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Understanding electrostatic effects in the function of biological systems

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Understanding electrostatic effects in the function of biological systems

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Content Understanding electrostatic effects in the function of biological systems
by
Mojgan Asadi
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 2023
Copyright 2023 Mojgan Asadi
For my parents, Javad and Farideh, to whom I owe everything.
ii
Acknowledgements
First I want to say thank you to my supervisor Professor Arieh Warshel, for your care, your
dedicationanddriveforscience, forallofyourquestions, discussions, andintuitionineveryproject
in our group, and of course your sense of humor. Thank you for letting me learn and grow for
five years under your supervision. The best part of my Ph.D. was the times our discussions went
back-and-forth to figure out something during our projects. I have kept all of your hand-drawn
illustrations from our discussions since day one. I wish I could compile all of the drawings you
made for all of your students and make a book out of it. I will carry the memories of working with
you these five years for the rest of my life.
Thank you to all previous and current group members that I have interacted with. I especially
thank Chen, WenJun, Gabriel, Arjun, Raphael, and Dibyendu, whom I worked more closely with.
Ilearneddifferent, valuablethingsfromeachoneofyouwhichIwilluseformyfuture. Ialsothank
Professor Igor Vorobyov for his kindness, support and intellectual discussions. Veselin, I’ll miss all
your wise words and of course the chocolates you sent us all the way from Europe. Thank you to
Matt, for his compassion and care, for always being there for the students, and for asking often
how our families are doing back home. I will miss all of the nice things of belonging to this group.
Thank you to my undergraduate advisor Wayne A. Hendrickson who first introduced me to
proteins and the deep intuition that goes into analyzing and understanding them. His passion and
iii
encouragement made me so interested in studying the functionality of proteins. Looking back, I
was very lucky to have the opportunity to learn from him and his amazing group.
Thankyoutomycommitteemembers,Prof.VadimCherezov,Prof.AiichiroNakano,Prof.Susumu
Takahashi,andProf.OlegPrezhdo. IreallyappreciatedencounteringProf.CherezovandProf.Taka-
hashi at conferences and receiving their encouragement and support. Thank you to Prof. Nakano
for his kindness and his enthusiastic encouragement to pursue further studies in computer science.
AndthankyoutoProf.Prezhdo,forallhisknowledgeandhistimededicatedascommitteemember
to my qualifying exam and dissertation defense.
Thank you to my best friends Humberto, Morteza, Alex, Aish, Michelle, and Judith. You guys
are true friends. Especially Humberto, thank you for always being there for me.
Thank you, to my strength, my family, my dad, my mom and my beautiful sister. You mean
the world to me. Whoever knows me will know that I have a very close relationship with my dad,
who worked non-stop, and still does, with passion for his family throughout his life. The fact he
allowed me to study abroad required a huge sacrifice of him. Forever I owe him a debt.
. AK
.
AK
.

àñ

JÜØ
iv
Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Electrostatic Energetics of Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2: Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Thermodynamic Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Potential of Mean Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Free Energy Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Protein Dipole-Langevin Dipole Method . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Empirical Valence Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Ab Initio methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 3: Membrane Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 Activity of Membrane Enzymes: Intramembrane Proteases . . . . . . . . . . . . . . 21
3.2 Characterizing Ion Channel Mutations . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 4: The Effect of Membrane Lipids on Protein Catalytic Activity . . . . . . . . . . . 25
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Computational Study Preparation . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 EVB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.3 Renormalization Evaluation of Conformational Barriers . . . . . . . . . . . . 29
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.1 EVB Energy Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.2 Coupling between Conformational Change and Substrate Movement . . . . . 31
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
v
Chapter 5: Reversal Potential Prediction of Channelrhodopsin Mutations . . . . . . . . . . . 40
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 The GHK Equation and Ionic Binding Energies . . . . . . . . . . . . . . . . . . . . . 41
5.3 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.1 Structure Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.2 Reversal Potential Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Chapter 6: Soluble Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Chapter 7: Modeling the Selective Covalent Inhibition of Tyrosine Kinases . . . . . . . . . . . 58
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.2 Kinetic Basis of TKI Selectivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3.1 Computational Study Preparation . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3.2 Ab Initio calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3.3 EVB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3.4 Kinetics Simulation of Inhibitor Selectivity . . . . . . . . . . . . . . . . . . . 64
7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.4.1 Ab initio calculations of reference reactions . . . . . . . . . . . . . . . . . . . 66
7.4.2 EVB Reaction Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.4.3 Kinetic Simulation of Inhibitor Selectivity . . . . . . . . . . . . . . . . . . . . 67
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 8: Examining Catalytic Proposals through Orotidine 5’-Phosphate Decarboxylase . . 77
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8.2 Examination of RSD Proposals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.2.1 The Circe Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.2.2 Induced fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.3 Simulation of the Catalytic Mechanism of ODCase . . . . . . . . . . . . . . . . . . . 81
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Chapter 9: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
vi
List of Tables
3.1 Comparison of turnover rates between homologous membrane and soluble enzymes.
The rate of soluble aspartic proteases is given as a substrate-depdendent range. . . 22
7.1 Comparison of experimentally measured inhibition potency of Acalabrutinib and
Ibrutinib with BTK and ITK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
8.1 CalculatedestimatesofODCaseactivationbarrierswiththecorrespondingobserved
results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
vii
List of Figures
2.1 Illustration of a two-state EVB profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 Phospholipids with two different head groups, POPC and POPG. . . . . . . . . . . . 24
4.1 Rhomboid Protease GlpG solved in detergent and lipid bilayer. . . . . . . . . . . . . 33
4.2 Active sites of different membrane and soluble serine proteases. . . . . . . . . . . . . 34
4.3 TatA substrate in GlpG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 The reaction mechanism of serine protease. . . . . . . . . . . . . . . . . . . . . . . . 36
4.5 EVB energy profiles for GlpG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.6 Energy barriers of conformational change and substrate movement. . . . . . . . . . . 38
4.7 Renormalized energy surface of conformational change and substrate movement. . . 39
5.1 Ionic binding Sites of C1C2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Ionic binding sites of GtACR1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Predicted GHK reversal potential shifts of C1C2 . . . . . . . . . . . . . . . . . . . . 51
5.4 Optimal model coefficients of C1C2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.5 Predicted GHK reversal potential shifts of GtACR1. . . . . . . . . . . . . . . . . . . 53
5.6 Optimal model coefficients of GtACR1. . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.1 Non-covalent and covalent tyrosine kinase inhibitors. . . . . . . . . . . . . . . . . . . 70
7.2 BTK and ITK with acalabrutinib. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3 Ab initio energy profiles for active region of BTK/ITK. . . . . . . . . . . . . . . . . 72
viii
7.4 Optimal reaction paths for BTK and ITK inhibition by acalabrutinib. . . . . . . . . 73
7.5 EVB energy profiles for the inhibitor binding reaction in water, BTK and ITK. . . . 74
7.6 Simulated inhibition progress at different initial acalabrutinib concentrations and
time windows for BTK and (b) ITK. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.7 Simulated k
calc
vs inhibitor concentration for BTK and ITK. . . . . . . . . . . . . . 76
8.1 Reaction mechanism of ODCase along a stepwise pathway. . . . . . . . . . . . . . . . 84
8.2 Active site and substrate of ODCase. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.3 Description of the Richard experiment that disproved the Circe RSD effect. . . . . . 86
8.4 Key experimental information about the catalytic reaction of ODCase. . . . . . . . . 87
8.5 Schematic reproduction of Richard’s induced fit proposal. . . . . . . . . . . . . . . . 88
8.6 EVB profiles of the reaction of ODCase. . . . . . . . . . . . . . . . . . . . . . . . . . 89
ix
Abstract
We examine the relationship between structure and functionality in several biological systems us-
ing computational modeling. The first study investigates the effect of environmental factors on
the activation barriers of intramembrane rhomboid protease. We used the empirical valence bond
approach to calculate chemical barriers in various environments and found that the physical envi-
ronment does not impact chemical catalysis. The second study proposes a computational strategy
to predict shifts in the reversal potential of ion channels due to point mutations. We employed the
protein dipole-Langevin dipole technique to analyze ion binding affinities and the GHK equation
to quantify shifts in the reversal potential, which can serve as an auxiliary tool in engineering
channelrhodopsins. The third study examines the selectivity of acalabrutinib, a covalent inhibitor,
for Bruton’s tyrosine kinase (BTK) over interleukin-2-inducible T-cell kinases (ITK). We devel-
oped a kinetic model of tyrosine kinase activity and inhibition using both chemical and binding
energetics. This approach is essential for studying covalent inhibitors with a highly exothermic
bonding process. The final study explores the catalytic effect of orotidine 5’-phosphate decarboxy-
lase (ODCase), which catalyzes the decarboxylation of orotidine monophosphate (OMP). We used
quantitative empirical valence bond calculations to replicate the catalytic action of ODCase and
the impact of the phosphate side chain in the ligand. We demonstrate that the overall catalytic
impact results from electrostatic transition state stabilization, indicating the lower reorganization
x
energyforthereactionenergyintheenzymethaninwater. Thesefindingshighlightthelimitations
of the induced fit hypothesis in explaining the origin of the catalytic effect of ODCase.
xi
Chapter 1
Introduction
1.1 General Background
Proteins are one of the fundamental elements of biological systems. The majority of the actions
necessary for an organism to operate and contribute to its structure are carried out by proteins.
Understanding a protein’s optimal thermodynamics and electrostatic energy is critical for estab-
lishing where its activities originate, finding its most probable reaction path, and designing new
proteins with improved functions or drugs with more efficacy against their targets. Proteins are
necessary components of all living creatures and provide a number of activities, including accel-
erating metabolic events, providing structural support, and allowing cell communication [1–7]. A
complete description of proteins requires a multidimensional energy landscape that defines the rel-
ative probabilities of the conformational states (thermodynamics) and the energy barriers between
them (kinetics).
Protein function may be traced back to the earliest beginnings of life on Earth. Knowing how
proteins changed through time might help us better comprehend how life began and diversified [8,
9]. Understanding the origins of protein activity may also aid in the creation of new proteins with
unique functions and applications, such as in medicine development, biotechnology, and materials
research [10, 11]. Furthermore, understanding the origin of protein function may also offer insight
1
into the molecular basis of illnesses and aid in the identification of novel therapeutic targets [12].
For example, by investigating how protein mutations impact their function, we may learn more
about the underlying causes of genetic illnesses and design more effective therapies [13, 14]. In
brief, knowing the origin of protein function is critical for furthering our understanding of the
natural world, generating new technologies, and improving human health [15].
Inthisdissertation,Iexaminetheoriginoftheactivityandfunctionalityofavarietyofbiological
systems from the perspective of multi-scale, computationally efficient evaluations of electrostatic
interactions in these systems. I focus on four different systems with diverse roles and applications,
two membrane proteins and two soluble proteins:
1. Rhomboid protease, a membrane enzyme in which catalytic activity take place within the
lipid bilayer.
2. EngineeringofChannelrhodopsinthroughbindingenergymodelsofmutantreversalpotential
shifts.
3. Covalent inhibition of tyrosine kinases.
4. The origin of catalysis in the Orotidine 5
′
phosphate decarboxylase enzyme.
Underlying each study are free energy calculations of catalyzed reactions and/or effects of elec-
trostatic interactions with a ligand, such as a chemically active drug or an ion, within the active
region of each protein [16, 17]. These methods are further developed and explain in Chapter 2. In
Section 1.2, we introduce the foundations of a consistent treatment of electrostatic interactions. A
more detailed summary and outline of each topic is provided in Section 1.3.
2
1.2 Electrostatic Energetics of Proteins
Electrostaticinteractionsprovidewhatisperhapsthemosteffectiveunderstandingofstructure–function
relations in different biological systems [1, 16–20]. This requires examining not only small-scale
electrostatic interactions (i.e. charged and polar groups), but also the effective macroscopic elec-
trostatics of the environment. The solvent is generally a high-dielectric, polarizable medium, while
proteins and lipid bilayers effectively are modelled as materials with an effectively smaller dielec-
tric constant [21, 22]. Consistent and convergent methods for evaluating the electrostatic energy
in these environments are necessary to reliably calculate binding energies as well as the rate of
reactions in enzymes [1, 7, 22–26].
The study of protein structure-function relationships has a very long history, beginning with
the macroscopic description by Linderstron-Lange, and Tanford & Kirkwood [27–31]. These ini-
tial views placed an emphasis on the relative energies of prototonation states and pH-titration
properties of ionizable groups in proteins, which were modeled as spherical, low-dielectric environ-
ments. As computational power advanced and detailed protein crystal structures became available
[32], microscopic electrostatic models became more accessible and critical to understanding the
functionality of proteins.
Underlying any electrostatic model is Coulomb’s law for the interaction (potential/free energy)
∆ G between any two charged atoms or groups i and j,
∆ G
Q
=K
Q
i
Q
j
εr
ij
, (1.1)
whereK =332
˚A
2
kcalmol
− 1
isCoulomb’sconstant,thechargesQ
i
andQ
j
areexpressedinatomic
units, r
ij
is the distance between the groups, and ε is the dielectric constant of the medium. The
physical meaning of the dielectric constant in proteins has been controversial, since proteins are
3
not homogeneous media at short length scales. However, it can be consistently viewed as a model-
dependent constant that depends on the degree of detail that is included in the model [7, 30,
31].
In addition to charge-charge interactions, the next order of electrostatic energies include dipole
interactions, which have potential energies
∆ G
µ =
X
i
1
2
K⃗ µ i
· ⃗
ξ i
, (1.2)
where
⃗
ξ i
is the local electric field applied on the dipole at atom i. The charge distributions of
solvent molecules and polar residues in proteins includes dipole moments that are not permanent,
but rather are polarized depending on the strength of the local electric field. The dipoles µ i
on a
protein atom i follows a linear dependence on the electric field
⃗ µ p,i
=α i
⃗
ξ i
, (1.3)
where
⃗
ξ i
and α i
are the local electric field and the atomic polarizability. On the other hand, the
polarizationofbulksolventismodeledbyagridofLangevindipoles. EachLangevindipolemoment
µ L,i
is determined by the self-consistent solution to the Langevin equation
⃗ µ L,i
=
ˆ
ξ i
µ 0
(coth(χ i
)− χ − 1
i
), (1.4)
whereξ i
∝
µ 0
k
b
T
|ξ i
|. Aself-consistentsolutionneedstobeobtained,i.e.throughiterativeevaluations
of the dipole moment, since the local electric field
⃗
ξ i
itself depends on the strength of nearby
Langevin dipoles [22, 33].
4
The above formulation of electrostatic energies in proteins form the basis of the Protein dipole-
Langevin dipole (PDLD) method for evaluating the interaction energies in proteins, including the
binding energies of ligands. PDLD does not calculate the absolute free energy. However, in some
cases it can be represented adequately by scaling the calculated energies with a dielectric constant,
so we apply its semi-macroscopic formulation (PDLD/S) by assuming the protein has a dielectric
constant ε
p
. Finally, in order to reduce the unknown factors in ε
p
it is useful to apply the linear
response approximation (LRA) to transform the PDLD/S model to the PDLD/S-LRA model.
In the LRA approximation, the PDLD/S energy is calculated and averaged over configurations
generated by molecular dynamics over charged and uncharged states. More details about the
PDLD method are provided in Chapter 2 [34–36].
Free energy perturbation/umbrella sampling (FEP/US) [37–41] calculations can accurately es-
timate enzyme catalysis, e.g. chemical reactions and electron transport, between atom within some
activeregion. Whileinprinciplethefreeenergyprofilesofreactionscanbeevaluatedwith ab initio
methods, a computationally simpler objective is to understand the effect of the new electrostatic
environmentthatthereactionissubjecttowithinanenzyme,comparedtothesamereactionunder
standardcondition,i.e.insolvent. Thisistheapproachtakenbytheempiricalvalencebond(EVB)
method. Thismethodleveragestheideasofvalencebondstructuresandionic-covalentresonanceto
build a simple Hamiltonian for the isolated molecule, and then assesses the reaction in solution by
adding the computed solvation energies to the diagonal matrix components of the ionic resonance
forms [42–44]. Further details of the EVB method is provided in Chapter 2.
1.3 Outline
We begin in Chapter 2 by giving a detailed introduction to the important computational methods
usedthroughoutthestudiesthatfollow. Fundamentally, thesemethodsaimtoevaluatefreeenergy
5
changes in a computationally efficient and stable manner and capture the energetics of binding and
chemical reactions in biological systems.
The study of membrane proteins is motivated in Chapter 3. Following that, in Chapter 4,
we present a study where the goal was to understand how a different physical (i.e. membrane)
environment affects intramembrane proteolysis using the EVB method. The primary question in
this work was the influence of the electrostatics of different lipid head groups on catalytic activity.
We examined the catalytic reaction barrier for each chemical step of the serine protease reaction.
Our study shows that the catalytic activity of a protein is unaffected by the incorporation of
electrostatic variations between lipid head groups when calculating the free energy profile of the
reaction. Inparticular, wefoundnosignificantchangesinenzymecatalyticratewhenchangingthe
charge composition of the lipid bilayer. In addition, we used renormalized dynamics to determine
whetherthereisacouplingbetweentheconformationalchangeandthesubstratesmovementatlong
time scales. We find that the enzyme conformational change is not caused by substrate movement,
and conclude that the induced-fit theory is not applicable in the case of rhomboid protease.
In Chapter 5, we present a computational mutation study of channelrhodopsin, a membrane
photoreceptor ion channel that is a central tool in the study of neurological systems [45–52].
We use solved structures of the C1C2 channelrhodopsin chimera as well as the anion channel-
rhodopsinGtACR1andevaluateionbindingenergieswiththePDLD-S/LRAmethod. Wedevelop
amodeltocorrelatetheshiftinreversalpotentialwithmutatedbindingenergiesthroughtheGold-
man–Hodgkin–Katz (GHK) equation [53–55]. The free energy profiles in relation to ion positions
are used to explore how different mutations in the pore impact the gain and loss of functionality
for both cation and anion channelrhodopsins. The results of our study indicate that computation-
ally calculating ion binding free energy can provide us with a good understanding of the role of
each mutation on electrostatic ion movement through the pore and how the predicted impact that
6
mutations can have on the free energy barriers of the ion movements and hence effective currents
and reversal potentials. Our work lays the ground for in silico assessment of the properties of
channelrhodopsin mutants as a tool for optogenetic engineering, particularly for the development
of novel channelrhodopsin with variant functionalities.
The second half of this dissertation focuses on soluble proteins, with our particular interests
motivated in Chapter 6. Next, Chapter 7 presents a comprehensive computational approach to
predicting the potency and selectivity of covalent inhibitors, a class of drugs that irreversibly
inactivate the function of a target protein by forming a covalently bonded pose in the binding
pocket of the protein that prevents any enzyme activity from taking place. We examine two closely
related enzymes from the tyrosine kinase family, BTK and ITK, and predict the observed high
selectivity of acalabrutinib for BTK over ITK. We performed ab initio and EVB calculations to
identify the optimal reaction pathway for the covalent inhibition step with the target cysteine
residue. A critical component of the high selectivity of acalibrutinib is the microenvironment of
the reaction, which is affected by the presence or absence of an i + 3 aspartate residue, which
results in a pKa shift that prevents the reacting group of acalabrutinib from bonding in ITK. With
both the reaction pathways and binding energies of the ligand, we quantify the selectivity using
the effective second order rate constant k
inact
/K
i
. The result of our study shows that examining
chemical reaction pathways is crucial to building selective covalent tyrosine kinase inhibitors.
In Chapter 8 we look at a foundational question of enzymology: what mechanism is responsible
for the large reduction in the reaction barrier in enzymes from the same reaction in water? We
present EVB simulations for the decarboxylation reaction of orotidine monophosphate (OMP) in
the Orotidine 5
′
phosphate decarboxylase enzyme (ODCase), as well as a critical examination of
modern proposals for the origin of catalysis. ODCase has a highly charged catalytic region and
a particularly high catalytic reaction rate for the decarboxylation of OMP. Our results strongly
7
suggest that a preorganized environment around OMP promotes transition state stabilization,
and are not consistent with proposals centered on ground state destabilization such as the Circe
mechanism [56, 57].
8
Chapter 2
Computational Methods
2.1 Thermodynamic Integration
Suppose a molecular system is modeled by a classical Hamiltonian H(⃗ r,⃗ p) = K(⃗ p)+U(⃗ r), where
⃗ r and ⃗ p denote the 3N Cartesian positions and momenta of N atoms, K(⃗ p) consists of the kinetic
energy terms, and U(⃗ r) is the potential energy of the system. Any thermodynamic quantities can
be derived from the partition function [58–60]
Z =
Z
e
− β H(⃗ r,⃗ p)
d
3N
⃗ rd
3N
⃗ p, (2.1)
where β = (k
B
T)
− 1
is the inverse temperature. The Helmholtz free energy is defined from the
partition function by
F =− k
B
T ln(Z). (2.2)
LetH
A
andH
B
be two Hamiltonian functions over the phase space of the same molecular system,
corresponding to some system states A and B. The change in Helmholtz free energy ∆ F(A→B)
of a process going from A to B can be written as
∆ F(A→B)=− k
B
T ln
Z
B
Z
A
=− k
B
T ln
R
exp(− β (H
B
(⃗ r,⃗ p)−H
A
(⃗ r,⃗ p)))e
− β H
A
(⃗ r,⃗ p)
d
3N
⃗ r
R
e
− β H
A
(⃗ r,⃗ p)
d
3N
⃗ r
, (2.3)
9
which we identify as a thermodynamic average over the Gibbs distribution of H
A
. That is,
∆ F(A→B)=− k
B
T ln
D
e
− β (H
B
(⃗ r,⃗ p)−H
A
(⃗ r,⃗ p))
E
A
, (2.4)
wherewewrite⟨·⟩
A
forthethermodynamicaverageoverstateA. Finally,wenotethatinprocesses
at fixed pressure for which changes in volume can be neglected, as we will only be concerned with,
changes in the Helmholtz free energy ∆ F are equal to changes in the Gibbs free energy ∆ G. In
addition, if the process involves no change in the kinetic energy term, the momentum component
of the partition function can be ignored, and Eq. (2.4) simplifies to
∆ G(A→B)=− k
B
T ln
D
e
− β (U
B
(⃗ r)− U
A
(⃗ r))
E
A
, (2.5)
This equation is formally exact for any state change. However, in practice it is difficult to use
directly to accurately sample and obtain a convergent average. Now suppose that the potential
energy U(⃗ r,λ ) can be parametrized by some real parameter λ such that it also differentiable with
respect to λ , where λ = λ A
and λ = λ B
place the system in state A and state B, respectively. By
differentiating the free energy with respect to λ , it can easily be shown that
∆ G(A→B)=− k
B
T
Z
λ B
λ A

