to comparison of the structures, we also studied FRET between the Tryptophan and the chromophore in all 4 systems. By comparing the results with the experimental FRET 197 Y/M145 H148 R96 W E222 T203 F/Y165 S205 Figure 6.3: Superimposed crystal structures of EGFP (green) and BrUSLEE (orange), with the chromophore’s center of mass set at the origin. E222 Cro F165 R96 H148 Y145 S205 T203 W E222 Cro-T65G R96 Y165 H148 M145 S205 S203 W Figure 6.4: Top: Hydrogen-bond network around the chromophore in EGFP and Bottom: BrUSLEE. 198 measurements we can further validate the simulations. FRET experiments and simulations are discussed in the Appendix C. The mutations affect both the chromophore is structure and its interactions with the nearby residues. As discussed in our previous work in Chapter 4, T65G mutation has significant effect on the structure and results in weakening of the hydrogen-bond network around the chromophore. In the mutants, there is no hydrogen bond between Glu222 and Thr65 (since it is substituted by Gly); instead a new bond between Glu222 and N-imidazoline is formed (see Fig. 6.4). Phe165Tyr mutation leads to the formation of the hydrogen-bond chain Tyr165:::Arg96:::O=C-imidazoline. Another important feature of BrUSLEE is that the spatial fixation of the chromophore’s tyrosine (Tyr66) is weakened. First, there is now no hydro- gen bond between Thr203 and Tyr66 due to changes in Thr203 side-chain conformation (it is twisted away from the chromophore). Second, hydrogen bonding between His148 and OH- Tyr66 is weaker than in the parental protein (bond length is 3.52 ˚ A vs 2.89 in EGFP). Third, Tyr145Met mutation leads to the increased range of motion of the chromophore (Tyr66 move- ments). Overall, in EGFP one can count up to 9 hydrogen bonds around the chromophore (Chro- HSD148, Chro-W, Chro-Thr203, CHro-GLUP(2), Chro-Arg96, W-Ser205, Ser205-Glup222, Chro-Tyr145), whereas in BrUSLEE only 6 hydrogen bonds can be formed. 6.2.2 Time-resolved fluorescence All four mutants exhibit maximum emission at approximately 510 nm (2.43 eV), which is characteristic for EGFP. In this region, fluorescence decay of EGFP is dominated by a charac- teristic lifetime of 2.8 ns (88.7 %) and a minor component2.0 ns (11.3 %). Mutations lead to the appearance of the fast (sub-nanosecond) component and a significant reduction of average fluorescence lifetime (Table 6.1). 199 Table 6.1: Lifetime distributions of EGFP and the mutants at 510 nm (2.43 eV). System 1 , ns A 1 , % 2 , ns A 2 , % 3 , ns A 3 , % hi, ns EGFP 2.0 11.3 2.8 88.7 2.71 T65G 0.82 88.5 2.0 11.5 0.96 T65G Y145M 0.52 91.0 1.5 9.0 0.61 T65G Y145M F165Y 0.51 83.3 1.4 16.4 2.3 0.3 0.66 Lifetimes represent fluorescence decay measured at 29 C. Average lifetime is computed as hi = P i A i i . 2 T65G 820 88.5 2.0 11.5 - - T65G/Y145 520 91.0 1.5 9.0 - - Trio 510 83.3 1.4 16.4 2.3 0.3 In the region from 5 to 27 °C fluorescence of eGFP was monoexponential, however at temperatures above 30 °C we observed gradual increase of another components yield (! " ) reaching approximately 60 % before the unfolding temperature (~ 80 °C). The fact that fast and slow components of eGFP decay converge at low temperatures indicate that the presence of these states is not determined by heterogeneity (or impurity) of the sample. We assume that these subpopulations represent chromophores with slightly different internal molecular degrees of freedom/conformation/environment or solvent accessibility which cause extremely high radiationless deactivation rates. Figure 2. Temperature dependencies of fluorescence lifetimes of eGFP and its mutants. Fluorescence decay was measured at 510 nm under 470 nm excitation by 50 ps FWHM laser pulses. Color represents the logarithm of amplitude of corresponding component. Temperature dependencies of fluorescence lifetimes of eGFP and its mutants (presented as Arrhenius plots) reveal principally linear parts for fast components, while transitions of slow components are characterized by more complex s-shaped dependency (except T65G/Y145M double mutant, in which slow component almost disappears at high temperatures (Figure 2). Such nonlinear behavior of temperature dependency of proteins characteristics is usually attributed to gradual changes of protein conformation. Main question, however is why these changes of protein structure do not affect fast components of the decay (or what isolates sub- population of rapidly decaying chromophores)? Several linear parts of temperature dependencies could be used for the estimation of activation energies (Ea) for internal conversion (see Table 2). Obtained value of Ea for the eGFP at low temperatures equal to 0.59 kcal/mol (~ 205 cm -1 ), for Figure 6.5: Temperature dependence of fluorescence lifetimes in EGFP and the mutants. Fluorescence decay was measured at 510 nm under 470 nm excitation by 50 ps FWHM laser pulses. Color represents the logarithm of the amplitude of the corresponding com- ponent (Data courtsey to Bogdanovetal. Temperature dependence of fluorescence lifetimes of EGFP and its mutants (presented as Arrhenius plots in Fig. 6.5) reveals principally linear parts for fast components, while tran- sitions of slow components are characterized by more complex s-shaped dependency, except 200 T65G/Y145M double mutant in which slow component almost disappears at high temperatures. Such nonlinear behavior is usually attributed to gradual changes of protein’s conformation. Several linear parts of temperature dependencies can be used to estimate effective activation energies (E a ) for internal conversion; the results are given in Table 6.2. We observe that the fastest component has the largest E a in all systems and that the respective value is similar among mutants and in the entire temperature range. Its value (4.4-8 kcal/mol) is close to the computed torsional barrier around the double bond of the isolated chromophore in the excited state (3.59 kcal/mol) 26 , suggesting that the fast component corresponds to the chromophore twisting. The excited-state dynamics simulations (discussed in Section 6.2.3) confirm that the timescale of the torsional motion is indeed similar to the timescales of the fast components. TheE a for the slow components are much smaller, suggesting that lower-frequency vibra- tional motions are responsible for radiationless relaxation of the chromophore locked in the planar configuration. For EGFP, E a extracted from low temperatures equals 0.59 kcal/mol (205 cm 1 ). At high temperatures energy barriers for the slow components increased up to 2.2-3.5 kcal/mol. A striking feature of the triple mutant (BrUSLEE) is the presence of a slow component of fluorescence decay, which has lifetime and activation energy close that of EGFP. Table 6.2: Activation energies (kcal/mol) for internal conversion of EGFP and its mutants. Range EGFP T65G T65G/Y145M BrUSLEE 2 3 1 2 1 2 1 2 3 Below 45 C 0.59 4.78 1.81 4.47 2.28 4.41 1.24 Above 45 C 3.76 2.93 4.78 3.21 4.47 2.28 4.41 3.22 1.79 Freezing initially causes reduction of lifetimes for all samples. Since at low temperatures lifetime of EGFP is lower than at room temperature (1) we can not use it as tau0 to calculate the quantum yield and (2) we have to postulate that this protein has (at least) two states with high fluorescent lifetimes. Almost no dependence of average lifetime of EGFP on temperature in 10 200 K region. Together with the absence of broadening of spectrum it suggests that 201 the chromophore is locked in a specific configuration which is not sensitive to temperature. Mutants also reach this state, but at significantly lower temperatures. Trio shows the highest average lifetimes at deep temperatures. 6.2.3 Computational results Analysis of ground state structure from MD simulations H148 F165 R96 TYG E222 S205 T203 Y145 W d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 Figure 6.6: Definition of the key distances in EGFP. d1 = CRO66:CE1-PHE165:CE2; d2= CRO66:CD1-PHE165:CZ; d3 = CRO66:OH-TYR145:OH; d4 = CRO66:OH- HSD148:ND1; d5 = CRO66:OH-W84:OH2; d6 = CRO66:O2-ARG96:NH2; d7 = CRO66:N2-GLUP222:OE2; d8 = CRO66:OH-THR203:OG; d9 = CRO66-CE2- SER205:OG; d10 = SER205:OG-W84:OH2; d11 = SER205:OG-GLUP222:OE2. Figures 3 and 4 compare EGFP and BrUSLEE (Trio) crystal structures. In this section, we analyze the results of equilibrium MD simulations for EGFP, BrUSLEE, and the two mutants; 202 for each we consider 3 different protonation states of His148. Fig. 6.6 shows the key distances used for structural analysis. Tables 6.6-6.9 and Figure 6.16 show the values of the key structural parameters extracted from the crystal structures and from the MD simulations (averaged along equilibrium trajectories at T=298 K). The main observations are: For EGFP, the best overall agreement with the crystal structure is observed for HSD148, whereas for BrUSLEE the best agreement is observed for HSE148. Focusing on the distance between His148 and Chro (d4) we note that for EGFP HSP148 shows better agreement with the crystal structure. We note that a study of a subatomic resolution X-ray structure of GFP in the neutral (T203I mutant) and anionic (S65T and E222Q mutants) forms 43 . For the neutral form, hydrogen atom densities show that the chromophore is in the neutral form, His148 is in HSD form, and Glu222 is in anionic form, which is consistent with our choices of protonation states in neutral GFP. For the anionic form, the maps confirm that Glu222 is in neutral form (in agreement with the proton wire picture), but His148 is positively charged (HSP)—this suggests that in the ground state there is an additional proton involved in protonation equilibrium. Comparing EGFP and BrUSLEE, BrUSLEE possess less planar chromophore compared to that in EGFP. Distance in Cro-HIS148 is