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Computational investigation of glutamatergic synaptic dynamics: role of ionotropic receptor distribution and astrocytic modulation of neuronal spike timing

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Computational investigation of glutamatergic synaptic dynamics: role of ionotropic receptor distribution and astrocytic modulation of neuronal spike timing

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Content COMPUTATIONAL INVESTIGATION OF GLUTAMATERGIC SYNAPTIC DYNAMICS: ROLE OF IONOTROPIC RECEPTOR DISTRIBUTION AND ASTROCYTIC MODULATION OF NEURONAL SPIKE TIMING By Sushmita Lakshmi Allam _____________________________________________________________________ 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 PHILOSPHY (BIOMEDICAL ENGINEERING) May 2013 Copyright 2013 Sushmita Lakshmi Allam ii Dedication To my family and my teachers iii Acknowledgements I wish to thank everyone who was directly and indirectly involved in the successful completion of my dissertation work. I express my sincere gratitude to Dr.Ted Berger for his generous support, inspiring wisdom, constant encouragement and for creating the best environment to succeed. I was very fortunate to have been a part of ‘The Center for Neural Engineering’ lab for all these years. My heartfelt thanks to Dr.Michel Baudry who first introduced me to this project and for his esteemed guidance filled with a lot of understanding and flexibility and for always being there. I would like to thank my committee members Dr. Bartlett Mel and Dr.Vasilis Marmarelis for their insightful questions, guidance and for reviewing my work. Words are not enough to express my gratitude towards Dr.Jean-Marie Bouteiller, without whose support and motivation, this project would not have been possible. I profusely thank him for his guidance and his infinite patience during the numerous discussions that streamlined my thought process and for his valuable contributions at every stage of this work. I would like to thank the entire Rhenovia team led by Dr. Serge Bischoff for facilitating the active collaboration I shared with his team members especially Renaud Greget, Nicolas Ambert and Arnaud Legendre. I would like to thank Eric Hu for a lot of the technical help he provided and for working with me on the EONS project. I thank Viviane for being a great teammate who made work fun and productive, it was very special to have won the Qualcomm Innovation fellowship with her. I would like to thank Dr. Dong Song, Dr. Rosa Chan, Dr. Ude Lu, Dr. Sageev George for providing me guidance whenever I needed. I would like to thank all the lab members Philip Hendrickson, Huijing Xu, Gene Yu, Brian Robinson, Shane Roach, Mickey and Penning Yu for their companionship. I will always cherish these years I spent at this lab with the most wonderful people who made this journey very special. I thank all the faculty members of the Biomedical department at USC, graduate student advisors and administrative staff who were instrumental in the completion of my degree. I am forever grateful to my friends, Joyita Dutta, Adarsh Shekhar, Krishnakali Dasgupta and Rumi Ghosh who were a family away from home and for taking care of me. iv I’m extremely grateful to all my family members for their love and support, especially Nirmala Chilamkurti, Rajeev Chilamkurthy and Siritha Akula for always being there for me. The last mile of the marathon is usually the toughest and I wouldn’t have achieved this proud moment, if not for the constant encouragement and understanding from my husband Murali Kota. Words are not sufficient to acknowledge the warm affectionate love and encouragement I received from my beloved parents and my brother Tejaswi Allam. It’s their lessons of perseverance and patience that got me this far. I’m grateful to Almighty and Google for leading me through my search. v Table of Contents Dedication ........................................................................................................................... ii Acknowledgements ............................................................................................................ iii List of Figures ................................................................................................................... vii List of Tables ..................................................................................................................... xii Abstract ............................................................................................................................ xiii Chapter 1: Introduction ....................................................................................................... 1 1.1 Overview ................................................................................................................... 1 1.2 Research Objectives .................................................................................................. 3 Chapter 2: A Novel Integrated Synaptic-Neuron Modeling Framework ............................ 5 2.1 Multi-Scale Modeling Framework ............................................................................ 5 2.1.1 EONS Synapse Model ........................................................................................ 7 2.1.2 Neuron Models ................................................................................................. 19 2.2 Software Implementation ........................................................................................ 21 2.2.1 EONS – XML representation ........................................................................... 22 2.2.2 Message Passing for Java (MPJ) ...................................................................... 23 2.2.3 NEURON – Python .......................................................................................... 24 Chapter 3: Synaptic Efficacy as a Function of Ionotropic Receptor Distribution ............ 26 3.1 Introduction ............................................................................................................. 26 3.2 Results ..................................................................................................................... 29 3.2.1 Synaptic potency as a function of AMPAR location ....................................... 30 3.2.2. Synaptic potency as a function of NMDAR location ...................................... 37 3.2.3. Summation of AMPA-R mediated EPSCs and NMDA-R mediated EPSCs, Mg 2+ as a tuning ratio ................................................................................................ 40 3.2.4. Paired-Pulse ratio as a function of the location of AMPA and NMDA receptors .................................................................................................................... 41 3.3 Discussion ............................................................................................................... 48 Chapter 4: A Computational Model to Investigate the Influence of Astrocytic Glutamate Uptake on Synaptic Transmission and Neuronal Spiking ................................................. 54 4.1 Introduction ............................................................................................................. 54 4.2 Results ..................................................................................................................... 60 4.2.1 Effect of astrocytic glutamate uptake on postsynaptic currents ....................... 60 4.2.2 Astrocytic glutamate uptake influences neuronal spiking ................................ 68 4.3 Discussion ............................................................................................................... 72 vi Chapter 5: Application To Drug Discovery ...................................................................... 79 5.1 Introduction ............................................................................................................. 79 5.2 Effect of CX614 ...................................................................................................... 81 5.3 Effect of NMDAR and GABA-A R antagonists ..................................................... 85 5.4 Conclusion ............................................................................................................... 87 Chapter 6: Conclusion ....................................................................................................... 89 6.1 Results Summary ..................................................................................................... 89 6.2 Future Work ............................................................................................................ 93 References ......................................................................................................................... 96 Bibliography .................................................................................................................... 104 Appendix……………………………………………………………………………….114 A1. Optimization Framework for Genetic Algorithm and Sensitivity Analysis ......... 114 vii List of Figures Figure 2.1: Schematic representation of the spatial and temporal span within the CNS. The spatial scales range from 1nm at molecular level to cm at systems level. The events taking place across these spatial scales span between microseconds to minutes and hours…………………………………….…5 Figure 2.2: A schematic representation of some of the synaptic level elements such as receptors, channels , buffers and transporters within EONS synaptic modeling platform. Each element is described as a Markov model with transitions into open conducting and desensitized states from resting/closed states dictated by kinetic rate constants. AMPA receptor model [12] is emphasized here in red. The kinetic state diagram of the receptor depicts the receptor in numerous states when glutamate is bound. The number of glutamate molecules (1,2,3,4) associated with the Resting (R), Desensitized (D), Deeply desensitized (E) and Open (O) states is represented here…………………………………………………………...6 Figure 2.3: Each synapse model is a fairly complex structure with presynaptic components, glutamate diffusions and postsynaptic structure. This unified model is then integrated into a morphologically realistic biophysical model of CA1 hippocampal pyramidal neuron……………………………7 Figure 2.4: Glutamate concentration profile (plotted in log scale - Yaxis) as a function of time (X-axis) available at the location of the receptor located at 0nm to 200nm (color coded) on the postsynaptic side…………………………...10 Figure 2.5: Schematic of 16 states AMPA receptor model adapted from Robert and Howe (2003) with kinetic rate constants provided in the table below…..12 Figure 2.6: Kinetic schema of 15 states NMDA receptor model with kinetic rate constants adapted from [22 ]provided in the table 2.1……………….…..15 Figure 2.7: Schematic of the glutamate transporter from [28] and kinetic rate constants described in the table 2.2………………………………………………...17 Figure 2.8: Schematic representation of the communication taking place between synapse and neuron instances on parallel nodes of a cluster. Information (postsynaptic currents and potentials) is exchanged between these processes at every time step and, at the end of a simulation, results are stored in a database………………………………………………………………….21 Figure 2.9: Core communication method behind synaptic processes programmed in JAVA and NEURON software programmed in Python. Many synapses processes in parallel update their values to a master process which organizes the order of synaptic data and transmits through Java client to the Python server. These synaptic currents drives voltage changes inside NEURON. Dendritic voltage data from NEURON is sent to python client and is transmitter back to the master process which distributes the viii respective postsynaptic potentials from the respective dendritic elements to all the EONS synaptic processes...........................................................25 Figure 3.1: Diversity in subsynaptic architecture and activity patterns give rise to variances in postystnaptic responses ……………………………………28 Figure 3.2: (Top row) Probability of AMPA receptors being in the open conducting states as a function of distance from release site when 2 , 3 and 4 glutamate molecules are bound (shown by filled circles – bottom row). Middle row shows the normalized maximum values scaled between 0 to 1 to highlight the location where the probability of being in that open state is maximum………………………………………………………………...32 Figure 3.3: AMPA receptor-mediated EPSCs in response to a single pulse stimulus. A gradual decrease in EPSC amplitude is observed when the distance between the release site and the receptors increases. The peak value of EPSC obtained at 0 nm is 52% more than the peak amplitude when AMPA receptors are located 200nm away from the release site. The resulting EPSP values as a result of the EPSC to the left are plotted as a function of distance. As expected the EPSPs mediated by AMPARs closest to the glutamate release site had the highest amplitude, 50% more than the peak amplitude of AMPAR located 200nm away……………...33 Figure 3.4: Time–to-EPSC peak response as a function of AMPA receptor location. The time-to-peak EPSC when AMPA receptors are 300nm (marked by blue asterisk) farther away show a 0.5 ms delay compared to receptors located at 0nm (marked by red asterisk)…………………………………34 Figure 3.5: Desensitization of AMPAR as a function of its location relative to the glutamate release site Individual plots from top represent probability of desensitization profile when (A) 2 glutamate molecules are bound. (B) 3 glutamate molecules are bound and (C) 4 glutamate molecules are bound. (D) Overall desensitization as a sum of all individual states including when 1 glutamate molecules is bound and no molecules are bound. There are trends in the profiles as a function of location as these are dependent on the glutamate concentration. However overall desensitization (sum of all desensitized D states) is relatively similar across all locations as the receptor is likely to be in desensitization state D0 (when no glutamate are bound) for a longer period of time……………………………………….35 Figure 3 6: Probability of glutamate occupancy (peak values) plotted when the AMPAR is present at locations 0 to 200nm (Plotted along the X-axis)…36 Figure 3.7: The two open states of NMDAR model used here, plotted as a function of receptor location. There is not much variation in the individual state probability of being in the open states whether the receptor was located close to the release site or farther away. Open state 2 did show a slight variation as a function of receptor location, but the scale s in the order of 10 -3 ……………………………………………………………………….38 ix Figure 3.8: NMDAR-mediated EPSCs and EPSPs as a function of NMDAR location. There is no significant contribution of NMDAR location on the NMDAR- mediated EPSCs and EPSPs. ……………………………………………39 Figure 3.9: EPSCs (shown in red) described here are a summation of AMPA-R (blue dotted line) mediated and NMDAR-mediated currents (green dotted line). When the Mg 2+ concentration varies from 1mM to 0.5mM, the NMDAR mediated current scales to higher amplitude, changing the envelop of EPSC (in red).……………………………………………………………41 Figure 3.10: A schematic of the PSD and the receptors located on it elicited by a paired pulse stimulus with an inter pulse interval of 10ms. The EPSC waveforms (shown in red and blue) as a result of ionic current flow from both AMPAR (located right opposite to the glutamate release site and at 200nm respectively) and NMDAR. The paired pulse ratio (PPR) as explained in Box B is a ratio of max. amplitude caused by second response to the maximum amplitude of the first response. When the AMPAR is closer to the release site the PPR~0.85 and when farther away PPR~0.96………..44 Figure 3.11: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations). The paired pulse ratios vary between 0.8 to 1.18 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals. ……………………………………45 Figure 3.12: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations) for a decreased concentration of Mg 2+ (to simulate the effect of partial unblocking of NMDA receptors by Mg 2+ ). The paired pulse ratios vary between 0.95 to 1.75 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals (10-100ms). For longer paired pulse intervals, we did not observe any dramatic changes in the PPR values. ………………………46 Figure 3 .13: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations) in the vicinity of glutamate uptake. The paired pulse ratios vary between 0.9 to 2 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals (20-30ms). ……………………………………………………..48 Figure 4.1: Multi-scale framework of the CNS hierarchy including molecular, synaptic, neuronal, and network level including glial cells., modified from Bouteiller et al. (2011). The molecular level is illustrated with a kinetic schema of the NMDA receptor. The synaptic level includes several molecular elements and their spatio-temporal interaction. The neuron level comprises morphologically realistic neuron model with synapses (blue x circles) randomly located on dendritic branches surrounded by astrocyte processes (green arcs). The network level takes into account the interaction between neurons and glial cells, especially the effect of glial glutamate uptake was modeled here……………………………………..54 Figure 4.2: Functional diagram of the EONS synapse model including: glutamate diffusion inside the cleft, AMPAR, NMDAR, mGluR, and glutamate uptake mediated by glial (EAAT2) and neuronal transporters (EAAT3). The green cylindrical ensheathment represents the astroglial process on which EAAT2s are expressed. This representation is referred to as the tri- partite synapse……………………………………………………………55 Figure 4.3: Simulated AMPAR and NMDAR mediated EPSCs in response to varying density of glial glutamate transporters (A) The increased number of glutamate transporters affects the peak amplitude of AMPAR-mediated current due to uptake of glutamate. (B) Normalized responses of AMPA mediated EPSCs elicited from a single input pulse for cases with no transporters, 50% density and 100% density of astrocytic glutamate transporters. The decay time course of normalized AMPAR currents with 50% density and without any transporters did not show any change. (C) Glutamate uptake by the glial transporters affects the decay time course of NMDA receptor-mediated EPSC. An increase in the density of transporters results in an increase in the rate of uptake thus decreasing the decay time of NMDA receptor-mediated EPSC. (D) NMDAR-mediated EPSCs with glial glutamate uptake (red), and with both glial and neuronal uptake (blue). The uptake mediated by neuronal transporters (EAAT3) is not significant…………………………………………………………….62 Figure 4.4: Astrocytic glutamate uptake effect on paired pulse responses is distinct for small and large input time intervals. (A) Composite EPSCs elicited by paired pulse stimulation plotted against input time intervals separated by 10–500 ms (Time axis in log scale to zoom into the effects at shorter input time intervals for all plots). First pulse response indicated by black arrow. Paired pulse depression (PPD) effect is observed for responses when no transporters are present (light gray, peaks marked by red asterisks). With the presence of transporters and astrocytic glutamate uptake (dark gray, peaks marked with blue asterisks), there is a paired pulse facilitation (PPF) effect observed for responses when the input time intervals are short. This reversal of effect from PPD to PPF is only apparent for shorter input time intervals. (B) The probability of the AMPARs to be in desensitization states as a function of input time intervals. These receptors are highly desensitized for shorter input time intervals. (C) The probability of NMDARs to be in desensitized states. The NMDARs are highly desensitized and this increases with increasing input time intervals. (D) HGN3To state probability of the glutamate transporter, when H+, Glu, 3 Na+ are bound to the transporter. Glutamate uptake ability is observed within this state, described in detail in section 2.1.1.4.1. The transporter xi recovers to this same state only after longer input time intervals >200 ms………………………………………………………………………...65 Figure 4.5: Influence of astrocytic glutamate uptake on spiking activity of a CA1 pyramidal neuron at different input frequencies. (A) Neuronal spiking activity elicited by a random input interval train with mean frequency of 2 Hz. The number of spikes occurring in the presence of glutamate uptake are much less (green) vs. when there are no transporters in the vicinity of synapses. (B) Number of spikes per trial within a span of 4 s without transporters (blue) and with transporters inducing glutamate uptake (green). Across trials we observe a consistent decrease in the spike count. (C) Neuronal spiking activity elicited by a random input interval train with a mean frequency of 5 Hz. Similar effects of spike failure as seen in 2 Hz are observed. (D) Number of spikes per trial across five trials show the consistent failure of spikes due to increased glutamate uptake in the presence of transporters. Two critical events marked by * show that the spikes elicited without glutamate uptake (no transporters) and with glutamate uptake have a timing difference between 1 and 2 ms and ** indicates when timing lies in between 3 and 8 ms. The input trains are indicated by the traces shown in black within each result panel………...71 Figure 5.1: Synaptic locations of EONS synapses (represented in blue) on the compartmental model of a CA1 pyramidal cell, adapted from [25]. All synaptic inputs receive a synchronous 4Hz random interval train. All synapses have similar configuration of receptor distribution with 80 AMPARs and 20 NMDARs……………………………………………..82 Figure 5.2: Simulated spiking patterns from the soma of a neuron elicited by a 4Hz random interval train. Different concentrations of CX614 at 5µM (b), 10µM (c) and 100µM (d) result in distinct spike timing pattern from the control (a), where no drug was administered. Published in [4]………….83 Figure 5.3: Simulated neuronal activity for a 10Hz RIT with NMDAR and GABA-A R antagonist effects at individual EONS synapses. Blocking 50% of the NMDAR conductance by simulating the effect of APV induces a significant reduction in the number of spikes obtained (blue). On the contrary, blocking an inhibitory effect of GABA-A R antagonist enhanced the excitability of the neurons and led to more number of spikes (red trace) than the control condition (black). However, including both the NMDAR antagonist effect and GABA-A R antagonist effect restored the same spike count as in control but the temporal pattern of the resulting spike train changed drastically. ……………………………………………………..86 Figure A1: Implementation on the global optimization procedure on a high performance distributed framework……………………………………..98. xii List of Tables Table 2.1: Kinetic parameters of AMPAR model used in EONS…………………...12 Table 2.2: NMDAR model parameters used in EONS……………………………...15 Table 2.3: GLT-1 model kinetic rate parameters used in EONS……………………18 Table 2.4: Neuronal transporter kinetic rate parameters from [32] used in EONS…18 Table 2.5: Neuron models used within this multi-scale framework………………...20 xiii Abstract Glutamatergic synapses and their subsynaptic elements play crucial roles in mediating neuronal communication. Any disruption to the normal functioning of these elements and/or their interactions has implications in neurological disorders. It is technically difficult to access synaptic space and explore subsynaptic parameters influence on the overall synaptic and higher-order functions through usual experimental methodologies. Computational models complement experimental findings and provide a means for better understanding of such complex systems by providing the framework to look at various dimensions of synaptic functions by simultaneous manipulation of subsynaptic parameters. EONS (Elementary Objects of the Nervous System) is a highly configurable synaptic modeling platform featuring subsynaptic elements and interactions between them. We developed a multi-scale framework, which combines the features of this unified glutamatergic synapse model (EONS) into hippocampal neuron models (within the NEURON simulation environment) within a parallel computing environment. This multi-scale architecture creates a link between molecular level processes and higher order neuronal spiking activity thereby creating a unique powerful tool with direct application to drug design and discovery. Two main topics were addressed through computer simulations, glutamate diffusion and uptake on synaptic function and neuronal spiking: A) We explored the functional consequences that arise as a result of subsynaptic localization of ionotropic receptors. There is evidence that AMPARs, NMDARs and xiv mGluR exist at different locations within the postsynaptic membrane. These receptors have different kinetics. Given that glutamate released from the pre-synaptic vesicles diffuses across the synaptic cleft, a reasonable hypothesis is that receptors located across the post-synaptic membrane encounter varying levels of glutamate and respond differently. Within this highly configurable synapse model, we varied the location of ionotropic receptors, extracellular environmental factors such as Mg 2+ , astrocytic glutamate uptake. Our simulations using single pulse and paired pulse protocols simulations suggests that it is the interplay between spatial location of AMPAR, density and conductance of these channels and the pre-synaptic pattern of activity combined that influence synaptic potency. B) We explored the influence of astrocytic glutamate uptake on synaptic transmission and neuronal spiking. This was tested with the multi-scale modeling framework developed. Astrocytic glutamate transporter models were added to the synaptic environment to simulate glutamate uptake. The reduced levels of glutamate activated receptors differently and influenced the amplitude and decay time course of EPSCs, which directly had an effect on the neuronal spiking ability. Overall this model will subsequently help us decipher how targeting molecular elements at the synaptic level can modify network function and could provide a unique method to design therapeutic approaches to alleviate and reverse pathological conditions. 