∂U
∂λ
λ dλ, (2.6)
whichresultsinthemethodofthermodynamicintegration,whichcanbeappliedwhenthederivative
∂U
∂λ is available in simulations. However, since the path for λ needs to be discretized to evaluate
the integral numerically, systematic errors can accumulate when the concavity of U is large. The
next two sections deal with alternative numerical approaches to the problem of evaluating the free
energy differences between two connected states.
10
2.2 Potential of Mean Force
While molecular dynamics (MD) samples the Gibbs distribution of a system in the long-time limit,
there are generally rare events with large energy barriers that are of interest, but are not reached
by MD within a reasonable budget of computation time. Some examples of this situation are ions
passing through a channel or a protein undergoing a conformational change. A general strategy
in this case is to “guide” the system through the under-sampled states that may otherwise be
inaccessible. This is accomplished by umbrella sampling (US), in which the Gibbs distribution
over the state space is reweighed to access additional states [61–64], for instance, by adding a
guiding potential w
i
(⃗ r)=w(⃗ r,⃗ r
i
) centered at coordinates ⃗ r
i
to the system HamiltonianH(⃗ r). The
simulations are carried out over N
W
windows, sampling the Hamiltonian biased by the potentials
{w
i
(⃗ r)}
i=1,...,N
W
[65–71]. This allows for the evaluation of the potential of mean force (PMF) of
some single- or multi-particle process along the path of the guiding potential.
Multiple methods exist to evaluate the PMF from US data. A notable one in widespread use
is the weighed histogram analysis method (WHAM) [72–74], which has the advantage of being
able to generating statistical error estimates through bootstrap or Bayesian bootstrap sampling
[74]. The WHAM equations are derived from the minimum error estimate of the unbiased density
of states P(ξ ) of some generalized coordinate ξ constrained under the guiding potential. For a
one-dimensional PMF at constant temperature, they are
P(ξ )=
P
Nw
i=1
g
− 1
i
h
i
(ξ )
P
Nw
j=1
n
j
g
− 1
j
e
− β (w
j
(ξ )− fm)
, (2.7)
and
e
− βf
i
=
Z
e
− βw
i
(ξ )
P(ξ )dξ, (2.8)
where
11
• h
i
(ξ ) is the number of samples from window i at ξ ,
• n
i
is the total number of samples drawn from window i,
• f
i
is the estimated value of the PMF in window i, and
• g
i
=1+2τ i
is a weight when the simulation at window i has an autocorrelation time of τ i
.
By discretizing the umbrella coordinate ξ , each umbrella window yields a discrete histogram h
i
(ξ )
with n
i
total observations, and Eq. (2.8) is evaluated as a sum. Since P(ξ ) and {f
i
} depend on
each other, Eqs. (2.7) and (2.8) are solved self-consistently, i.e. though iterative evaluation until
the{f
i
} values converge.
2.3 Free Energy Perturbation
Free energy perturbation (FEP) is another general method used to calculate the change in free
energy ∆ G of a transformation on a Hamiltonian function H(λ ) depending on some parameter λ [70, 75–78]. Let δG be the change in the free energy subject to a small parameter perturbation δλ ,
then from Eq. (2.5),
δG (λ )=− k
B
T ln
D
e
− β (U(λ +δλ )− U(λ ))
E
λ , (2.9)
where U(λ ) is the potential energy term of the Hamiltonian and ⟨·⟩
λ denotes the expectation
value with respect to the Gibbs distribution ofH(λ ). Suppose we wish to evaluate the free energy
∆ G(λ 0
→ λ N
) of a process where λ is changed from λ 0
= 0 to λ N
= 1 in N small increments.
Thus,usingEq.(2.9),thesmallincrementsδG canbesummedoveraseriesofparameterincrements
δλ m
=λ m+1
− λ m
, yielding
∆ G(λ 0
→λ f
)=
N− 1
X
m=0
δG (λ m
→λ m+1
)=− β − 1
N− 1
X
m=0
ln

D
e
− β (H(λ m+1
)−H (λ m))
E
λ m

. (2.10)
12
The free energy perturbation method therefore consists of sampling the Gibbs distribution at each
λ M
, e.g. through molecular dynamics, and evaluating each free energy increment δG (λ m
→λ m+1
).
A canonical application of the FEP method is evaluating the electrostatic interaction between
twomoleculargroups,e.g.aligandandaprotein[7,79]. Inthiscase,thestrengthoftheelectrostatic
interaction between the protein and the ligand is linearly parametrized by λ , which turns the
interaction off. The resulting Hamiltonian increment is therefore
H(λ m+1
)−H (λ m
)=(λ m+1
− λ m
)
X
ij
K
Q
i
q
j
ϵr
ij
, (2.11)
where Q
i
is a charge in the ligand group and q
i
is a charge in the protein group, ϵ is the dielectric
constant and r
ij
is the distance between charges i and j.
While FEP is a very common tool in molecular dynamics, it is prone to convergence problems
on its own when the step size is too large, which results in either large statistical errors in the
thermodynamic averages or expensive simulation times. In the next section, we build up a stable
method for evaluating electrostatic as well as complete binding energies for ligand-protein interac-
tions. We then follow with a method for evaluating reaction free energies in enzymes utilizing FEP
to effectively map a reaction profile.
2.4 Protein Dipole-Langevin Dipole Method
The protein dipole-Langevin dipole (PDLD) method aims to evaluate electrostatic energies in a
computationally efficient and stable manner. To this end, it utilizes polarizable dipole interactions
asdescribedinSec.1.2. Inaddition,the linear response approximation (LRA)isanotherimportant
element that sidesteps the issue of FEP convergence [35, 75, 80]. Under the LRA approximation,
we assume that the linearized coupling between the system and the solvent are approximately the
13
same in both the initial state A and the final state B, i.e. the environment has the same “force
constant” in both states. The change in free energy is therefore found to be
∆ G
LRA
(A→B)=
1
2
(⟨U
B
− U
A
⟩
A
+⟨U
A
− U
B
⟩
B
) , (2.12)
To apply the LRA to a binding process, where U
B
=U
p
elec,l
is the potential energy with the ligand
in protein and U
B
= U
w
elec,l
is the potential energy with the ligand in water, the states that can
be reliably approximated by the LRA are accessed by the relevant thermodynamic cycles, which
results in a process of uncharging the ligand, inserting it into the protein, then turning its charge
back on. In all, the total binding energy of a ligand in protein can be evaluated as
∆ G
LRA
bind
=
1
2
hD
U
p
elec,l
E
l
′
+
D
U
p
elec,l
E
l
i
− 1
2
h