larger in BrUSLEE compared to EGFP. This may be indicative of the fact that HSE is suitable protonation state for BrUSLEE where as HSD is suitable for EGFP. THR203 exists in different conformation in BrUSLEE com- pared to EGFP. Distance in SER205-GLUP222 is larger in BrUSLEE compared to EGFP. This is indicative of a weaker hydrogen bonding around the chromophore. Chromophore planarity and hydrogen-bond pattern The key structural parameters related to the photophysical properties are chromophore planarity and the number of hydrogen bonds around the chromophore. We also analyzed partial 203 stacking between the chromophore and residue 165 (Phe165 in EGFP) but found that it does not change significantly among the mutants and does not correlate with photophysical properties. Fig. 6.12 shows the key parameters characterizing the planarity of the chromophore. Deviation from the planarity can be characterized by the sum of the two torsion angles: = +. Fig. 4 in the main draft shows the hydrogen-bond network around the chromophore. Hydrogen bonds were characterized by the VMD hbond analyzer plugin, with the distance cutoff in polar atoms set to 3.5 ˚ A and the angle cutoff set to 30 . Table 6.3 Shows the chromophore’s planarity and the range of twisting motion is sensitive to mutations and depends on the protonation state of His148. The chromophore is most planar in Duo-HSD, EGFP-HSP, and EGFP-HSD (main form). BrUSLEE shows quite noticeable deviations from planarity for all 3 protonation states of His148. The average number of hydrogen bonds around the chromophore is smaller in the mutants than in EGFP. For each structure, the number of hydrogen bonds is smallest for HSE, because this form cannot form hydrogen bonds with the chromophore. Table 6.3: Chromophore planarity and the number of hydrogen bonds around the chro- mophore. (Averaged over 400 snapshots from MD at 298 K, standard deviation is in paren- thesis). Mutant HIS148 H-bond EGFP HSD 6.88 (5.08) 5.50 (0.98) HSE 8.96 (6.67) 4.16 (0.80) HSP 6.41 (4.67) 4.45 (1.00) T65G HSD 8.48 (6.10) 3.69 (0.95) HSE 8.87 (6.51) 3.76 (0.89) HSP 8.74 (5.97) 4.49 (0.96) Duo HSD 6.21 (4.58) 4.31 (0.87) HSE 7.20 (5.32) 3.44 (0.90) HSP 7.89 (5.56) 4.54 (1.06) BrUSLEE HSD 10.06 (6.87) 4.19 (0.83) HSE 8.33 (5.41) 3.54 (0.63) HSP 7.98 (5.75) 4.35 (0.78) 204 Ground-state structure analysis and populations of different protonation states We considered 3 different protonation states of His148: HSD (protonated at N ), HSE (pro- tonated at N ), and HSP (protonated at both nitrogens), see Fig. 6.10 in the Appendix A1. The computed Gibbs free energy differences are summarized in Table 6.12 and the respective popu- lations are shown graphically in Fig. 6.7. At 298 K, the calculated Gibbs free energies suggest that in EGFP and T65G, the main protonation state are HSD (87% and 86%, respectively), with HSP (13% and 14%) being also present. In contrast, in Duo and Trio, the main protonation state is HSE (97 and 70%). In BrUSLEE, the two other states are also present (HSD 29% and HSP 2%). These computed populations correlate well with the populations extracted from fluorescence decay. The calculations at T=100 K show that the distinct populations can be present at low ener- gies. This is because Gibbs free energies include entropic factor and are also temperature- dependent. In EGFP, the population of HSD drops to 68 %. In BrUSLEE, the population of the main form (HSE) increases to 91 %, with the rest being HSD (the population of HSP drops below 1%). The most important thing to note is that distinct population can coexist in a wide temperature range. Excited-state dynamics The results of MD simulations on the excited states are shown in Fig. 6.8.Fig. 6.9 shows the population decay of planar population due to excited-state twisting. For each protonation state, we observe nearly perfect linear fit of the twisting kinetics, which means that in our simulations there are no inter-converting conformers that could give rise to multi-exponential fluorescence decay. The respective lifetimes (shown in each panel of Fig. 6.9) are obtained by linear fit. As documented in our previous study 26 (see also Chapter 4), the twisting rate is different in mutants because T65G mutation weakens the hydrogen-bond network around the chromophore. 205 HSD HSE HSP 87.1 % population in different protonation state 5.20 26.8 12.9 0.00 67.8 EGFP-HSD, 298K EGFP-HSD, 100K EGFP-HSE, 298K EGFP-HSE, 100K EGFP-HSP , 298K EGFP-HSP , 100K HSD HSE HSP 85.7 % population in different protonation state 5.91 33.9 14.3 0.00 60.2 T65G-HSD, 298K T65G-HSD, 100K T65G-HSE, 298K T65G-HSE, 100K T65G-HSP , 298K T65G-HSP , 100K HSD HSE HSP 0.0 % population in different protonation state 99.0 1.0 2.60 97.4 0.0 Duo-HSD, 298K Duo-HSD, 100K Duo-HSE, 298K Duo-HSE, 100K Duo-HSP , 298K Duo-HSP , 100K HSD HSE HSP 28.5 % population in different protonation state 91.0 0.1 1.80 69.7 8.90 Trio-HSD, 298K Trio-HSD, 100K Trio-HSE, 298K Trio-HSE, 100K Trio-HSP , 298K Trio-HSP , 100K Figure 6.7: Relative populations (at 298 K and 100 K) of different protonation states of His148 in EGFP (top left), T65G (top right), Duo (bottom left), and BrUSLEE (Trio) (bot- tom right). Protonation states of His148 also affects the twisting rate—in particular, HSE exhibits the fastest twisting, which can be explained by the inability of this state to form a hydrogen bond with the chromophore. These markedly different lifetimes suggest that the observed multi-exponential fluorescence decay might be due to the co-existence of multiple protonation states of His148. Table 6.4 shows computed populations and average excited-state lifetimes and estimated FQY . The radiationless times extracted from twisting kinetics agree rather well with experi- mental results. 206 The extracted radiationless lifetimes are given in the main text. The percentage of the planar chromophore (< 50 ) after 3 ns is indicated on the figure. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 EGFP-HSD EGFP-HSE EGFP-HSP % population of planar conformation (A) Simulation time (ns) 76.25% 47.50% 32.50% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 T65G-HSD T65G-HSE T65G-HSP % population of planar conformation (A) Simulation time (ns) 41.50% 14.00% 3.00% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 Duo-HSD Duo-HSE Duo-HSP % population of planar conformation (A) Simulation time (ns) 32.75% 22.75% 0.00% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 Trio-HSD Trio-HSE Trio-HSP % population of planar conformation (A) Simulation time (ns) 34.75% 29.75% 12.00% Figure 6.8: Evolution of planar population in excited-state molecular dynamics simula- tions of EGFP, T65G, Duo, and BrUSLEE (Trio). The numbers indicate the surviving population of the planar chromophore after 3 ns of dynamics. 6.3 Conclusions Photophysical properties of EGFP, T65G, Duo, BRUSLEE are determined by an interplay between chromophores intrinsic electronic structure, its interactions with the surrounding residues, and several competing excited-state processes. We begin connecting the macroscopic observables (extinction coefficients, brightness, and photostability) with the microscopic 207 τ = 8.60 ns τ = 2.96 ns τ = 1.87 ns 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 EGFP-HSD; R 2 =0.99 EGFP-HSE; R 2 =1.00 EGFP-HSP; R 2 =0.97 Linear fit of planar conformation Simulation time (ns) τ = 2.66 ns τ = 0.98 ns τ = 0.69 ns 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 T65G-HSD, R 2 =0.99 T65G-HSE, R 2 =0.97 T65G-HSP, R 2 =0.98 Linear fit of planar conformation Simulation time (ns) τ = 1.78 ns τ = 1.41 ns τ = 0.47 ns 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -5 -4 -3 -2 -1 0 Duo-HSD, R 2 =0.99 Duo-HSE, R 2 =0.97 Duo-HSP, R 2 =0.99 Linear fit of planar conformation Simulation time (ns) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Trio-HSD, R 2 =0.99 Trio-HSE, R 2 =0.98 Trio-HSP, R 2 =0.98 Linear fit of planar conformation Simulation time (ns) τ = 1.87 ns τ = 1.69 ns τ = 0.97 ns Figure 6.9: Excited-state dynamics: Decay of planar population in EGFP, T65G, Duo, and BrUSLEE. Lifetimes are obtained as linear fit for ln[A]. Table 6.4: Computed values of average lifetime (in ns), percentage population of each pro- tonation states, and fluorescent quantum yield. Experimental values are given in paren- thesis. Mutant HIS148 , population, hi FQY hFQYi, theory (exp) theory (exp) theory (exp) EGFP HSD 3.93 (2.8) 0.871 (0.887) 3.69 (2.71) 0.54 0.51 (0.60) HSE 1.48 — 0.21 HSP 2.10 (2.0) 0.129 (0.113) 0.29 T65G HSD 0.85 (0.82) 0.857 (0.885) 1.00 (0.95) 0.13 0.15 (0.10) HSE 0.63 — 0.09 HSP 1.90 (2.0) 0.143 (0.115) 0.28 Duo HSD 1.16 — 0.46 (0.61) 0.17 0.07 (0.08) HSE 0.44 (0.52) 0.974 (0.91) 0.07 HSP 1.40 (1.5) 0.026 (0.09) 0.21 Trio HSD 1.34 (1.4) 0.285 (0.164) 1.00 (0.65) 0.20 0.15 (0.3) HSE 0.85 (0.51) 0.697 (0.833) 0.13 HSP 1.46 (2.3) 0.018 (0.003) 0.22 208 properties of the chromophores. The most interesting features of EGFP and BRUSLEE are the existence of multiple decay channels, which are temperature dependent. As one can see from population analysis, different population of HIS148 twists in excited-state at different time (varying in the range of 1-8 ns). This explains the reason behind multiple subpopulations in mutants. Structural analysis, especially hydrogen-bonding analysis, indicates more hydrogen bonds prevent the twisting in excited-state. For example, HSD form possesses the maximum number of hydrogen bonds in mutants whereas HSE possesses the lowest number of hydrogen bonds, resulting in a faster twist of that form. Competition of enthalpy and entropy at different temperature explains free energy change upon change in protonation state and temperature dependence of that process in equilibrium. On the other hand, intrinsic lifetime is a function of excitation energy and oscillator strength. To conclude, with the help of series of electronic structure calculations and MD simulations (both in ground and excited-state) we have rationalized the properties of the newly developed variant of EGFP, BRUSLEE, which will lead us designing new FPs with desirable properties. 