1 Chapter 1: Introduction 1.1 Overview Synapses are the most critical points of neuronal communication. Plasticity and memory related processes take place at these hippocampal synapses[2-4]. Excitatory neurotransmitter glutamate is responsible for activating ionotropic receptors: α-amino-3- hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) and N-Methyl-D- aspartic acid (NMDAR) [5]. The ionic channels associated with these receptors mediate the flow of ions and give rise to excitatory postsynaptic currents (EPSCs), which then depolarize the neuron’s membrane to produce excitatory postsynaptic potentials (EPSPs); when these potentials are near spiking threshold values, action potentials are generated. Glutamate also activates metabotropic glutamate receptors (mGluR) that trigger a cascade of other second messenger mechanisms. Any disruptions to the circuit elements at a glutamatergic synapse, such as glutamate release, glutamate receptors binding, and glutamate uptake will give rise to various neurological disorders and also interrupt neuronal information flow. The current state of the art technology allows the experimental manipulations to approach a single spine level and sometimes even to tracking of single receptors. Despite this progress, it is difficult to get a complete picture of the synapse and how the interactions between subsynaptic elements influence synaptic transmission. The reason most often being that the experimental protocol only allows the manipulation of a single or very few parameters at a time. In such cases, computational models complement our 2 understanding of such complex systems by providing the framework to look at various dimensions of synaptic functions by simultaneous manipulation of multiple subsynaptic parameters with complete control over the rest of the in-silico synaptic substrate. There are many computational models that combine the features of synaptic models as conductance changes and neurons as cable equations. However, in reality, there is a lot more complexity that drives synaptic machinery and the subsequent neuronal communication. For example, synapses usually formed on dendritic spines have complex morphologies and contain numerous subsynaptic elements within. It is not very clear, how the structural heterogeneity and the diversity of subsynaptic architecture give rise to variances in postsynaptic responses. With a growing interest in multi-scale modeling and increased availability of parallel computing resources, several groups in the recent decade proposed to build multi-scale models of the CNS with specific aims targeted to specific brain regions. Some of the notable ones are Blue Brain Project [6], NEURON [7], GENESIS[8], PyMOOSE[9]. Some of these simulation methodologies have been reviewed in [10]. Though some of these modeling platforms are capable of simulating large networks of neurons, it is difficult to accommodate synaptic and subsynaptic level information in these models due to the computational complexity of simulating reaction diffusion equations such as the ones demonstrated with MCELL [11]. Our computational model, within a multi-scale framework, combines the features of fairly complex models of glutamatergic synapses into hippocampal neuron models (CA1 Pyramidal cells) to foster our understanding of neuronal spiking activity that arises from subsynaptic element interactions, especially at glutamatergic synapses. Our approach is 3 novel as this framework spans the nervous system hierarchy across three levels, subsynaptic, synaptic and neuronal levels, with capabilities of extending to large networks. The subsynaptic elements are described using mathematical models of receptors and transporters (Markov processes) and diffusion at single synapses, which are highly configurable parametrically. This platform is combined with the NEURON simulation environment to systematically test various experimental paradigms and predict the neuronal activity for variants of synaptic input activity. Understanding this neuronal activity and its spiking and temporal pattern is important as the information across the brain regions is conveyed through spatiotemporal patterns. These spatiotemporal patterns in the form of spike trains are processed by a wide variety of neurons, diverse synaptic connections and subsynaptic elements to create a ‘meaningful’ code, which form the means of communication across brain regions. We need to understand the subsynaptic mechanisms that cause such input-output transformations to interpret higher order brain functions. 1.2 Research Objectives The present study was motivated by our interest in understanding the physiological role of the diverse elementary objects of glutamatergic synapses (especially ionotropic glutamate receptors), their distribution at spines and astrocytic glutamate transporters and their respective influence on different levels of neuronal function. To approach this goal, we developed a computational framework of a multi-scale model of nervous system hierarchy that could provide a quantitative description of the biological processes from the bio-molecular level to the neuron level and that could not only reproduce experimental results, but also make predictions that could be tested and 4 verified experimentally. The two major specific aims will be addressed in this thesis: a) At the synaptic level, the role of ionotropic receptor distribution and its implications on synaptic potency will be described in Chapter 3. Synapses express several classes of receptors at various locations on their specialized postsynaptic structures, which activation dynamics are determined by glutamate concentration available at the receptor and the receptors’ characteristics. We explored the AMPAR and NMDAR internal behavioral states of activation, desensitization, and resulting postsynaptic currents as a function of their location. b) At the neuron level, we investigated the role of glutamate uptake mediated by astrocytic glutamate transporters on synaptic transmission and neuronal spiking, presented in Chapter 4. In addition to that, this multi-scale framework has applications in drug discovery platform RHENOMS TM for testing and predicting synergies between different drugs that act at these synaptic pathways. Some of the examples tested using this framework are described in Chapter 5. Chapter 6 briefly summarizes the work presented and some of the limitations that can be improved upon to further address a multitude of scientific questions. 5 Chapter 2: A Novel Integrated Synaptic-Neuron Modeling Framework 2.1 Multi-Scale Modeling Framework The CNS has a highly parallel architecture that spans hierarchically across several spatial and temporal scales as shown in Figure 2.1 Spatial scales range from ‘°A’ to ‘cm’, considering molecular sizes and cortical columns. Temporal scale spans from microseconds to minutes, taking into account the fast processes of ion movements, diffusion and hours for memory formation and stabilization such as LTP. The novel multi-scale approach that was developed here integrates across some of these layers of spatial and temporal complexity. Figure 2.1: Schematic representation of the spatial and temporal span within the CNS. The spatial scales range from 1nm at molecular level to cm at systems level. The events taking place across these spatial scales span between microseconds to minutes and hours. Source:[1] 6 Figure 2.2: A schematic representation of some of the synaptic level elements such as receptors, channels , buffers and transporters within EONS synaptic modeling platform. Each element is described as a markov model with transitions into open conducting and desensitized states from resting/closed states dictated by kinetic rate constants. AMPA receptor model [12] is emphasized here in red. The kinetic state diagram of the receptor depicts the receptor in numerous states when glutamate is bound. The number of glutamate molecules (1,2,3,4) associated with the Resting (R), Desensitized (D), Deeply desensitized (E) and Open (O) states is represented here. Under the current framework, we looked closely at three levels of the hierarchy. At the subsynaptic level, the glutamate binding with receptors and several internal states of the receptor (AMPAR internal states highlighted in red box) as shown in Figure 2.2. At the synaptic level, non-linear interactions between glutamate receptors and transporters are modeled. At the neuronal level, we can determine how these synaptic mechanisms will influence the neuron’s spiking ability by passing synaptic currents (Figure 2.3). 7 Figure 2.3: Each synapse model is a fairly complex structure with presynaptic components, glutamate diffusions and postsynaptic structure. This unified model is then integrated into a morphologically realistic biophysical model of CA1 hippocampal pyramidal neuron. 2.1.1 EONS Synapse Model EONS (Elementary Objects of the Nervous System) synaptic modeling platform is available online at http://synapticmodeling.com [13] based upon a parametric modeling approach. A parametric model is defined by a finite dimensional parameters space. Parametric models are beneficial when the user seeks controllability of the system as the parameters of the model remain close to the physiological mechanisms observed and 8 these parameters help us understand the system behavior by changing known parameters and analyzing their influence on the entire system. This platform was developed to help better understand how changes in parameters of constitutive elements of the glutamatergic synapse, such as receptor distribution and density, relative position of postsynaptic receptors with respect to the release site, and ionic concentration within the synaptic environment influence synaptic responses such as currents and potentials. Figure 2.2 illustrates some of the mechanisms and elements that are incorporated in the current synaptic model: presynaptic calcium buffers, voltage-dependent calcium channels, a single vesicular release site for glutamate, glutamate diffusion in the synaptic cleft, Markov models of postsynaptic ionotropic and metabotropic receptors, which represent the behavior of receptors on glutamate binding. AMPA receptors are responsible for fast synaptic transmission while NMDA receptors mediate EPSC with slower kinetics. In addition to the complexity at synaptic level, NMDA receptors are highly nonlinear, as their activity is influenced by changes in magnesium concentration and membrane potential. Other second messenger mechanisms are triggered by activation of metabotropic glutamate receptors (mGluR), which lead to a cascade of calcium- mediated events, which play a major role in short and long-term potentiation of synaptic transmission. This software is implemented using JAVA. A library of elementary models is available within this platform. Each elementary model within this is developed using Cell Designer TM platform. After testing and validating using several protocols, we integrated these into the EONS software, where elementary models interact with each other, i.e., one model’s output represents an input to another model. 9 For example, the elementary model of the receptors behavior represented in various intermediate states such as resting to inactive to open states. The input to these models is the local glutamate concentration available at the receptor site. The time- dependent evolution of the receptor states is calculated using ODEs driven by the kinetic rates of association and dissociation of glutamate to the receptor. Only a few models relevant to this thesis topic will be presented in detail in this document. For this, the features of the modeling platform are separated in three sections (i) Presynaptic component (ii) Glutamate diffusion (iii) Postsynaptic component and (iv) Extrasynaptic components. 2.1.1.1 Presynaptic Component Action potentials invade the presynaptic terminals to depolarize the membrane, which triggers the voltage dependent calcium channels (VDCCs) to allow flow of Ca 2+ through the ion channels. L-type, N-type and T-type channels account for most of the Ca 2+ influx in this component[14, 15]. Presynaptically, calcium buffers, mitochondria and calcium pumps are responsible for the extrusion of calcium. The influx, out flux and diffusion of intracellular calcium diffusion determines Ca 2+ concentration levels, which regulate the amount of neurotransmitter (NT) glutamate released [16, 17]. This modeling platform gives the flexibility to change the location and number of the presynaptic channels away or towards the release site, which influences the amount of NT release [13]. Quantal release is highly stochastic in nature, though this feature is modeled; all simulations that will be described in the rest of this thesis use a deterministic release, i.e. for similar presynaptic stimulus, the amount of NT released is always same. This choice 10 was made due to avoid any variability in results due to presynaptic noise, since the focus of the present study is to determine the influence of postsynaptic arrangement of receptors on synaptic transmission. The glutamate concentration values thus obtained are described in the next section. 2.1.1.2 Glutamate Diffusion Figure 2.4: Glutamate concentration profile (plotted in log scale - Yaxis) as a function of time (X-axis) available at the location of the receptor located at 0nm to 200nm (color coded) on the postsynaptic side. The diffusion model used here has been adapted from [18] to calculate glutamate concentration inside the cleft as a function of the distance of the receptor from the release site using Equation (1). The glutamate diffusion coefficient is 0.4 µm 2 ms -1 . The total number of transmitter molecules released from the vesicle in the model is 3,000 per 11 release event. The concentration of glutamate inside the cleft is determined by the following equation: Dt r e Dt Q D Q t r Glu 4 2 4 ) , , , , ( − = πε δ (1) Where Glu, r and D represent the concentration of glutamate inside the cleft, the radial distance and the diffusion coefficient, respectively. Q represents the number of glutamate molecules released instantaneously. ‘δ’ stands for the height of the cleft and is maintained constant throughout the simulations at 20 nm. The glutamate profile seen by postsynaptic receptors is shown in Figure 2.4. 2.1.1.3 Postsynaptic Components At most CA1 hippocampal synapses, EPSCs are produced by the summation of ionic currents mediated by AMPARs and NMDARs. Each of these receptors has pore- forming subunits, the differences in their structure and homology sequence is the reason for different subunit types giving rise to different kinetic properties[5]. We present AMPARs of GluR1 type models and NMDAR NRA types, as these are the most often present within the postsynaptic densities. However, other sub-types/receptor models with different kinetic parameters can be easily plugged into the synaptic modeling platform. 2.1.1.3.1 AMPAR Model We used the AMPA receptor model described in detail in [12] which represents a 16 states model describing the receptor transitions between resting, desensitized and conducting open states (Figure 2.5). Successive binding of 2, 3, and 4 glutamate 12 molecules produces conformational changes leading to fast opening and closing of the channel. Figure 2.5: Schematic of 16 states AMPA receptor model adapted from Robert and Howe (2003) with kinetic rate constants provided in the table below. Parameter Values k1 10 mM -1 ms -1 k-1 7 ms -1 k2 10 mM -1 ms -1 k-2 4.1e -4 ms -1 γ o 0.001 ms -1 δ o 3.3e -6 ms -1 γ 1 0.42 ms -1 δ 1 0.017 ms -1 γ 2 0.2 ms -1 δ 2 0.035ms -1 Β 0.55 ms- 1 Α 0.3 ms -1 Table 2.1: Kinetic parameters of AMPAR model used in EONS The current through the channel is calculated by: ) ( ) ( 4 4 3 3 2 2 rev AMPA AMPA V V O g O g O g nb I − × + + × = 13 i i O Glu M O )]. ( [ =  (4) where I AMPA is the current mediated by AMPA receptors, nb AMPA is the number of AMPA receptors (in this study nb AMPA is 80), consistent with reported AMPAR numbers between 46-147 at CA1 hippocampal synapses [19]. g2, g3, g4 are unitary conductances with values 9, 15 and 21 pS associated with the channel in open states when 2, 3 and 4 glutamate molecules are bound respectively. The probabilities for the O 2, O 3, O 4 states are calculated based on ODEs simulated using SBML (Systems Biology Markup Language). Different ODE solvers are used within EONS modeling platform. Some of these solvers used in this platform such as RK4, TRBDF2, Rosenbrock, IMEX are compared for performance and results are presented in [20]. The derivatives of open states i O  (where i=2, 3, 4) are calculated as a product of matrix M containing other states transition rate constants with input Glu and vector of currents states O i . Vrev is the reversal potential of the AMPAR (Vrev is 0 mV) and V is the membrane potential that changes dynamically during the simulation. 2.1.1.3.2 NMDAR Model NMDAR model represented in a 15-state kinetic scheme (Figure 2.6), which includes agonist (glutamate) and co-agonist (glycine) binding sites, channel blockers (memantine and magnesium), as well as several antagonist sites. The kinetics of this model are borrowed from [21]. For validation of the NMDAR model, various protocols were tested. For a single short pulse of glutamate, experimental results reported by [22] were used to validate the model. For long or repetitive glutamate inputs to the model, the 14 kinetic parameters were adjusted to properly capture effects of desensitization and match experimental data from [23]. The equations to calculate NMDAR-mediated synaptic current are: RT m zF o o NMDA NMDA e K Mg I nb I ψ δ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 2 1 ) ( ) ( t O V V g I rev o − = m e g g g g αψ + − + = 1 1 2 1 (5) Figure 2.6: Kinetic schema of 15 states NMDA receptor model with kinetic rate constants adapted from [22] provided in the table below. 15 Parameter Values k e 8.3 mM -1 ms -1 k -e 0.0263 ms -1 k g 10 mM -1 ms -1 k -g 0.0291 ms -1 g b 0.0671 ms -1 g -b 0.15 ms -1 g a 2.03 ms -1 g -a 22.8 ms -1 β 1 35.2 ms -1 α 1 0.728 ms -1 β 2 0.787 ms- 1 α 2 11.2 ms -1 d on 0.03 ms -1 d off 9.5e -4 ms -1 Table 2.2: NMDAR model parameters used in EONS where I NMDA is the current mediated by NMDA receptors. nb NMDA is set at 20 for this study consistent with observations made in [24, 25]. I o is the current associated with the open conducting state O(t) calculated using ODEs solved with kinetics described in [21]. The magnesium concentration in the external solution is set to 1 mM ; Ψm is the electrical distance of the magnesium binding site from the outside of the membrane (set at 0.8); R, the molar gas constant (8.31434 J.mol −1 .K −1 ); F, the Faraday constant (9.64867.104 C.mol −1 ); T, the absolute temperature (273.15 °K); g 1 and g2 are the conductances associated with the open states when one or two glutamate molecules are bound and are 40 pS and 247 pS respectively; α=0.01 is the steepness of the voltage- dependent transition from g1 to g2. The EPSCs thus obtained are a summation of responses of currents mediated by AMPARs and NMDARs. 16 2.1.1.4 Extrasynaptic Components Since a neuron’s pre- and postsynaptic nerve terminals are often ensheathed by astrocytes, which participate in synaptic signal processing, the term tripartite synapse was coined [26]. Within a tripartite synapse, biochemical and morphological studies suggest that excitatory amino-acid transporters (EAATs) expressed on astrocytes are of the type EAAT2. These glutamate transporters maintain low extracellular glutamate concentration, which prevents neurotoxicity in spinal cord, striatum, and hippocampus [27], and may play a functional role in regulating synaptic currents by clearing glutamate after its synaptic release [28]. To model this mechanism, we used the glial glutamate transporter model shown in Figure 2.7. 2.1.1.4.1 Glial Glutamate Transporter The astrocytic glutamate uptake is calculated by the following rate equation for glutamate flux: (6) where N2ToH, N2ToGH, N2To, N2ToG are the intermediate states that determine glutamate bound and transported by the transporter (See Figure 2.7). The values for parameters , is 6 mM -1 ms -1 and for , , is 0.5 ms -1 . The other rate constants and ion concentrations are the same as reported in [29]. The uptake rate in the equation above is for a single transporter channel. The diameter of the postsynaptic disk is 200nm [25] the height of the synaptic cleft is fixed at 20nm [18]. The astrocyte membrane and its ToG N k To N Glu k ToGH N k Glu ToH N k dt dGluo 2 2 2 2 3 3 6 6 × − × × + × − × × = − − 17 transporters are set at a distance of 400 nm from the release site. The distance of the transporter from the release site does not influence its uptake rate (Diamond, 2005). Transporters are expressed on astrocytes surrounding synapses with densities within a range of 6500-13,000/µm 2 [30, 31]. The astrocyte is modeled as a cylindrical surface of height 20 nm and radius 400 nm. Assuming the maximum transporter density (13,000/µm 2 ) and a 50% astrocytic coverage surrounding the synapse, we calculate the number of glutamate transporters per synapse to be 650. For the same conditions but with 50% density, we calculate the number of transporters to be 325. Glutamate uptake from neuronal transporters is calculated in a similar manner to that by glial transporters (Equation 2) with the kinetic rate constants adapted from [32] (presented in Table 2.4) and a transporter density of 90/µm 2 [33]. The total amount of glutamate cleared from the receptor vicinity is obtained by multiplying the cleared glutamate rate dGluO/dt (integrating over the time steps of the simulation) and the number of transporters. This amount of cleared glutamate is then subtracted from the glutamate input concentration available at the receptors. Figure 2.7: Schematic of the glutamate transporter from [28] and kinetic rate constants described in the table below. 