U
w
elec,l

l
+

U
w
elec,l

l
′
i
, (2.13)
where
• ⟨·⟩
l
and ⟨·⟩
l
′ denote thermodynamic averages over the charged ligand l and the uncharged
ligand l
′
, respectively,
• U
p
elec,l
is the energy of the ligand in protein in the charged state, and
• U
w
elec,l
is the energy of the ligand in water in the charged state.
2.5 Empirical Valence Bond
The empirical valence bond (EVB) approach is a QM/MM method that simplifies the state of the
QM region into a linear combination of diabatic states (e.g. valence bond structures), formulated
by Warshel in 1980 [23, 42, 43, 81–84]. The key aspect of EVB is that environmental effects on a
reaction can be reliably considered even with a simplified representation of the electronic structure
14
by calibrating the parameters of the model using a reference reaction in solution. This makes it a
powerful and computationally efficient tool for evaluating reactions in enzymes.
The diabatic states correspond to the electronic configuration states of the reactant, product,
and any intermediate states. If there are n such states, the effective quantum Hamiltonian H is
an n× n matrix whose diagonal elements are classical energy functions of the nuclear coordinates,
and whose off-diagonal elements quantify the mixing between two diabatic states, especially in a
reaction. Quantitatively,
H
ij
(
⃗
R,⃗ r)=











h
ij
(
⃗
R,⃗ r), i̸=j,
ε
i
(
⃗
R,⃗ r), i=j,
(2.14)
where the Hamiltonian is a function of the solute coordinates
⃗
R and solvent coordinates ⃗ r, h
ij
is
the mixing element between state i and j, and ε
i
(
⃗
R,⃗ r) is the total energy of the i-th state under
some classical force field representation. That is,
ε
i
(
⃗
R,⃗ r)=U
i,intra
(
⃗
R)+U
i,Ss
(
⃗
R,⃗ r)+U
i,ss
(⃗ r)+α i
, (2.15)
where U
i,intra
is the intramolecular solute energy, U
ss
is the solvent energy, and U
i,Ss
is the inter-
action energy between the solute and the solvent. The gas phase shift α i
includes any additional
(quantum-mechanical) formation energy for the molecular fragments represented by the diabatic
state in the gas state. As a general rule, the mixing term h
ij
is modeled with either a constant or
exponential between two adjacent diabatic states in the reaction.
In principle, any classical MD force field with appropriate electrostatic energy terms and bond
dissociation effects can be used for the potential energy interactions, which can result in different
energy minima. Furthermore, the physics of the quantum system is invariant to energy shifts in
all of the diabatic states. For this reason, we conventionally take α 1
= 0 and treat the gas shifts
15
for the other states as parameters that take into account any formation energy difference relative
to the first state. Since the force field should include the ability to model bond dissociation, any
chemical bonds thatarebrokenor formedbetween anytwo differentstates aremodeledbya Morse
potential
V
M
(b)=D
M
(1− e
a(b− b
0
)
)
2
, (2.16)
where b is the bond length, b
0
is the equilibrium bond length, D
M
is the dissociation energy of the
bond, and the force constant near equilibrium is 2D
M
a
2
.
To evaluate the free energy profile of a reaction traversing two states, for instance from state 1
to state 2, a FEP/US approach is used. The guiding potential is chosen to be a linear combination
of the diabatic energy states
ϵ i
=(1− λ i
)ε
1
+λ i
ε
2
, (2.17)
where λ i
∈ [0,1] and i = 0,...,N
w
− 1, where N
w
is the number of windows (also called frames).
The free energy profile is mapped by sampling the ground state energy of the Hamiltonian along a
reaction coordinate x,
∆ g
0
(x
′
)=∆ G
m
− k
B
T ln
D
δ (x− x
′
)e
− β (E
G
(x)− ϵ m(x))
E
m
, (2.18)
where E
G
is the ground state energy and ∆ G
M
is the FEP energy mapped using λ ,
∆ G
m
=− k
B
T
m− 1
X
k=0
ln
D
e
− β (ϵ k+1
− ϵ k
)
E
k
. (2.19)
Generally, ∆ g
0
(x
′
) is evaluated by a binning procedure along the reaction coordinate. For each
simulation window m, if the reaction coordinate x of a sampled configuration is within the bin
16
[x
′
i
,x
′
i+1
], then a count of e
− β (E
G
− ϵ m)
is added to the bin. The reaction coordinate itself is most
naturally taken to be the energy gap between the diabatic states, i.e. x=ε
1
− ε
2
.
In addition to the energy profile, the expected values of the diabatic energy curves ∆ g
1
(x
′
) and
∆ g
2
(x
′
) can be evaluated by an analogous equation as (2.18) replacing E
G
with ε
1
or ε
2
. These
profiles are analogous to Marcus parabolas in electron transfer theory, and their intersection yields
an estimate of the reorganization energy of the reactions, which is important for characterizing the
effect of the solvent environment, whether in water of in protein, on the reaction.
In the absence of resonance or concerted pathways, many reactions only involve two chemical
states. The adiabatic surface ∆ g
0
(x) and diabatic surfaces ∆ g
1
(x) and ∆ g
2
(x) are therefore a
complete description of the energetics of the reaction. An illustration of the energy surfaces of a
typicaltwo-statereactionisgiveninFigure2.1. Theenergiesofthereactionitselfareextractedfrom
the minima and maximum of ∆ g
0
(x). The diabatic surfaces also provide important information
about the influence of the environment on the reaction. Stabilization of the product state in
protein compared to water, for instance, would result in a lowered ∆ g
2
(x). A shift in the concavity
of each diabatic surface would also result in a shift in the reorganization energy λ . This energy is
conceptually important to the origin of catalysis, and is central to the analysis in Chapter 8.
2.6 Ab Initio methods
Every reaction results in a change in the electronic structure of molecular systems, whose en-
ergy must be calculated through quantum-mechanical methods. Such methods, typically based
on solving the Schr¨ odinger equation after separating nuclear and electronic degrees of freedom
(i.e. the Born-Oppenheimer Approximation), are called ab initio methods [85, 86]. As solving
the Schr¨ odinger equation directly is highly computationally expensive, the starting point for these
17
methods is the Hartree-Fock (HF) approximation [87–90], which treats interactions between elec-
trons through a mean-field approximation and neglects electronic correlations. The HF equations
are solved iteratively and basis of molecular orbitals, which are filled by electrons up until some
“Fermilevel”. TheHFenergyisgenerallynotaccurateincaseswherestrongcorrelationsmayexist,
such as in transition states or in systems involving transition metals. However, the HF molecular
orbitals can be used as a starting point for post-Hartree Fock (PHF) methods such as MP2 and
coupled cluster (CC) methods, which include correlation energy contributions to the total energy
through perturbative corrections. The quality of HF and PHF computations is contingent upon a
choice of basis sets for electronic orbitals. Basis sets composed from Gaussian functions have been
developed the most in software [91–95]. Factors including the size of the chemically active region,
net charge, and computational budget should be considered in the choice of basis set.
Densityfunctiontheory(DFT)isanabinitio methodthattakesadifferentapproachtointreat-
ing correlations between electrons [96–103]. The correlation energy is evaluated from a functional
of the electron density rather than through perturbative corrections. The form of the functional
thatisoptimalfordifferentapplicationsisanactiveareaofresearch. Forreactionsinorganicchem-
istry, the B3LYP and M06-2X functionals give strong agreement with experiment and generally see
widespread use [104–112].
18
Reaction Coordinate (Energy Gap)
Free Energy
Figure 2.1: Illustration of a two-state EVB profile, showing the adiabatic free energy surface
(solid) and the diabatic surfaces of the reactant (dashed blue) and product states (dashed green).
The reaction energy and activation energy are obtained from the minima and maximum of the
adiabatic surface and are denoted by ∆ G
‡
ad
and ∆ G
0
, respectively. The diabatic surfaces intersect
at∆ G
‡
d
, whichisreducedbytheoff-diagonalmixingenergy H
12
toyieldtheactivationenergy. The
reorganization energy is denoted by λ .
19
Chapter 3
Membrane Proteins
Membrane proteins are proteins that are partially or fully embedded in cell membranes [113]. The
membrane itself is a film composed of lipids (fat) and protein molecules. The transmembrane
portions of membrane proteins live in a hydrophobic environment where there is virtually no wa-
ter. Although membrane proteins make up almost half of the total mass of membrane and lipid
complexes, so far they make up less than 1% of protein structures collected in Protein Data Bank
[114], which can be attributed to the difficulties of crystallizing membrane proteins caused by their
tendency for disordered association [115–117]. Membrane proteins are involved in various roles:
allowing transmembrane diffusion transport of various molecules, ions, signal reception, catalysis,
etc... [118]. In the present work, we will focus on two type of integral membrane proteins, the ion
diffusion and catalytic activity roles [119] of membrane proteins. The former role is accomplished
bytheclassofproteinscalledionchannels[120,121],whilethelatterisaccomplishedbymembrane
enzymes [122–126].
Viewed as electrical elements, the lipid of a membrane works as a kind of insulator, while its
embedded proteins can act as conductors. A particular ion channel can be permeable to different
ioniccompounds,allowingthemtopassthroughthemembrane. Ifanionchannelismorepermeable
to one kind of ion than to another, it is said to be selective for that particular kind [127–130]. The
20
transportselectivitydeterminesthespecificfunctionoftheionchannelandisdependentonvarious
factors. A particularly strong factor is the pore diameter and size of the molecule that tries to pass
throughthechannel: moleculesthataretoolargewillnotbeabletopenetratethroughit[131,132].
Theselectivityalsoisstronglydeterminedbythefactthatthemembraneisessentiallyimpermeable
to polar functional groups, particularly charged groups.
The impermeability of the membrane to charged elements can be quantified through high-level
physical arguments. The free energy of a charge q in the medium with permittivity ε is equal
to +q
2
/2εr, where r is the van der Waals radius of the charge. It can be easily estimated that,
with q equal to the electron charge and r = 1.5
˚A (the typical radius of a charged ion), the value
of +q
2
/2εr is close to 1.5 kcal/mol at ε = 80 (in water), while at a membrane permittivity of
ε
memb
=3, this value will amount to nearly 37 kcal/mol. This is a resulting free energy increase of
∆ F =35kcal/molresults. BasedontheBoltzmannfactor, theprobabilityofaccumulationofsuch
free energy is approximately exp(− ∆ F/kT) = exp(− 35/0.6) ≈ 10
− 25
. This means that only one
in 10
25
ion attacks on the membrane will be successful. Given that the attack time is no less than
10
− 13
s, an ion passing through a purely lipid membrane would require at least ∼ 10
12
s before a
penetration event, i.e. about 10,000 years [133].
3.1 Activity of Membrane Enzymes: Intramembrane Proteases
In Chapter 4, we looked at the role of the lipid bilayer composition on the catalytic activity of the
serine protease GlpG. At this time, there are not many experimentally solved membrane protease
structures yet. Evolution may often make use of protein-lipid interactions as a mechanism for con-
trolling enzymes [134–138]. The effect of different lipid head groups on membrane protein function
has been observed experimentally in membrane proteins, such as the potassium channel KcsA, and
recently GlpG [132, 139–141]. The membrane composition is generally controlled through varying
21
Soluble Enzymes
Proteases Active Side Residues k
cat
(s
− 1
)
Aspartic protease [142, 143] Asp-Asp 0.003–0.9
Serine protease (chymotrypsin) [144–146] Ser-His-Asp 6.3× 10
− 4
–120
Membrane Enzymes
Proteases Active Side Residues k
cat
(s
− 1
)
Aspartic protease (γ -Secretase) [147] Asp-Asp 0.00120
Serine protease (Rhomboid) [148, 149] Ser-His-Asn 0.0069
Table3.1: Comparisonofturnoverratesbetweenhomologousmembraneandsolubleenzymes. The
rate of soluble aspartic proteases is given as a substrate-depdendent range.
ratios of the neutral phospholipid POPC and the charged phospholipid POPG (Figure 3.1). This
composition changes the probability that the KcsA channel is in its open conformation, and thus
changesthecurrent-voltagecurves. InthecaseofKcsA,thelipidactsasaco-factor,influencingthe
potassium channel’s conformational shift. Similarly, our concern for rhomboid protease is whether
altering the lipid head groups from neutral to charged may also affect the enzyme’s catalytic ac-
tivity. Recently after the publication of our work, another experimental group conducted tests on
GlpG catalytic activity and discovered that the lipid head group has no effect on catalytic activity,
although the lipid thickness is actually crucial [141].
In general, it is still difficult to determine what effect the lipid has on the rate of the catalytic
process. Even though membrane and soluble proteases have different evolutionary histories and
their similar catalytic function is an instance of convergent evolution, it is still quite interesting
to study the origin of the drastically different catalytic rates in solute and in protein. A promis-
ing approach is to characterize the differences between the soluble and the membrane proteases
that correspond to the same catalytic function. For instance, a soluble analog of the rhomboid
serine protease, chymotrypsin, has a reaction rate of 7.5s
− 1
[146], although the reaction rate of
rhomboid protease is three orders of magnitude slower. A similar situation holds for the analogous
aspartyl protease of γ -secretase (Table 3.1). Unfortunately, currently available experimental rates
and theoretical rate calculations for membrane proteases remain limited [147, 150].
22
3.2 Characterizing Ion Channel Mutations
The amino acid residues that are present in the channel are also particularly important in deter-
mining the its selectivity [132, 151]. Electrostatic interactions play an intimate role in the function
of membrane proteins, and the low-dielectric nature of the membrane has a large influence on the
electric fields and energetics of proteins and small molecules at or near the lipid bilayer. Neverthe-
less, there is currently no consistent model that predicts the effect of mutations on the function of
ion channels [152–155].
In Chapter 5, we take a step in developing models to predict the reversal potential of an ion
channel, which is a function of the permeability of the channel to both anions and cations that are
commonlypresentinintracellularandextracellularfluid. Wefocusonthechannelrhodopsinfamily
of proteins, light-activated ion channels that are important in their application to optogenetics
and have a number of experimentally measured mutant reversal potentials. Channelrhodopsins
are relatively non-selective, so their properties can be easily influenced and engineered through
selected mutations, making them a suitable and challenging test-bed for computational prediction
of reversal potentials. We develop a linear model relating the calculated binding energies using the
PDLD/S-LRA/β method to the reversal potential [33, 48, 50, 75].
23
Figure 3.1: Two different lipid head groups: (a) 2-oleoyl-1pamlitoyl-sn-glyecro-3-phosphocholine
(POPC) and (b) 2-oleoyl-1-pamlitoyl-sn-glyecro-3-glycerol (POPG).
24
Chapter 4
The Effect of Membrane Lipids on Protein Catalytic Activity
Abstract
The cleavage of protein within cell membranes controls pathogenic processes. Consequently, the
link between the physical environment and the function of such proteins has lately drawn major
experimental and theoretical attention. Without separating chemical and environmental compo-
nents, experimental and theoretical research cannot identify the coupling’s nature. Calculations
of the intramembrane rhomboid protease’s activation barriers in neutral and charged lipid bilayers
and detergent micelles are presented in this study to investigate environmental effects. Chemical
barrier calculations use the empirical valence bond (EVB) approach. The conformational change’s
energetics and dynamics are also captured by the renormalization approach. The simulations show
thatthephysicalenvironmentsurroundingtherhomboidproteasedoesnotaffectchemicalcatalysis
and that conformational and substrate dynamics do not display long-term correlation.
25
4.1 Introduction
Intramembrane serine proteases are a family of transmembrane proteases, which hydrolyze the
transmembrane regions of their substrate in the lipid region. At present, much of the current un-
derstandingoftheserineproteasesuperfamilycomesfromstudiesofsolubleproteins[145,156–161].
Among the known intramembrane proteases, Metalloprotease (Site-2 protease) [162–164], Aspartyl
proteases (γ -secretases)[165–167], and Serine proteases [168], the rhomboids are a well-conserved
family of intramembrane serine protease [169]. The E. coli rhomboid protease GlpG is an interest-
inganduniquesignalingtransmembraneproteaseinvolvedinmanyvitalprocessesandparticipates
indevelopmentalcontrolthroughtheepidermalgrowthfactorreceptor(EGFR)pathway[149,169–