6.4 Appendix A: Computational details 6.4.1 Appendix A1: Model structures and ground-state dynamics We begin with the crystal structures of EGFP and BrUSLEE (Trio). EGFP structure was taken from protein data bank (PDB) id: 2Y0G 27 . The mutants are built from the 2Y0G crystal structure by single (T65G) and double (T65G-Y145M, Duo) mutations using the VMD Mutator plugin. Hydrogen atoms were added using the VMD plugin and a modified (to include the chromophore) CHARMM27 topology file. Protonation states of titratable residues were initially assigned by Propka 28 and then manually set for the chromophore and His148. 209 In EGFP, the chromophore is deprotonated. The two most important residues near the chromophore are His148 and Glu222. Glu222 can be GLU (anionic) or GLUP (protonated); Propka 28 suggested GLUP state (pKa 9.2) for the Glu222, which was validated by geometry optimizations and MD simulations in our previous work 26, 29 . Hence, in this study we consider Glu222 to be protonated in all structures. For His148, we considered 3 different protonation states (shown in Fig. 6.10) for each system: HSD (protonated at N ), HSE (protonated at N ), and HSP (protonated on both N, positively charged). δ ϵ ϵ ϵ δ δ + Figure 6.10: Different protonation states of histidine: HSD (left), HSP (middle), and HSE (right). Charged amino acids on the surface were locally neutralized by adding counterions close (4.5 ˚ A) to them. Charged residues that do not form salt bridges inside the protein barrel were also neutralized by adding appropriate counter-ions at the surface. This protocol resulted in the addition of 21 Na + and 14 Cl for the HSD and HSE structures, and and 20 Na + and 14 Cl for the HSP structures. The proteins were solvated in water boxes producing a solvation layer of 15 ˚ A. The TIP3P water model was used to describe water. Ground-state MD simulations were performed using these solvated neutralized model struc- tures as follows: 1. Minimization using steepest descent algorithm for 2,000 steps (protein, crystal water, counterions). 2. Minimization using steepest descent algorithm for 2,000 steps of the fully solvated struc- ture (keeping protein frozen), with the subsequent equilibration of the solvent (keeping 210 the protein frozen) for 500 ps with 1 fs time step using the NPT (isobaric-isothermal) ensemble. 3. Full equilibration of the system for 2 ns (with 1 fs time step) with periodic boundary con- dition (PBC) using the NPT ensemble (Noose-Hoover barostat with Langevin dynamics). 4. Production run for 2 ns with 1 fs time step using the NPT ensemble. Pressure and tem- perature were kept at 1 atm and 298 K. These simulations provided snapshots (taken from the production run, step 4) represent- ing ground-state equilibrium dynamics and were used to analyze ground-state structures and hydrogen-bond pattern around the chromophore. They also served as a starting point for calcu- lating free energies of different protonation states of His148 (See Appendix D), for computing excitation energies by the QM/MM protocol (Appendix A2), and as starting structures to per- form MD simulations on the excited-state surfaces (Appendix A3). MD simulations were performed with NAMD 30 . 6.4.2 Appendix A2: QM/MM setup for excited-state calculations We computed electronic properties (vertical excitation energies, oscillator strengths) using snapshots from equilibrium trajectories (production runs in the MD simulations) using the fol- lowing QM/MM scheme. The chromophore and selected residues were included in the QM region and the rest of the system was treated as fixed MM point charges via electrostatic embed- ding. Figure 6.11 shows the definition of the QM subsystem. Hydrogen atoms were added at the QM/MM boundary to saturate the valencies. Point charges on the atoms adjacent to the QM/MM boundary (such as red and green atoms in Fig. 2 in the main text) were set to zero and the excess charge was redistributed over the rest of the atoms of the respective residues to avoid over-polarization of the QM atoms at QM/MM boundary. 211 H148 F165 R96 TYG E222 S205 T203 Y145 W Y165 R96 GYG E222 S205 M145 H148 W T203 Figure 6.11: Top: Residues involved in QM/MM calculations of EGFP, Bottom: BrUSLEE. Chromophore, water, residues 145, 148, 165, 96, 203, 205, 222 were included in the QM region in calculations of spectra and electronic properties. Electronic structure calculations were performed at the !B97X-D/aug-cc-pVDZ 31, 32 level of theory. All quantum chemistry and QM/MM calculations were carried out using the Q-Chem electronic structure package 33, 34 . 212 φ τ - Figure 6.12: Definition of the two torsional angles and describing chromophore twist- ing. describes twist around the single bond (phenolate flip) and describes twist around the double bond (imidozalinone flip). 6.4.3 Appendix A3: Molecular dynamics simulations on the excited-state surfaces Following the same procedure as in our earlier work 26 , we modified forcefield parameters of the chromophore to account for the changes in the bonding pattern upon photoexcitation. Specifically, we changed the parameters for methyne bond-lengths, angles, and torsional potential, as well as selected partial charges. The values of these parameters were computed in the ground and excited states using DFT (!B97X-D/aug-cc-pVDZ). We then computed the difference (for charges, bond-lengths, and angles) or ratio (for force constants) in the ground and excited states and used these values to either shift or scale the respective parameters from the CHARMM27 forcefield. The resulting forcefield parameters are given in Ref. 26. Below we explain the key differences. The most important parameters are the two torsional angles and (see Fig. 6.12). The PES scans (Fig. 6.13) show that the minimum in the ground state corresponds to the planar chromophore, whereas in the excited state the planar structure is separated by relatively low barriers from the two minima corresponding to the strongly twisted chromophore. We fitted the excited-state potential to reproduce the location of the new minima (Fig. 6.13). From this fit, 213 we extracted the force contact. The resulting torsional potential for excited-state calculations has the following form: E =k[1 +cos(n)]; (6.5) wheren is periodicity, is phase, being the optimized torsional angle. The parameters are given in Table 6.5 and the resulting torsional potential (computed with the modified forcefield is shown in Fig. 6.14. As one can see, our fit reproduces the barriers for twisting reasonably well, but does not reproduce the depth of the well of the twisted structures (the fitted potential is too shallow). Hence, to prevent the trajectories from re-crossing, in the excited-state MD simulations we simply stop the trajectories once they twist by more than a specified threshold value (50 ). Figure 6.13: Ground- and excited-state torsional potentials for (twisting of the phenolic ring) and (twisting of the imidazolinone ring) of the bare HBDI chromophore. Black dots are ab initio calculations whereas red and black lines mark ab initio force-field. The barrier heights for twisting along and in the excited state are 3.5 kcal/mol and 3.2 kcal/mol, respectively. The respective ground-state barriers are 32.1 and 34.9 kcal/mol. Reproduced from Ref. 26. Table 6.5: Parameterized force constant and periodicity (n) for torsional potentials for angles and. Dihedral k gs;charmm n (gs) n (ex) k gs;qm k ex;qm k ex;charmm 2.7 2 4 15.05 3.79 0.68 3.9 2 4 14.99 4.90 1.27 214 -877.510 -877.505 -877.500 -877.495 -877.490 -877.485 -225 -180 -135 -90 -45 0 45 90 135 180 225 Energy (hartree) dihedral angle f fitting potential Torsional angle φ Electronic energy (a.u.) -200 -150 -100 -50 0 50 100 150 200 -877.51 -877.50 -877.49 -877.48 -877.47 -877.46 Energy (hartree) dihedral angle t Torsional angle τ Electronic energy (a.u.) Figure 6.14: Excited-state torsional potentials for (left) and (right) of the bare HBDI chromophore. Red curves: fit to ab initio calculations (from which the parameters were extracted). Pink and black curves: torsional potentials computed with the modified force- field. 6.4.4 Appendix A4: Ab initio molecular dynamics (AIMD) As an additional validation of our force-field parameters, we carried outabinitio molecular dynamics (AIMD) simulations on the excited-state surfaces. These calculations were performed using the ONIOM embedding with large QM (shown in Fig. 6.11), !B97X-D/cc-pVDZ, and CHARMM27 force-field. 11 trajectories intimated from random snapshots and with initial velocities corresponding to 298 K thermal distribution were propagated for 3 ns with 1 fs time step (3,0000,000 steps) with constant energy (NVE) ensemble. All atoms were allowed to move, except for the link atoms, which were pinned to their positions from the MM-relaxed structures. 