18 Glial Transporters: Parameter Values k 1 ; k -1 0.01 mM -1 ms -1 ; 0.1 ms -1 k 2 ; k -2 0.01 mM -1 ms -1 ; 0.5 ms -1 k 3 ; k -3 6 mM -1 ms -1 ; 0.5 ms -1 k 4 ; k -4 60000 mM -1 ms -1 ; 0.7 ms -1 k 5 ; k -5 60000 mM -1 ms -1 ; 0.7 ms -1 k 6 ; k -6 6 mM -1 ms -1 ; 0.5 ms -1 k 7 ; k -7 0.01 mM -1 ms -1 ; 1 ms -1 k 8 ; k -8 2 ms -1 ; 1.9 ms -1 k 9 ; k -9 1 ms -1 ; 0.04 mM -1 ms -1 k 10 ; k -10 3 ms -1 ; 90000 mM -1 ms -1 k 11 ; k -11 3 ms -1 ; 0.1 mM -1 ms -1 k 12 ; k -12 100 ms -1 ; 20 mM -1 ms -1 k 13 ; k -13 100 ms -1 ; 100 mM -1 ms -1 k 14 ; k -14 1 mM -1 ms -1 ; 1 ms -1 k 15 ; k -15 0.04 ms -1 ; 0.01 ms -1 k 16 ; k -16 20 ms -1 ; 1 mM -1 ms -1 k 17 ; k -17 0.0014 ms -1 ; 1.0e -5 ms -1 Table 2.3: GLT-1 model kinetic rate parameters used in EONS Parameter Values k 1 ; k -1 0.01 mM -1 ms -1 ; 2.5 ms -1 k 2 ; k -2 0.01 mM -1 ms -1 ; 2.5 ms -1 k 3 ; k -3 6.8 mM -1 ms -1 ; 0.3 ms -1 k 4 ; k -4 60000 mM -1 ms -1 ; 0.7 ms -1 k 5 ; k -5 60000 mM -1 ms -1 ; 0.7 ms -1 k 6 ; k -6 6 mM -1 ms -1 ; 0.5 ms -1 k 7 ; k -7 0.01 mM -1 ms -1 ; 1 ms -1 k 8 ; k -8 0.5 ms -1 ; 0.55 ms -1 k 9 ; k -9 0.8 ms -1 ; 0.04 mM -1 ms -1 k 10 ; k -10 6 ms -1 ; 90000 mM -1 ms -1 k 11 ; k -11 3 ms -1 ; 1 mM -1 ms -1 k 12 ; k -12 0.5 ms -1 ; 2 mM -1 ms -1 k 13 ; k -13 4 ms -1 ; 1 mM -1 ms -1 k 14 ; k -14 0.1 mM -1 ms -1 ; 10 ms -1 k 15 ; k -15 0.05 ms -1 ; 0.005 ms -1 k 16 ; k -16 0.8 ms -1 ; 0.01 mM -1 ms -1 k 17 ; k -17 0.008 ms -1 ; 1.0e -5 ms -1 Table 2.4: Neuronal transporter kinetic rate parameters from [32] used in EONS 19 2.1.2 Neuron Models Classical cable theory proposed by Rall is used to explain the flow of currents in passive dendrites [34]. Here neurons are treated as long leaky cables, and the dendritic compartment properties such as membrane resistance, membrane capacitance and axial resistance, influence the synaptic current and subsequent membrane depolarization. The NEURON simulation environment [35] used for creating realistic morphological models of biological neurons is primarily based on the cable theory of neurons with dendritic compartments defined as electrical compartments with resistance and capacitance. Also, biophysical properties such as multiple channel types, ion diffusion and second messengers can be easily integrated into the neurons. The neuron models used in this thesis are adapted from existing neuron models accessible from the ModelDB database. Neuron’s response to synaptic inputs depends on three factors: Dendritic geometry, location of synapses, passive and active membrane properties of neurons. In the initial development phase of this framework, Migliore model adapted from [36] was used. The CA1 pyramidal neuron was modeled with sodium current, INa, delayed rectifying, IK DR, and A-type potassium channel, IK A . All these distributions were consistent with experimental data of CA1 pyramidal neurons [37, 38]. Another CA1 pyramidal neuron model [39] was used for the neuron level simulations presented in Chapter 4. Jarsky Model: Neuron had four types of conductance: (a) Voltage-gated Na+ conductance (b) Delayed rectifier K+ conductance and (c) Two A-type conductance 20 Neuron Models: Models used ModelDB link: Passive properties: Rm = 28000 Ωcm 2 Cm =1 µF/cm 2 For active channels properties and distributions, please see [36]: http://senselab.med.yale.edu/modeldb Accession: 119283 Cm =0.75 µF/cm 2 Rm = 40000 Ωcm 2 For active channels properties and distributions, please see [39]: http://senselab.med.yale.edu/modeldb Accession: 116084 Table 2.5: Neuron models used within this multi-scale framework These neuron models are simplistic compared to other complex models [40] but they exhibit spiking behavior, which is the main criteria needed to test the hypothesis of how subsynaptic level parameters and interactions influence neuronal spiking abilities. This decision was based on the rationale to keep the neuron model as simple as possible to elicit spiking responses without too many nonlinear effects induced by voltage dependent channels and also to reduce computational burden in simulating a multitude of mechanisms. For the Jarsky model used to study neuronal spiking behaviour, we used 16 instances of the EONS synapse computational model at 16 different dendritic locations and conductance of each synapse amplified by 6 times (which represents synchronous activation of 6 synaptic inputs) to elicit a neuronal spiking response. 21 2.2 Software Implementation A significant amount of our time and effort was devoted to developing the multi- scale system, specifically toward integrating the synaptic modeling platform into the NEURON modeling platform and adapting the system to work on the high-performance computing cluster in order to launch large-scale simulations in a parallel fashion. To deploy this simulation model on the computing cluster, the user instantiates the neuron process and synapse processes on the nodes as illustrated in Figure 2.8. The neuron instance runs with Python as the back end and several of the synapse instances run using JAVA and MPJ Figure 2.8: Schematic representation of the communication taking place between synapse and neuron instances on parallel nodes of a cluster. Information (postsynaptic currents and potentials) is exchanged between these processes at every time step and, at the end of a simulation, results are stored in a database. 22 (Message Passing for Java) protocols[41] to communicate information, postsynaptic currents and potentials are exchanged back and forth. At every time step, information is exchanged between the synapses and the neuron. As suggested in Rall and Rinzel models, spines have high impedance and the low impedance of the parent dendrite makes them behave like current sources [42], and the postsynaptic potentials drive various voltage dependent mechanisms at the synapse. Since some events occur at a time scale of 0.5 µsec at the molecular level, information is exchanged at small time steps; however, in order to speed up communication time, the user can configure the system to exchange information at longer intervals. At the end of the simulation, all results are stored inside the database to enable access and retrieval of dynamic relevant information recorded at several levels (biomolecular, synaptic and neuronal). The complex synaptic models used add additional computational capability to neurons making them very powerful in handling multiple interactions. While these synapses can be scaled up, large-scale systems may present load-balancing problems. Though there are 10,000 to 30,000 synapses per neuron, activation of only a few of them (16-26) is sufficient to elicit a spike response [43], and depending on the scientific question, these synapses can be used as per required numbers and the rest replaced with alpha synapses, as defined within the NEURON simulation platform. The capabilities of such integration are innumerable, especially for identifying drug modulators that act at the synaptic level and potentially influence neuronal spiking abilities and further more neuronal network’s synchrony. 2.2.1 EONS – XML representation EONS synaptic modeling platform is based in JAVA with a GUI (Graphic user interface) through which the user can modify parameters of the models through 23 interactive components on the GUI. To enable these synapse models to high-performance computing architecture, a non-interface version of this computational model was created where the underlying parameters of the system are loaded from XML files. Extensible Markup Language (XML) is a language to annotate a document that is both human readable and machine readable[44]. XML files exhibit simplicity in the layout of the data and are also easily interpretable to the human eye. The parameters of the synapses are now defined within ‘tags’ that define the data objects called language elements. There is a hierarchy of relationships among the language elements that are used to create XML schema, where there are parent and children nodes to define objects within objects such as a receptor being parent node and all its kinetic rate parameters being defined as child nodes. Since XML follows strict rules, there are standard parsers to process these files such as DOM (Document Object Model) and SAX (Simple API for XML). Parsers go through these files and make the values available to the JAVA program for further number crunching. Within the scope of this project, this XML based input file formats allow the users to configure the synapse models with different combination of parameters. In addition to that, having multiple files gives the flexibility to run synapses on parallel nodes, as each synapse can be setup to define a unique parameter set. Several custom scripting files were also developed to allow users to change the parameters easily and create numerous files with unique parameter sets. 2.2.2 Message Passing for Java (MPJ) The source code of EONS is entirely implemented in JAVA; to adapt this multisynapse architecture to high-performance architecture, message-passing libraries for 24 JAVA [41] were used to execute parallel applications on computing clusters and parallel processors. This was critical for enabling communication/information transfer between synapses (on slave nodes) and the master node in-charge of simulating the neuron. 2.2.3 NEURON – Python NEURON simulation environment is traditionally based on hoc (higher order calculator) programming. NEURON simulation program developers introduced a newer version of NEURON and extended its capabilities to use with Python [45]. Python is a modern programming language used extensively for scientific and engineering applications. Its well received for its expressive syntax, modularity support and ease of debugging [45]. In addition, it also has the capabilities to easily interface and read XML files. Python wrappers are also used to communicate with JAVA processes. Implementing a communication channel between NEURON simulation environment with Python and JAVA processes of EONS simulation platform was a major technical task in developing this integrated multi-scale platform. Using port communication protocols, we were able to develop the communication channel between the EONS synaptic modeling platform’s master node which collects all individual synapse currents and communicates to Python server through JAVA client and Python server. The NEURON simulation environment calculates the next step and passes the voltage values back to JAVA server, which sends the respective dendritic data to the respective synapses as described schematically in the Figure 2.9 below. 25 Figure 2.9: Core communication method behind synaptic processes programmed in JAVA and NEURON software programmed in Python. Many synapses processes in parallel update their values to a master process –which organizes the order of synaptic data and transmits through Java client to the Python server. These synaptic currents drives voltage changes inside NEURON. Dendritic voltage data from NEURON is sent to python client and is transmitter back to the master process which distributes the respective postsynaptic potentials from the respective dendritic elements to all the EONS synaptic processes. 26 Chapter 3: Synaptic Efficacy as a Function of Ionotropic Receptor Distribution 3.1 Introduction It has been observed that synapses in the mammalian central nervous system often differ significantly in terms of their potency, and that synaptic strengths can change significantly as a function of time and/or use. Most often, these sources of variances in the synaptic strengths have been attributed to presynaptic mechanisms[46]. Studies emphasizing postsynaptic factors, however have given far less importance to the geometry of synapses, and in particular to the postsynaptic arrangement of receptors and/or receptor sub-types. There is evidence that AMPARs, NMDARs and mGluRs exist at different locations within the postsynaptic membrane [47]. These receptors have different kinetics. Given that glutamate released from the pre-synaptic vesicles diffuses across the synaptic cleft, a reasonable hypothesis is that receptors located across the post- synaptic membrane encounter varying levels of glutamate depending on their location. We therefore propose to explore the functional consequences that arise as a result of subsynaptic localization of ionotropic receptors. Also, there is evidence of glial cells ensheathing central synapses, buffering large amount of glutamate within the synaptic vicinity[28]. There are also extracellular ions and exogenous compounds such as magnesium and glycine, which intervene with the receptor activation of NMDA receptors at these synapses. All these factors thus shape the synaptic responses. However, it is difficult to individually test the influence of such contributing factors on synaptic potency experimentally, due to the difficulty in controlling multiple factors at single synapses. In 27 this study, we use the EONS (Elementary Objects of the Nervous System) synaptic modeling platform, which was specifically developed to allow for the exploration of the roles of synaptic geometry, specifically ionotropic receptor localization relative to the release site of glutamate, and receptor kinetics, in the regulation of synaptic efficacy. This biophysical modeling approach allowed us to systematically vary the system’s parameters, which is very hard to realize through usual experimental techniques. In this chapter, we will investigate how interaction between the subsynaptic location of the receptor and its kinetics affects glutamatergic synaptic responses. This is also of interest due to the nonlinearities that arise in response to multiple stimuli due to receptor desensitization. Desensitization is defined as the receptor state in which the receptor is no longer able to open even when an endogenous molecule is bound. Understanding the influence of spatial location of receptors is essential because clustering of glutamate receptors at synapses plays an important role during brain development and in synaptic plasticity of excitatory transmission. The surface trafficking of AMPA receptors either through insertion into the PSD or lateral diffusion can account for tuning synaptic transmission [48] and the receptor alignment with the presynaptic release site can account for STP and LTP [49]. Similarly, synaptic morphology might undergo changes during LTP [50], which leads to alterations in the receptor content and expression at the spine. This could also lead to providing clues to how network stability might arise from the synapse level and how mechanisms like receptor localization might play a crucial role in determining synaptic efficacy. Beyond just understanding the contribution of receptor locations to synaptic potency, it is also crucial to underscore that disruptions of receptor positioning that alter 28 PSD protein mutations and deletions may lead to functional disturbances, which have implications for the pathogenesis of autism spectrum disorders and epilepsy [51]. Figure 3.1: Diversity in subsynaptic architecture and activity patterns give rise to variances in postystnaptic responses Source MacGillavry, H.D., et al., Lateral organization of the postsynaptic density, Mol. Cell. Neurosci. (2011), doi:10.1016/ j.mcn.2011.09.001 In this chapter, we will explore synaptic potency as a function of ionotropic receptor location and other factors such as Mg 2+ concentration, glutamate uptake that may influence the receptor location effects. 29 3.2 Results The synaptic modeling platform allows the investigation of receptor localization influence on synaptic currents at single synapses especially characterized for CA1 hippocampal type neurons, due to their crucial role in synaptic plasticity. Our results section begins with a systematic demonstration of synaptic potency as a function of AMPAR location relative to the source of release for a single quantum of release elicited by single input pulse. In this section, our simulation results show the probabilities of the receptor in a desensitization state or open conducting states as a function of glutamate occupancy, based on the location of the receptor. Next, we apply the same input simulation protocol to analyze the synaptic currents mediated by NMDAR and how its localization on the membrane influences its internal states. In addition, since AMPARs and NMDARs co-exist in most CA1 hippocampal synapses, we provide a few examples to demonstrate EPSCs scaling as a function of ratio of AMPAR to NMDAR using Mg 2+ concentration as a tuning factor to control scaling of EPSC responses. Relative timing between two input events is critical to determine if a receptor exhibits higher or lower response to the second event compared to the first. Hence we simulated the ionotropic receptor responses to paired pulse input stimulus over a large range of interpulse intervals, 10ms to 2s. Lastly, we also model the effect of astrocytic glutamate uptake at synapses to examine if glutamate uptake activity enhances or suppress the receptor location effects on paired pulse ratios of EPSCs. 30 3.2.1 Synaptic potency as a function of AMPAR location We first focused on studying the influence of the location of AMPA receptor population, which was varied along the PSD relative to the release site on synaptic potency. AMPA receptor(s) were placed in concentric circular strips separated by 20nm. The location of the receptors was varied from 0 to 200nm in increments of 20nm. AMPA receptors have 4 glutamate binding sites. These receptors require at least 2 glutamate molecules to be bound for the associated Na+ channel to open. Based on the number of glutamate molecules bound, the receptor enters into different states such as desensitized, deactivated, open, or closed. There are many mathematical models that closely depict the kinetics of AMPA receptor response to glutamate binding ([52],[12]). The AMPA receptor model used here [12], shown in Figure 2.5, is an elaborate model built to capture desensitization effects induced by glutamate occupancy. This model captures the AMPAR desensitization state when 1,2,3 and 4 glutamate molecules are bound. In general, there is variability in AMPAR location across the PSD [25, 53]. Based on its proximity to the source of glutamate release, the receptor could be occupied by ‘n’ molecules at any point in time (n=1,2,3,4). We tested here if the probability of the receptor being in individual states was influenced by its location. AMPAR’s intermediate state responses were simulated for a single pulse of glutamate for 50ms. The location of the receptor was varied from 0nm to 200nm away from the source of release. The results of some key states O2, O3, O4 (open conducting state when two, three and four glutamate molecules are bound respectively simulated for a single pulse) are presented as below (Figure 3.2 Top row). 31 As expected, the responses of AMPAR open states O2, O3, O4 varied as a function of location. However, within the state O2, the receptor located at 140nm had the highest probability of being in that state. In state O3, the receptor located around 20- 40nm indicated a higher probability of occurrence when 3 glutamate molecules are bound. In state O4, the receptor located closest to the glutamate source indicated the highest probability of occurrence. Interestingly, each conducting state has a preferred location where their probability of being in that state is maximum. To show this effect more clearly, the peak values of the responses were captured and normalized between 0 and 1, the ratio of Po n /Po n_max (n=2,3,4) are plotted as a function of the location of the receptor in Figure 3.2 (middle row). The legend below shows the number of glutamate molecules occupied in the four available binding sites. The location where the receptor has the highest probability of being in that open conduction state varied when 2,3 and 4 glutamate molecules are bound. The normalized maximum value shifts towards smaller distances with respect to the release site as the number of bound glutamate molecules increases. However, though we observe such variability in each of the individual states, the conductance associated with each open state (based on the number of glutamate molecules bound) is different. For this AMPAR model, the conductance associated with O2 state is 9pS, O3 state is 15pS and O4 state is 21pS. The weighted sum of all these states gives rise to currents that are dominated by the state O4 and its highly weighted conductance of 21 pS. 32 Figure 3.2: (Top row) Probability of AMPA receptors being in the open conducting states as a function of distance from release site when 2 , 3 and 4 glutamate molecules are bound (shown by filled circles – bottom row). Middle row shows the normalized maximum values scaled between 0 to 1 to highlight the location where the probability of being in that open state is maximum. 33 This weighted sum of conductance times the probability of occurrence in each states, multiplied with the postsynaptic voltage give rise to AMPAR mediated EPSC responses as shown below. The AMPAR mediated EPSC responses as a function of locations of the receptor are plotted in Figure 3.3. The EPSC and EPSP response elicited by the AMPAR closest to the release site had the maximum amplitude. Figure 3.3: AMPA receptor-mediated EPSCs in response to a single pulse stimulus. A gradual decrease in EPSC amplitude is observed when the distance between the release site and the receptors increases. The peak value of EPSC obtained at 0 nm is 52% more than the peak amplitude when AMPA receptors are located 200nm away from the release site. The resulting EPSP values as a result of the EPSC to the left are plotted as a function of distance. As expected the EPSPs mediated by AMPARs closest to the glutamate release site had the highest amplitude, 50% more than the peak amplitude of AMPAR located 200nm away. 34 Figure 3.4: Time–to-EPSC peak response as a function of AMPA receptor location. The time-to-peak EPSC when AMPA receptors are 300nm (marked by blue asterisk) farther away show a 0.5 ms delay compared to receptors located at 0nm (marked by red asterisk) All the EPSC responses were stacked on the same time axis to examine if there was a variation in the time-to-peak response as shown by the red markers (Figure 3.4). AMPA receptors located 300nm farther away from the glutamate source showed a 0.5 ms delay in reaching the maximum amplitude of response compared to receptors located at 0nm. AMPA Receptor occupancy and Desensitization: Receptor desensitization is an important property, as it determines the time during which receptors cannot respond to subsequent pulses of glutamate. The individual states D2, D3, D4 (desensitized when two, three and four glutamate molecules are bound) showed much variation in the desensitization responses as shown in Figure 3.5 below. Especially D3, D4 states, the AMPARs closest to the release site, show a high probability of being in these states. However, the overall desensitization response (summation of all 35 these individual desensitized states, including the state when no glutamate is bound) Figure 3.5: Desensitization of AMPAR as a function of its location relative to the glutamate release site Individual plots from top represent probability of desensitization profile when (A) 2 glutamate molecules are bound. (B) 3 glutamate molecules are bound and (C) 4 glutamate molecules are bound. (D) Overall desensitization as a sum of all individual states including when 1 glutamate molecules is bound and no molecules are bound. There are trends in the profiles as a function of location as these are dependent on the glutamate concentration. However overall desensitization (sum of all desensitized D states) is relatively similar across all locations as the receptor is likely to be in desensitization state D0 (when no glutamate are bound) for a longer period of time. 36 did not vary significantly. The results showed that the receptor had a higher probability of being in state D0 (when no glutamate is bound) and overall desensitization is dictated by the dynamics of this state, hence we did not observe much variation. Receptor occupancy is also a key determinant of synaptic potency, as receptor saturation would limit the range of synaptic responses at a single synapse. We thus calculated receptor occupancy based on binding probabilities of 0.5 when 2 out of 4 glutamate binding sites are occupied, 0.75 when 3 out of 4 binding sites are occupied and 1 when 4 out 4 binding sites are occupied and weighted the sum of all states to obtain the values shown in Figure 3.6. The mean value of AMPA receptor occupancy (marked by red dots) across all locations is around 0.59, consistent with the observation of peak open probability of AMPARs is 0.6 [52, 54]. Figure 3 6: Probability of glutamate occupancy (peak values) plotted when the AMPAR is present at locations 0 to 200nm (Plotted along the X-axis). 