174]. The substrate binding likely involves a significant conformational change in the rhomboid en-
zyme, reflected in the shifting of TM5 and the connected loop L5 [175–177]. The transmembrane
domain of GlpG for different configuarations is illustrated in Figure 4.1. The substrate enters the
active site in the open state conformation, then the rhomboid undergoes a conformational change.
The catalytic reaction takes place in a closed conformational state within the membrane bilayer.
Finally, the product is released upon returning to an open state conformation.
Rhomboid protease has a slower reaction rate than other analogous serine proteases (see Table
S6 in [148]). The reason is most likely due to the fact that the catalytic dyad of rhomboid (His
254-Ser201)islesseffectivethantheSer-His-Asp/Glucatalytictriadsintheserineproteasesfamily
(Figure4.2). Themaindifferenceisassociatedwiththeelectrostaticstabilizationoftheprotonated
His, which leads to about a 4 kcal/mol stabilization of the transition state [159].
There has been some conflicting conclusions regarding the rate-limiting step of rhomboid pro-
tease. Urbanandco-workers[149]haveconcludedthattheconformationalchangesareratelimiting.
On the other hand, Arutyunova et al. [171] found out that mutations of the oxyanion hole led to
a very significant change in the rate constant, and thus the chemical barrier is likely to be rate
26
limiting. Furthermore, prior studies have not clearly elucidated the coupling between the environ-
ment, i.e. the composition of the membrane, and the catalytic effect. In our study [148], we try to
advanceinresolvingtheseissues,startingbyevaluatingtherateofthechemicalstepofthereaction
of rhomboid in the open and half-open conformations in different environments [149, 178].
The chemical barriers were calculated with the empirical valence bond (EVB) method [42].
Furthermore,weusedtherenormalizationapproach[179,180]toevaluatetheconformationalenergy
barrier from the closed to the open conformation and its potential coupling to the binding of the
TatA substrate over an equivalent low-dimensional system. Our EVB study found that changes in
the membrane environments of the protein do not significantly affect the intramembrane protease’s
catalytic activity. In addition, our renormalization study also indicated no dynamical coupling
between the substrate movement and the conformational change.
4.2 Methods
4.2.1 Computational Study Preparation
The crystal structures for our studies were obtained from the Protein Data Bank (PDB) [114]. We
usedtheopen(PDBcode2IRV)[181],halfopen(PDBcode2NRF)[182],andclosedconformations
of GlpG (PDB code 2IC8) [173]. The ligand in this study was a five-amino acids TatA substrate,
which was docked to each systems using Autodock [183, 184]. The docked substrate is illustrated
in Figure 4.3.
POPG and POPC were used to moduled the lipid composition of charged and uncharged head
groups. We prepared the system in a lipid bilayer using a ratio of 3:1 for POPC:POPG, as well
as in DPPC detergent micelle, using CHARMM-GUI [185, 186]. After generating the different
27
environmentswithembeddedproteins,theywereequilibratedinGROMACS[187]usingtheAmber
force [188] field for 10 ns.
4.2.2 EVB
The EVB method is a QM/MM approach in which the relevant diabatic states are mixed to
represent the chemical reactions (see Chapter 2). The chemically active region in EVB, Region 1,
is designated as the few atoms that are involved in the chemical process. The remaining portion
of the enzyme-solvent-membrane system, referred to as region 2, consists of the remaining enzyme
together with the membrane and all the water molecules in the system.
We calibrated the EVB reaction surface as described in prior work [160]. The MOLARIS-
XG [34] package used the relaxed structures for the EVB computations. In place of an explicit
membrane, we used a coarse-grained (CG) membrane grid [189, 190] to represent the membrane
region’s atoms. We modified the charge and van der Waals parameters of the outermost layers of
the corresponding CG model to replicate the characteristics of the head-group of the phospholipids
of the lipid bilayer and the detergent micelle. The van der Waals parameters and charges of the
lipid head groups were randomly adjusted with a Monte Carlo procedure to reflect the composition
of the membrane.
The relevant ESP charges [191] from Gaussian 03 [192] were used to calculate the charges of
area 1 atoms. In the Antechamber program of AmberTools16 [193], the substrate charges and the
reactive residues were eventually transformed into RESP charges. The ENZYMIX force field’s [34]
vanderWaalsandbondingparameterswereused. Todeterminethelocationofthecoresimulation
sphere, the geometric center of the EVB reacting atoms was used. In an 18
˚A water sphere, the
system was submerged using the surface-constrained all-atom solvent (SCAAS) model [194].
28
The backbone atoms and all residues were constrained by K = 0.3
˚A
2
kcalmol
− 1
during the
simulation. Treatment of the long-range effects was carried out using the local reaction field (LRF)
approach[195]. Atthebeginningofeachreactionstep,eachprotein-membranesystemwasbrought
to equilibrium by gradually increasing the temperature from 5 K to 300 K for 400 ps. Each
free energy perturbation/umbrella sampling (FEP/US) calculation was based on these relaxed
structures as its starting point. There were six different FEP/US calculations for each EVB step,
each from a different relaxation point.
4.2.3 Renormalization Evaluation of Conformational Barriers
In order to further understand the conformational barriers and any potential connections between
the conformational change and the mobility of the TatA substrate, as was described in the intro-
duction, moreresearchmustbedone. Apossibledynamicalcontributiontothislinkshouldalsobe
investigated, whichisveryessential. Takingintoaccountthechallengesofusingamassiveall-atom
conformational barrier generation within the atomic chemical and structural space, we tried multi-
level modeling with reduced dimensions and expanded time scales through the “renormalization”
approach [179, 180].
This technique, discussed and put to use for chemical-conformational coupling in [179], is em-
ployed by renormalizing the dynamical data obtained from specific MD simulations to simplify
the conformational and dynamical processes to a two-dimensional model. In effect, the complete
atomicmodelisusedasthebasisforatwo-dimensionalrepresentation. Asastrongforcedrivesthe
system from one state to another, standard MD simulations are used for the entire model, while
LD simulations are used to treat the low-dimensional model with effective friction.
This approach starts with the full atomic model and then maps it onto a 2-D model. The full
modelistreatedwithregularMDsimulations,andLDsimulationstreatthelow-dimensionalmodel
29
with effective friction that is adjusted so that the 2-D and the full models have similar dynamics
under the effect of a strong force that moves the system from one state to another. The energy
landscape in the 2-D model is taken as the ground state of an EVB Hamiltonian with diagonal
matrix elements of the form
H
lm,lm
=ϵ lm
=
ℏω
Q
2
(Q− δ lm
Q
)
2
+
ℏω
R
2
(R− δ lm
R
)
2
+α lm
, (4.1)
where Q and R are, respectively, dimensionless conformational and substrate coordinates, ω
Q
and
ω
R
are effective frequencies, and δ lm
Q
are the minima locations. The energy landscape in the 2-D
model is fitted to the full surface using the proper α lm
.
4.3 Results
4.3.1 EVB Energy Barriers
The reaction mechanism is shown in Figure 4.4. The final deacylation step was not studied since
the formation of a covalent intermediate is the limiting step of the reaction. We explored whether
each path may occur in a stepwise or concerted way, and found that a concerted mechanism has
a lower barrier in both paths. The EVB free energy profiles are shown in Figure 4.5 for reactions
in the open and half-open conformations in three different environments: neutral lipid, composite
lipid, and detergent micelle. In all, the EVB simulations with different conformations of rhomboid
protease do not show a significant difference in the activation energy barrier as the environment of
each protein is varied.
Usingtransitionstatetheory,thecalculated k
cat
inneutralmembraneanddetergentwerefound
to be 0.008s
− 1
and 0.006s
− 1
, respectively. In comparison, the observed catalytic rates in a native
lipid environment and micelle were found to be 0.02s
− 1
and 0.04s
− 1
, respectively, while the rate in
30
a neutral membrane was found to be 0.007s
− 1
. We see that the agreement between the calculated
and observed results is reasnoable, within a margin of error of 1–2 kcal/mol for the EVB barriers.
4.3.2 Coupling between Conformational Change and Substrate Movement
ThefrictionandeffectivebarriersintherenormalizedLDdynamicswereparametrizedtomaximize
the agreement withthe time-dependent responseof MD undervariouspulling forces. Theresulting
energy landscape for the conformational and substrate movement is illustrated in Figure 4.7, along
withatypicalmillisecondtimescaletrajectory. TheLDtrajectorieswereinitializedwitharandom
Maxwell-Boltzmann velocity at 300 K. We observed that the kinetic energy of each trajectory
dissipates quickly, so the system reaches the energy minimum before overcoming the substrate
energy barrier. Consistent with prior studies [179], the renormalized trajectories do not retain
substantial memory of the kinetic energy associated with substrate binding or the conformational
barrier before reaching the beginning of the chemical barrier.
4.4 Conclusion
In this study, we explored the free energy barriers of the catalytic reaction in rhomboid protease
in a variety of lipid environments using EVB as well as the energy landscape of the closed to open
conformationalchangewithsubstratemovementusingtherenormalizationmodel. Wefindthatthe
changeoftheenvironmenthasnosignificanteffectonthecatalyticactivityforbothopenhalf-open
conformations. Furthermore, the calculated barrier for conformational change appears similar to
the corresponding observed barrier, and it is unlikely that there is significant dynamical coupling
between the conformation change and the ligand binding step. A similar conclusion should apply
to the coupling between the conformational and chemical barriers.
31
Wefacetheproblemthattheconformationalchangebarriermaybealimitingstep,withvarious
studies reaching different conclusions (see Section 4.1). Thus, the exact observed chemical barrier
is hard to determine. It is also possible that the conformational barrier is close to the chemical
barrier. This ambiguity makes our theoretical findings particularly important.
Understandingthecatalyticmechanismofintramembraneserineproteasecanserveasanimpor-
tant tool in the design of covalent inhibitors for this enzyme. Despite great advances in designing
inhibitors [196–198], our present and previous study [199] should be beneficial in the design of
highly selective covalent inhibitors.
Ourstudynaturallyleadstoanobservationoftheslowreactionratesofotherknownmembrane
proteases,suchasintramambraneaspartylproteases(e.g.γ -secretase)[147]andpossiblyintramem-
brane glutamate proteases (e.g. Rce1) [200]. Intramembrane metalloproteases such as S2P [201]
also share common features, so their reaction rates would be interesting to investigate. While we
cannot conclude that all membrane proteases have slow catalytic activity, this is a topic of great
interest that warrants further study.
32
Figure 4.1: Superimposed open, half-open, and closed structures, shown in purple, orange, and
green, respectively, solved in detergent (A) and in lipid bilayer (B). In all three conformations, the
position of histidine and serine are identical. Loop 5 is responsible for opening and closing the
conformations, where it is connected to transmembrane 5.
33
Figure 4.2: Active sites of different membrane and soluble serine proteases: (A) rhomboid serine
protease (PDB 2NRF-A), (B) chymotrypsin (PDB 1AFQ), (C) rolyl oligopeptidase (PDB code
2XDW), and (D) subtilisin protein (PDB code 2SIC). The presence of aspartic acid in soluble
serine proteases makes the active site triads residues and more effective compared to membrane
serine protease, which has asparagine instead.
34
Figure 4.3: (A) The portion of the TatA substrate used in the present study, which is cleaved
between P1 and P1
′
before release. (B) The hydrophobic surface of rhomboid protease: red and
blue show density of negatively and positively charged residues, yellow shows density of sulfur
atoms in cysteine, and white otherwise denotes neutral carbon atoms. (C) Detailed view of the
docked substrate in the active site, showing how it is stabilized by neighboring residues.
35
Figure4.4: Thereactionmechanismofserineprotease,consistingof(i)thefirstprotontransferfrom
serinetohistidine,(ii)nucleophilicattackfromtheserineresiduetothesubstrate’scarbonylcarbon,
(iii) the second proton transfer from protonated histidine to the amide group of the substrate, (iv)
bond breaking step, and (v) the intermediate state prior to deacylation.
36
Figure 4.5: The EVB reaction energy barriers for open and half-open conformations for paths 1
and 2 in (A) lipid and (B) detergent environments.
37
Figure 4.6: Energy barriers for the conformational change Q and the substrate movement R, taken
as cross sections of the 2-D energy surface employed in the renormalized model. The projection
of Q onto the r coordinates is shown here, while the projection of R onto the z coordinates is
provided. The angstrom scale is used for both.
38
Figure 4.7: The two-dimensional renormalized energy surface with different states illustrated and
a function of generalized coordinates Q and R, defined in the supplementary information of [148].
State I: Rhomboid is in a closed conformational state. State II: Rhomboid is in an open conforo-
mational state. State III: The substrate reaches the active site of rhomboid in its open state.
39
Chapter 5
Reversal Potential Prediction of Channelrhodopsin Mutations
Abstract
The reversal potential is an important property of an ion channel quantifying its electrochemical
equilibrium conditions. In this study, we propose a computational strategy to predict shifts in the
reversal potential of ion channels subject to point mutations. To anticipate changes in ion channel
permeabilities to various ions induced by mutations, we employ the protein dipole-Langevin dipole
(PDLD) technique to analyze ion binding affinities. The GHK equation is used to quantify shifts
in the reversal potential and develop a model based on shifts in ion binding affinities. We apply
this technique to predict reversal potential measurements from a cation channelrhodopsin (Ch.R.
C1C2 chimera) and an anion channelrhodopsin (GtACR1). We demonstrate that the binding ener-
gies computed from PDLD/S-LRA/β may be utilized to detect mutation-induced electrochemical
equilibrium alterations in GHK equation-applicable conditions. The prediction strategy proposed
here can be used as an auxiliary tool in the engineering of channelrhodopsins.
40
5.1 Introduction
Channelrhodopsins are light-activated ion channels that are used and engineered for neurological
systems [45, 48, 201–207]. The transmembrane portion of channelrhodopsin comprises seven reg-
ular α -helices that form a membrane-spanning bundle slightly tilted with respect to the plane of
the membrane, while the single β -hairpin and all irregular segments (connecting loops) protrude
from the membrane [208–210]. Despite the importance of membrane photoreceptors, efficient com-
putational methods and approaches to evaluate their functionality in different mutation are not as
established as soluble proteins.
Inthisproject,wedevelopedanapproachforpredictingphotoreceptorionchannelfunctionality
subject to point mutations. We used the protein dipole-Langevin dipole (PDLD) method [22, 35]
to evaluate ion binding affinities to predict changes in the permeability of the ion channel to
different ion species due to point mutations. This in turn shifts the reversal potential through
the Goldman-Hodgkins-Katz (GHK) equation [211, 212]. We applied this approach to reported
reversal potential measurements from both a cation channelrhodopsin (Ch.R. C1C2) [213] and an
anion channelrhodopsin (GtACR1) [214]. The predicted GHK reversal potentials of many mutants
are in strong agreement with the reported experimental measurements. Provided that the reversal
potential of the native wild-type ion channel is characterized, we show that the binding energies
calculated from PDLD can be reliably used for assessing shifts in electrochemical equilibrium due
to mutations in settings where the GHK equation is applicable.
5.2 The GHK Equation and Ionic Binding Energies
Here we will review the GHK equation, specializing it to the selectivity of channelrhodopsin, and
establish the physical relation between the reversal potential and relevant ionic binding energies.
41
We start by assuming that monovalent ionic concentrations are the main ionic contribution to the
reversal potential V
rev
. In the case of channelrhodopsin, V
rev
is then given by the GHK equation
[55, 215]
V
rev
=
RT
F
ln