6.4.5 Appendix A5: Calculation of free-energy difference between differ- ent protonation states of His148 To compute free-energy differences, we employ the thermodynamic cycle shown in Fig. 6.15. This approach 36, 37 , called quantum mechanical thermodynamic cycle perturbation (QTCP), allows one to compute high-level QM/MM free energy changes between two states A and B based on classical (MM) sampling and a relatively modest amount of QM/MM cal- culations. In this approach, the free energy change between A and B described by QM/MM 215 A, QM/MM B, QM/MM A, MM B, MM ΔA qm/mm (A B) - ΔA mm qm/mm (A) ΔA mm qm/mm (B) ΔA mm (A B) Figure 6.15: The quantum mechanical thermodynamic cycle perturbation (QTCP) method employing a thermodynamic cycle to calculate QM/MM free-energy changes 36 . is calculated as the sum of three terms: (1) free energy change between A described by MM and by QM/MM (-A mm!qm=mm (A)), (2) the free energy change between A and B, with both described by the MM potential (A mm (A!B)), and (3) the free energy change between B described by the MM potential and by QM/MM ( A mm!qm=mm (B)). Hence A qm=mm (A!B) =A mm!qm=mm (A) + A mm (A!B) + A mm!qm=mm (B); (6.6) A mm (A!B) =k B T lnhe [E tot mm (B)E tot mm (A)]=k B T i mm;A ; (6.7) A mm!qm=mm =k B T lnhe [E tot qm=mm (X)E tot mm (X)]=k B T i mm;X ; (6.8) where k b = 0.0257 eVK 1 . To adapt this scheme to different protonation states, we follow the strategy by Warshel 38 . For HSP!HSD energy difference, this scheme means: A qm=mm (HSP!HSD) =k B T lnhe [E tot qm=mm (HSP)E tot mm (HSP)]=k B T i mm;HSP k B T lnhe [E tot mm (HSD)E tot mm (HSP)]=k B T i mm;HSP k B T lnhe [E tot qm=mm (HSD)E tot mm (HSD)]=k B T i mm;HSD : (6.9) 216 Once free energies are computed, one can evaluate the populations of different forms by using Maxwell-Boltzmann equation: P A P B =e A qm=mm (A!B) k b T : (6.10) We considered three protonation states of the HIS148 (HSD, HSE, HSP, see Fig. 6.10) to compute HSP!HSD and HSP!HSE free-energy differences. Free energy difference for HSD!HSE is the computed as the difference between the HSP!HSD and HSP!HSE free- energy differences. The three terms involved were computed as follows: 1. We carried out QM/MM electronic energy calculation on 400 ground-state snapshots from MD using the mechanical embedding scheme (ONIOM) and !B97X-D/aug-cc-pVDZ. We compute QM/MM (with His148 in QM and the rest of the protein in MM) and pure MM energies (all atoms are in MM) for all protonation states. These energies are used to evaluate A mm!qm=mm terms: Eqns. (6.6) and (6.8). 2. We then consider snapshots for the HSP state for each mutant. We remove protons from either or nitrogen (giving rise to the HSD and HSE forms, respectively) and place an extra proton at a fixed position in bulk (making sure there are no bad contacts to water). We then compute MM energies for these two structures (original snapshot and the mod- ified one) and use them them to evaluate A mm (HSP!HSD/HSE). These calculations are done for 400 snapshots. The calculations at room temperature (298 K) were carried out using the respective equilib- rium MD simulations. Free-energy calculation at low temperature (100 K) were carried out as follows. For each model system (mutant/protonation state), we took 20 snapshots from room- temperature simulations and re-equilibrated them for 1 ns (with reinitialized velocity). The MD 217 simulations were performed as described above. From each trajectory, we took 20 snapshots for the QM/MM free-energy calculation (total 20x20 = 400). 6.4.6 Appendix A6: Calculation of radiative lifetimes and extinction coef- ficients Radiative lifetime is given by 39 : 1 r = ! 2 0 f abs 2(c 0 ) 3 ; (6.11) wherec 0 is the speed of light in the medium (c 0 =c=n;c is the speed of light in vacuum andn is the index of refraction) and is the dielectric constant. For vacuum,=1 andc=137. The index of refraction of water is 1.33; the refractivity of protein solutions is generally larger, around 1.6 Dielectric constant in proteins is small (i.e., 28) 40, 41 . We compute macroscopic extinction coefficient using the following expression 42 : (~ !) = X i N a e 2 4m e c 2 0 ln 10 p f i exp " ~ ! ~ ! i 2 # ; (6.12) where (~ !) is the molar extinction coefficient measured in Lmol 1 cm 1 ; ~ ! is the excitation wavenumber,N a is the Avogadro number,e is the electron charge,m e is the electron mass,c is the speed of light in cm s 1 , 0 is the vacuum permittivity in F cm 1 ,f i is the oscillator strength of the statei, and is the broadening factor in cm 1 . We used wavenumbers, since the units are L mol 1 cm 1 and so is in cm 1 . The coefficient is: N a e 2 4m e c 2 0 ln 10 p = 1:277 10 8 L mol 1 cm 2 : (6.13) 218 The choice of is the biggest uncertainty in the calculations, as we cannot compute it from first principles. In calculation we use = 0.3 eV . 6.5 Appendix B: Analysis of structures from equilibrium MD simulations Table 6.6: EGFP. Comparison of the key distances in the crystal structure and in MD simulations (T=298 K) considering 3 different protonation states for His148. distance 2Y0G 6JGI EGFP-HSD EGFP-HSE EGFP-HSP d1 4.01 4.07 4.02 (0.29) 3.93 (0.34) 4.33 (0.32) d2 3.94 4.11 4.12 (0.32) 3.88 (0.31) 4.25 (0.31) d3 4.43 4.39 3.89 (0.56) 5.32 (0.22) 3.21 (0.42) d4 2.85 2.87 3.28 (0.39) 3.80 (0.26) 2.75 (0.12) d5 2.62 2.74 3.21 (0.48) 2.74 (0.14) 3.78 (0.41) d6 2.73 2.75 2.68 (0.08) 2.70 (0.09) 2.72 (0.10) d7 2.59 2.67 2.85 (0.17) 2.85 (0.15) 2.88 (0.21) d8 2.66 2.67 2.84 (0.19) 2.70 (0.12) 3.08 (0.39) d9 3.94 4.18 4.54 (0.43) 4.32 (0.40) 4.97 (0.37) d10 2.69 2.76 2.92 (0.19) 4.67 (0.44) 2.84 (0.16) d11 3.88 3.81 4.01 (0.42) 3.87 (0.39) 4.34 (0.52) 6JGI is the crystal structure of the S65T variant of EGFP at 0.85 ˚ A(from Ref. 43). Table 6.7: T65G. Comparison of the key distances in the crystal structure and in MD simulations (T=298 K) considering 3 different protonation states for His148. distance 2Y0G T65G-HSD T65G-HSE T65G-HSP d1 4.01 4.23 (0.39) 4.09 (0.40) 4.36 (0.42) d2 3.94 4.33 (0.36) 4.01 (0.39) 4.43 (0.42) d3 4.43 3.80 (0.53) 5.34 (0.42) 3.32 (0.47) d4 2.85 3.53 (0.45) 3.83 (0.28) 2.73 (0.13) d5 2.62 3.23 (0.56) 2.83 (0.21) 3.39 (0.44) d6 2.73 2.68 (0.09) 2.73 (0.09) 2.71 (0.09) d7 2.59 4.61 (0.89) 3.45 (0.49) 3.54 (0.71) d8 2.66 2.93 (0.33) 2.94 (0.51) 3.13 (0.33) d9 3.94 4.29 (0.51) 4.13 (0.50) 4.12 (0.48) d10 2.69 2.89 (0.24) 4.49 (0.60) 2.88 (0.21) d11 3.88 4.21 (0.60) 4.49 (0.49) 4.35 (0.45) 219 d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 0 1 2 3 4 5 6 Distance Å 2Y0G EGFP-HSD EGFP-HSE EGFP-HSP d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 0 1 2 3 4 5 6 2Y0G T65G-HSD T65G-HSE T65G-HSP Distance Å d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 0 1 2 3 4 5 6 2Y0G Duo-HSD Duo-HSE Duo-HSP Distance Å d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 0 1 2 3 4 5 6 Trio- Crystal Trio-HSD Trio-HSE Trio-HSP Distance Å Figure 6.16: Key distances in EGFP (top left), T65G (top right), Duo (bottom left), and BrUSLEE (Trio, bottom right). 3.30 Å 2.59 Å 3.59 Å 2ns equilibration Rotamer A Rotamer B Rotamer A 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Cro-Glup distance A time (ns) Rotamer-A of GLUP Rotamer-B of GLUP Figure 6.17: Left: Two rotamers of Glu222and the definition of the key distance affected y the rotamers. Right: Equilibrium MD trajectories starting from the two rotameric forms in GLUP222 (T=298 K). The structure of the second rotamer is unstable: it flips after 0.25 ns into the main form and never comes back. 220 Table 6.8: Duo. Comparison of the key distances in the crystal structure and in MD simulations (T=298 K) considering 3 different protonation states for His148. distance 2Y0G Duo-HSD Duo-HSE Duo-HSP d1 4.01 4.27 (0.34) 4.20 (0.46) 4.27 (0.37) d2 3.94 4.32 (0.39) 4.37 (0.42) 4.21 (0.38) d3 – – – – d4 2.85 3.29 (0.37) 3.92 (0.31) 2.75 (0.11) d5 2.62 2.81 (0.22) 2.89 (0.31) 2.98 (0.36) d6 2.73 2.69 (0.09) 2.71 (0.09) 2.71 (0.09) d7 2.59 4.34 (0.98) 4.53 (0.82) 3.63 (0.84) d8 2.66 2.76 (0.14) 2.76 (0.14) 2.82 (0.19) d9 3.94 4.24 (0.30) 4.05 (0.43) 4.14 (0.40) d10 2.69 2.80 (0.12) 4.58 (0.78) 2.83 (0.15) d11 3.88 4.26 (0.55) 4.66 (0.60) 4.48 (0.46) Table 6.9: BrUSLEE (Trio). Comparison of the key distances in the crystal structure and in MD simulations (T=298 K) considering 3 different protonation states for His148. distance Trio-crystal Trio-HSD Trio-HSE Trio-HSP d1 3.85 4.27 (0.43) 4.64 (0.41) 5.04 (0.46) d2 4.01 4.46 (0.43) 4.85 (0.43) 5.24 (0.46) d3 – – – – d4 3.52 2.93 (0.22) 4.65 (0.56) 2.73 (0.11) d5 2.70 2.71 (0.11) 2.74 (0.13) 2.76 (0.14) d6 2.64 2.69 (0.09) 2.68 (0.08) 2.67 (0.08) d7 2.80 3.01 (0.17) 2.96 (0.15) 2.97 (0.15) d8 5.14 3.80 (0.28) 5.02 (0.42) 5.09 (0.33) d9 3.60 4.90 (0.41) 3.58 (0.24) 3.66 (0.24) d10 2.87 2.90 (0.23) 2.96 (0.26) 2.89 (0.22) d11 4.59 4.16 (0.40) 4.07 (0.39) 4.10 (0.35) 221 6.6 Appendix C: F¨ orster energy transfer between trypto- phane and chromophore Here we describe experiments and simulations of the quenching of the fluorescence of tryp- tophane (Trp57) at different temperatures, which help to further validate the structures and ground-state equilibrium motions of the protein. The experiment measures fluorescence lifetime at 360 nm (3.44 eV), which can be inter- preted as fluorescence lifetime of Trp. From these raw data efficiency of FRET (E, %) is calculated as: E = (1 da fast d slow ) 100%; (6.14) where da fast and d slow are fast and slow components of fluorescence decay at 360 nm. The assumption is that the fast component of fluorescence decay of Trp is due to FRET to the chro- mophore, whereas slow component is intrinsic Trp excited-state lifetime. The results are shown in Fig. ??. The actual definition of E is given by the rations of the lifetime (or fluorescence intensity,F ) of the donor in the presence and absence of the acceptor: E = 1 0 D D = 1 F 0 D F D : (6.15) The efficiency of FRET energy transfer is given by: E = 1 1 + (r=R 0 ) 6 ; (6.16) wherer is the distance betweenD andA andR 0 is F¨ orster distance: R 6 0 = 2:07 10 4 128 5 N A 2 Q D J n 4 ; (6.17) 222 Fig. 1. Temperature dependency of Trp lifetimes in FPs. Fig 2. Efficiency of excitation energy transfer, calculated as ! =1− % &'() *' % (+,- * . Fig. 3. Overlap of Trp emission and GFP absorption. Gray area indicates spectral range in which calculations of R0 were performed. Figure 6.18: Temperature dependence of Trp lifetimes in selected mutants. whereQ D is the FQY of the donor in the absence of the acceptor, 2 is the dipole orientation factor,n is refractive index of the medium (1.33 used here),N A is the Avogadro number, andJ is the spectral overlap of the absorption of the acceptor and emission of the donor: J = Z f D () A () 4 d: (6.18) Here f D () is donor’s emission spectrum normalized to a unit area and A () is molar extinction coefficient of the acceptor. These equations are used in the software PhotochemCAD, which was used to analyze the experimental data. The calculation also requires extinction coefficients; .Q D is taken as 0.12. is: = A D 3( D R)( A R); (6.19) where A and D are normalized transition dipole vectors of the acceptor and the donor, andR is the normalized radius vector betweenD andA. For randomly orientedD andA (which is 223 certainly not the case in FPs!), = 2=3. Zero corresponds to the perpendicular orientation, 2 = 1 corresponds to parallel orientation, and 2 = 4 to collinear. While can be extracted from the experimental data (as described above), it can also be computed from the equilibrium MD trajectories of mutants using Eq. (6.19); this is described in section 6.6.1 below. Table 6.10 summarizes the analysis of the experimental FRET measurements. Measured were E, thenR 0 were extracted (usingr=13.5 ˚ A), then was computed fromR 0 andJ. The experimental data were averaged over lower-temperature measurements, 20-40 . In the analysis of experimental data, Eugene used r=13.5 ˚ A (as in EGFP x-ray structure). We note that the choice of r depends of how one defines the distance (between closest atoms? Or center-of- mass?) and choosing different values affects the values of (and vise verse). Specifically, Eqns. (6.16) and (6.17) mean that if one multipliesr by a factor ofx, than the values of need to be multiplied byx 3 for the (r=R 0 ) 6 remain the same (or, if 2 is multiplied byy, thenr needs to be multiplied byy 1=6 ). Table 6.10: Summary of the FRET experiments. System E% 20 C R 0 , ˚ A E , M 1 cm 1 J, cm 6 2 EGFP 87.80 18.7586 55,000 1.860310 14 0.07021 T65G 90.59 19.4460 70,000 2.026110 14 0.0860 T65G Y145M 92.80 19.6322 84,500 2.452010 14 0.1021 T65G Y145M F165Y 92.63 21.3096 86,000 2.807110 14 0.0816 n = 1:33,r=13.5,Q D =12%. 6.6.1 Appendix C1: Calculations of the dipole orientation factor from equilibrium MD simulations The MD simulations were carried out for HSD protonation state. The computed average dis- tance between the donor and acceptor (defined as the CRO66:N2-TRP57:CD2 distance) agrees 224 well with the crystal structure (CRO66:N2-TRP57:CD2 distance is 13.5 ˚ A in 2Y0G). To com- pute using Eq. (6.19), we carried out TDDFT calculations for 21 QM/MM snapshots. For each snapshot, we performed 2 calculations: one with the chromophore in QM and one with Trp57 in the QM. We used Eq. (6.19) to compute. We used two different approaches. In one calculation, we first computed average transition dipole moments for the chromophore and for Trp57 and then computed using average values. In the second calculation, we computed for each snapshot and averaged them. The second approach is more rigorous as it correctly treats the equilibrium averaging. The first approach can give an idea of how much static orientation of the Chro and Trp is responsible for the observed values. Table 6.11 shows the results of the two calculations. Fig. 6.19 shows experimental versus calculated 2 — as you can see, there is an excellent correlation between the theory and experiment (R 2 =0.98). The values of are relatively small, which is consistent with nearly perpendicular orientation of the two dipoles, < >=82-98 . The calculations using average structure overestimate , which shows that dynamic fluctuations are important, however, the correlation is very good for both static and dynamic values, meaning that static (average) structures of the mutants are sufficiently different to explain the observed trend. The differences in the magnitude of 2 cannot be reconciled by using different value for the chromophore-Trp57 distance in the experimental analysis or in the calculations. For example, dividing theoretical 2 by 2, leads to an adjusted value ofhri=13.51.26=17.01 ˚ A, which is too large. Besides, our current definition ofr seems to be consistent with what was used in the experiment, as evidenced by<r>. So the discrepancy is likely due to a combined effect of the uncertainties inQ D ,J, andn that enter the equation forR 0 . It is quite likely that we accumulate a factor of 2 from the uncertainty inQ D and J. 225 Table 6.11: Computed average distance (standard deviation in parenthesis), angle between average transition dipoles, and 2 . His148 is in the HSD state. system hri, ˚ A hi (theory a ) hi (theory b ) 2 (theory a ) 2 (theory b ) 2 (exp) EGFP 13.48 (0.26) 111.59 95.97 0.209 0.143 0.070 T65G 13.14 (0.26) 103.65 91.31 0.309 0.169 0.086 T65G Y145M 13.31 (0.28) 91.83 96.89 0.472 0.209 0.102 T65G Y145M F165Y 13.16 (0.30) 107.6 97.69 0.276 0.154 0.082 a Computed using the average values of the dipoles. b Computed by averaging the instantaneous values at each snapshot. 226 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 R 2 =0.97 k 2 (exp) k 2 (theory a ) 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 R 2 =0.95 k 2 (exp) k 2 (theory b ) Figure 6.19: Correlation plot of theoretical and experimental dipole orientation factor. Top: Computed using average dipoles. Bottom: Computed by averaging 2 at each snap- shot. 227 6.7 Appendix D: Free-energy differences between different protonation states 228 Table 6.12: Gibbs free-energy differences (in eV) and relative populations of different protonation states at room tem- perature (298 K) and at 100 K (numbers in parenthesis). System HIS148 G mm HIS148 G HIS148 G HIS148 popul. (mm! qm/mm) EGFP HSP!HSD 0.085 HSP -4.360 HSP!HSD -0.049 HSP 0.129 (-0.033) (-1.452) (-0.008) (0.268) HSP!HSE 0.064 HSD -4.494 HSP!HSE 0.125 HSD 0.871 (-0.023) (-1.427) (0.014) (0.678) HSD!HSE – HSE -4.299 HSD!HSE 0.174 HSE – – (-1.415) (0.022) (0.052) T65G HSP!HSD 0.067 HSP -4.691 HSP!HSD -0.046 HSP 0.143 (-0.026) (-1.601) (-0.005) (0.339) HSP!HSE 0.029 HSD -4.804 HSP!HSE 0.180 HSD 0.857 (-0.017) (-1.625) (0.015) (0.602) HSD!HSE – HSE -4.540 HSD!HSE 0.226 HSE – – (-1.569) (0.020) (0.059) Duo HSP!HSD 0.045 HSP -3.832 HSP!HSD 0.194 HSP 0.026 (0.019) (-1.297) (0.106) (0.010) HSP!HSE 0.020 HSD -3.683 HSP!HSE -0.093 HSD — (-0.011) (-1.210) (-0.040) (–) HSD!HSE – HSE -3.945 HSD!HSE -0.101 HSE 0.974 – (-1.326) (-0.146) (0.990) Trio HSP!HSD 0.058 HSP -3.944 HSP!HSD -0.071 HSP 0.018 (0.017) (-1.301) -0.056 (0.001) HSP!HSE 0.026 HSD -4.073 HSP!HSE - 0.094 HSD 0.285 (-0.009) (-1.374) -0.076 (0.089) HSD!HSE – HSE -4.064 HSD!HSE -0.023 HSE 0.697 – (-1.368) -0.020 (0.910) 229 Tables 6.12 and 6.13 show computed free energy differences at room temperature (T=298 K) and at T=100 K. The entropic factor favors HSD and HSE over HSP: entropy is increasing upon deproto- nation, because the number of particles increases. This explains the increase of the HSP fraction at low temperatures for all 4 systems. The HSD-HSP G shows much weaker temperature dependence. Seems like distinct populations survive at low T, which is what experiment shows. 230 Table 6.13: Free-energy differences (in eV) between different protonation states at room temperature (298 K) and at 100 K (numbers in parenthesis), difference in enthalpy (H in eV) and entropy (S in eVK 1 ). Mutant HIS148 G(298K) G(100K) H S -TS(298K) -TS(100K) EGFP HSP!HSD -0.049 -0.008 0.013 2:07 10 4 -0.061 -0.021 HSP!HSE 0.125 0.014 -0.042 -5:61 10 4 0.167 0.056 HSD!HSE 0.174 0.022 -0.055 -7:68 10 4 0.229 0.077 T65G HSP!HSD -0.046 -0.005 0.016 2:07 10 4 -0.061 -0.021 HSP!HSE 0.180 0.015 -0.068 -8:33 10 4 0.248 0.083 HSD!HSE 0.226 0.020 -0.084 -1:04 10 3 0.310 0.104 Duo HSP!HSD 0.194 0.106 0.061 -4:44 10 4 0.132 0.044 HSP!HSE -0.093 -0.040 -0.013 2:68 10 4 -0.080 -0.027 HSD!HSE -0.101 -0.146 -1.68 -2:27 10 3 0.676 0.227 Trio HSP!HSD -0.071 -0.056 -0.048 7:57 10 5 -0.022 -0.007 HSP!HSE - 0.094 -0.076 -0.067 9:09 10 5 -0.027 -0.009 HSD!HSE -0.023 -0.020 -0.018 1:51 10 5 -0.004 -0.001 231 Analysis of the computed free energies and entropy: If the reaction is assumed to be it gas phase, one may expect S to be largely positive in reaction HSP!HSD/HSE making free energy change more negative. This is due to creation of two particles (one H + from one leading to increase in degree of disorderness. However, the situation is much more complex in solution and in condense phase. The effect of created H + is expected to be minimized due to solvation. Enthalpy-entropy compensation (EEC) is widely accepted for playing a key role in protein-ligand binding, protein-protein interaction, solvation in proteins in water etc. This was previously understood as explained by assuming that if a molecular change in the ligand leads to more and/or tighter van der Waals contacts and H-bonds with the sub- strate (giving a more negative H), this inevitably leads to reduced mobility/ flexibility in either or both components of the interaction, i.e., a reduction in the overall conformational entropy, and that change compensates the enthalpy decrease. However, a recent study shows, in macromolecules, a little change in Gibbs free energy and and the large changes in enthalpy and entropy are too great to be a consequence of only conformational changes.it does not follow that conformational changes are the sole contributor to the entropy: overall protein flexibility should be considered to be a greater contributor to change in entropy. To check, if EEC exists in EGFP and mutants, we will plot H and -TS at 298 K and 100 K to check if they correlates. There exists linear correlation in H and -TS at 298K and 100K for each mutants. However, trends are not similar for all of them. Trio behaves differently compared to rest of the mutants. 