37 3.2.2. Synaptic potency as a function of NMDAR location A similar analysis was conducted for NMDAR localization. NMDAR location was varied from 0nm to 200nm away from the source of release in steps of 20nm. The NMDAR mediated EPSCs and the internal receptor states such as desensitization and open states are reported here. The NMDA receptor model borrowed from Ambert et al., takes into account two binding sites each for glutamate and its co-agonist, glycine. It also captures receptor desensitization and has been validated in comparison with several experimental protocols [22, 55]. Two open states of the NMDAR model were examined here as a function of location of the NMDA receptor. Unlike the AMPAR, which demonstrated a location dependent conducting effect, the NMDAR did not show much variation in each of its open conducting states (See Figure 3.7). The probability of opening remained in the range of 0.3 for NMDARs at different locations. The open states Open1 is associated with a conductance of 40pS and Open 2 with 247pS. The resulting synaptic currents are a weighted sum of conductance values with their respective open state probabilities, also taking into account voltage dependent Mg 2+ blockade of NMDAR channel. The Mg 2+ concentration used for these simulations is 1mM. 38 Figure 3.7: The two open states of NMDAR model used here, plotted as a function of receptor location. There is not much variation in the individual state probability of being in the open states whether the receptor was located close to the release site or farther away. Open state 2 did show a slight variation as a function of receptor location, but the scale s in the order of 10 -3 39 Figure 3.8: NMDAR-mediated EPSCs and EPSPs as a function of NMDAR location. There is no significant contribution of NMDAR location on the NMDAR-mediated EPSCs and EPSPs. Since experimental evidence indicates a range of 5-30 NMDA receptors per synapse [24], we used 20 NMDA receptors in our study to scale the EPSC responses. 40 NMDA receptor-mediated EPSCs as a function of receptor location are shown in Figure 3.8a. As previously reported [56],[57] there is no significant difference between the responses of receptors placed close to the release site compared to those placed farther away. In our simulation results, there were not much location dependent amplitude differences NMDA receptor-mediated EPSPs (Figure 3.8b); these results reflect the relatively high affinity of glutamate for NMDA receptors, which essentially eliminates the influence of location based on receptor occupancy. Along the same lines, in a separate study, we analyzed the effects of glial glutamate transporters on NMDA receptor kinetics [58], and showed that the time course of decay of NMDA receptor-mediated synaptic responses was inversely related to the density of glutamate transporters, but that this influence remained quantitatively limited. 3.2.3. Summation of AMPA-R mediated EPSCs and NMDA-R mediated EPSCs, Mg 2+ as a tuning ratio In 85% of all matured CA1 hippocampal synapses, AMPARs and NMDARs co- exist [59, 60]. The ratio of AMPAR versus NMDAR numbers and their conductance values are important determinants of the shape of EPSC waveform. The EPSC quantal size and quantal content may vary with the developmental stage of the animals as shown in some experimental studies. The AMPA receptor content increases with development [61], resulting in EPSCs having a much sharper rise time. In addition to that, a factor such as extra-cellular magnesium concentration shapes the NMDA-mediated EPSC component. For example, in the following Figure 3.8 one would notice the sharp AMPA- R mediated component when the Mg 2+ concentration was set to 1 mM. At that concentration, Mg 2+ blockade reduced the NMDA-mediated component of the EPSC. 41 However for a moderate concentration at 0.5mM, the EPSC had a predominant NMDAR mediated component. We should be cognizant that these variations in extracellular concentration of compounds can indeed have a profound effect on the shape of the EPSC waveform. This information is important for the reader to understand the analysis of the results in the following section, which includes these Mg 2+ dependent effects on EPSC waveforms elicited by paired pulse protocol simulations. Figure 3.9: EPSCs (shown in red) described here are a summation of AMPA-R (blue dotted line) mediated and NMDAR-mediated currents (green dotted line). When the Mg 2+ concentration varies from 1mM to 0.5mM, the NMDAR mediated current scales to higher amplitude, changing the envelop of EPSC (in red). 3.2.4. Paired-Pulse ratio as a function of the location of AMPA and NMDA receptors The timing interval between two subsequent input spikes may have a profound impact on the post-synaptic activity of neurons. We propose to analyze in the next section 42 the effects of synaptic localizations of both AMPA and NMDA receptor-channel population in response to paired-pulse stimuli. For these simulations, we will use the term paired pulse ratio to quantify synaptic efficacy. The paired pulse ratio is generally calculated as the ratio of the maximal peak amplitude of the EPSC elicited by the second of two pulses divided by the maximum amplitude obtained for the first EPSC. In the context of a pair of inputs, the amplitude of the EPSC associated with the second input can be smaller or larger compared to the response to the first pulse. After the first release event, a number of factors involved in the release event can change the response to the second input. For example, paired pulse facilitation is explained as an increase in a cell’s release probability on the arrival of a second input spike following a first spike. This is most commonly associated with presynaptic factors; however, there is also evidence supporting postsynaptic origination of paired pulse facilitation [62]. The increase or decrease in the presynaptic response is attributed to many mechanisms such as residual calcium hypothesis, vesicular depletion (which are pre-synaptic in origin) [63], and postsynaptically Ca 2+ driven AMPA-R properties are shown to regulate synaptic facilitation [64]. The facilitation or depression effect of the second postsynaptic response is also determined by the input timing intervals [65]. For the purpose of this study, all conditions that determine presynaptic NT release, driven by calcium buffers and calcium pumps are the same for the two input pulses, i.e. the amount of neurotransmitter released for both pulses is the same (See methods) – this condition was set to isolate all presynaptic sources of quantal variability. The variations in postsynaptic responses obtained are purely a result of postsynaptic receptor properties and the glutamate binding associated with them. 43 We examined the EPSC responses elicited by a paired pulse stimulus for various inter pulse intervals; the EPSC responses elicited by paired pulse stimulation where the inter pulse interval is 10ms is shown as an example in Figure 3.10. When AMPARs are at 0nm, the peak EPSC amplitude to the second pulse is 80% of the first pulse shown in red (Figure 3.10). However this difference in peak response between the first and second pulse decreases as AMPA receptor distance from the release site increases. When receptors are at 200nm, the response to the second pulse is almost 96% of the first pulse response. Indeed, there is a gradual decrease in the amplitude of the first pulse response as a function of receptor location since the glutamate concentration available is less at a farther location. One factor seen in these results is that the EPSCs simulated here are summations of AMPAR and NMDAR mediated responses. The second sharp peak of EPSC (evoked by AMPAR) rests on the baseline of the EPSC response contributed by NMDARs response to the first peak. 44 Figure 3.10: A schematic of the PSD and the receptors located on it elicited by a paired pulse stimulus with an inter pulse interval of 10ms. The EPSC waveforms (shown in red and blue) as a result of ionic current flow from both AMPAR (located right opposite to the glutamate release site and at 200nm respectively) and NMDAR. The paired pulse ratio (PPR) as explained in Box B is a ratio of max. amplitude caused by second response to the maximum amplitude of the first response. When the AMPAR is closer to the release site the PPR~0.85 and when farther away PPR~0.96 In all the simulations that follow, the AMPAR locations were varied from 0 to 300nm in increments of 20nm. NMDARs were held at a constant location since they did not demonstrate any location dependent contribution towards EPSC amplitudes (as shown in section B). The AMPARs locations were varied along one axis. The simulations were repeated for time interval between the two pulses (inter pulse interval) at 10ms, 20ms, 30ms, 50ms, 100ms, 200ms, 300ms, 500ms, 1000ms and 2000ms. The paired pulse ratio obtained from each simulation is then plotted on the z-axis of the surface plot. 45 Figure 3.11: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations). The paired pulse ratios vary between 0.8 to 1.18 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals. The above Figure 3.11 shows that the paired pulse ratios varied within a range of 0.8 to 1.15, a PPR value of 0.8 corresponds to the case when the second peak amplitude is 80% of the first peak amplitude, occurs when the AMPARs are located close to the release site and PPR=1.15 corresponds to second peak being 15% more than the first peak amplitude, occurs when the AMPARs are located 30nm away the release site. This range is predominant for the paired pulse interval of 30ms. The range of ratios is indicated by the color bar index on the right. These ratios varied as a function of both AMPAR location and inter pulse interval. We simulated for even longer inter pulse intervals at 500ms, 1000ms and 2000ms. We did not observe any location dependent variation in the paired pulse ratios. 46 In subsequent simulations Mg 2+ concentration was reduced to 0.5mM to analyze the relation between paired pulse ratios as a function of AMPAR location and inter pulse intervals. Since Mg 2+ plays an important role in mediating currents through NMDA channel, Mg 2+ concentration determines the amplitude/shape of the EPSC response as demonstrated previously (Figure 3.9). Decreasing the Mg 2+ blockade could enhance the synaptic response envelope, which means the AMPAR mediated peak now rests on a higher baseline and hence a higher amplitude in response. The 3D surface plot for this condition of 0.5mM Mg 2+ is shown below. As expected, the paired pulse ratios were now distributed over a wider range from 1 to 1.7. Figure 3.12: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations) for a decreased concentration of Mg 2+ (to simulate the effect of partial unblocking of NMDA receptors by Mg 2+ ). The paired pulse ratios vary between 0.95 to 1.75 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals (10-100ms). For longer paired pulse intervals, we did not observe any dramatic changes in the PPR values. 47 In addition to factors such as Mg 2+ that modulate the synaptic waveforms, there are additional contributing factors such as glutamate uptake mediated by astrocytic processes, which flank the synapses. Depending on the area of coverage and the density of glutamate transporters within the astrocytes, the glutamate concentration value varies within the synaptic cleft. The glutamate transporters within the astrocytic ensheathment around synapses act as huge sinks for glutamate. This is important because the glutamate uptake itself can alter the time decay of EPSC responses as shown experimentally [31] and in simulation studies. Inclusion of glutamate uptake activity by surrounding glutamate transporters changed the paired pulse ratio range from 0.9 to 1.9 (Figure 3.13). This is the largest range observed across all the paired pulse simulations, indicating that glutamate uptake modifies the decay time course which directly influences the baseline NMDA mediated EPSC waveform and AMPAR mediated peak amplitudes. Also the peak values are now more inclined towards lower input pulse intervals indicating that the glutamate uptake effect is more predominant at these intervals. 48 Figure 3 .13: Figure 3 l: Paired pulse ratios (collected from 16x11 simulations - AMPARs located from 0nm to 300nm (16 data points along X-axis) and for inter pulse intervals for 10 to 2000ms (11 data points along Y-axis) simulations) in the vicinity of glutamate uptake. The paired pulse ratios vary between 0.9 to 2 (as indicated on the color bar). These PPR variations scale as a function of AMPAR locations, however only for certain inter pulse intervals (20-30ms). 3.3 Discussion Within the scope of this chapter, we specifically focused on the effect of postsynaptic geometry i.e., receptor localization effects on synaptic response. We tested this hypothesis and varied ionotropic receptors location while recording synaptic efficacy using the EONS synaptic modeling platform. We observed the influence of subsynaptic localization of AMPAR and NMDAR on synaptic responses such as postsynaptic currents (EPSCs) and potentials (EPSPs). In addition, we also identified some key parameters such as Mg 2+ and glutamate uptake that can shape these influences. We believe that the numerous elements present at the synapses give rise to multi- dimensionality feature and specificity for synapses. 49 It is important to study the influence of spatial location of receptors and the functional implications they will have on the synaptic responses. Immunogold labeling studies show variations in subsynaptic localization of NMDARs, which are more centrally located within the PSD and AMPARs and are more uniformly distributed across the PSD [24, 66]. Also, there is evidence of receptor movements demonstrated by single particle tracking experiments showing the lateral movement of AMPAR trafficking [67]. These movements of the receptor itself could be associated with synaptic maturation and tuning synaptic transmission [68], indicating that receptor localization dependent effects may influence synaptic function in different ways. Variability in postsynaptic currents could also be a result of such location dependent effects of receptors. (i) We have validated the amplitude variances in AMPAR and NMDAR mediated EPSCs as a function of their spatial locations in response to a single release event. Our results are qualitative in good agreement with some phenomena reported in previous studies [56], [51, 57, 69]. However, both simulation and experimental results obtained from SDL- digested freeze-fracture replica labeling studies in corticogeniculate and retinogeniculate synapses showed minor influence of density and distribution of ionotropic receptors on postsynaptic responses [70]. In fact assuming a uniform distribution and density of AMPARs will average out the responses across individual receptors. This could be the reason why results from these studies [29] show averaged responses. Here we varied the AMPAR location systematically in increments of 20nm assuming imaginary concentric circles within a PSD. A single AMPA response was multiplied with 80 (80 being the number of receptors) to match the quantal responses of the range 5-20pA as reported within single boutons [71]. Modeling the response of one 50 AMPAR and scaling it by a factor of 80 is equivalent to the response of 80 AMPARs because the radial distance of activation is similar and they summate linearly. This modeling choice was made to avoid the computational burden of simulating so many ODEs. (ii) The parametric structure of the modeling platform allowed us to explore the internal state receptor dynamics such as desensitization and receptor occupancy as a function of the receptor location. AMPA receptors, which are sensitive to their position relative to the release site, seemed to have an optimal distance where they have the maximal probability of being in open conducting state. Depending on the number of glutamate molecules bound to the receptor. The glutamate concentration available to the receptor is a key determinant of glutamate occupancy. This value varies within the surrounding environment with glutamate uptake and glutamate spillover from neighboring synapses. For this simulation study, single vesicular release architecture was used. There is evidence of most hippocampal synapses having univesicular sources of glutamate release [72-74]. Moreover, though many studies point to the evidence of multi- vesicular release [75-77], there are arguments that, vesicles are not released at the same time, instead even if a presynaptic compartment had two vesicles, what really determines the receptor response is the glutamate concentration available at the receptor binding sites, which is determined by the location of the receptor, relative to the source of glutamate release. (iii) AMPA receptor responses were more sensitive to its spatial location while the NMDA receptors, due to their high binding to glutamate and slower unbinding rate [55, 78] did not show much variation in response as a function of their location. The 51 binding affinity of glutamate to receptors varies across receptor sub-types and their responses are highly frequency dependent [79]. Here we focused on a generic NMDAR present at the hippocampal synapses. We did not delve into the details of the subtypes in this study, which will be the focus of our future studies as the platform gives the flexibility to use any receptor sub-type model. (iv) The timing between subsequent inputs/release events is a critical determinant of receptor recovery and saturation. We used paired pulse inputs to determine synaptic efficacy, i.e. the peak amplitude value elicited on the second pulse to the peak amplitude elicited by the first pulse. This kind of evaluation will determine the postsynaptic determinants of facilitation or depression at these synapses. We used location of AMPARs as one such postsynaptic factor that could influence the synaptic facilitation or depression. We observe a sharp facilitative effect on all of the 3D surface plots for a time interval of 20-30ms. This could be due to the underlying dynamics of NMDAR responses whose rise time is 30ms, which means the maximum amplitude of the NMDAR mediated occurs around 30ms after the instantiation of the pulse. If the AMPAR mediated peak response elicited by the second pulse is added to the NMDAR mediated amplitude during the rising phase, the second pulse response could be facilitative. If the AMPAR-mediated peak occurs on the decay phase or the normal base line, the second pulse response can appear depressive. If the time interval is very large between the two pulses, the receptor’s response decays back to base line and the peak amplitudes elicited by both input pulses will be similar giving rise to a paired pulse ratio of 1. We observed a paired pulse ratio of 1 for all inter stimulus intervals ranging from 500ms – 2000ms, given that the NMDAR response decay for this model is 500ms in agreement with experimental data [55]. Hence, 52 the amplitude fluctuations induced by AMPARs location and the timing dependent effects together give rise to EPSC variations. (v) In addition to the simple additive effects of EPSC responses from both the ionotropic receptors, factors such as Mg 2+ concentration and glutamate uptake within the synaptic vicinity have a direct influence on the peak amplitude and time decay responses. This was explicitly discussed in other publications [21, 58]. These factors indirectly will have an effect on the EPSC waveforms and the facilitation and depression effects. We believe that critical modulators such as glutamate uptake capacity add additional dimensions to synapses that induce variability in synaptic amplitudes. (vi) We also acknowledge the complexities that arise due to the changing ratio of NMDA and AMPA receptor numbers. At some stage of the synapse, NMDARs outnumber the AMPARs supported by the evidence of silent synapses [80]. Under such conditions, location dependent effects of receptor distribution will not contribute to postsynaptic variances because receptor location has almost negligible effect on NMDAR-mediated responses. For this simulation study we assumed a constant density of 80 AMPARs and 20 NMDARs per concentric circular ring, consistent with the reported numbers of NMDARs between 5 and 30 [24, 25]. This is usually a scenario in adult synapses. Two-photon uncaging of glutamate technique was used to map functional glutamate receptors at the level of single synapse, such studies have shown that mushroom spines have larger more complex PSDs and there are up to 40-140 per spine, but much sparsely distributed in thin spines [81]. So we have chosen the average value for the numbers, consistent with that reported in literature. 53 (vii) Overall, it is the interplay between spatial location of AMPAR, density and conductance of these channels and the pre-synaptic pattern of activity combined that influence synaptic potency. Our results underscore the importance of ionotropic distribution that mediates filtering synaptic responses. They support our beliefs that alterations in synaptic structure and the underlying receptor distribution contribute to synaptic plasticity. Synapses act as interfaces for neuronal information processing. Alterations in their subsynaptic architecture due to neurological disorders, which cause disruptions to structural machinery, will eventually lead to alterations in neuron spike processing abilities. The computational synapse model developed here and its integration into a morphologically realistic neuron model within our integrated multi-scale framework [1] will enable us to achieve greater insight into how ionotropic receptor distribution can influence neuronal spike timing. This will be focus of our future work. Identifying these subtleties at synapses that arise due to minor variations in the distribution of receptors might eventually give clues to the functional diversity that arise from these varieties of receptor expression. 