Q
EC
Q
IC

, (5.1)
where the reversal potential depends on the permeability-weighed compartment charges
Q
EC
=P
Na
+[Na
+
]
EC
+P
K
+[K
+
]
EC
+P
H
+[H
+
]
EC
+P
Cl
− [Cl
− ]
IC
(5.2a)
Q
IC
=P
Na
+[Na
+
]
IC
+P
K
+[K
+
]
IC
+P
H
+[H
+
]
IC
+P
Cl
− [Cl
− ]
EC
, (5.2b)
where P
Na
+, P
Cl
− , P
K
+, and P
H
+ are the ionic membrane permeabilities, RT = 0.596kcal/mol,
and F =0.0231kcal/(molmV) is the Faraday constant. Equivalently, it can be written in the form
V
rev
=
RT
F
ln

[Na
+
]
EC
+r
K
+[K
+
]
EC
+α [H
+
]
EC
+r
Cl
− [Cl
− ]
IC
[Na
+
]
IC
+r
K
+[K
+
]
IC
+α [H
+
]
IC
+r
Cl
− [Cl
− ]
EC

, (5.3)
which is in terms of the permeability ratios
r
Cl
− =
P
Cl
− P
Na
+
, r
K
+ =
P
K
+
P
Na
+
, α =
P
H
+
P
Na
+
. (5.4)
The hydrogen permeability ratio α is known to be on the order of 10
6
in ChR2. In addition, ChR2
is not significantly selective between K
+
and Na
+
, so r
K
+ ≈ 1 [207, 216]. We will assume that α is
constant and that the pH is the same in both the extracellular and intracellular solvent.
Based on microscopic models used for other ion channels [217, 218], we assume that the log-
permeability of an ion X is proportional to its highest binding energy while in the channel,
P
X
=Ce
− ∆ G
‡
bind
(X)/RT
. (5.5)
42
Hence, for the permeability r
Cl
− , which we are interested in calculating, we have
r
Cl
− =exp

∆ G
†
bind
(Na
+
)− ∆ G
†
bind
(Cl
− )
RT
!
. (5.6)
We will make some assumptions as well as set the concentrations following experimental condi-
tions following those of [219],
1. Both EC and IC are at pH 7.3 (same concentration [H
+
]), and channelrhodopsin has a fixed
hydrogen permeability α =10
6
,
2. The EC solvent contains 147 mM NaCl, and the IC solvent contains 4mM[Cl
− ], and
3. We assume r
K
+ = 1 and that the remaining concentrations are [Na
+
]
IC
= 4mM, [K
+
]
IC
=
147mM and [K
+
]
EC
=4mM .
Given the above assumptions, we can determine the wild-type chloride permeability r
Cl
− from
the reversal potential found in [219]. Solving for r
Cl
− in the GHK equation
r
WT
Cl
− =
[Na
+
]
EC
− u[Na
+
]
IC
+α (1− u)[H
+
]+r
K
+([K
+
]
EC
− u[K
+
]
IC
)
u[Cl
− ]
EC
− [Cl
− ]
IC
, (5.7)
where u = e
VrevF/RT
. Thus, using the measured wild-type V
rev
= − 7mV in C1C2, we have
r
WT
Cl
− =0.442.
We are now ready to define our reversal potential model in terms of mutation binding energies.
For each mutation µ , we calculate the permeability ratio
r
µ Cl
− =r
WT
Cl
− e
∆∆ G
‡
bind,µ
(Cl
− →Na
+
)/RT
, (5.8)
where ∆∆ G
‡
bind,µ
(Cl
− →Na
+
)=∆∆ G
‡
bind,µ
(Na
+
)− ∆∆ G
‡
bind,µ
(Cl
− ).
43
Provided the permeability ratio is sufficiently small, the reversal potential from the GHK equa-
tion can be linearized with its derivative
dV
rev
dr
Cl
− =
RT
F

[Cl
− ]
IC
Q
IC
− [Cl
− ]
EC
Q
EC

Q
EC
Q
IC
. (5.9)
Thus,writingr
Cl
− (g)=e
g/RT
,thelinearizationofthereversalpotentialwithrespecttothebinding
energy difference g is
dV
rev
dg
=
dV
rev
dr
Cl
− dr
Cl
− dg
=
1
F

[Cl
− ]
IC
Q
IC
− [Cl
− ]
EC
Q
EC

Q
EC
Q
IC
r
Cl
− . (5.10)
This leads the linearized GHK equation as a function of mutated binding energies
V
rev
(µ )≈ V
WT
rev
+

dV
rev
dg

WT
∆∆ G
‡
bind,µ
(Cl
− →Na
+
). (5.11)
5.3 Computational Methods
5.3.1 Structure Preparation
We used the wild-type structure of activated C1C2 (PDB ID 7E6X) and dark state GtACR1
(PDB ID 6CSM). For each structure, five binding sites throughout the channel were chosen with
approximately even spacing through the channel. The structures were mutated and relaxed using
Rosetta 3 [220] with a membrane protein score function protocol to locally optimize the placement
of the ions and the side chain configurations. We then evaluated ionic binding energies using
Molaris-XG [34] for our PDLD calculations. The hydrophobic portion of the membrane around the
proteins was represented in Molaris using a coarse-grained atom model with a thickness of 30
˚A.
After equilibrating the 25
˚A region around the ion with weak restrains of K = 0.3
˚A
2
kcalmol
− 1
44
using the Enzymix force field, the binding energies were calculated with the PDLD/S-LRA/ β method.
5.3.2 Reversal Potential Prediction
We used PDLD-S/LRA/β [22] to evaluate the binding energies of Na
+
and Cl
− ions. Since chan-
nelrhodopsin is not a symmetric ion channel, the location of the ion is not as clearly defined as
a function of the membrane coordinate z. Therefore, we have selected a sequence of 5 reasonable
binding sites and optimized the ion positions and side chain configurations with Rosetta 3 before
evaluating the PDLD binding energies. Figures 5.1 and 5.2 show the selected binding sites for
C1C2 and GtACR1, respectively, as well as residues involved in notable mutations.
Inaddition,duetotheuncertaintyandsensitivityoffindingthebindingbarrierofanasymmetric
channel, we assume the effective rate-limiting binding energy may be a general linear combination
of the calculated binding energies,
∆∆ G
‡
bind,µ
(Cl
− →Na
+
)=
X
i

c
i,Cl
− ∆∆ G
i
bind,µ
(Cl
− )+c
i,Na
+∆∆ G
i
bind,µ
(Na
+
)