232 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 -T DS (eV) DH (eV) EGFP: 298K, R 2 =1.00, k= -4.229 EGFP: 100K, R 2 =1.00, k= -1.429 HSD →HSE HSP →HSD HSP →HSE HSD →HSE HSP →HSE HSP →HSD HSD →HSE HSP →HSD HSP →HSE HSD →HSE HSP →HSE HSP →HSD -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 -T DS (eV) DH (eV) T65G: 298K, R 2 =1.00, k= -3.699 T65G: 100K, R 2 =1.00, k= -1.246 HSD →HSE HSP →HSD HSP →HSE HSD →HSE HSP →HSE HSP →HSD -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -T DS (eV) DH (eV) Duo: 298K, R 2 =0.90, k= -0.432 Duo: 100K, R 2 =0.90, k= -0.127 HSD →HSE HSP →HSD HSP →HSE HSD →HSE HSP →HSE HSP →HSD -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 -0.030 -0.025 -0.020 -0.015 -0.010 -0.005 0.000 Trio: 298K, R 2 =0.96, k= 0.481 Trio: 100K, R 2 =0.98, k= 0.166 -T DS (eV) DH (eV) Figure 6.20: Plots of H versus -TS in different protonation states of mutants. In EGFP, HSP!HSD shows a +ve entropy (as expected), whereas the reaction is also seen to be endothermic (+ve). At room temperature, entropy term dominates over enthalpy. As the temp goes down, enthalpy term starts being dominant changing the favorable proto- nation state at low temperature. This explains, why population of HSD decreases at 100K compared to 298K. For Trio HSP!HSE shows a +ve entropy and the reaction is also seen to be exothermic (-ve). Therefore, here entropy and enthalpy are not competing with each other. Rather it is complementing. At low temperature, HSE remain the dominant population due to large -ve enthalpy. This explains why population of HSE increases upon lowering the temperature. 233 Using H and S we have extrapolated G at different temperatures which shows change in dominant population at low temperature for EGFP and T65G whereas no change in observed for Duo and Trio; this is shown in Figs. 6.21 and 6.22. -50 0 50 100 150 200 250 300 350 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 EGFP, (HSP-->HSD) EGFP, (HSP-->HSE) EGFP, (HSD-->HSE) DG (eV) T (K) -50 0 50 100 150 200 250 300 350 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 DG (eV) T (K) T65G, (HSP-->HSD) T65G, (HSP-->HSE) T65G, (HSD-->HSE) -50 0 50 100 150 200 250 300 350 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 DG (eV) T (K) Duo, (HSP-->HSD) Duo, (HSP-->HSE) Duo, (HSD-->HSE) -50 0 50 100 150 200 250 300 350 -0.10 -0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 DG (eV) T (K) Trio, (HSP-->HSD) Trio, (HSP-->HSE) Trio, (HSD-->HSE) Figure 6.21: Extrapolation of G with respect to temperature in mutants. 234 0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 Population Temperature(K) EGFP-HSD EGFP-HSE EGFP-HSP 0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 Population Temperature(K) T65G-HSD T65G-HSE T65G-HSP 0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 Population Temperature(K) Duo-HSD Duo-HSE Duo-HSP 0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 Population Temperature(K) Trio-HSD Trio-HSE Trio-HSP Figure 6.22: Extrapolation of population of different protonation state with respect to temperature in mutants. 235 6.7.1 Appendix E: AIMD results Table 6.14 compares twisting times in AIMD trajectories compared with the MD simu- lations initiated from the same snapshot (same structures but different velocities; see section 6.4.4). Specifically, we record time at which phenolate ring twists (defined as > 30 ). Fig 6.23 shows this comparison graphically. We observe very close correlation between the MD and AIMD trajectories, which provides validation for our modified fore-field parameters. Table 6.14: AIMD simulation in 1st excited state for 3 ns showing the twist around in 11 snapshots for EGFP and BrUSLEE. Time of the twist of the same snapshot in excited-state MD is shown in parenthesis (in ns). Snapshot EGFP-HSD EGFP-HSE EGFP-HSP Trio-HSD Trio-HSE Trio-HSP 0 2.44 (–) 1.93(1.55) 0.29 (0.56) 0.67 (0.52) 2.27 (–) 0.78 (0.98) 40 2.38 (2.27) 1.00 (0.77) 1.63 (1.47) 2.36 (–) 2.09 (2.26) 1.03 (1.15) 80 – (–) 2.28 (2.06) 2.61 (–) 0.69 (0.93) 2.40 (–) 2.88 (2.32) 120 2.08 (–) 1.14 (1.57) 2.66 (2.57) 2.57 (–) 2.65 (–) 2.79 (–) 160 1.42 (1.65) 0.62 (0.34) 0.74 (0.46) 2.83 (–) 0.19 (0.06) 2.21 (–) 200 1.27 (0.93) 1.55 (1.89) – (–) – (2.70) 1.63 (2.14) 1.13 (1.63) 240 2.77 (–) 2.06 (2.28) 2.70 (2.17) 0.39 (0.04) 2.23 (–) 2.06 (1.43) 280 1.69 (1.81) 0.43 (0.60) 1.06 (0.92) 2.31 (–) 2.27 (2.62) 1.85 (1.42) 320 2.36 (–) 1.19 (1.15) 0.28 (0.03) – (2.98) 0.63 (0.41) 1.33 (0.97) 360 2.41 (–) 1.11 (0.77) 0.84 (1.25) 0.69 (0.71) 0.72 (0.50) 2.16 (–) 400 1.33 (0.83) 2.23 (2.32) 0.79 (0.81) 0.56 (0.37) 1.37 (1.57) 0.97 (0.61) 236 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 EGFP-HSD, R 2 = 0.77 EGFP-HSE, R 2 = 0.82 EGFP-HSP, R 2 = 0.91 Time of chromophore twist in excited state MD (ns) Time of chromophore twist in AIMD (ns) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Trio-HSD, R 2 =0.92 Trio-HSE, R 2 =0.96 Trio-HSP, R 2 =0.61 Time of chromophore twist in AIMD (ns) Time of chromophore twist in excited state MD (ns) Figure 6.23: Correlation plot of twisting time for MD and AIMD excited-state trajectories initiated from 11 snapshots for each protonation state of His148 of EGFP and BrUSLEE. 237 6.8 Appendix F: Calculations of radiative and radiationless lifetimes Radiative lifetimes are computed using Eq. (6.11). For the protein-bound chromophore, we usen=1.6 (as in Ref. 26). Radiationless lifetimes were computed from the excited-state MD by using linear fit of the planar population decay. Then we compute apparent excited-state lifetime as for each form as: 1 = 1 r + 1 nr (6.20) = nr r r + nr (6.21) (6.22) For example, for the HSD form: HSD = nr;HSD r;HSD r;HSD + nr;HSD : (6.23) Then we use the following procedure to compute apparent excited-state lifetimes and FQY averaged over distinct populations: hi = X i A i i (6.24) In this case, hi =A HSD HSD +A HSE HSE +A HSP HSP (6.25) For FQY: FQY = nr r + nr (6.26) 238 For HSD: FQY HSD = nr;HSD r;HSD + nr;HSD (6.27) hFQYi = X i A i FQY i (6.28) In this case, hFQYi =A HSD FQY HSD +A HSE FQY HSE +A HSP FQY HSP (6.29) Table 6.15: Theoretical estimates of radiative lifetime for different mutants. Computed excitation energies and oscillator strengths are also shown. QM/MM absorption energies and oscillator strengths are averaged over 400 snapshots taken from ground-state equilib- rium MD simulations. r ,rel values are relative lifetimes calculated with respect to r in EGFP-HSD. Mutant HIS148 E ex , eV (f l ) E ex ,eV (f l ) r , ns r , ns r rel, ns (gas) (QM/MM) (gas,n=1) (QM/MM,n=1.6) EGFP HSD 3.101 (1.02) 3.026 (1.06) 29.50 7.254 1.00 HSE 3.101 (1.02) 3.046 (1.07) 28.25 7.091 0.98 HSP 3.101 (1.02) 3.019 (1.06) 28.25 7.286 1.00 T65G HSD 3.123 (1.05) 3.079 (1.14) 28.25 6.496 0.89 HSE 3.123 (1.05) 3.062 (1.09) 28.25 6.778 0.93 HSP 3.123 (1.05) 3.067 (1.13) 28.25 6.642 0.91 Duo HSD 3.123 (1.05) 3.055 (1.14) 28.25 6.622 0.91 HSE 3.123 (1.05) 3.058 (1.14) 28.25 6.616 0.91 HSP 3.123 (1.05) 3.096 (1.12) 28.25 6.581 0.91 Trio HSD 3.123 (1.05) 3.079 (1.13) 28.25 6.577 0.91 HSE 3.123 (1.05) 3.128 (1.15) 28.25 6.242 0.86 HSP 3.123 (1.05) 3.061 (1.13) 28.25 6.660 0.92 239 Table 6.16: Computed non-radiative decay times (ns), populations of different protona- tion state of His148, and % of non-planar chromophores at the end of the excited-state simulation (3 ns). Mutant HIS148 nr population %planar conformation EGFP HSD 8.60 0.871 76.25 HSE 1.87 — 32.50 HSP 2.96 0.129 47.50 T65G HSD 0.98 0.857 14.00 HSE 0.69 — 3.00 HSP 2.66 0.143 41.50 Duo HSD 1.41 — 22.75 HSE 0.47 0.974 0.00 HSP 1.78 0.026 32.75 Trio HSD 1.69 0.285 29.75 HSE 0.97 0.697 12.00 HSP 1.87 0.018 34.75 240 Table 6.17: Computed values of average lifetime (in ns), percentage population of each protonation states, and fluores- cent quantum yield. Experimental values are given in parenthesis. Mutant HIS148 , theory (exp) population, theory (exp) hi FQY hFQYi, theory (exp) EGFP HSD 3.93 (2.8) 0.871 (0.887) 3.69 (2.71) 0.54 0.51 (0.60) HSE 1.48 — 0.21 HSP 2.10 (2.0) 0.129 (0.113) 0.29 T65G HSD 0.85 (0.82) 0.857 (0.885) 1.00 (0.95) 0.13 0.15 (0.10) HSE 0.63 — 0.09 HSP 1.90 (2.0) 0.143 (0.115) 0.28 Duo HSD 1.16 — 0.46 (0.61) 0.17 0.07 (0.08) HSE 0.44 (0.52) 0.974 (0.91) 0.07 HSP 1.40 (1.5) 0.026 (0.09) 0.21 Trio HSD 1.34 (1.4) 0.285 (0.164) 1.00 (0.65) 0.20 0.15 (0.3) HSE 0.85 (0.51) 0.697 (0.833) 0.13 HSP 1.46 (2.3) 0.018 (0.003) 0.22 241 0 2 4 6 8 10 3.5 4.0 4.5 5.0 5.5 R 2 =0.78 Hydrogen bonds t nr (ns) -10 0 10 20 30 40 50 60 70 80 3.5 4.0 4.5 5.0 5.5 Hydrogen bonds % of planar conformation R 2 =0.90 Figure 6.24: Correlation between the average number of hydrogen bonds in the ground state and computed non-radiative lifetime (top) and the % of surviving planar conforma- tion after 3 ns of excited-state dynamics (bottom). 242 Table 6.18: Computed and experimental values of photophysical parameters EGFP, T65G, Duo, and Trio (in parenthesis, the experimental values are shown). Protein Ext. coeff.