54 Chapter 4: A Computational Model to Investigate the Influence of Astrocytic Glutamate Uptake on Synaptic Transmission and Neuronal Spiking 4.1 Introduction 1 Until a few decades ago the quest to better understand high-level brain functions, such as learning, memory and cognition, mainly focused on investigating the rapid, spike-based information processing performed by neurons. Glial cells, and among them astrocytes, were largely regarded as passive support cells, providing neurons with nutrition and structural support without directly participating in information processing functions [82]. Over the past twenty years, however, a growing body of evidence has demonstrated that astrocytes do participate in bidirectional signaling with neurons and, therefore, possibly play an important role in shaping communication in the brain [83, 84]. These findings demand a revision of the traditional neuron-centric model used to explain higher order brain functions to include astrocytes as part of a neuron-glia network model. Within this new framework, signaling includes both, fast spike-based processing and slower modulation mediated by astrocytic elements [85]. In this chapter, we propose to study the effect of astrocytic glutamate transporters on neuronal spiking within this improved framework (Figure 4.1). We used the framework presented in Chapter 2, where molecular level processes can be linked to neuron level spiking activity to investigate the effect of astrocytic glutamate uptake on the classical presynaptic-postsynaptic synaptic model. 1 Content published in [58] 55 Within this new framework, including the astroglial effects of glutamate uptake (Figure 4.1), interact with elements at the molecular level and more specifically on the three classes of glutamate receptors, ionotropic receptor-channels, AMPAR (α-amino-3- hydroxy-5-methyl-4-isoxazolepropionic acid receptor) and NMDAR (N-Methyl-D- aspartate receptor), and mGluR (metabotropic glutamate receptor). At the synaptic level, ion fluxes through these receptor-channels give rise to synaptic responses of varying time courses and amplitudes depending on channel kinetics. These responses sum in a nonlinear spatio-temporal manner and evoke spiking activity in neurons. A network of these neurons constitutes the system that emulates a physiological function including the astrocytic influence. Figure 4.1: Multi-scale framework of the CNS hierarchy including molecular, synaptic, neuronal, and network level including glial cells., modified from Bouteiller et al. (2011). The molecular level is illustrated with a kinetic schema of the NMDA receptor. The synaptic level includes several molecular elements and their spatio-temporal interaction. The neuron level comprises morphologically realistic neuron model with synapses (blue circles) randomly located on dendritic branches surrounded by astrocyte processes (green arcs). The network level takes into account the interaction between neurons and glial cells, especially the effect of glial glutamate uptake was modeled here. 56 Figure 4.2: Functional diagram of the EONS synapse model including: glutamate diffusion inside the cleft, AMPAR, NMDAR, mGluR, and glutamate uptake mediated by glial (EAAT2) and neuronal transporters (EAAT3). The green cylindrical ensheathment represents the astroglial process on which EAAT2s are expressed. This representation is referred to as the tri-partite synapse. 57 One particular type of glial cell, the astrocyte, has thousands of processes and extensions that are often found in close proximity to hundreds of synapses, which it can potentially modulate [86]. Additionally, it has been discovered that astrocytes express large amounts of neurotransmitter receptors and transporters [87]. Since a neuron’s pre- and postsynaptic nerve terminals are often ensheathed by astrocytes, which participate in synaptic signal processing, the term tripartite synapse was coined [26]. We modeled this tripartite synapse model by extending the existing EONS modeling platform by adding an astrocytic component as illustrated in Figure 4.2. Within a tripartite synapse, biochemical and morphological studies suggest that excitatory amino-acid transporters (EAATs) expressed on astrocytes are of the type EAAT2. These glutamate transporters maintain low extracellular glutamate concentration, which prevents neurotoxicity in spinal cord, striatum, and hippocampus [27], and may play a functional role in regulating synaptic currents by clearing glutamate after its synaptic release [28]; [31]. Neuronal transporters (EAAT3) also take up glutamate from the extracellular space, however, at a significantly lower rate than astrocytes due to their lower expression levels [27]. The role of neuronal transporters could be to limit glutamate spillover and to slow down glutamate clearance by glial transporters [88, 89]. The importance of astrocytes in the regulation of glutamate uptake, the transformation of glutamate to glutamine [90] for re-usage in synaptic transmission, and epilepsy pathogenesis has recently been reviewed [91]. Several studies demonstrated that astrocytes not only uptake glutamate inside a tripartite synapse, but under certain conditions, can also release glutamate [92], through a process termed gliotransmission [93]. This term describes the process of glutamate 58 release from astrocytes due to an increase in intracellular calcium via mGluR-mediated mechanisms in response to neural signaling inside a tripartite synapse [94-96]. Because of the astrocyte’ structural characteristics and biochemical signaling mechanisms, these cells may play an important role at the neuron and network levels of the CNS hierarchy [97]. However, the exact manner in which astrocytes communicate with neurons in vivo is still unclear. For example, the effect of glutamate uptake in synaptic transmission, and on neuronal spiking, is difficult to verify using state-of-the-art experimental procedures. Furthermore, several experimental and review articles have been published that challenge the tripartite synapse concept [98] [85], and raised a number of issue regarding the way astrocytes contribute to synaptic signaling by performing feedforward and/or feedback action through the uptake and release of neuro- and gliotransmitters [99]. One of the primary reasons why these disagreements cannot easily be resolved, is the lack of experimental techniques to directly study astrocytes and their biochemical signaling mechanisms [85]. Since astrocytes are generally not electrically excitable (do not generate action potentials), techniques for measuring glial cell activity mainly rely on imaging for in vitro studies or genetic manipulations for in vivo experiments. Hence, experiments are often performed under non-physiological conditions [85], as in vitro experiments do not represent the natural environment of these cells and their responses might be drastically amplified. Disabling astrocytes through genetic manipulations is equally non-physiological and might result in compensatory effects in vivo [99]. One promising approach that can resolve these uncertainties is to use computational models. Such models provide opportunities to analyze the behavior of the system in 59 response to various stimuli in physiological conditions otherwise difficult to conduct experimentally. In recent years, many computational modeling groups have demonstrated the glial influence within synaptic, neuronal, or network dynamics. Astrocytic effects on spontaneous activity at the postsynaptic level were characterized [100]. The effects of glutamate release from astrocytes on neuronal depolarization and activity were also modeled [101]. Computer simulations also demonstrated that neuron-glia interactions, which are in part mediated by potassium ion fluxes between the two entities [102]. Finally, a modeling approach with bi-directional communication and synchrony between astrocytes and neuron clusters was also presented [103, 104]. Our modeling approach integrates the dynamics from the molecular to the neuronal level and provides an original framework that allows for a better understanding of the effects of glia in a hierarchical manner. This modeling methodology mimics the structure of the central nervous system which spans several spatial and temporal scales and forms a hierarchical system from the bottom–up: molecular to synapse level, synapse to neuron level, and neuron to network level, with the inclusion of glial interactions. In this chapter, we will focus on studying the role of astrocytic glutamate uptake on synaptic responses and how it can modify neuronal spiking within the context of this modeling framework (Figure 4.1). We observe that glial glutamate uptake is important to decrease desensitization of ionotropic glutamate receptors resulting in enhanced paired pulse facilitation for very short input intervals. Based on these observations, we propose that the time interval between input pulses and the interactions between receptors and transporters significantly contribute to neuron spiking patterns. Our model provides a 60 unique method to assess critical parameters that can influence neural network behavior in relation to glutamate uptake. 4.2 Results 4.2.1 Effect of astrocytic glutamate uptake on postsynaptic currents The EONS/Rhenoms TM modeling platform allows the investigation of critical parameters that modulate synaptic transmission and neuronal spiking. In this chapter we study the effects of EAATs within the astrocyte membranes surrounding CA1 hippocampal neurons on neuronal activity. The result section begins with a demonstration of the model’s fidelity in replicating the influence of astrocytic glutamate uptake at the synapse level, as previously shown [28, 31, 105]. We then build on these results and propose to investigate how astrocytic glutamate uptake influences ionotropic receptors’ responses for different input stimulation protocols such as paired-pulse and random interval trains. The molecular level effects, such as receptor desensitization and transporter saturation, arising from the relative timing between the inputs (glutamate release from single vesicular sites) are demonstrated. We believe that understanding the interactions between these molecular level elements through simulation studies provide insights into synaptic level responses that are difficult to explore experimentally. In this work, we demonstrate how sub-cellular responses can affect neuronal spiking. 4.2.1.1 Astrocytic glutamate uptake decreases peak amplitudes of AMPAR- mediated EPSCs AMPARs are known for their crucial role in mediating fast excitatory synaptic transmission. AMPARs and NMDARs co-exist at many central glutamatergic synapses 61 [59] and have very distinct kinetics contributing to the fast and slow components of the EPSCs respectively [106]. It was previously shown that astrocytic glutamate transporters do not shape the decay of non-NMDA receptor-mediated synaptic responses [105]. We proposed to test if our synapse model (described in chapter 2) yielded the same effects and studied the role of glutamate uptake on current going through the AMPARs channels in response to a single vesicular release. We simulated AMPAR- mediated EPSCs for a single pulse input with 50%, 100% glutamate transporter densities which correspond to transporter numbers between 325-650 and without glutamate transporters. These three cases were chosen to demonstrate the effect of glutamate transporters at moderate and extreme cases of transporter density on astrocytes. Figure 4.3A shows the values of peak amplitude responses of AMPAR-mediated EPSCs plotted against varying density of glutamate transporters. AMPAR currents obtained here are in response to a single presynaptic input pulse eliciting a single vesicular release of glutamate as a function of the number of surrounding astrocytic glutamate transporters. Due to increased density of transporters and hence more glutamate uptake, glutamate input to AMPARs is decreased. As expected, the amplitude of AMPAR-mediated synaptic responses decreased with increasing number of transporters. The red line in Figure 4.3A is a linear regression fit to the data (in black) with a correlation coefficient of r 2 =0.69. Figure 4.3B shows the normalized AMPAR-mediated EPSCs in response to a single release event with (50% and 100% density) and without transporters. These results indicate that the decay of the time course remains the same with 50% transporter density and without the transporters. However, at 100% density of transporters, the peak itself is shifted, which could be due to elevated glutamate uptake, but the time course decay is 62 also unchanged. Since AMPARs are sensitive to glutamate concentration, removal of glutamate from the cleft due to buffering or uptake by EAATs modifies this concentration and thus affects the AMPAR-mediated responses. Figure 4.3: Simulated AMPAR and NMDAR mediated EPSCs in response to varying density of glal glutamate transporters (A) The increased number of glutamate transporters affects the peak amplitude of AMPAR-mediated current due to uptake of glutamate. (B) Normalized responses of AMPA mediated EPSCs elicited from a single input pulse for cases with no transporters, 50% density and 100% density of astrocytic glutamate transporters. The decay time course of normalized AMPAR currents with 50% density and without any transporters did not show any change. (C) Glutamate uptake by the glial transporters affects the decay time course of NMDA receptor-mediated EPSC. An increase in the density of transporters results in an increase in the rate of uptake thus decreasing the decay time of NMDA receptor-mediated EPSC. (D) NMDAR-mediated EPSCs with glial glutamate uptake (red), and with both glial and neuronal uptake (blue). The uptake mediated by neuronal transporters (EAAT3) is not significant 63 4.2.1.2 Astrocytic glutamate uptake influences decay phase of NMDAR-mediated EPSC time course Unlike for AMPARs, the responses of NMDARs are slower [55]. Numerous experimental studies report that glutamate uptake mediated by glia and neuronal transporters significantly influences the decay phase of NMDAR-mediated EPSCs [28, 29, 31]. It is important to study the role of glutamate uptake on NMDARs. Figure 4.3C shows the simulated responses of normalized NMDAR-mediated postsynaptic currents to a single release event with 50% and 100% densities, and without transporters. Our simulations confirm previously reported results suggesting that an increased number of EAATs leads to an increase in glutamate uptake, which causes a faster decay of NMDAR-mediated EPSC. Thus, increased expression and density of glutamate transporters could possibly account for the increased glutamate uptake observed as developmental changes that occur with age in NMDAR-mediated EPSCs between P14 and adult rat pyramidal cells (Diamond, 2005). We also explored the role of the neuronal transporters, which are located within perisynaptic regions (He et al, 2000) on NMDAR-mediated EPSCs. Neuronal transporters at a density of 90/um 2 [33] were placed within the presynaptic annulus of radius 100-400 nm. Figure 4.3D shows NMDAR-mediated EPSCs elicited in response to a single pulse taking into account glutamate uptake mediated by glial transporters (EAAT2) shown in red and the combined effect of glial and neuronal transporters (EAAT3) shown in blue. Our simulation results showed that uptake by neuronal transporters at the reported numbers [33] did not significantly affect NMDAR- mediated EPSC responses, in contrast to glia-mediated glutamate uptake, which showed a stronger effect NMDAR-mediated EPSCs 64 4.2.1.3 Astrocytic glutamate uptake effect on paired pulse responses is different for small and large input time intervals In this section we investigate the influence of astrocytic glutamate uptake on EPSCs mediated by both AMPARs and NMDARs for a paired pulse input. The fast component of the EPSC is mediated by AMPARs and the slow component is mediated by NMDARs [106]. The quantal value of EPSCs may vary with developmental stage or age of the animals [61], as differential expression and density of AMPA and NMDA receptors will result in different values of AMPAR- and NMDAR-mediated components. For this study, we use AMPA to NMDA receptor ratio of 80 to 20 (See methods). The paired pulse protocol is commonly used for testing presynaptic effects on EPSCs [107] by changing the timing between two release events. Figure 4A shows the composite EPSCs to paired pulse inputs for different input intervals from 10 to 500 ms with (dark gray traces) and without glutamate transporters (light gray traces). The asterisks highlight the peak amplitudes of the EPSC with (red) and without (blue) glutamate uptake. To better demonstrate the effects of glutamate uptake for shorter input intervals, the results are plotted on a logarithmic time scale. In Figure 4.4A, the difference in the peak amplitude of the response to the first pulse with and without glutamate uptake is significant. For input intervals up to 100 ms, we observe paired pulse facilitation (peak amplitude of the second pulse is larger, as compared to that of the initial pulse) with glutamate transporters, and paired pulse depression (peak amplitude of the second pulse smaller, as compared to that of the initial pulse) when there are no transporters. For larger intervals, however, this facilitation/depression effect becomes less prominent in both cases, with and without glutamate transporters. 65 Figure 4.4 Astrocytic glutamate uptake effect on paired pulse responses is distinct for small and large input time intervals. (A) Composite EPSCs elicited by paired pulse stimulation plotted against input time intervals separated by 10–500 ms (Time axis in log scale to zoom into the effects at shorter input time intervals for all plots). First pulse response indicated by black arrow. Paired pulse depression (PPD) effect is observed for responses when no transporters are present (light gray, peaks marked by red asterisks). With the presence of transporters and astrocytic glutamate uptake (dark gray, peaks marked with blue asterisks), there is a paired pulse facilitation (PPF) effect observed for responses when the input time intervals are short. This reversal of effect from PPD to PPF is only apparent for shorter input time intervals. (B) The probability of the AMPARs to be in desensitization states as a function of input time intervals. These receptors are 66 highly desensitized for shorter input time intervals. (C) The probability of NMDARs to be in desensitized states. The NMDARs are highly desensitized and this increases with increasing input time intervals. (D) HGN3To state probability of the glutamate transporter, when H+, Glu, 3 Na+ are bound to the transporter. Glutamate uptake ability is observed within this state, described in detail in section 2.1.1.4.1. The transporter recovers to this same state only after longer input time intervals >200 ms. To better explain these effects, we take advantage of the modeling platform features to access the individual desensitization states (probability of receptors being desensitized) of AMPARs and NMDARs. The probability of the desensitized state of AMPARs with two glutamate molecules bound is plotted as a function of paired pulse intervals in Figure 4.4B. At smaller input time intervals, the AMPAR enters into a desensitized state more rapidly, thus reducing its probability of being open or more responsive to the second pulse of glutamate, thereby decreasing the current through its channel. As shown in Figure 4.4C, the NMDA receptor also enters into a desensitized state and the probability of being in this state increases with increase in the time intervals between input pulses, as the receptor takes a much longer time to return to its original resting state. This desensitization property reduces the receptor’s ability to be in the open state in response to subsequent pulses for almost all interval ranges examined here. Figure 4.4D shows the dynamics of the EAAT2 transporter in its HGN3T 0 state (when glutamate, Na + , and H + ions are bound and the transporter is facing outward). These results show that the glutamate transporter has to go through a recovery phase during which the clearance rate is slowed down. This indicates that the transporter may not be in its full capacity shortly after an initial pulse, thereby reducing its responsiveness to glutamate released on subsequent pulses. Evidence for changes in glutamate 67 transporter’s uptake rate and its effects has been reported for different input pulse intervals [31]; [108] and supports our findings. In these studies, glutamate uptake rate was assessed through synaptically activated transporter–mediated anion currents (STCs). In Figure 4.4A, the light gray traces show EPSCs responses elicited by paired pulse inputs. Blue asterisks mark the peak amplitude of the responses. The peak amplitudes on the second pulse elicited after intervals of 10 ms and up to 300 ms are much lower than the peak amplitude of the first pulse. We hypothesize that this effect (paired pulse depression) is due to the desensitization of the receptors during these input intervals, as our results described above suggest. As time intervals lengthen, the peaks elicited by the second pulse slowly recover towards the value of first peak as receptors return to their original responsive state. In the case where glutamate uptake occurs, paired pulse facilitation can be observed, indicated by the red asterisks on the peaks of the dark gray traces for the shorter input intervals. This effect could be due to (i) a significant reduction in the amplitude of the first peak of AMPARs response due to glutamate uptake, as shown in Figure 4.3A for single pulse, as well as (ii) transporter’s recovery time to uptake glutamate with the same efficiency. As seen from these simulation studies, we hypothesize that interplay between receptor desensitization and transporter recovery explains the clear differences in paired pulse responses in the presence (facilitation) or absence (depression) of astrocytic glutamate uptake. These differences disappear as interpulse intervals lengthen, as the transporter recovers to its initial state and receptors recover from desensitization. These simulation results highlight the importance of understanding the interactions between glutamate receptors and transporters at the molecular level and how they modulate responses observed in classical paradigms such 68 as the paired-pulse protocol. They also demonstrate the power of such computational modeling approach to facilitate our understanding of the behavior observed and the interplay between its underlying mechanisms. 