, (5.12)
where the coefficients c
i,X
are optimized by linear regression on (5.11). We perform the linear
regression using Lasso regression with the L1 penalty strength optimized through leave-one-out
cross-validation to prevent overfitting the coefficients.
5.4 Results
ThepredictedreversalpotentialsshiftsforC1C2areshowninFigure5.3,withthemodelcoefficients
in Figure 5.4. This model results in a correlation coefficient R=0.576. While many mutations are
predicted within 5 mV, the model has some notable outliers. The mutations with the largest four
45
prediction errors are N297Q (16.5 mV), E136N (16.0 mV), S102N (13.9 mV), E140S (12.7 mV),
V156K (11.7 mV), and V146R (10.9 mV). A closer examination reveals that the reversal potential
shiftislessaccurateformutationsthathaveimportantstabilizationeffectsonneighboringresidues
within5
˚A. Themutationswherethepredictedvaluesareinbetteragreementwiththeexperimental
values with do not have a nearby residue to stabilize them electrostatically. For example, E129S
mutates Glu-129, which was not stabilized by any nearby basic residues in the first place. In
addition, in Q95K, the Gln-95 mutation to a basic residue like Lys is better stabilized by the
nearby Glu-140 and Glu-136 residues.
In contrast, the mutations with a large reversal potential perdiction error originally had a
significant stabilization effect. In the E136N and E140S mutation, the position of the residue
Lys-132 was originally held steady by the acidic residue Glu-136. Furthermore, the S102N and
N297Q point mutations both affect the stable interaction between Ser-102 and Asn-297. Finally,
theV156KandV146Rmutationswerebothoriginallystabilizedthroughhydrophobicinteractions,
alongwithTyr-148,andarestronglydestabilizedbythesurroundingArg-159andLys-154residues.
The residues involved in these mutations are illustrated in Figure 5.1(b).
The predictions of the model for GtACR1 are shown in Figure 5.5, with the coefficients shown
in Figure 5.6. This model has a stronger correlation coefficient of R = 0.651. However, the L1
penalty results in a dependence on the anion binding energy only at two binding sites. In this
case, the largest prediction result from the double mutations: Q46A-K188A (22.0 mV), R53Q-
K188A (14.9 mV), and K188A-R259A (14.8 mV). Figure 5.2(b) shows these mutations and their
neighboring residues in GtACR1. The K188A mutation, which on its own also has a large error,
Lys-188 originally stabilizes Glu-191, making this mutation have a highly destabilizing effect. The
errors of these three double mutations appear highly related to the mutation of Lys-188 to a
smaller residue such as Ala. The position of Lys-188 is critical to the “aperture” of the channel,
46
so the volume-reducing effect of this mutation may be underestimated by the binding energy. The
R53Q mutation on its own is overall stabilizing, since Arg-53 is surrounded by various hydrophobic
residues, Trp-246, Val-57 and Phe-49. Similarly, the R259A mutation on its own results in a more
favorable hydrophobic interaction with Phe-17 and is predicted relatively accurately. Nevertheless,
the R53Q-K188A and K188A-R259A double mutation still result in a large error.
5.5 Conclusion
The cationic channelrhodopsin C1C2 chimera is non-selective and allows for the transport of H
+
,
Na
+
, K
+
, and Ca
2+
ions. Through a selection of mutations, this channel was engineered for the
selective transport of Cl
− ions and hence an extensive shift in its reversal potential [219]. Con-
versely, theanionicchannelrhodopsinwasengineeredintheoppositedirectiontoacationicchannel
through selected mutations [214, 221]. Systematic computational approaches for the behavior of
ion channels, such as conductance and reversal potential, under varying conditions are not, to our
knowledge, developed to a significant degree. We have attempted to make headway for these ap-
proaches by developing a model based on a linearization of the GHK equation to predict reversal
potential shifts from key binding energies in ion channels. By performing a regression scheme
that avoids overfitting, our predictions correlate with experimentally measured reverasal potential
shifts in both C1C2 (R = 0.57) and GtACR1 (R = 0.65). While these predictions are robust, our
models are currently parametric and require prior data to fit to predict mutants for a particular
channel. Furthermore, we found instances of mutations whose predictions deviated strongly from
their experimental measurements. We aim to address these limitations in future work.
The reversal potential of an ion channel is an equilibrium property that depends only on exper-
imentalconditions(ionicconcentrationsandexternalappliedpotential)thatarestraightforwardto
control. The conductance of an ion channel is another property that is important to characterize.
47
However, itsmeasuredvaluehasastrongdependenceonthespecificexperimentalconditions. Ulti-
mately, a reliable, non-parametric model of the properties of ion channel mutants will is necessary
to enhance the study and engineering of ion channels.
48
a b
E136N
E140
E129
N297Q
L101
S102N
Y148 K154
V146R
V156K
R159
Figure 5.1: Binding sites used to evaluate ionic binding energies in C1C2 channelrhodopsin, de-
picted using Na
+
ions in purple. (a) Location of the selected binding sites in C1C2 (PDB ID
7E6X), showing the location of the retinal and the TM domains guiding the ion. (b) Close-up view
of notable mutations along the channel and key neighboring residues.
49
a b
R53Q
V57
W246
I243
F49
Q46A
R192A
K188A
L252
T248 E191
R259A
F178
Figure 5.2: Binding sites used to evaluate ionic binding energies in GtACR1 anionic channel-
rhodopsin, depicted using Cl
− ions in green. (a) Location of the selected binding sites in C1C2
(PDB ID 7E6X), showing the location of the retinal and the TM domains guiding the ion. (b)
Close-up view of notable mutations along the channel.
50
− 20 − 15 − 10 − 5 0
GHK Δ V
rev
(mV)
− 25
− 20
− 15
− 10
− 5
0
5
Experimental Δ V
rev
(mV)
WT
N82R
K88R
Q95K
T98S
S102N
Y109F
E129S
E136S
E136R
E136N
H139K
E140S
E140K
F141K
D142K
D142N
E143K
V146R
N153R
V156K
E162S
H173R
L180D
V281K
Y282K
T285R T285D
T285N
N297S
N297Q
R307H
H311D
I314D
L315D
H317N
H317D
R =0.57604
GHK Reversal Potential - Linear ΔΔ G
‡
bind
- PDLD-S/LRA/β Figure 5.3: Predicted GHK reversal potential shifts of C1C2 from the regression model, correlated
withthemeasuredpotentials. Thisisacationicchannelwithmutationspromotingananionicshift.
51
1 2 3 4 5
Binding Site
− 0.06
− 0.04
− 0.02
0.00
0.02
0.04
0.06
c
i
Linearized GHK - Linear ΔΔ G
‡
bind
coefficients
Ion
Na
Cl
Figure 5.4: Optimal coefficients of ∆∆ G
‡
bind,µ
in Eq. (12) for C1C2 in the linearized GHK model
Eq. (11).
52
− 5 0 5 10 15 20 25 30
GHK Δ V
rev
(mV)
0
10
20
30
40
Experimental Δ V
rev
(mV)
WT
K24A
K33A
K33E
R53Q
K56A
R83Q
K88A
K116A
K188A
K188E
R192A
R192E
K194A
K256A
R259A
Q46A K188A
K188A R259A
K188A R192A
R53Q K188A
R =0.65127
GHK Reversal Potential - Linear ΔΔ G
‡
bind
- PDLD-S/LRA/β Figure 5.5: Predicted GHK reversal potential shifts from WT GtACR1 correlated with the mea-
sured potentials. This is an anionic channel with mutations promoting a cationic shift.
53
1 2 3 4 5
Binding Site
− 0.05
0.00
0.05
0.10
0.15
c
i
Linearized GHK - Linear ΔΔ G
‡
bind
coefficients
Ion
Na
Cl
Figure 5.6: Optimal coefficients of ∆∆ G
‡
bind,µ
for GtACR1.
54
Chapter 6
Soluble Proteins
6.1 Introduction
Water-soluble globular proteins, or simply soluble proteins, are the most-studied group of proteins.
For many hundreds of them, their spontaneous self-organization is known; for many thousands,
their three-dimensional atomic structures are solved. If mutants and various functional states are
taken into account, these numbers are increased many-fold [222, 223]. The present work analyses
aspects of soluble proteins with enzymatic mechanism roles: tyrosine kinase and orotidine 5’-
phosphatedecarboxylase(ODCase). Enzymicreactionsplayacriticalimportantroleincontrolling
and performing most life processes [26, 76]. Thus, understanding how enzyme work and interact
with their environment are key to fundamental questions in biology. Furthermore, the design of
drugs that modify the functions of specific enzymes is central to the study of pharmaceutics.
Givenacompoundthatonewouldliketobringtomarketasmedicine,manyyearsoftheoretical
and clinical steps are necessary to answer effectively two questions: Does the drug accomplish its
intended purpose, and does it do so with as few side effects as possible? Major progress to the
first question can be made at pre-clinical stages with carefully-designed computational studies. As
emphasized in previous chapters, the electrostatic interactions between the drug and its target are
the key influence to its binding and catalytic role. The methods we have previously introduced
55
with this view in mind, protein diple-Langevin dipole (PDLD) and empirical valence bond (EVB),
are thus desirable tools of choice to understand if and when a drug works. The second question is
mainly in the purview of pharmaceutics, particularly when we wish to understand the toxicity and
metabolic pathways of the drug. Nevertheless, it includes the important theoretical study of the
compound’s effects on a protein it was not intended for. That is, for the compound to be suitable
medicine, its function should not simply be potent enough for its intended target, but should also
be selective for it [224–226].
One can attempt to take the converse approach to pharmaceutics: given that we want a po-
tent and selective drug for a particular, what is a suitable molecular structure for the drug? A
data-driven answer to this question is the approach of drug discovery, which has received strong
attention and research effort from machine learning practitioners [227–229]. While not a complete
replacement for designing drugs from fundamentals, a sufficiently advanced generative drug discov-
ery model could have an analogous effect as that which the advent of GPT-4 has had on technical
and creative writing [230].
InChapter7,wetakeacovalentinhibitor,adrugthatstopsthefunctionofitstargetirreverisibly
through covalent bonding, as a case study for evaluating drug selectivity. Tyrosine kinases (TKs)
are involved in important signal cascades, and their malfunction can result in cancer. Covalent
inhibitors can be highly potent, making it all the more important to ensure they are selective for
their intended TK. The electrostatic environment of the active site of the covalent bond influences
the inhibition rate, the central subject of this study.
In the first place, the question of how enzymes can catalyze reactions is as old as the study of
enzymesthemselves. Nevertheless,competingviewsabouttheenergymechanismsinvolvedremain.
The ODCase enzyme has been an important case study in the understanding of the catalytic
power of enzymes [1, 231, 232]. ODCase has one of the largest known catalytic effects, catalyzing
56
a decarboxylation reaction in the ring of its substrate, orotidine 5’-monophosphate (OMP), by
bringing down the activation barrier by 23-24 kcal/mol from the same reaction in water. Many
proposals have attempted to explain the origin of this large catalytic power, and can broadly
be grouped by whether they result in reactant state destabilization (RSD) or in transition state
stabilization (TSS). In the former case, the reaction proceeds because the decarboxylation reaction
begins with a reactant state at a destabilized free energy after the binding of the ligand, while in
the latter case the reaction proceeds due to a favorable environment for the transition state. We
present an investigation and analysis of the active site of ODCase in Chapter 8, which has yielded
strong support for the TTS proposal due to a preorganized electrostatic environment around the
ligand, and that recent RSD proposals do not appear to be self-consistent.
57
Chapter 7
Modeling the Selective Covalent Inhibition of Tyrosine Kinases
Abstract
Tyrosinekinaseenzymesactivatenumerousproteinsviasignaltransductioncascades. Thedysfunc-
tion of these enzymes disrupts these cascades and causes various illnesses. Thus, tyrosine kinases
are often targets of drug development with the intention to inhibit their function. In this study,
we examine the origin of the selectivity of acalabrutinib, a covalent inhibitor, for Bruton’s tyro-
sinekinase(BTK)overinterleukin-2-inducibleT-cellkinases(ITK).Designingpotentandselective
inhibitors is challenging due to the identical ATP-binding pockets of these tyrosine kinases. Our
work examines the reaction step of acalabrutinib in the binding and inhibition process. We find
that a water-assisted mechanism of acalabrutinib’s 2-butynamide reactive group is the most favor-
able reaction mechanism in protein. We use both chemical and binding energetics to develop a
kinetic model of tyrosine kinase activity and inhibition. This novel approach is crucial for studying
covalent inhibitors with a highly exothermic bonding process. Our findings illustrate the relevance
of chemical reaction stages in building selective covalent tyrosine kinase inhibitors.
58
7.1 Introduction
Protein tyrosine kinases (TKs) are enzymes found in the cytoplasm and are responsible for trans-
ducingseveralsignalsinmetazoans[233–235]. TheTECfamily[236,237]isthesecondlargest,and
is composed of five mammalian members: BTK, BMX, ITK, TEC and TXK. Mast cells express
four out of five TEC family kinases: BTK, ITK, TEC, and TXK (also known as RLK) [237–240].
Mast cells are generally recognized as effector cells in allergic reactions and innate immunity. Mast
cells play an important role in adaptive immune responses, according to mounting data. Overall,
these cells have a broad range of effect owing to the astonishing array of mediators, both pro-
and anti-inflammatory, that they release during simulations [241, 242]. The disfunction of tyrosine
kinases, especiallyITKandBTK,leadstovarietyofdiseasesrelatedtothesignalingpathway, such
as certain infectious, autoimmune, and inflammatory diseases [243–245].
Tyrosine kinase inhibitors (TKIs) are drugs aimed at reducing the activity of targeted tyrosine
kinases. Among these inhibitors, covalent inhibitors, whose action includes the formation of a
covalent bond, have an increased biochemical efficiency and duration, thereby allowing the use
of lower doses, which minimizes side effects resulting from off-target activity [246–248]. Covalent
inhibitorsgenerallyincludeanelectrophilicreactivegroupthatwillparticipateinaMichaeladdition
reactionstotargetserine,threonine,orcysteineresiduesinproteintargets[249–253]. Somenotable
non-covalent and covalent tyrosine kinase inhibitors are illustrated in Figure 7.1.
Indeed, covalent inhibitors make up a substantial portion of our arsenal of successful medica-
tions. An example of a common drug acting through an irreversible mechanism is aspirin, which
cancovalentlybondtoaserineresidue[254]ofcyclooxygenases. Therearealso β -lactamantibiotics
such as penicillins, which covalently bond to DD-transpeptidase [255–257]. However, due to safety
issuesandthedifficultyofcreatingcovalentinhibitors,covalentbondinghasbecomealessdesirable
approach for rational drug design [258].
59
Acalabrutinib is a covalent inhibitor currently undergoing clinical trials. It is highly selective
for BTK, much more so than the first-in-class ibrutinib inhibitor. Here, we investigate the origin
of the selectivity of acalabrutinib by proposing and characterizing the reaction path of the covalent
step. We focus on the mechanism of two tyrosine kinases: BTK and ITK (Figure 7.2(a)). The
crystalstructuresfortheseenzymeshavewell-superimposed3Dstructures, includingatthe“DFG-
flip.” In Figure 7.2(b), we observe some key residues that differ between the two enzymes. The
inhibitor reacts by targeting a homologous cysteine residue Cys-481 (BTK)/Cys-442 (ITK), whose
microenvironment is influenced by the i+3 residue Asn-484 (BTK)/ Asp-445 (ITK). While no
direct experimental studies characterize the pKa shift of the targeted cysteine in these TKs, the
pKaoffreecysteinethiolinsolutionis8.6, while, inthepresenceofanearbyAspresidueinEGFR,
computational research suggests a pKa of 11.1 [259]. We therefore infer that the i+3 residue is
likely to play a significant role in the reaction mechanism.
7.2 Kinetic Basis of TKI Selectivity
TKIs mainly compete with ATP for the same binding site and prevent phosphorylation from tak-
ing place by targeting a cysteine residue of the kinase to form a covalent bond and irreversibly
occupy the binding site [260]. An inhibitor first binds to the pocket via noncovalent interactions,
bringing its reactive group close to the cysteine nucleophile. Following noncovalent binding, the
inhibitor–enzyme complex is formed by covalent bond formation. The inhibition process competes
60
with the phosphorylation catalyzed by tyrosine kinases that are quantified using Michaelis–Menten
kinetics [261]. The entire process is depicted by the scheme
E+I
k
1
⇌ k
− 1
E· I
k
inact
−−−→ EI (7.1a)
E+S
ks
⇌ k
− s
E· S
ks,cat
−−−→ E+P, (7.1b)
where K
i
=
k
− 1
k
1
is the noncovalent binding affinity between the enzyme (E) and the inhibitor (I),
k
inact
measures the reaction rate of the inhibitor with the enzyme, and K
m
=
k
− s
+ks,cat
ks
is the
Michaelis constant for ATP as the native substrate (S), which binds to the free enzyme and forms
the catalytic phosphorilation product (P). For simplicity, we model the phosphorylation catalyzed
by tyrosine kinases with Michaelis-Menten kinetics.
There are two ways to measure the potency of an inhibitor in an experiment: one can measure
its IC50 (concentration needed to inhibit 50% of an enzyme) or its inactivation efficiency k
eff
=
k
inact
/K
i
, which is an effective second-order rate constant for the inhibition. The selectivity of an
inhibitor is the quantified as the fraction of its potency for a target kinase over its potency for
another off-targetkinase, where potencyis quantifiedinversely toIC50 orproportionallyto k
eff
. In
general, the measurement of IC50 is a convenient way to assess the inhibitor’s potency. However,
under steady-state conditions, it can be used to determine K
i
using the Cheng–Prusoff equation
[262] and the substrate concentration.
Nevertheless, a direct measurement of k
eff
is preferable as it is intrinsic to the inhibitor–enzyme
reactionanddoesnotdependonthesubstrate. Awaytoobtainitisbyvaryingtheinitialinhibitor
61
concentration within a range of small values and measure the asymptotic effective rate constant
k
obs
of product formation. In the limit of small initial concentration,
dk
obs
d[I]
0
≈ k
eff
1+[S]/K
m
. (7.2)
Hence k
eff
can be obtained by linear regression between k
obs
and [I]
0
.
The problem is that, in some cases, it is hard to directly measure the parameters of molecular
origin related to IC50 and k
eff
. Nevertheless, the selectivity of acalabrutinib as measured by IC50
has been found to be as much as 8000 for BTK relative to ITK, in contrast to 117 for ibrutinib.
A similar difference is found when selectivity is measured by the inactivation efficiency k
eff
of a
kinetic assay (Table 7.1) [263, 264].
Acalabrutinib
System IC50 (nM) k
inact
(kcal/mol) k
inact
/K
i
(M
− 1
s
− 1
)
BTK (Asn) 2.5 20.5 3.0× 10
4
ITK (Asp) >20,000 - 7
Ibrutinib
System IC50 (nM) k
inact
(kcal/mol) k
inact
/K
i
(M
− 1
s
− 1
)
BTK (Asn) 0.47 19.6 1.0× 10
6
ITK (Asp) 55 - 2.8× 10
3
Table 7.1: Comparison of experimentally measured inhibition potency of Acalabrutinib and Ibru-
tinib with BTK and ITK [265, 266]. The i+3 residues from the targeted cysteine for BTK and
ITK are Asn and Asp, respectively.
7.3 Methods
7.3.1 Computational Study Preparation
Our study simulated the inhibition process using the crystal structures of BTK (PDB ID 6J6M)
[267]andITK(PDBID4HCV)[268]asinitialstructures. Theywerechosenbecauseoftheirsimilar
superimposed conformations, particularly in the activation loop known as the “DFG-flip,” which
62
is known to affect the measurement of IC50 and selectivity. We obtained the three-dimensional
struct ure of acalabrutinib from PubChem, superimposed it to the covalently bound inhibitors in
the active sites of both crystal structures, and validated the docking poses using AutoDock Vina
[184]. Werelaxedeachsystemfor40nsinGROMACS(2021)[269]usingtheAmberforcefieldand
selectedappropriateinitialconfigurationsfromthetrajectoryforthedownstreamEVBcalculation.
The force field parameters for the ligand atoms were determined from the generalized Amber force
field (GAFF) using AmberTools21 [270].
7.3.2 Ab Initio calculations
We used the 2-butynamide group truncated with methane caps on the nitrogen to model the re-
active group of the inhibitor. All ab initio calculations, including geometry optimization, energy
evaluation, and charge calculations, were performed with Gaussian16 [271] using density functional
theory (DFT) at the M06-2X/6-311+G(d,p) level of theory [272–275] and the CPCM polarizable
continuum model [276] for implicit solvent. This DFT method was found to yield reaction exother-
micities within a few kcal/mol of CCSD(T) in a systematic ab initio study of Michael acceptor
reactions, which includes the 2-butynamide reaction with cysteine [277]. The calculated barriers
for the reference reactions were used for calibrating the EVB Hamiltonian to model the reaction
between acalabrutinib and BTK/ITK.
7.3.3 EVB
The EVB method is a quantum mechanics/molecular mechanics (QM/MM) approach where the
chemical reactions are described by mixing the relevant diabatic states, allowing efficient sampling
of the chemical reaction process (see Chapter 2). An example of the successful application of the
EVBmethodinthekineticsofirreversibleinhibitorswasinacomputationalstudyoftheinhibition
63
of monoamine oxidases, which are drug targets for the treatment of neurodegenerative disorders
[278]. Our EVB calculations were performed using the Q6 simulation package [279]. In these
simulations, the region comprising the few atoms that directly participate in the chemical reaction
is referred to as region 1, which includes the acalabrutinib reactive group and cysteine (Cys-481 in
BTK and Cys-442 in ITK) as well as a catalytic water. The rest of the enzyme-solvent system is
referredtoasregion2. FortheschemepresentedinFigure7.4,theAsn-484inBTKandAsp-445in
ITK are included in region 2. These residues are expected to influence the covalent bond formation
between acalabrutinib and kinases through electrostatic interactions.
The charges of region 1 atoms were taken as the corresponding ESP charges obtained from
Gaussian16. The substrate charges and the reacting residues were subsequently converted into
RESP charges in the Antechamber program of AmberTools21. The initial position of sulfur in
cysteine was used to set the central simulation sphere. The system was immersed in a water sphere
with a diameter of 20
˚A, where the water molecules were described by the TIP3P model [280] and
subjected to the SCAAS boundary conditions [281], where the long-range effects were treated by
the local reaction field [195]. At the first stage of each reaction step, each system was optimized
to a local energy minimum, with all heavy atoms initially restrained by K =20
˚A
2
kcalmol
− 1
con-
straint, and then equilibrated by progressively relaxing atomic position restraints and raising the
temperature from 5 to 300 K for 1 ns. Finally, we performed production runs of free-energy per-
turbation/umbrella sampling (FEP/US) on the relaxed structure. For each reaction, we performed
5 replicas of umbrella sampling with 100 frames and 5 ps of sampling per frame.
7.3.4 Kinetics Simulation of Inhibitor Selectivity
Atthispoint,wemustdealwiththetaskofconnectingtheestimatedandobservedkinetics. Wecan
expect that IC50 and K
i
are connected in the situation of reversible inhibitor binding. However,