(exp.) FQY (exp.) R.B. (exp.) FL, ns (exp.) RPS (exp.) EGFP 48948.1 (55000) 0.51 (0.6) 1 (1) 3.69 (2.71) 1 (1) T65G 53668.8 (70000) 0.15 (0.1) 0.32 (0.21) 1.00 (0.95) 3.69 (1.87) Duo 56774.6 (84500) 0.07 (0.08) 0.16 (0.203) 0.46 (0.61) 8.02 (4.3) Trio 58157.8 (86000) 0.15 (0.3) 0.35 (0.8) 1.00 (0.65) 3.69 (8.8) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5 3.0 R 2 =0.75 t, ns (experiment) t, ns (theory) EGFP-HSD EGFP-HSP T65G-HSP T65G-HSD Duo-HSE Duo-HSP Trio-HSD Trio-HSE Trio-HSP 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 R 2 =0.88 FQY (experiment) FQY (theory) EGFP Trio T65G Duo EGFP-HSD EGFP-HSP T65G-HSP T65G-HSD Duo-HSE Duo-HSP Trio-HSD Trio-HSE Trio-HSP 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 R 2 =0.97 % population (experiment) % population (theory) 48000 50000 52000 54000 56000 58000 55000 60000 65000 70000 75000 80000 85000 90000 Extinction coefficient R 2 =0.99 Extinction coefficient (Lmol -1 cm -1 [Experiment] Extinction coefficient (Lmol -1 cm -1 ) [Theory] 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Relative brightness (R.B) R 2 =0.63 Relative brightness (experiment) Relative brightness (theory) EGFP Trio Duo T65G EGFP T65G Duo Trio 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 R 2 =0.09 Relative photostability (RPS) [experiment] Relative photostability (RPS)[theory] Figure 6.25: Correlation plots in RB, FQY, extinction coefficient, RPS, lifetimes. 243 6.9 Chapter 6 references 1 M. 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Astafiev, A. Acharya, K. A. Lukyanov, A. I. Krylov, and A. M. Bogdanov, Influence of the first chromophore- forming residue on photobleaching and oxidative photoconversion of EGFP and EYFP, Int. J. Mol. Sci. 20, 5229 (2019). 27 A. Royant, M. Noirclerc-Savoye, Stabilizing role of glutamic acid 222 in the structure of Enhanced Green Fluorescent Protein, J. Str. Biol. 174, 385 (2011). 28 M. H. M. Olsson, C. R. Sondergaard, M. Rostkowski, and J. H. Jensen, PROPKA3: Consis- tent treatment of internal and surface residues in empirical pKa predictions, J. Chem. Theory Comput. 7, 525 (2011). 29 B. L. Grigorenko, A. V . Nemukhin, I. V . Polyakov, D. I. Morozov, and A. I. Krylov, First- principle characterization of the energy landscape and optical spectra of the green fluorescent protein along A-I-B proton transfer route, J. Am. Chem. Soc. 135, 11541 (2013). 30 J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R.D. Skeel, L. Kale, and K. Schulten, Scalable molecular dynamics with NAMD, J. Comput. Chem. 26, 1781 (2005). 31 J.-D. Chai and M. Head-Gordon, Systematic optimization of long-range corrected hybrid density functionals, J. Chem. Phys. 128, 084106 (2008). 32 J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionals with damped atom-atom dispersion interactions, Phys. Chem. Chem. Phys. 10, 6615 (2008). 33 Shao, Y .; Gan, Z.; Epifanovsky, E.; Gilbert, A.T.B.; Wormit, M.; Kussmann, J.; Lange, A.W.; Behn, A.; Deng, J.; Feng, X., et al., Advances in molecular quantum chemistry contained in the Q-Chem 4 program package, Mol. Phys. 113, 184 (2015). 34 A. I. Krylov, P. MW. Gill, Q-Chem: an engine for innovation. Wiley Interdisciplinary Reviews: Computational Molecular Science 3, 317 (2013). 35 S. Faraji, A. I. Krylov, On the nature of an extended Stokes shift in the mPlum fluorescent protein, J. Phys. Chem. B. 119, 13052 (2015). 36 T. H. Rod, U. Ryde, Accurate QM/MM free energy calculations of enzyme reactions: methy- lation by catechol O-methyltransferase, J. Comput. Chem. 1, 1240 (2005). 37 T. H. Rod, U. Ryde, Quantum mechanical free energy barrier for an enzymatic reaction, Physical Review Letters, 94, 138302 (2005). 38 A. Warshel, Calculations of enzymic reactions: calculations of pKa, proton transfer reactions, and general acid catalysis reactions in enzymes, Biochemistry, 20, 3167 (1981). 39 T. R. Gosnell, Fundamentals of Spectroscopy and Laser Physics, Camb. Univ. Press 3 (2002). 246 40 D. B. Hand, The refractivity of protein solutions, J. Biol. Chem. 108, 703 (1935). 41 T. L. MacMeekin, M. L. Merton, N. J. Hipp, Refractive indices of amino acids, proteins, and related substances, Advances in Chemistry 44, 54 (1964). 42 M. de Wergifosse, C. G. Elles, A. I. Krylov, Two-photon absorption spectroscopy of stilbene and phenanthrene: Excited-state analysis and comparison with ethylene and toluene, J. Chem. Phys. 146, 174102 (2017). 43 K. Takaba, Y . Tai, H. Eki, H.-A. Dao, Y . Hanazono, K. Hasegawa, K. Mikia, and K. Takeda, Subatomic resolution x-ray structures of green fluorescent protein, IUCrJ 6, 387 (2019). 44 M. Taniguchi, H. Du, J. S. Lindsey, PhotochemCAD 3: diverse modules for photophysical calculations with multiple spectral databases, Photochem. Photobiol. 94, 277 (2018). 45 A. V . Mamontova, A. M. Shakhov, K. A. Lukyanov, A. M. Bogdanov, Deciphering the Role of Positions 145 and 165 in Fluorescence Lifetime Shortening in the EGFP Variants, Biomolecules 10, 1547 (2020). 46 A. V . Mamontova, I. D. Solovyev, A. P. Savitsky, A. M. Shakhov, K. A. Lukyanov, A. M. Bogdanov, Bright GFP with subnanosecond fluorescence lifetime, Scientific reports 8, 1 (2018). 247 Chapter 7: Future Work The thesis focuses on excited-state photophysics of FPs. We aimed to understand the effect of mutations on radiative and nonradiative relaxation process, which control properties such as excited-state lifetimes, FQY , RB, etc. However, important phenomena such as photobleaching remain largely unexplored. One important example is redding: EGFP is known to undergo oxidative redding in presence of an external oxidants 1 . Understanding such processes is important for understanding photostability 7.1 Understanding the photostability in EGFP mutants For a given rate of the bleaching process (via photo-oxidation or other photochemical processes), the yield of the bleached forms is smaller for systems with shorter apparent excited-state lifetimes. As photostability is inversely proportional to Y bl , the ratios of 1/Y bl can be interpreted as relative photostabilities. Bleaching rates can vary significantly among different proteins, because electron-transfer (ET) pathways and the rates are sensitive to mutations 1, 2 . Because of the high cost of such calculations, the effects of mutations on the rates of electron transfer are not fully investigated in the present thesis. 248 Within the first-order kinetics, the yield of bleaching Y bl is given by: Y bl = bl ; (7.1) where is excited-state lifetime, bl is related to rate of electron transfer processes. In our study in Chapter 4 and 6, we computed Y bl as a ratio of lifetimes of mutants to that in EGFP. Table 7.1: Computed and experimental values of relative photobleaching rate (relative to EGFP). Experimental values are in PBS+Ox. (Reproduced from Chapter 4). Protein relative photostability (theory) relative photostability (exp.) EGFP 1.0 1.0 EGFP-T65G 10.0 17.0 EYFP 2.5 0.4 EYFP-G65T 0.71 6.4 Table 7.1, shows that we fail to achieve qualitative agreement in computed and experimental photostability in mutants 4 . This suggests that indeed ET pathways and the rates are sensitive to mutations. The oxidative redding in EGFP can be expressed as a series of reactions as follows 1, 2 : Chro h !Chro fast;1e !Chro slow;Chemistry !Redform (7.2) A detailed mechanistic study by Bogdanov et al. focused on the initial step; ET from the chromophore (electron donor) to a nearby aromatic residue (electron acceptor). The rate of ET between different sites are given by Marcus rate expression 5, 6 : k ET =jH DA j 2 1 p 4k B T exp ( (G +) 2 4K B T ) (7.3) 249 where G, andH DA are the free energy change, reorganization energy, and coupling between the electronic states involved in ET. Computation of rate of ET in different mutants, as dis- cussed in Chapter 4 and 6, may provide a new approach towards enhancing phtostability of FPs. 7.2 Exploring the role of a triplet state in oxidative photo- chemistry in EGFP Two recently discovered phenomena in EGFP have generated considerable interest. The first one is oxidative redding, which was observed in 2009 by Bogdanov et al 7 . The other one is primed photoconversion, which was observed in 2015 by Dempsey et al. 8 in some photoconvertible FPs such as Dendra2. Both phenomena have in common that, upon absorption of light, the green chromophore changes its color to red. This happens with low quantum yield. For oxidative redding, the authors favor an excited singlet precursor developing into a radical state that further reacts in the dark although the possibility of the involvement of a triplet state was also briefly mentioned 9 . In contrast, for the primed conversion, Mohr et al. 10 proposed a triplet state with millisecond lifetime that absorbs a second photon forming a higher excited triplet state, serving as a doorway for further chemical transformation. Formation of the triplet state was characterized by phosphorescence emission (time-resolved phosphorescence spectroscopy) and an intermediate with 5 ms lifetime was observed in transient absorption (TA) 11 . The proposed mechanism of that process involves an S 1 ! T 1 intersystem crossing. The chromophore then ends up in a low lying triplet state. In presence of an oxidant, ET transfer takes place from the chromophore to the oxidant. However, very little is known about the 250 Figure 7.1: Summary of the mechanism of primed conversion: 488 nm excitation or prim- ing of the anionic cis chromophore, C . populates the S 1 (C ) state. De-population of the S 1 (C ) state may occur via (i) fluorescence emission or (ii) low-yield intersystem crossing to the lowest triplet state, T 1 . Excitation of T 1 with the red conversion beam causes a T 1 T n transition. The ensuing relaxation process to the singlet ground state involves reverse intersystem crossing (RISC) and excited state chemical transformation generating the red species. (Reproduced from Ref. 10) electronic structure of this triplet state, and the entire mechanism of the process of redding via primed photoconversion. Because primed photoconversion is used as an alternate way of green to red conversion of EGFP, a mechanistic study of that process would help to understand the photophysics of FPs and hopefully, design better FPs for super resolution imaging. 251 7.3 Chapter 7 references 1 A. M. Bogdanov, A. Acharya, A. V . Titelmayer, A. V . Mamontova, K. B. Bravaya, A. B. Kolomeisky, K. A. Lukyanov, A. I. Krylov, Turning on and off photoinduced electron transfer in fluorescent proteins by-stacking, halide binding, and Tyr145 mutations, J. Am. Chem. Soc. bf 138, 4807 (2016). 2 A. Acharya, A. M. Bogdanov, K. B. Bravaya, B. L. Grigorenko, A. V . Nemukhin, K. A. Lukyanov, and A. I. Krylov, Photoinduced chemistry in fluorescent proteins: Curse or bless- ing?, Chem. Rev. 117, 758 (2017). 3 R.Y . Tsien, The green fluorescent protein, Annu. Rev. Biochem. 67, 509 (1998). 4 T. Sen, A. V . Mamontova, A. V . Titelmayer, A. M. Shakhov, A. A. Astafiev, A. Acharya, K. A. Lukyanov, A. I. Krylov, and A. M. Bogdanov, Influence of the first chromophore- forming residue on photobleaching and oxidative photoconversion of EGFP and EYFP, Int. J. Mol. Sci. 20, 5229 (2019). 5 R. A. Marcus, On the theory of oxidation-reduction reactions involving electron transfer. I, J. Chem. Phys. 24, 966 (1956). 6 R. A. Marcus, Chemical and electrochemical electron-transfer theory, Annu. Rev. Phys. Chem. 15, 155 (1964). 7 A. M. Bogdanov, A. S. Mishin, I. V . Yampolsky, V . V . Belousov, D. M. Chudakov, F. V . Subach, V . V . Verkhusha, S. Lukyanov, K. A. Lukyanov, Green fluorescent proteins are light- induced electron donors, Nat. Chem. Biol. 5, 459 (2009). 8 W. P. Dempsey, L. Georgieva, P. M. Helbling, A. Y . Sonay, T. V . Truong, M. Haffner, P. Pantazis, In vivo single-cell labeling by confined primed conversion, Nat. Method 12, 645 (2015). 9 R. B. Vegh, K. B. Bravaya, D. A. Bloch, A. S. Bommarius, L. M. Tolbert, M. Verkhovsky, A. I. Krylov, K. M. Solntev, Chromophore photoreduction in red fluorescent proteins is responsible for bleaching and phototoxicity, J. Phys. Chem. B. 118, 4527 (2014). 10 M. A. Mohr, A. Y . Kobitski, L. R. Sabater, K. Nienhaus, C. J. Obara, J. Lippincott-Schwartz, G. Nienhaus, P. Pantazis, Rational Engineering of Photoconvertible Fluorescent Proteins for Dual-Color Fluorescence Nanoscopy Enabled by a Triplet-State Mechanism of Primed Conversion, Angew. Chem. Int. Ed. 56, 11628 (2017). 252 11 M. Byrdin, C. Duan, D. Bourgeois, K. Brettel, A long-lived triplet state is the entrance gateway to oxidative photochemistry in green fluorescent proteins, J. Am. Chem. Soc. 140, 2897 (2018). 253
Abstract (if available)
Abstract
Fluorescent proteins from the family of Green Fluorescent Protein (GFP) are unique in that they are the only fluorescent probes of natural origin. Their photoproperties make them suitable for a wide variety of applications. Fluorescent proteins are useful devices for studying the mechanistic details of various processes in cells, both in vitro and in cellulo. Excited-state lifetime is of the fundamental importance, as it limits the time-scales of competing relaxation channels of the excited chromophore. Structural changes in an excited state can cause temporary and permanent loss of fluorescence. For example, cis-trans photoisomerization often proceeds via a transient dark state, whereas a stable twisted geometry in excited state leads to a long-living dark state with a loss of fluorescence. This thesis covers studies of different fluorescent proteins and provides a mechanistic/operational insights into phenomena such as photoswitching in Dreiklang and loss of fluorescent quantum yield upon specific mutations in enhanced green fluorescent protein (EGFP). Chapter 1 presents an overview of GFP-like proteins. ? Chapter 2 presents the theoretical methods for computing radiative and nonradiative lifetimes and discusses requisite computational tools. An equation for radiative lifetime can be derived from first principles with classical harmonic oscillator, which allows us to estimate radiative lifetime with a help of electronic structure calculations. The dominant channel responsible for nonradiative decay is discussed in Chapter 1. To capture the essential physics and to quantify nonradiative lifetime, we performed dynamics simulations of excited-state chromophores. Towards this end, we re-parameterised the ground-state forcefield parameters of the chromophore to describe excited-state potential energy surface (PES) with ab initio calculations. We then use excited-state lifetime to estimate fluorescent quantum yield in model systems. We then discuss multiple decay channels operational in proteins like EGFP and how the protonation states of the key residues affect excited-state dynamics. We utilize thermodynamic cycles to estimate free-energy changes upon changing the key protonation states to compute relative populations of different protonation states. ? In Chapter 3 fluorogenic dyes based on the GFP chromophore are discussed. The compounds contain a pyridinium ring instead of phenolate and feature large Stokes shifts and solvent-dependent variations in the fluorescence quantum yield, which facilitates their use for imaging the membrane structure of endoplasmic reticulum. Electronic structure calculations explain the trends in their solvatochromic behavior. ? Chapter 4 focuses on EGFP?one of the most popular genetically encoded fluorescent probes, which carries the threonine-tyrosine-glycine (TYG) chromophore, undergoes efficient green-to-red oxidative photoconversion (redding) with electron acceptors. In contrast, enhanced yellow fluorescent protein (EYFP), a close EGFP homologue (5 amino acid substitutions), with glycine-tyrosine-glycine (GYG) chromophore, is much less susceptible to redding and requires halide ions in addition to the oxidants. We clarified the role of the first chromophore-forming amino acid in photoinduced behavior of these fluorescent proteins. To that end, we compared photobleaching and redding kinetics of EGFP, EYFP, and their mutants with reciprocally substituted chromophore residues, EGFP-T65G and EYFP-G65T. Experimental measurements showed that T65G mutation significantly increases EGFP photostability and inhibits its excited-state oxidation. Remarkably, while EYFP-G65T demonstrated highly increased spectral sensitivity to chloride, it is also able to undergo redding independent of chloride. Atomistic calculations revealed that the GYG chromophore has an increased flexibility, which facilitates radiationless relaxation leading to the reduced fluorescence quantum yield in the T65G mutant. The GYG chromophore also has larger oscillator strength relative to TYG, which leads to a shorter radiative lifetime (i.e., a faster rate of fluorescence). The faster fluorescence rate partially compensates for the loss of quantum efficiency due to radiationless relaxation. The shorter excited-state lifetime of the GYG chromophore is responsible for its increased photostability and resistance to redding. In EYFP and EYFP-G65T, the chromophore is stabilized by ?-stacking with Tyr203, which suppresses its twisting motions relative to EGFP. ? Chapter 5 presents the results of high-level electronic structure and dynamics simulations of the photoactive protein Dreiklang. With the goal of understanding the details of Dreiklang’s photocycle, we carefully characterized the excited states of the ON- and OFF-forms of Dreiklang. The key finding of our study is the existence of a low-lying excited state of a charge-transfer character in the neutral ON form and that population of this state, which is nearly isoenergetic with the locally excited bright state, initiates a series of steps that ultimately lead to the formation of the hydrated dark chromophore (OFF state). These results allowed us to refine the mechanistic picture of Dreiklang’s photocycle and photoactivation. ? Chapter 6 introduces BrUSLEE?BRight Ultimately Shorttime Enhanced Emitter?a new fluorescent protein derived from the enhanced green fluorescent protein (EGFP) by 3 mutations: T65G/Y145M/F165Y. BrUSLEE shows an unusual combination of high fluorescence brightness and short fluorescence lifetime. To explain the peculiarities of its photobehavior, we investigated fine structural determinants of the fluorescence lifetime in connection with brightness by combination of time-resolved fluorescence measurements and atomistic simulations. High-resolution fluorescence measurements revealed 2 distinct subpopulations co-existing in a wide temperature range (4-300 K). The fluorescence lifetimes of these emissive states change considerably with temperature, converging to low temperature (intrinsic) lifetimes that are vastly different from each other and from that of the parental EGFP. The crystal structure and 15N-NMR spectroscopy of BrUSLEE show no obvious structural heterogeneity. Atomistic simulations suggest that the heterogeneity arises due to co-existing populations of different protonation states of chromophore-adjacent titratable residues. Different protonation states of His148 alter the hydrogen-bond network around the chromophore, which significantly affects its twisting flexibility in the excited state. Changes in the hydrogen-bond network also explain the variations in photo-physical properties among EGFP and the T65G, T65G/Y145M, and T65G/Y145M/F165Y (BrUSLEE) mutants.
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Sen, Tirthendu
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The role of the environment around the chromophore in controlling the photophysics of fluorescent proteins
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College of Letters, Arts and Sciences
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Doctor of Philosophy
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Chemistry
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2021-08
Publication Date
07/18/2021
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06/18/2021
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Krylov, Anna I. (
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chromophore
EGFP
enhanced green fluorescent protein
excited-state lifetime
fluorescent protein
GFP
green fluorescent protein