4.2.2 Astrocytic glutamate uptake influences neuronal spiking The results presented in the previous sections demonstrate that glutamate uptake influences EPSC kinetics at the synaptic level. Given the hierarchical organization of the nervous system, a critical question we propose to address in this section is whether the local effects at the synaptic level can significantly affect neuronal signaling. The changes in input glutamate concentration profile due to EAATs affect ionotropic receptors and modify the kinetics of excitatory synaptic currents. These currents subsequently change membrane potential in dendrites and thus influence neuronal spiking activity. In order to effectively model these aforementioned phenomena, we simulated a neuron model using the NEURON simulation software that incorporates our detailed synaptic models, as described in the methods section. The neuron model used here [39] has a realistic CA1 pyramidal cell morphology with synapses distributed at random locations within 100-200 µm from the soma. The input to the system is a random interval train (RIT) (average rates at 2 and 5 Hz) to mimic low frequency spiking activities of the CA3 inputs to CA1 under physiological conditions. The synaptic input strength was chosen such that a spike was elicited by synchronous firing of all synapses. This condition makes the neuron very sensitive to threshold levels for firing. The neuron configuration described here is a specific case, and can be configured in multiple ways with respect to synaptic distributions and locations, strengths and ion channel distributions. Previous work has shown how the rate of change 69 of membrane potential contributes to neuronal firing by modifying spiking threshold. In addition to these parameters, the synchrony of excitatory synaptic inputs and previous occurrence of an action potential can also determine the probability of occurrence of the next action potential [109, 110]. Figure 4.5A illustrates the spiking activity of a CA1 pyramidal neuron elicited by a 2 Hz RIT input in the absence (blue) or presence (green) of EAATs. The average number of spikes elicited in the presence of EAATs is smaller throughout the simulation, as compared to that in the absence of EAATs. Figure 4.5C shows a similar result displaying for a 5 Hz RIT input. In addition to spiking activity, the figure shows two critical events marked by * when spikes elicited without glutamate uptake and those with glutamate uptake have a timing difference between 1 and 2 ms and by ** when timing differences are between 3 and 8 ms indicating that glial glutamate transporters may not only affect spiking frequency, but also have an impact on spike timing properties. In Figure 4.5A, a RIT with mean frequency of 2Hz containing 9 pulses within a span of 4s (black trace) is the input to the presynaptic terminals of all synapses. In the case without glutamate uptake or when no transporters were present, the neuron evoked 9 output spikes at the soma, but only 4 spikes were elicited with glutamate uptake. Based on the paired pulse effects on EPSCs with and without glutamate transporters presented in Figure 4.4A, we expected to observe these effects on the number of spikes elicited at the neuron level. Between the two cases in Figure 4.5A, without (blue) and with (green) glutamate transporters, spike numbers 1, 2, 3, 5 and 7 failed to appear when there is glutamate uptake. Spike numbers 4, 6, 8 and 9 are not suppressed but arrive with a small delay. Looking at the time intervals between spikes 3 and 4, 5 and 6, and 8 and 9, which 70 are all less than 200 ms, we can see from the results in Figures 4.5A and 4.5C that the probability of a spike being suppressed due to glutamate uptake is increased when the input inter-spike interval is longer than 200-300ms. Indeed, for longer inter-spike intervals, glutamate transporters have recovered to their full potential for efficient uptake thereby reducing the amount of glutamate available to bind on the postsynaptic receptors. Also, the subtle timing differences that occur between the two cases could be potentially due to the relative changes in NMDAR-mediated EPSC time course decay. The change in peak amplitude responses, mainly mediated by AMPARs, due to glutamate uptake may or may not drive the neuron’s membrane potential to spiking threshold values. This indicates that the inter-play between the kinetics of AMPARs, NMDARs and the transporters can potentially lead to varying spiking patterns in neurons. We repeated a similar experiment, but with a higher input frequency of 5 Hz RITs (Figure 4.5C), which elicited between 19 and 22 spikes in the span of 4 s. Our results indicate that less spikes were elicited in the presence of glutamate uptake, in agreement with the observations on the 2 Hz RIT responses. However, the spiking failure is comparatively less as there is a lower probability of spikes occurring with intervals longer than 200-300 ms due to the increased mean frequency: 5 Hz RIT contains inputs which are separated by intervals most likely shorter than 200 ms and all those paired pulse effects observed in Figure 4.4A at these intervals could possibly explain the spiking effects seen here. 71 Figure 4.5: Influence of astrocytic glutamate uptake on spiking activity of a CA1 pyramidal neuron at different input frequencies. (A) Neuronal spiking activity elicited by a random input interval train with mean frequency of 2 Hz. The number of spikes occurring in the presence of glutamate uptake are much less (green) vs. when there are no transporters in the vicinity of synapses. (B) Number of spikes per trial within a span of 4 s without transporters (blue) and with transporters inducing glutamate uptake (green). Across trials we observe a consistent decrease in the spike count. (C) Neuronal spiking activity elicited by a random input interval train with a mean frequency of 5 Hz. Similar effects of spike failure as seen in 2 Hz are observed. (D) Number of spikes per trial across five trials show the consistent failure of spikes due to increased glutamate uptake in the presence of transporters. Two critical events marked by * show that the spikes elicited without glutamate uptake (no transporters) and with glutamate uptake have a timing difference between 1 and 2 ms and ** indicates when timing lies in between 3 and 8 ms. The input trains are indicated by the traces shown in black within each result panel. To test the robustness of these simulations, several trials with RIT with the same mean frequency were run. It appears that the spike failure across trials elicited by 5 Hz was relatively consistent. However, as shown in Figure 4.5B, across trials elicited by 2 Hz RITs, there was more spike failure in some trials (such as 3 and 4). When we analyzed the simulation results, we observed that these trains had spikes separated by 72 intervals longer than 300 ms. This interesting behavior in spike failure may be attributed to the hypothesis described above, i.e. the transporters have recovered their uptake capacity thereby reducing amplitude and time course of AMPAR-mediated EPSCs. These results are preliminary and were meant to demonstrate how simulation studies can be used to show that subtle changes in synaptic currents induced by glutamate uptake contribute to distinct neuronal spiking and temporal patterns. Changes in amplitude and time course of AMPAR- and NMDAR-mediated EPSCs, as shown in Figure 4A, were translated into subtle changes in spike arrival timings (Figures 4.5A and 4.5C) and spike failure (Figure 4.5B and 4.5D) with and without glutamate uptake. We built a model that could take into account receptors dynamics at elaborate synapses. Some of these dynamics, such as time course decay and amplitudes, were influenced by glutamate uptake mediated by glutamate transporters present on the astrocytic membrane surrounding these synapses. These results thus show the relevance of astrocytic mediated glutamate uptake and its interactions between synapses and thus their effects on neurons. 4.3 Discussion In this chapter we focused on the role of glutamate uptake mediated by glutamate transporters present on astrocytic membranes surrounding CA1 hippocampal synapses on synaptic transmission and neuronal spiking. First we showed that the model was able to reproduce previously observed phenomena regarding the influence of glutamate uptake on responses mediated by AMPA and NMDA receptors. This was achieved by removing glutamate molecules that are bound to or transported by glutamate transporters from those available at the levels of the receptors. Previous studies have emphasized the 73 importance of taking into account both glutamate diffusion and binding to transporters to determine changes in the decay kinetics of synaptic glutamate concentration [111]. In agreement with this study, glutamate is removed from synaptic cleft by diffusion, bound to and transported by glutamate transporters. Some of the phenomena demonstrated here under the conditions we used are: (i) An increase in the density of astrocytic glutamate transporters results in a decrease in AMPAR-mediated EPSC’s peak amplitude. This effect is due to the rapid decrease in glutamate concentration mediated by the transporters. For an average density of transporters and under the assumption that there is 50% ensheathment surrounding these synapses, the time-course of AMPAR-mediated EPSCs is not influenced, as previously reported [105]. Some experimental and simulation studies however show that there is no effect on AMPAR peak amplitudes [112]. This lack of effect could be due to a much lower density of transporters and also to Monte Carlo diffusion studies that assumed a different configuration of glutamate diffusion, receptors kinetics and transporters arrangement. (ii) Astrocytic glutamate uptake has a more predominant effect on the decay phase of NMDAR-mediated EPSCs. This result is consistent with previously reported experimental results (Diamond, 2005). Our simulations allowed us to closely examine the effect of glutamate uptake on the desensitization properties of these receptors as well. (iii) The resulting effects of glutamate uptake on amplitude and time course on EPSCs, combined with the transporter’s recovery behavior following paired pulse stimuli separated by short time intervals give rise to interesting dynamics. When glutamate uptake is not considered, there is paired pulse depression for responses to stimuli 74 delivered at short intervals. However in the presence of glutamate uptake, paired pulse facilitation is observed. The transporter’s recovery kinetics are often neglected based on the assumption that, at physiological temperature, they have a large capacity and respond to high frequency stimuli in a similar way [113] [114]. However, modifying their kinetics as a function of temperature and pH may give rise to different outcomes. The importance of neuronal transporters was shown in studies where reduced expression of neuronal transporters (EAAT3) can lead to behavioral abnormalities [115]. In the current work, we included the EAAT3 kinetic model described in [32]. EAAT3 type transporters are localized at dendrites and soma, and especially at perisynaptic regions [116]. However, their role in mediating glutamate uptake is debated because of their low expression density, 1%, as compared to other types of EAATs expressed mainly by glia with densities of 20% for GLAST and 80% for GLT-1 [33]. Experimental and simulation studies by [88] show that neuronal transporters may slow down glutamate clearance time by astrocyte transporters and that they can influence NMDAR-mediated synaptic transmission. Glutamate molecules bound to efficient neuronal transporters are more likely to be transported once bound, than to be unbound [108]. Studies using knock out models of EAAC1/EAAT3 showed no significant changes in AMPAR- and NMDAR-mediated EPSCs for single vesicle release [88], which was the basic assumption of the synapse model used here (see methods section). From other simulation studies by [89] it is hypothesized that neuronal transporters might influence perisynaptic NMDA receptors response, as they are more likely to be activated by glutamate spillover from neighboring synapses. We tested the influence of neuronal transporters on NMDAR-mediated EPSCs at 90/um 2 density with NMDA receptors located ~100nm 75 away from release site and found that they had no significant effect on EPSC profile. Higher densities of neuronal transporters and changes in AMPA-R and NMDA-R locations might induce a greater influence on EPSCs, but given the experimental findings mentioned above, it is generally accepted that they have a low impact on transmission. Since the effects contributed by neuronal transporters were negligible, we focused in this study on understanding the changes in neuron-spiking behavior induced by glutamate uptake mediated by astrocytic transporters. This focus was also a modeling choice to reduce the computational load in simulating synapses with too many elements. Exploring the influence of neuronal transporters with different kinetic parameters and density may or may not have an effect, as previously discussed and explored in previous studies. (iv) All the effects described above at the molecular and synaptic levels are translated into conductance changes with varying amplitudes and time courses that impact the temporal coding and spiking of neurons. Blocking glial glutamate uptake may have serious consequences on raising glutamate concentration to neurotoxic levels and causing epileptic conditions [27]. These effects have been shown in both experimental and simulation studies [117]. In our simulations, we examined the effects of glutamate uptake on neuron spiking behavior elicited by 2 Hz and 5 Hz RIT stimuli. Neurons with blocked astrocytic glutamate uptake showed higher spike counts. We attribute the failure of spikes in the presence of glutamate uptake mainly to the reduced levels of glutamate (i) that decrease synaptic amplitudes mediated by AMPARs and (ii) time course decay mediated by NMDARs, which also cause subtle differences in spike arrival. A closer look at the pattern of spike generation between the two cases without and with glutamate uptake shows that, spike usually occurs even after glutamate uptake, when the timing 76 between the input pulses is less than 200-300 ms, implying that sometimes, the spike could be evoked because the transporters have not cleared glutamate levels up to levels required for suppressing spike generation. Note that in this model the strength and number of synapses were chosen such that the neuron membrane potential reached threshold values easily. These parameters were selected in order to test the influence of glutamate uptake on spike activity around the membrane potential threshold for spike generation. Under our assumed conditions, the simulation studies show that glutamate uptake mediated by astrocytic transporters have a significant impact on neuronal spiking. To test the robustness of these results we ran several 5 trials (shown in Figure 4.5 (B) and (D) and found that the spike failure rates were more predominant for 2 Hz RITs, because there seems to be a higher probability of input trains with inter spike intervals separated by more than 500 ms, when transporters and receptors have completely recovered for efficient glutamate uptake and responses, respectively. Also, temporal integration [REF] in neurons may be the reason for one of the two neighboring spikes being elicited when the timing interval is very small. Further investigation needs to be done by simulating multitude of cases with varying time intervals to understand neuronal spiking behavior. We also underscore the diversity of synapses that arises from the variability in spatial location of the receptors, which we are investigating in a separate study. It is interesting to note that most of the receptors, such as NMDARs and mGluRs, have many modulatory sites, which consequently increase the number of parameters needed in the simulation. Our highly configurable geometric synapse model allows for the exploration of various parameters that influence sub-cellular/molecular level interactions and their direct or indirect influence on the synapse and neuron levels. By linking such complex 77 unified model of a synapse to morphologically realistic models of neuron within the NEURON simulation environment, we can investigate this complexity in an orderly and hierarchical fashion. This modeling effort allows for the investigation of key phenomena that are otherwise difficult to explore through mainstream reductionist modeling approaches. The main technical drawback of this kind of approach is the computational overhead involved. The modeling paradigm itself is complex in its nature due to (i) the level of parametric details and (ii) the time scale of processing of some elementary models, which in some cases takes place within tenths of microseconds, thereby slowing down the entire system. The astrocyte model presented here is not a complete model, and astrocytes are known for their role in influencing synaptic transmission beyond glutamate uptake and clearance. This model needs to be expanded to incorporate other important features, such as direct neurotransmitter release from astrocytes and signaling to neurons. All synapses are wrapped differently by astrocyte processes, covering smaller or larger areas with different levels of transporter expression. We have assumed for simplicity a constant wrapping for each individual synapses, which may not be necessarily true in vivo. Parametric models, where the model behavior is explained by a set of parameters, are in general limited by the scope of available experimental evidence. However, with a parametric modeling paradigm, we can test the reliability and sensitivity of these parameters. The observations described through our simulation studies are still preliminary and the modeling architecture established here will enable us to further investigate the effects caused by changing the amount of ensheathment around the synapses, as the density of EAATs in both glia and neurons 78 appears to play an influential role in shaping synaptic glutamate concentration profile and its functional consequences. Including other details of a tortuous path for glutamate and including extrasynaptic NMDARs, may also affect synaptic responses. Future modeling efforts will be directed towards investigating the hierarchical effects of astrocytes on sub- populations of neurons and synapses contacted by astrocyte processes, by incorporating geometry-related considerations. Here, we demonstrated the hierarchical link between synaptic currents to spike generation while also taking into account astrocytic glutamate uptake effects on molecular elements. This is a novel approach and one of the few times such a link has been shown. These results may have significant implications for understanding glial cell effects on nerve cell membrane potential and thus, nerve cell spiking, i.e., neuronal information flow. These results also are important because they strongly suggest that glial cell uptake of synaptic glutamate during neuron-to-neuron synaptic transmission should influence spike-dependent processes that are relevant to secondary messenger pathways and other long-term effects. This comprehensive framework will allow the investigation of complex mechanisms within large neuron/glia networks, including neurodegenerative diseases and their underlying processes. We can identify the most sensitive parameters in neuron glial interactions and develop different testing paradigms to understand the molecular basis of diseases associated with astrocytic dysfunction. 79 Chapter 5: Application To Drug Discovery 5.1 Introduction Neuronal communication is mediated by neurotransmitters such as glutamate, acetyl choline, dopamine to name a few and their binding and subsequent effect on receptors. Neurotransmitter diffusion, uptake and their binding capacity can be modulated by several synaptic elements such as transporters, exogenous molecules. All these sites in and around synapses are potential pharmacological targets. Exogenous compounds are used to modulate the physiological effects in a manner useful for alleviating neurological disorders. Drugs can be classified as (i) agonists, which are substances that bind to receptor and trigger its response (e.g. neurotransmitters), (ii) antagonists which, on the contrary, are compounds that inhibit the response and block or suppress the action of agonist. Action of agonists and antagonists are dose-dependent. There are multiple targets at synapses such as the ionotropic receptors such as AMPAR, NMDAR that mediate excitatory transmission, GABA receptors, which mediate inhibitory effects on neurons and are activated by inhibitory neurotransmitter GABA. In addition there are much more complex pathways such as the mGluR which are coupled to G-Proteins and trigger a cascade of calcium-mediated mechanisms. All these receptors and second messenger pathways are potential targets for designing drugs that drastically or moderately influence the neuronal response. 80 The multi-scale modeling platform described here provides an excellent framework to test the effects of agonists and antagonists at the synaptic level in a dose- dependent manner and determine: 1) the most effective concentrations and 2) potential synergistic combinations of drug compounds that will give rise to a desired neural response. This kind of integrative approach provides tremendous opportunity to identify lead compounds for neuropsychiatric disorders before they enter the clinical trials phase, potentially saving pharmaceutical companies of huge amount of time and financial resources. In this chapter, I will describe some of the capabilities of this platform that were developed with an active collaboration from scientists, engineers and developers from Rhenovia Pharma. Computational models play a pivotal role in explicitly bringing out a phenomenon that is not evident from experimental procedures. An example of such role was highlighted in our study [1] on the functional differences observed with different NMDA- R antagonists. Memantine is a noncompetitive NMDAR blocker and is widely used in the treatment of mild to moderate Alzheimer’s disease (AD). NMDARs are known for their role in learning and memory. They are also vulnerable targets in AD conditions. AP5, a well known antagonist exhibits an inhibitory effect on NMDAR that is shown to be stimulation frequency dependent, while being independent of changes to membrane potential. On the contrary, Memantine’s inhibitory effects decrease with both stimulation frequency and Vm, in particular, produces a tonic blockade of the channel at resting Vm. It is not as effective at high frequency stimulation, thereby limiting the risk of its negative 81 effects on learning and memory, which are often driven by frequency protocols useful for learning and memory. These effects are non obvious and simulation approaches provide a great platform to study such paradigm and test the efficacy of compounds under various stimulation conditions. In this chapter, two examples are provided demonstrating the capabilities of this novel multi-scale modeling framework for drug discovery. One example demonstrates the effect of AMPAkine CX614. AMPAkines are positive AMPA receptor modulators that modify desensitization and deactivation kinetics of AMPA receptors. Computer simulations were performed for different concentration values of this drug to determine the neuronal spiking responses. This platform also gives the flexibility to simultaneously test multiple parameters, and this will be demonstrated briefly with the application of NMDAR and GABA-A receptor antagonists at the synapse level and their subsequent effects on neuronal spiking behavior. 5.2 Effect of CX614 Ionotropic receptors are major targets for many CNS disorders. At the molecular level, we focused on AMPA receptors, a class of ionotropic receptors that mediate the majority of fast excitatory transmission. CX614 is a positive AMPA receptor modulator, aka AMPAkine, and has been shown to result in cognitive enhancement in rodents, primates and humans [2, 3]; AMPAkines are allosteric modulators of AMPA receptors and interfere with desensitization and deactivation properties of the AMPA receptor channel. We simulated the responses of CX614 effects at 5, 10 and 100µM concentration values and observed the changes in synaptic current amplitude and decay responses 82 induced by the above changes in concentration and their subsequent effects on neuronal spiking probability. Figure 5.1 Synaptic locations of EONS synapses (represented in blue) on the compartmental model of a CA1 pyramidal cell, adapted from [25]. All synaptic inputs receive a synchronous 4Hz random interval train. All synapses have similar configuration of receptor distribution with 80 AMPARs and 20 NMDARs. The AMPA receptor model [15] presented in Figure 2.5 used here describes subunit occupancy of glutamate and its temporal evolution from resting state to open and desensitized states. The time constants determine the rate of changes between the probability of occurrences of any one of the states. The agonist CX614 is assumed to modify AMPA receptor function by modulating the kinetic constant δ. 83 Figure 5.2: Simulated spiking patterns from the soma of a neuron elicited by a 4Hz random interval train. Different concentrations of CX614 at 5µM (b), 10µM (c) and 100µM (d) result in distinct spike timing pattern from the control (a), where no drug was administered. Published in [4] Rhenovia Pharma generously provided the modulation parameters of kinetic constants by CX614. The value of δ was set at 0.42ms -1 in the control condition and was modified as a function of Ampakine concentration. These values were obtained by fitting dose response curves from [5]. As observed with our model, changing the kinetic 84 constants of AMPAR at the receptor level did indeed produce a different spiking pattern at the neuron level for different concentrations of CX614. Notice the changes from 4 spikes to 6 spikes when 5µM of CX614 was administered. At 10µM, not only there were 2 more spikes, but additional spikes occurred a little earlier than the case of CX614 at 5µM indicating a slight difference in temporal spiking pattern. With 100µM of the drug, pyramidal neurons exhibited a rhythmic burst behavior (Figure. 