64
we expect that the reaction of an irreversible inhibitor will be highly exothermic. As a result,
it is ideal to use the calculated reaction free-energy profile and kinetic simulations to replicate
the experimental observable, namely, IC50 and its time-dependent observable (IC50(t)) as well as
the effective second-order rate constant, k
eff
. Initially, we used the traditional kinetic scheme of
Eq. (7.1) to generate the trend of the experimentally observed kinetics. The kinetics of BTK was
simulated using the same initial conditions as the assay used by Liclican in [263] ([S]
0
= 300µ M
and [E]
0
= 5nM). In addition, the initial conditions for ITK were taken as [S]
0
= 100µ M and
[E]
0
= 5nM. (Additional assay-dependent parameters are listed in Tables S1 and S2 of [282].)
While the above simulations are a useful baseline, our true goal is to use the computed binding
and catalytic profiles to model the corresponding kinetics and compare them to the experimental
results. Thus, we used a multi-step kinetic simulation to model the enzyme-inhibitor reaction,
where each step corresponds to a step in the reaction mechanism. In particular, we model the
enzyme-inhibitor reaction using a three-step mechanism
E+I
k
1
⇌ k
− 1
E· I
∗ 1
k
2
⇌ k
− 2
E· I
∗ 2
k
inact
−−−→ EI, (7.3)
where E· I
∗ 1
and E· I
∗ 2
are the chemical intermediates of the enzyme–inhibitor complex. The equi-
librium constant K
i
= k
− 1
/k
1
was determined from the PDLD/S-LRA/β binding energy ∆ G
bind
of the inhibitor [75], where K
i
/(1M)=e
∆ G
bind
/k
B
T
and determined k
− 1
using an estimated disso-
ciation barrier of 12 kcal/mol. Finally, the rates k
2
and k
inact
were determined from the barrier in
EVB profiles using the Arrhenius relation.
65
7.4 Results
7.4.1 Ab initio calculations of reference reactions
We investigated the free energy profiles of a variety of candidate reaction mechanisms in solvent
that were likely to be included in the covalent binding action of acalabrutinib in BTK/ITK. Our
results are summarized in Figure 7.3, which shows the reaction energies and barriers for various
mechanisms. Weinvestigatedtwoclassesofreactionpathways: either(a)theAspresidueisdirectly
involvedinprotontransfer, or(b)theAsp/Asnresidueispassivelyinvolved, andnotpartofregion
1.
WeobservedthatdirectPT-NAandtautomerizationhaveverylargeenergybarriers,andhence
areunlikelytooccur. Thus,wefocusedontheremainingmechanismsteps: solvent-assistedPT-NA,
solvent-assisted tautomerization, and Asp-mediated PT and NA.
7.4.2 EVB Reaction Mechanism
We investigated several distinct reaction pathways for acalabrutinib in both BTK and ITK before
settlingonthecovalentinhibitionpathwayswiththelowestfree-energybarriersineachprotein. (A
comprehensive list of attempted schemes can be found in the Supplementary Information of [282].)
ThesereactionpathsareshowninFigure7.4forbothBTK(a)andITK(b). Wefoundthatthefree-
energy barriers for both BTK and ITK decrease when a water molecule engages in the processes.
The crystal structures of both BTK and ITK, which have different docked inhibitors, suggest that
no water molecule is present near the cysteine residue. However, a water molecule is present near
the cysteine residue througout the equilibration of the enzyme with docked acalabrutinib, and in
general the free energy of inserting a water molecule is rather small. Therefore, a water-mediated
reaction path is likely to be the best mechanism for both proteins.
66
The free energy profiles for these reaction paths are depicted in Figure 7.5. The PT-NA step
was found to be the rate-limiting step for BTK, with a barrier of 19 kcal/mol (k
cat
= 0.06s
− 1
),
which is close to the experimentally reported barrier of 20.5 kcal/mol (k
cat
= 0.007s
− 1
). The
rate-limiting step for acalabrutinib in ITK was also found to be the PT-NA step (∆ G
‡
= 23
kcal/mol, k
cat
= 0.0001s
− 1
). However, it is the tautomerization step in both cases that is highly
exothermicandirreversible. Thus, itwarrantsdetailedkineticsimulationstoexamineapotentially
morecomplicatedrelationshipbetweentheindividualreactionstepsandtheobservedexperimental
kinetic parameters.
7.4.3 Kinetic Simulation of Inhibitor Selectivity
Weobtainedbindingaffinities∆ G
bind
of-6.8kcal/molforBTKand-4.4kcal/molforITKfromour
PDLD/S-LRA/β calculations. Using the binding affinities and the energy profiles, we calculated
the rates for the steps in the enzyme-inhibitor reaction (7.3) and simulated the kinetics over time
for competitive inhibition.
Thesimulated time-dependentIC50curvesareshowninFigure7.6forbothBTKandITK.We
see that the IC50(t) estimated from the EVB kinetics is approximately 80–100 nM within an hour
timescale(4,000s)andreducesbyanorderofmagnitude(10nM)atmuchlongertimes(40,000s≈ 11 h). ITK, on the other hand, requires significantly longer times for inhibition with acalabrutinib
compared to BTK. Our simulations using the EVB profile clearly show that the inhibition of ITK
will not take place within a reasonable amount of time. Even with a concentration of acalabrutinib
around 1µM, ITK hardly reaches 50% inhibition over the timescale of multiple days. Interpreted
fromapharmacokineticview, adosageofacalabrutinibthatiseffectiveforinhibitingBTKwillnot
inhibitITKwithinmetabolicallyrelevanttime,consistentwithpre-clinicalstudiesofacalabrutinib,
which found no inhibition of ITK signaling [283, 284].
67
We also numerically evaluated the asymptotic pseudo-first-order rate constant ( k
calc
) from the
calculated product formation velocity at extended times. We assumed an asymptotically exponen-
tially decay of the velocity
v =v
i
e
− k
calc
t
, (7.4)
where v
i
is the initial velocity of product formation, which depends on the initial inhibitor con-
centration [I]
0
. The k
calc
values obtained for BTK and ITK are shown in Figure 7.6. Within the
simulated ranges of inhibitor concentration, the rate constant has linear behavior with respect to
[I]
0
, from which we can extract from the slope the simulated value of k
eff
=k
inact
/K
i
. (Section 7.2)
Our simulations for BTK yielded (k
eff
)
sim
= 5.5× 10
− 6
s
− 1
nM
− 1
. Note that this is fairly close
to the estimated k
eff
from approximating k
inact
with the rate-limiting chemical step (k
inact
≈ k
2
),
which yields (k
eff
)
sim
= 5.7× 10
− 6
s
− 1
nM
− 1
. However, it is about an order of magnitude smaller
than the experimentally reported 2.4× 10
− 4
s
− 1
nM
− 1
. Similarly, the simulation of ITK results
in a substantially smaller (k
eff
)
sim
= 1.8× 10
− 10
s
− 1
nM
− 1
, again smaller than the experimentally
reported (k
eff
)
sim
=7.0× 10
− 9
s
− 1
nM
− 1
. Nevertheless, the ratio of our simulated efficiencies yields
a selectivity of 30,000 for BTK over ITK, which is consistent experimental estimates.
7.5 Conclusion
To a large extent, the high selectivity of acalabrutinib appears to be linked to the i+3 cysteine
residue (Asn-484 in BTK and Asp-445 in ITK), [285] which increases the pKa of the targeted cys-
teineresidueforcovalentbindingbyroughly1pKaunitinITKcomparedtoBTK.Thepresenceof
anegativelychargedAsp-445destabilizesthetransitionstateofthereactionwiththe2-butynamide
group, which is electronegative and stabilized by resonance during the reaction, making this path-
way more plausible.
68
According to our ab initio and EVB calculations, the 2-butynamide group of acalabrutinib is
more amenable to solvent-assisted-type reactions than the acrylamide group of ibrutinib, which
was shown in previous QM/MM studies. Our results provide quantitative information on the en-
ergetics of the irreversible inhibition mechanism of acalabrutinib, highlighting the utility of our
computational approach in the design of potent and selective inhibitors of additional tyrosine ki-
nases. Our simulated kinetics using separate EVB and PDLD/S-LRA/β computations for each
kinase do not entirely duplicate the experimental kinetics, but the selectivity obtained is consistent
with the corresponding data. As a result, we anticipate that our method will be more successful
at predicting the ratios of the expected k
eff
, i.e. the selectivity, for additional covalent inhibitor
enzyme complexes than the values themselves.
Inconclusion,welookedintohowdrugselectivityisaffectedbytheindividualchemicalreaction
stepsinvolvedinthecovalentinhibitionoftyrosinekinases. Currentdrugdesignwisdompostulates
that the chemical reaction stage is largely determined by the nature of the reactive groups involved
and the targeted residues. In contrast, we demonstrate here that the local protein environment
around the binding site can have a major effect on the inhibition reaction rate. This is a primary
rationale for the high selectivity of currently available BTK inhibitors. Our results imply that
a thorough analysis of the chemical process is necessary for the rational design of powerful and
selective inhibitors. As the technology for developing inhibitors and our understanding of the
inhibitionprocessprogress,weanticipatethatcovalentinhibitorswillplayanincreasinglyimportant
role in medicinal treatments.
69
Fenebrutinib Vecabrutinib
a
b
Acalabrutinib Ibrutinib Zanubrutinib
Figure7.1: Twodifferentsetsoftyrosinekinaseinhibitors. (a)Non-covalentinhibitorsFenebrutinib
and Vecabrutinib [286]. (b) Covalent inhibitors Ibrutinib, Zanubrutinib and Acalabrutnib [287,
288]. The Michael acceptor group for the first two is acrylamide, while the group for the last one
is 2-butynamide.
70
Figure 7.2: (a) Superimposed BTK (yellow) and ITK (purple) structures showing the docked
inhibitor. (b) Close-up view of the docked acalabrutinib and nearby key residues in the active site
that differ between BTK and ITK.
71
Proton Transfer-
Nucleophilic Attack
PT
ΔG
‡
=19.8
ΔG
‡
=8.1
ΔG
‡
=24
NA
PT2
160°Bend
ΔE=6.5
Tautomerization
SolventAssisted
Direct
a
-20
0
20
40
ReactionCoordinate
Energy (kcal/mol)
Proton Transfer-
Nucleophilic Attack
PT
ΔG
‡
=27
ΔG
‡
=21
ΔG
‡
=8.1
ΔG
‡
=24
Tautomerization
NA
160°Bend
ΔE=6.5
SolventAssisted
Direct
b
-20
0
20
40
ReactionCoordinate
Energy (kcal/mol)
Figure7.3: Ab initio energyprofilesfor(a)thereactionwithanactiveaspartate-mediatedstepand
(b)apassiveasparagineoraspartateinthePT-NAstep. Onlythesolvent-assistedPT-NAandPT2
steps are shown in the aspartate-mediated pathway. Direct and solvent-assisted tautomerizations
areshowninbothprofiles. Inpanel(a),theperturbationofthelineargeometryoftheproductstate
of the PT-NA (PT2) step to the slightly bent reactant state of solvent-assisted tautomerization is
also indicated.
72
Figure 7.4: Scheme of the most likely catalytic inhibition mechanism scheme for (a) BTK and (b)
ITK. The mechanisms are identical except for the electrostatic interaction with the i+3 residue
from the targeted cysteine.
73
Proton Transfer-
Nucleophilic Attack Tautomerization
Water
BTK
ITK
-40
-20
0
20
Reaction Coordinate
Energy (kcal/mol)
Figure 7.5: The EVB energy profiles for the inhibitor binding reaction in water, BTK and ITK. In
the rate-limiting PT-NA step, BTK catalyzes the inhibition, while ITK suppresses it.
74
0.1 10
0
10
1
10
2
0.0
0.2
0.4
0.6
0.8
1.0
[I]
0
(nM)
Inhibition
a
Time (s)
0.1  10
3
1.0  10
3
2.0  10
3
4.0  10
3
10.0  10
3
14.0  10
3
20.0  10
3
30.0  10
3
40.0  10
3
50 100 500 1000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
[I]
0
(nM)
Inhibition
b
Time (s)
0.60  10
6
1.00  10
6
1.50  10
6
2.00  10
6
2.50  10
6
3.00  10
6
3.50  10
6
4.00  10
6
Figure 7.6: Simulated inhibition progress at different initial acalabrutinib concentrations and time
windows for both (a) BTK and (b) ITK. The simulated progress suggests that while BTK can be
half-inhibited with a dosage as little as 100 nM within an hour, inhibition of ITK does not occur
within a meaningful amount of time even at larger doses.
75
0 20 40 60 80
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
[I] (nM)
k
calc
 10
3
(s
-1
)
a
0 500 1000 1500 2000 2500
0.00
0.05
0.10
0.15
0.20
[I] (nM)
k
calc
 10
6
(s
-1
)
b
Figure 7.7: Simulated k
calc
vs inhibitor concentration for (a) BTK and (b) ITK from kinetic
simulations using the calculated EVB free energy profiles.
76
Chapter 8
Examining Catalytic Proposals through Orotidine 5’-Phosphate
Decarboxylase
Abstract
Orotidine 5’-phosphate decarboxylase (ODCase), an enzyme that decarboxylates orotidine mono-
phosphate(OMP),hasaverysignificant23kcal/molcatalyticeffectonthesamereactioninwater.
Previous analyses and critical tests have shown that the binding energy (the strain imposed by
a link to a phosphate group) does not contribute to catalysis. In this work, we use quantitative
empirical valence bond calculations to reproduce the catalytic action of ODCase and the impact of
the phosphate side chain in the ligand. The phosphate’s action contributes to the reorganization
energy shift, and does not participate in a Circe effect mechanism nor an induced fit mechanism.
Wealsodemonstratethatelectrostatictransitionstatestabilitycausestheoverallcatalyticimpact,
reflecting the lower reorganization energy for the reaction energy in enzyme than in water. We also
discuss the induced fit proposal’s shortcomings, such as its failure to explain the catalytic effect’s
genesis.
77
8.1 Introduction
The origin of the catalytic power of enzymes has a very long history, with the validity of many
proposals having been explored with both computer simulations and experimental studies [1, 231,
232, 289–294]. However, there remains controversial views on the factors contributing to enzyme
catalysis. Catalytic proposals are generally grouped into two kinds: ground state destabilizing
(GSD) or transition state stabilizing (TSS). While Pauling originally offered a solution to the
enzyme catalysis problem involving the reduction of the transition state energy [294], he was not
abletodescribehowthiswasdone. AlmostallsubsequentproposalsinvolvedGSDfactors,including
the strain proposal, the entropic proposal, the desolvation proposal, the Circe proposal and more.
To examine the controversial views of the origin of the catalytic power of enzymes, it is worth
usingaparticularcasewherethecatalyticeffectisknowntobelarge,makingithardtoaccountfor
with incorrect proposals. We therefore examine the case of orotidine 5’-phosphate decarboxylase
[295]. Thisenzymehasoneofthelargestknowncatalyticeffectsofabouta23-24kcal/molreduction
in the activation barrier of the same reaction in water. The substrate of this enzyme, orotidine
monophosphate (OMP), has negatively charged orotidine ring with a carboxylate group that is
converted to CO
2
, while the negatively charged ring accepts a proton from a Lys residue. The
catalytic process is illustrated in Figure 8.1. An early proposal suggested that the active site
behaves like an “oil drop” that destabilizes the charged reactant state in order to reduce the
activation barrier [296], though this strongly contrasted with Warshel’s prediction of a highly polar
active site [297], and indeed the latter was found to be the case when the ODCase structure was
solved [298, 299].
The structure contains two aspartate groups (Asp-70 and Asp-75B) in the vicinity of the sub-
strate and the Lys-72 proton donor (Figure 8.2). A different proposal [299] taking the solved
structure into account took the view that the reaction is still an RSD reaction due to the repulsion
78
between the ionized Asp-70 and the carboxylate. However, this overlooks that the pKa of Asp
70 would be significantly shifted in this interaction, in which case it would accept a proton and
the active site would lose the RSD property. In contrast, Warshel’s calculations of the reaction
supported a scenario where the Asp and Lys residues were preorganized to support the transition
state. That is, the reduced reorganization energy of the active site effectively reduces the energy
of the transition state, resulting in a TTS scenario.
Nevertheless, while the explicit idea that ODCase uses an RSD mechanism has declined, two
major RSD-based proposals remain: the induced fit effect [300, 301] and the Circe effect [231,
299]. Here, we discuss these proposals in detail and carefully consider their ability to explain the
catalytic power of ODCase. In addition, we provide calculations using the empirical valence bond
(EVB) method to reproduce the experimentally observed energetics. Overall, we present strong
support for the TSS mechanism by addressing inconsistencies in RSD proposals and presenting
computational simulations of the catalysis that demonstrate a TSS mechanism.
8.2 Examination of RSD Proposals
8.2.1 The Circe Effect
The Circe proposal originally posed by Jencks works by a RSD mechanism where the binding of
a nonreactive part of the substrate “pulls” the chemical part into the active site. In the case
of ODCase, the phosphate tail presumably pulls the ring and positions the carboxylate into an
unstable position. Quantitatively, the binding energy of the phosphate, which is not chemically
active, allows the chemical part to be subject to a destabilizing environment and thus make the
reaction proceed.
79
AnexperimentbyRichard et. al., [302]whooriginallysupportedtheCirceeffect, setouttotest
thisproposalinasimplebutinsightfulexperiment. (Figure8.3)First, theyremovedthephosphate
tailfromthesubstrateandfoundthatthecatalysisdisappeared. Thiswouldappeartolendsupport
to the Circe effect if it is interpreted as the loss of strain in the substrate making the destabilized
reactant state unfeasible. However, they performed a second experiment that included inorganic
phosphatewhichsurprisinglyshowedthattheenzymewouldcatalyzethereactionagain. Therefore,
only the presence of the phosphate in the binding site, and not its “pull” on the orotidine ring, has
any contribution to the catalysis. This experiment not only directly refutes the Circe effect, but is
also in strong opposition to any plausible RSD mechanism, since in this experiment the reaction
energy barrier is still dramatically reduced from that in water even without the phosphate tail.
The key observations of the experiment are illustrated in Figure 8.4.
8.2.2 Induced fit
Amorerecentproposal[301]takestheviewthatODCasecatalysiscanbeexplainedbytheinduced
fit effect, [300] in which the catalysis can be attributed to a structural change occurring in response
to the substrate binding. The RSD mechanism originates from the enzyme itself, in this proposal.
A schematic of the induced fit effect is shown in Figure 8.5, which postulates the existence of a
hypotheticalbound[E
O
S]intheopenstateoftheenzymewhichiselevatedtoaclosedboundstate
E
C
S. The reaction then proceeds via the transition state (E
C
S)
‡
.
However, the induced fit proposal presents some conceptual issues. First, if the E
O
S state has
a lower energy than E
C
S, then it should be more favorable for the system to remain in the former
state unless there are significant conformational barriers between then. Second, a critical aspect
of this proposal is the implicit assumption that the energy barrier for the reaction in the open
configuration is larger than that in the closed configuration, which is not justified a priori. Finally,
80
system ∆ G
0,EVB
λ ∆ G
‡
HAW
∆ G
‡
EVB
∆ G
‡
obs
water 30.0 352 63.4 40 38.0
ES
′
14.5 250 32.4 24 19.7
ES 6.0 228 23.9 20 15.0
Table 8.1: Calculated estimates of ODCase activation barriers with the corresponding observed
results. All energies are expressed in units of kcal/mol.
the proposal does not provide sufficient explanation for the stabilization of the transition state.
Thisisnecessarybecausetheenormousenergydifferenceof23kcal/molfromtheactivationbarrier
in water cannot be rationalized from binding energy alone. Indeed, the largest observed binding
energies in biochemistry, found in acetylcholinesterase inhibitors, only go up to 18 kcal/mol [303].
The lack of explanatory power in the induced fit proposal, in conjunction with the fact from
the Richard experiment that the phosphate tail does not play a strong in the activation energy
difference from water, compels one to conclude that the catalysis must be promoted by a suitable,
preorganized active site that reduces the transition state energy.
8.3 Simulation of the Catalytic Mechanism of ODCase
We now present an analysis of the reaction of ODCase in enzyme and in solution based on careful
EVB calculations using the three diabatic states shown in Figure 8.1. We used similar force field
parameters as those used in [304] and performed our calculations with the Q6 program [279]. In
addition to the energy barriers obtained from the EVB free energy profile, we also evaluate the
energy barriers predicted using the Hwang-
˚Aqvist-Warshel equation [305]
∆ G
‡
HAW
=
(∆ G
0
+λ )
2
4λ −| H
12
(X
‡
)| +
H
12
(X
0
)
2
∆ G
0
+λ , (8.1)
where ∆ G
0
in the reaction energy, λ is the reorganization energy, H
12
(X
‡
) is the mixing energy at
the transition state, and H
12
(X
0
) is the mixing energy at the reactant state.
81
The results of our calculations are summarized in Table 8.1 and shown in Figure 8.6. We
note that the magnitude of our calculated EVB barriers are consistent with the observed values.
Furthermore, our results reproduce the observed catalytic effect of the phosphate. However, the
energy barriers calculated through Eq. (8.1) have much less satisfactory agreement, reflecting that
the reorganization energies are not symmetric in the forward and backward directions. The re-
organization energies listed in Table 8.1 are evaluated from the actual full diabatic curves. With
the reorganization energies and reaction energies ∆ G
0
, we can analyze the factors that affect the
change in the activation barriers. The largest effect occurs upon moving the substrate from so-
lution to the enzyme-substrate complex (ES). In the solution reaction, ∆ G
0
is very large, and in
this limit ∆∆ G
‡
is approximately ∆∆ G
0
. The reduction of 24 kcal/mol in ∆ G
0
is not due to the
reorganization energy λ along the reaction coordinate. Nevertheless, the reaction still reflects a
reduction in reorganization energy. In moving from state I to state II, the Lys residue moves closer
totheC6atominOMPwhenthereactionoccursinprotein,butstaysatalargerdistanceinwater.
The reduction in the ion-pair distance leads to a significant stabilization effect in the active site,
but not so much in water [306].
8.4 Conclusion
This study focused on the enormous catalytic power of the ODCase enzyme, establishing several
important points about the key factors in enzyme catalysis. We establish that the catalytic effect
cannotbeduetotheCirceeffect,whichpostulatesthatthephosphatebindingenergyholdsthering
in an unstable reactant state configuration [299]. We also show that the reaction rate is sufficiently
accounted for by electrostatic reorganization energy, and not by an induced fit or similar proposal.
Evidence is demonstrated from careful EVB calculations that are consistent with catalytic effects
occurring through a shift in the reorganization energy.
82
A particular emphasis is placed on the effect of the phosphate, which provides very instructive
information. This includes the analysis of the fact that the effect of cutting the bond between the
phosphateandtheringisrestoredbyinorganicphosphate,establishingthatthecatalysiscannotbe
duetotheRSDCirceeffect. Inaddition,ourEVBcalculationsshowthatthedifferencebetweenthe
reaction rates with and without the phosphate is accounted for by the electrostatic reorganization
energy. Our study emphasizes that the key question is how enzyme catalyze their reactions, rather
than assigning labels to qualitative, loosely-defined possibilities. Having an unbiased computer
program that reproduces catalytic effects is the best (and arguably the only) way of assessing the
importance of catalytic effects.
83
N
H
N O
O O
O
H
H
N
H
H
OMP
Lys72
N
H
N O
H
2
N
C O O
H
N
H
N O
H
N
H
H
C O O
7
6
5
4
ASP75B
ASP70
ASP70
ASP75B
ASP75B
ASP70
-
-
+ +
-
-
-
-
-
-
H H