3.2). In all the above simulations, the output spikes were elicited for every input spike. One reason is this model is completely deterministic. Since all synapses are activated simultaneously, the system is activated by a strong synchronous synaptic input, hence the neuronal output closely followed the input pattern. The additional spikes occur when the EPSC mediated currents continue to keep the membrane potential near the spiking threshold values. EPSC kinetics are strongly correlated with spiking probability of the neuron and this phenomena was demonstrated through simulations [5] for several EPSC rise time and decay time ratios. Although these are still preliminary results, they provide a proof of principle that a model integrating molecular models into synaptic and neuronal models can facilitate the understanding of the effects of pharmacological agents on neuronal function. In addition, this approach can provide critical information regarding the effects of modulators [6] on hierarchical multi-scale readouts. 85 5.3 Effect of NMDAR and GABA-A R antagonists We also explored the neuronal spiking behavior when NMDAR and GABA-A R antagonists at 50% of their maximum effective inhibition are simulated at synapses located on CA1 Pyramidal neuron [7]. The stimulation protocol used here is a 10Hz RIT. The simulated effects of GABA A-R antagonist (bicuciline at IC50) and NMDAR antagonist APV for 50% inhibition are individually presented. Under the control conditions of the simulation, the ratio of glutamate to GABA synapses is set to 8:1. Unlike the results in the previous section, where every input pulse elicited an output spike, here (black traces) the output spikes were less in number due to the contributing inhibitory effect of GABA current on the membrane potential. When 50% NMDAR antagonist effect was simulated, there was a drastic reduction of the total number of spikes (blue trace) indicating that a decreased amplitude of NMDAR mediated EPSC did influence somatic membrane potential. When 50% inhibition of GABA-A receptor antagonist was simulated, more output spikes were elicited (shown in red traces). As expected, reduction in the inhibitory effect did have an enhancing influence on the membrane potential, which, when near spiking threshold values elicited more spikes. When a combination of both antagonists was used, the obtained output response (green trace) had a similar spike count as in the control condition but the temporal pattern of the resulting output spikes has completely changed. We should also note that the output responses obtained here are for a specific case of simulation setup of the biophysical neuron model and the synapses connecting them. 86 Figure 5.3: Simulated neuronal activity for a 10Hz RIT with NMDAR and GABA-A R antagonist effects at individual EONS synapses. Blocking 50% of the NMDAR conductance by simulating the effect of APV induces a significant reduction in the number of spikes obtained (blue). On the contrary, blocking an inhibitory effect of GABA-A R antagonist enhanced the excitability of the neurons and led to more number of spikes (red trace) than the control condition (black). However, including both the NMDAR antagonist effect and GABA-A R antagonist effect restored the same spike count as in control but the temporal pattern of the resulting spike train changed drastically. 87 These results should be treated as an example to demonstrate, how spike-timing patterns could indeed be varied by combination of exogenous molecules. This platform provides a framework to test such drug modulatory effects on spiking patterns for several input frequency protocols and different biophysical neurons models and synapse configurations. 5.4 Conclusion The simulations showing AMPAkine activity or NMDAR and GABA-A R antagonists are based on modifications to their internal model parameters, which directly modulate EPSC and IPSC amplitudes and decay times. Since there is a strong correlation between EPSC kinetics and neuronal spiking probability [5] the framework described here was able to demonstrate the link between drug effects and spiking probability. However, the results obtained are true for certain specific assumptions and input protocol and more rigorous testing with additional input frequency patterns are needed to hypothesize strongly the drug effects on spike timing and spiking probability. To understand the action of the drugs on the neuronal activity, in all detail, just modulating the kinetic parameters through the action of agonists or antagonists is not sufficient. Many additional factors need to be considered; the simulations described above and the simulation platform used emphasize the importance of incorporating the multiple factors that influence synaptic transmission and their subsequent effects on neuronal spiking probability and spike timing. The emphasis on drug modulatory effects on spike timing is important because, the timing between pre-synaptic, postsynaptic events is a critical factor for induction of plasticity and also has a basis in neurobiology of disease. Such integrated platforms 88 provide in-depth insights on the synaptic basis of timing modulation and provide directions in drug discovery to predict neuronal spiking behavior based on the concentration of exogenous compounds. Using the parallel hardware of the high- performance computing cluster, it will be possible to expand this work to neural circuits consisting of several neurons and study the effects of modulating key mechanisms at the synaptic level on network synchrony and asynchrony. 89 Chapter 6: Conclusion Computational models that can capture a wide range of dynamic biological processes are extremely resourceful to test various hypotheses and gain knowledge of the CNS from micro to macro scales, where experimental methods show their limitations. In this thesis, we have proposed and developed a novel multi-scale modeling framework that creates a link between molecular level processes to higher order neuronal spiking activity. This architecture can have profound implications in applications to drug design and discovery. This model will subsequently help us deciphering how targeting molecular elements at the synaptic level modify network function and could provide a unique method to design therapeutic approaches to alleviate pathological conditions. Two specific aims were addressed within the scope of this thesis using the EONS synaptic modeling platform and this multi-scale framework: 1) The influence of ionotropic receptor arrangement on synaptic efficacy 2) The influence of glutamate uptake on synaptic transmission and neuronal spiking 6.1 Results Summary At glutamatergic synapses, glutamate released from the pre-synaptic vesicles diffuses across the synaptic cleft, and receptors located across the post-synaptic membrane encounter varying levels of glutamate. We explored the functional consequences of subsynaptic localization of ionotropic receptors. The results presented in chapter 3, are obtained from simulations performed at the synaptic level. The quantal amplitude variances in AMPA-R and NMDA-R mediated 90 EPSCs as a function of their spatial locations were presented. We also explored the internal state receptor dynamics such as receptor desensitization and receptor occupancy with detailed models of postsynaptic receptors. Our synaptic model faithfully reproduced previously observed phenomena while also providing additional insights into the location-dependent effects on ionotropic receptor properties such as desensitization and receptor occupancy on synaptic potentiation. AMPA-R mediated responses were more sensitive to their spatial locations while the NMDA-R mediated responses did not show much variation as a function of its location relative to the release site. The descriptive mathematical model of AMPA-R from (Robert and Howe, 2003) provides the internal states of the receptor when 2, 3 and 4 glutamate molecules are bound. Our simulation results suggest that glutamate molecules occupy the binding sites based on the receptor’s location relative to the release site (Figure 3.2). AMPA-Rs closer to the release site have a higher probability of all the four glutamate binding sites being completely occupied. The glutamate occupancy levels decrease as the receptor is further away from the source of glutamate release. However, a lot of factors influence the glutamate occupancy levels, such as, the number of glutamate molecules released from the release site, the tortuosity of glutamate diffusion path and other uptake mechanisms within synaptic vicinity. We also looked at paired pulse stimuli because the timing between subsequent inputs/release events is a critical determinant of receptor recovery and saturation. We analyzed the paired pulse facilitation and depression as a function of spatial location of AMPA-Rs. Our simulation results, under the conditions assumed and at a ratio of 80:20 of AMPARs to NMDARs indicate that at very low input time intervals, the spatial location of receptors show variations in the paired pulse ratios of EPSCs i.e. the 91 responses sometimes show facilitation or depression depending on the location of AMPARs. This spatial location dependent facilitation/depression is however not seen at longer input intervals. The composite EPSCs obtained from the summation of AMPA-R and NMDA-R mediated EPSCs vary in the peak amplitudes and exponential decays when the ratios of AMPARs and NMDAR densities change. Such changes in the ratios of receptor densities vary with developmental age of animals [8]. In addition, factors such as Mg 2+ concentration and glutamate uptake within the synaptic vicinity have a direct influence on the peak amplitude and time decay responses of EPSCs, which indirectly modify these PPRs under different simulation conditions. Our simulations suggest that, it is the interplay between spatial location of AMPARs, density and conductance of these channels and the pre-synaptic pattern of activity combined that influence synaptic potency. Chapter 4 describes the computational model we developed to investigate the influence of astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking. Glial cells are known for their role of acting as large sinks for synaptically released glutamate. Astrocytes within the CA1 hippocampal neurons are moderately ensheathed by astrocytic processes and their contribution to synaptic transmission varies across synapses and brain regions, for which its role is often debated. We used a model of glial glutamate transporter and studied its impact on synaptic currents. Our computational model allows a systematic exploration of such parameters to test the extent to which parameters such as the density of glutamate transporters based on the amount of ensheathment might influence synaptic transmission. In this chapter, we have shown through simulations that glutamate transporters present on astrocytic processes buffer and 92 transport glutamate. This decrease in glutamate availability at synaptic sites affected the peak amplitudes of AMPA-R mediated responses and decay phase of the NMDA-R mediated responses. This relation is dependent on the density of glutamate transporters. We also showed that astrocytic glutamate uptake effect on paired pulse responses is distinct for small and large input time intervals. In the presence of glutamate uptake, there appears to be less desensitization of the receptors for longer input time intervals for AMPARs and NMDARs due to glutamate uptake. The glutamate transporter also takes time for recovery reducing its ability to uptake glutamate on subsequent pulses. These phenomena were demonstrated through paired pulse simulation results of internal state dynamics of receptors. This clearly helped to understand the spike failure in the presence of glutamate uptake at the neuronal level and this appeared to be frequency-dependent. Under the conditions assumed for spiking probability of neuron, a neuron configuration with random distribution of synapses, there was suppression of spiking behavior when the input time interval between the previous input spike and current input spike is large. Here, we demonstrated the hierarchical link between synaptic currents to spike generation while also taking into account astrocytic glutamate uptake effects on molecular elements. This is a novel approach and one of the few times such a link has been shown. These results may have significant implications for understanding glial cell effects on nerve cell membrane potential and thus, nerve cell spiking, i.e., neuronal information flow. In Chapter 5, we have demonstrated through simulation results a conceptual link between modulating receptor kinetics through application of specific agonists and antagonists and their effects on the spiking properties of the CA1 pyramidal neuron. We chose two examples, one with CX614 which, blocks AMPA-R desensitization and 93 deactivation properties. Another example, with two different antagonists at two modulatory sites of GABA-ARs and NMDA-Rs. These results bring out the unlimited possibilities of testing agonist and antagonists at various modulatory sites in neurons and neuronal circuits on neuronal spiking to determine the concentrations that can switch the neuron from a normal spiking behavior to a bursting mode. This framework is useful for estimating the right amounts of dosage and the combination of drugs that can produce a desirable neural response. 6.2 Future Work The synaptic models presented here are complex parametric synaptic models and encompass a large number of parameters used to describe the structure and function of the synapse. They capture the essential details of glutamate diffusion, relative distance between release site and receptors and their location dependent effects on synaptic responses. These are often neglected in generic synaptic models owing to the computational burden of simulating all these mechanisms. With the growing evidence of receptor sub-type dependent localization at synapses, an interesting future investigation would be to understand the functional consequences of synaptic localization of receptor sub-types of various kinds and their subsequent influence on neuronal spiking properties. This is again important because alterations in subsynaptic architecture due to neurological disorders, which may cause disruptions to structural machinery, will eventually lead to alterations in neuron spike processing abilities. Identifying these subtleties at synapses that arise due to minor variations in the distribution of receptors and their sub-types could eventually give clues to the functional diversity that arise from the varieties of receptor expression. 94 From the work based on astrocytic glutamate uptake described in Chapter 4, we appreciate that astrocytic elements indeed influence synaptic transmission in numerous ways beyond glutamate uptake. Glutamate release models from astrocytes need to be investigated and incorporated into the current model. A specific aim relating to modifying the amount of astrocytic ensheathment around CA1 stratum radiatum synapses could be of significant interest in pathology of mesial temporal lobe epilepsy (MTLE). Recent findings from serial section transmission electron microscopy in CA1 startum radiatum in human hippocampus revealed that mild to moderate cases of MTLE had normal spines and are surrounded by astrocyte processes, however in severe cases, only multisynaptic spines remained with a lower occurrence of presisynaptic astroglial processes, as they were disrupted with densely packed filaments [9]. We can explore even a broader spectrum of such pathological conditions by simulating cases of varying astrocytic ensheathment around synapses and test their effects on neuronal spiking abilities. Also changing the synapse configurations, such as their distribution on neurons and inherent receptor properties may have additional effects on neuron spiking probabilities, which will be an interesting direction to pursue. The synapse model and the astrocytic component presented here is a perfect example of model that can be used to hypothesize and test the influence of astrocytic ensheathment around synapses as a replica of various pathological cases and identify therapeutic mechanisms to reverse such conditions. At the neuron level, mechanisms relevant for demonstrating the simplest link between synaptic integration and spiking probability were included, however adding other voltage dependent mechanisms and channels will add to the complexity of temporal processing. Addition of such 95 mechanisms and spontaneous activity will make the model capable of simulating conditions similar to in vivo. Development of the synapse model will be continued with the incorporation of other important mechanisms. Computational modeling of biological phenomena requires making reasonable choices to include and ignore certain sets and sub-sets of models and or parameters based on the scientific question, one is trying to explore. Most often, its not the best choice to simulate all the known mechanisms as this creates a trade-off between the computational load and simulation time it takes to execute these processes and the relevance of such mechanisms to the scientific study. The synapse model presented here is unique and is highly configurable with the flexibility to plug and test several subsynaptic mechanisms. To facilitate extremely large-scale simulations of neural networks with the same amount of complexity at synapse, efforts are underway to generate a dynamic non-parametric synapse models. 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However, it is extremely challenging to validate the accuracy of these models due to the lack of consistent experimental data at the sub-synaptic scale. In this section, we discuss the current state-of-the-art optimization procedures used for neuronal parameter fitting. As already established, there is no one best fitting optimization procedures to test the goodness of all models, let alone multi-scale models. To tackle this multi-level optimization challenge, we propose to use multi-parameter annealing optimization method for sub-synaptic scale and more heuristic search methods using evolutionary algorithms with other combinatorial optimization techniques at higher levels of complexity. This approach allows validating the models used in the platform at different levels of complexity while minimizing computational complexity. We then provide a design paradigm within the high-performance computing framework to achieve large- scale deployment of these optimization tasks. This design thus facilitates testing of mathematical models for several experimental paradigms to determine the best 115 combination of model parameters for a desired output. The current platform also allows testing the effects of exogenous molecules on neuronal network activity. Since our model incorporates all levels of a detail in a realistic neuronal network, we expect to be able to fit parameters at all levels. Hence, the simulation block within the framework described below should be considered as a black box so that the algorithms for the communication framework are independent of the simulation run. At the start of the algorithm, the node determines whether it is a master or a slave. The messages are passed in a one to all and all to one communication, where the master broadcasts all the initial values to the nodes and mutation (parameters are changed at one significant bit as shown by a binary representation above.) The minute change is referred to as mutation and the simulations use these changed parameters and have the simulated results. At the end of the simulation, each of the slave nodes would have received the experimental data for comparison. Here a sub-routine that does a least squares minimization is planned. The errors from all the slave nodes are computed and sent to the master node. On the master node, the errors are ranked in an ascending order, with the minimum error receiving the highest rank. The best of the ranks are further selected for crossover, where a combination of these two best parameters are generated and sent for the next generation of simulations. Genetic Algorithms (GA) are biologically inspired. The initial parameters are considered as parents and the next generation will have traits different form the original parents. These traits are evolved from a combination of genetic factors from both the parents and individual changes acquired independently. Independent changes are known 116 as mutation and combination of genetic factors to create a new population of species is considered as crossover in this type of GA Figure A1: Implementation on the global optimization procedure on a high performance distributed framework. Implementation: Given the object oriented nature and ease of debugging and most importantly our legacy code being in JAVA, JAVA is our choice of programming language for this project. We have been using Java’s message passing interface MPJ Express for inter- process/inter-node communication. MPJ Express is an implementation of the Java bindings for the MPI standard in C and has the functionality of almost every MPI function. This system implements thread-safe communication in a Java messaging system 117 to make it compliant with Java’s threading features. Several instances of the simulation can be launched on multiple threads on multiple cores, similar to OpenMP implementation. The speed of communication makes JAVA a compromising choice over other programming languages, but MPJ is comparable with other MPI standards in terms of latency and bandwidth [5] if the message being passed is of a definite size. Significance: This work will be unique in several ways. First, this simulation platform is one of its kind, which models the multi-scale level of detail from the synapse level to a neuron level. Second, SBML is adopted as an industry standard by the modeling community and this work has potential to benefit all SBML users, as our objective functions are not model specific and are based on least squares error fit between experimental and simulation data. a) Evolutionary algorithms have proved to be by far the most popular methods for global optimization procedures. b) We propose to use combinatorial optimization procedures using genetic algorithms, simulated annealing in addition to the sensitivity analysis procedures to make a good estimate of parameter space. Initial guess of parameters are very important to converge to the global optimum rapidly. c) The high-performance computing resources available allow us to optimize and validate models integrated into the multi-scale neuronal platform with several protocols of the available experimental data. d) The above approaches will provide us with a good understanding of the relevance of parameters at the sub-synaptic scale and their influence at a neuronal network level. This 118 knowledge will help us identify targets for exogenous molecules more efficiently and rapidly. Utilization of information from sensitivity analysis results in a better estimation of parameter values. The GA search evolves towards convergence in a methodical way such that the most important parameters of the model are stabilized first and later those parameters which influence the model output the least. This approach allows us to rank the importance of parameters in their order of maximum contribution to the model output.

Abstract (if available)

Abstract Glutamatergic synapses and their subsynaptic elements play crucial roles in mediating neuronal communication. Any disruption to the normal functioning of these elements and/or their interactions has implications in neurological disorders. ❧ It is technically difficult to access synaptic space and explore subsynaptic parameters influence on the overall synaptic and higher-order functions through usual experimental methodologies. Computational models complement experimental findings and provide a means for better understanding of such complex systems by providing the framework to look at various dimensions of synaptic functions by simultaneous manipulation of subsynaptic parameters. EONS (Elementary Objects of the Nervous System) is a highly configurable synaptic modeling platform featuring subsynaptic elements and interactions between them. We developed a multi-scale framework, which combines the features of this unified glutamatergic synapse model (EONS) into hippocampal neuron models (within the NEURON simulation environment) within a parallel computing environment. This multi-scale architecture creates a link between molecular level processes and higher order neuronal spiking activity thereby creating a unique powerful tool with direct application to drug design and discovery. ❧ Two main topics were addressed through computer simulations, glutamate diffusion and uptake on synaptic function and neuronal spiking: A) We explored the functional consequences that arise as a result of subsynaptic localization of ionotropic receptors. There is evidence that AMPARs, NMDARs and mGluR exist at different locations within the postsynaptic membrane. These receptors have different kinetics. Given that glutamate released from the pre-synaptic vesicles diffuses across the synaptic cleft, a reasonable hypothesis is that receptors located across the post-synaptic membrane encounter varying levels of glutamate and respond differently. Within this highly configurable synapse model, we varied the location of ionotropic receptors, extracellular environmental factors such as Mg²⁺, astrocytic glutamate uptake. Our simulations using single pulse and paired pulse protocols simulations suggests that it is the interplay between spatial location of AMPAR, density and conductance of these channels and the pre-synaptic pattern of activity combined that influence synaptic potency. B) We explored the influence of astrocytic glutamate uptake on synaptic transmission and neuronal spiking. This was tested with the multi-scale modeling framework developed. Astrocytic glutamate transporter models were added to the synaptic environment to simulate glutamate uptake. The reduced levels of glutamate activated receptors differently and influenced the amplitude and decay time course of EPSCs, which directly had an effect on the neuronal spiking ability. ❧ Overall this model will subsequently help us decipher how targeting molecular elements at the synaptic level can modify network function and could provide a unique method to design therapeutic approaches to alleviate and reverse pathological conditions.

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Creator Allam, Sushmita Lakshmi (author)

Core Title Computational investigation of glutamatergic synaptic dynamics: role of ionotropic receptor distribution and astrocytic modulation of neuronal spike timing

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 02/19/2014

Defense Date 01/10/2013

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

Tag astrocyte glutamate uptake,glutamate synapse computational model,ionotropic receptor distribution,multi-scale model,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Berger, Theodore W. (committee chair), Bartlett, Mel (committee member), Baudry, Michel (committee member), Bouteiller, Jean-Marie C., (committee member), Marmarelis, Vasilis Z. (committee member)

Creator Email sushmita.allam@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-220971

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Legacy Identifier etd-AllamSushm-1443.pdf

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Document Type Dissertation

Rights Allam, Sushmita Lakshmi

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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 a...

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