O O

Figure8.1: ReactionmechanismofODCasealongastepwisepathway. Thepresenceoftwocharged
Asp residues is strong evidence that the active site of ODCase is not an oil drop.
84
Asp75B
OMP Asp70
Lys72
Figure 8.2: Active site and substrate of ODCase, shown with Lys-72, which is involved in the
catalytic reaction, along with the Asp-70 and Asp-75B residues that are assumed to destabilize the
carboxylate. Only hydrogens in the chemically active region are explicitly shown.
85
Asp75B
OMP Asp70
Lys72
A B C
Asp75B
OMP
Asp70
Lys72
Asp75B
Asp70
Lys72
OMP
Figure 8.3: Description of the Richard experiment that disproved the Circe RSD effect, showing
(A) the ODCase enzyme-substrate complex, in which the Circe proposal assumes that the binding
of the phosphate tail pushes the substrate to a state with a very large RSD, (B) an illustration of
the experiment with the tail group chopped off, resulting in the catalysis stopping and suggesting
support for the Circe proposal, and (C) an illustration of the experiment with the truncated OMP
but adding inorganic phosphate, which restores the catalysis. This establishes that the catalysis is
not related to the strain between the tail and the reactive part.
86
-10
0
10
20
30
40
ΔG (kcal/mol)
E
0
+S'+P
2-
E
0
+S
E
0
+S
W
‡
ES
(ES)
‡
ES'P
2-
(ES'P
2-
)
‡
ES'
(ES')
‡
39
-9.6
15
14.3
19.7
Figure 8.4: Key experimental information about the catalytic reaction of ODCase. E
O
is the
unbound ODCase. ES is the ODCase with the bound OMP substrate. ES is the ODCase with a
bound OMP where the side chain with the phosphate is removed. ESP
2–
is ES in the presence of
inorganic phosphate. The uncatalyzed reaction in water has a barrier of 39 kcal/mol. The binding
affinityofOMPinODCaseis-9.6kcal/mol,whilethecatalyzedreactionhasachemicalbarrierof15
kcal/mol. The observations of Richard and coworkers [302] show that removing the phosphate tail
increases the barrier of the catalytic reaction to 19.7 kcal/mol. However, the catalysis is recovered
even in the presence of inorganic phosphate with a barrier of 14.3 kcal/mol.
87
ΔG (kcal/mol)
E
O
+S
W
E
C
+S
W
[E
O
S]
Hyp
E
C
S
(E
C
S)
‡
(E
O
S)
‡
(?)
(E
O
+S
W
)
‡
Figure 8.5: Schematic reproduction of the induced fit diagram of [301]. In this proposal, the
substrate binding energy stabilizes the open state E
O
and drives the conformation to the closed
stateforming(E
C
S),whichinturncatalyzesthereactionmovingthesystemto(E
C
S)
‡
. Theenergy
of the complex with the open state is indicated by [E
O
S]
Hyp
. The energy of the transition state
with the open state (E
O
S)
‡
is not indicated in the original diagram and is probably assumed to be
the same as (E
C
S)
‡
.
88
a
b
c
- 200 - 100 0 100 200
0
20
40
60
80
Free energy (kcal/mol)
- 200 - 100 0 100 200 300
0
20
40
60
80
Free energy (kcal/mol)
- 200 - 100 0 100 200
0
20
40
60
80
Free energy (kcal/mol)
Figure8.6: EVBprofilesofthereactionofODCase,whereallenergiesareinkcal/mol. Eachfigure
describes the free energy functionals of the two diabatic states and the adiabatic state obtained
from their mixing ∆ G
EVB
The intersection of the diabatic states gives the diabatic barrier ∆ G
‡
and the maximum of the adiabatic functional gives the actual barrier. Figures (a–c) describe,
respectively, the EVB results for the reaction in water, the reaction of ES
′
, and the reaction of
ES. The calculations evaluated the free energy barrier for the first step (I–II), which provides a
reasonable estimate for the barrier of the concerted path.
89
Chapter 9
Conclusion
In this dissertation, a broad variety of topics were explored, all with the underlying intent to move
forward our understanding of protein structure-function relationships and the role of electrostatic
interactionsinbindingandcatalysis. Thecentralintellectualcontributionsinthisdissertationwere
as follows:
1. We investigated the effect of membrane composition on the catalytic activity of rhomboid
proteaseusingtheempiricalvalencebond(EVB)methodandcapturedproteinconformational
changecouplingusingtherenormalizationmethod. Wediscoveredthattherearenosignificant
differences in catalytic activity between different lipid head groups environments and that
thereisnoacouplingbetweentheconformationalchangetheligandmotion. However,thereis
apotentiallyrichdirectioninstudyingtheoriginofthedrasticallydifferentratesofanalogous
soluble and membrane protease [148].
2. We developed a model to predict the reversal potential shift of cation and anion channel-
rhodopsin mutants using binding energies evaluated with the protein dipole-Langevin dipole
90
(PDLD) Method. We used the Goldman-Hodgkins-Katz (GHK) equation to establish a lin-
earizedmodelbetweenthebindingfreeenergycalculationandthereversalpotential. Compu-
tational methods for evaluating and screening mutation candidates for further experimental
steps will be valuable in the engineering of channelrhodopsins in neural science and medicine.
3. Weproposedandsimulatedthechemicalbasisforthehighselectivityofthecovalentinhibitor
acalabrutinib for BTK over ITK. The active sites of these two kinases primarily differ in
their Asn-485/Asp-445 residue, respectively. We used the EVB method to find the optimal
reactionmechanismforBTKandITK.Ournovelfindinghereisthatthisreactionmechanism
is water-facilitated in the case of acalabrutinib. Kinetic modeling of BTK and ITK activity
basedonourcalculatedreactionenergyprofilesreproducedtheresultsofexperimentalassays
quantifying the selectivity of acalabrutinib [282].
4. Finally, we critically discussed the origin of the catalytic power of enzymes. We performed
EVBcalculationsonODCaseandshowedthatthepreorganizedenvironmentofthisenzymeis
responsibleforitsenhancedcatalyticeffect. ThephosphatedianionofOMPcontributestothe
reducedorganizationenergyanddoesnotparticipateinproposedreactantstatedestabilizing
mechanism [307].
Electrostatics plays an important role in predicting the function of proteins. Soluble and mem-
brane proteins each have their set of challenges, and we have attempted to tackle a small selection
withimplicationsinmedicine,bioengineering,andourfundamentalunderstandingofbiology. There
are many instances of membrane proteases whose activity and structure are not yet characterized.
Systematic computational approaches to the functionality of ion channel mutants still need further
development. Selective inhibitor design has remained challenging, and it is hoped this may be
changed with the advent of generative artificial intelligence. Central aspects of the behavior of
91
enzymes continue to be debated, and more questions may be raised than settled as fundamental
biology research advances. This is just a small part of potential directions for future work, and a
careful computational approach to these problems across many length and time scales is crucial for
making advances in them.
92
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118

Abstract (if available)

Abstract We examine the relationship between structure and functionality in several biological systems using computational modeling. The first study investigates the effect of environmental factors on the activation barriers of intramembrane rhomboid protease. We used the empirical valence bond approach to calculate chemical barriers in various environments and found that the physical environment does not impact chemical catalysis. The second study proposes a computational strategy to predict shifts in the reversal potential of ion channels due to point mutations. We employed the protein dipole-Langevin dipole technique to analyze ion binding affinities and the GHK equation to quantify shifts in the reversal potential, which can serve as an auxiliary tool in engineering channelrhodopsins. The third study examines the selectivity of acalabrutinib, a covalent inhibitor, for Bruton’s tyrosine kinase (BTK) over interleukin-2-inducible T-cell kinases (ITK). We developed a kinetic model of tyrosine kinase activity and inhibition using both chemical and binding energetics. This approach is essential for studying covalent inhibitors with a highly exothermic bonding process. The final study explores the catalytic effect of orotidine 5’-phosphate decarboxylase (ODCase), which catalyzes the decarboxylation of orotidine monophosphate (OMP). We used quantitative empirical valence bond calculations to replicate the catalytic action of ODCase and the impact of the phosphate side chain in the ligand. We demonstrate that the overall catalytic impact results from electrostatic transition state stabilization, indicating the lower reorganization energy for the reaction energy in the enzyme than in water. These findings highlight the limitations of the induced fit hypothesis in explaining the origin of the catalytic effect of ODCase.

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Asset Metadata

Creator Asadi, Mojgan (author)

Core Title Understanding electrostatic effects in the function of biological systems

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2023-08

Publication Date 07/18/2023

Defense Date 07/17/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag binding affinity,channelrhodopsin,decarboxylase,empirical valence bond,energy barrier,enzyme efficiency,enzymes,ion channels,OAI-PMH Harvest,pre-organized electrostatics,reactivity,reorganization energy,rhomboid protease,tyrosine kinase

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Warshel, Arieh (committee chair), Cherezov, Vadim (committee member), Nakano, Aiichiro (committee member), Prezhdo, Oleg (committee member), Takahashi, Susumu (committee member)

Creator Email masadi@usc.edu,mojgan.asadi67@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113281393

Unique identifier UC113281393

Identifier etd-AsadiMojga-12102.pdf (filename)

Legacy Identifier etd-AsadiMojga-12102

Document Type Dissertation

Format theses (aat)

Rights Asadi, Mojgan

Internet Media Type application/pdf

Type texts

Source 20230719-usctheses-batch-1069 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu