Modelling Vesicular Release at Hippocampal Synapses

We study local calcium dynamics leading to a vesicle fusion in a stochastic, and spatially explicit, biophysical model of the CA3-CA1 presynaptic bouton. The kinetic model for vesicle release has two calcium sensors, a sensor for fast synchronous release that lasts a few tens of milliseconds and a separate sensor for slow asynchronous release that lasts a few hundred milliseconds. A wide range of data can be accounted for consistently only when a refractory period lasting a few milliseconds between releases is included. The inclusion of a second sensor for asynchronous release with a slow unbinding site, and thereby a long memory, affects short-term plasticity by facilitating release. Our simulations also reveal a third time scale of vesicle release that is correlated with the stimulus and is distinct from the fast and the slow releases. In these detailed Monte Carlo simulations all three time scales of vesicle release are insensitive to the spatial details of the synaptic ultrastructure. Furthermore, our simulations allow us to identify features of synaptic transmission that are universal and those that are modulated by structure

A tale of two stories: astrocyte regulation of synaptic depression and facilitation

Short-term presynaptic plasticity designates variations of the amplitude of synaptic information transfer whereby the amount of neurotransmitter released upon presynaptic stimulation changes over seconds as a function of the neuronal firing activity. While a consensus has emerged that changes of the synapse strength are crucial to neuronal computations, their modes of expression in vivo remain unclear. Recent experimental studies have reported that glial cells, particularly astrocytes in the hippocampus, are able to modulate short-term plasticity but the underlying mechanism is poorly understood. Here, we investigate the characteristics of short-term plasticity modulation by astrocytes using a biophysically realistic computational model. Mean-field analysis of the model unravels that astrocytes may mediate counterintuitive effects. Depending on the expressed presynaptic signaling pathways, astrocytes may globally inhibit or potentiate the synapse: the amount of released neurotransmitter in the presence of the astrocyte is transiently smaller or larger than in its absence. But this global effect usually coexists with the opposite local effect on paired pulses: with release-decreasing astrocytes most paired pulses become facilitated, while paired-pulse depression becomes prominent under release-increasing astrocytes. Moreover, we show that the frequency of astrocytic intracellular Ca2+ oscillations controls the effects of the astrocyte on short-term synaptic plasticity. Our model explains several experimental observations yet unsolved, and uncovers astrocytic gliotransmission as a possible transient switch between short-term paired-pulse depression and facilitation. This possibility has deep implications on the processing of neuronal spikes and resulting information transfer at synapses.Comment: 93 pages, manuscript+supplementary text, 10 main figures, 11 supplementary figures, 1 tabl

Efficient approximations for stationary single-channel calcium nanodomains

Mathematical and computational modeling plays an important role in the study of local Ca2+ signals underlying many fundamental physiological processes such as synaptic neurotransmitter release and myocyte contraction. Closed-form approximations describing steady-state distribution of Ca2+ in the vicinity of an open Ca2+ channel have proved particularly useful for the qualitative modeling of local Ca2+ signals. This dissertation presents several simple and efficient approximants for the equilibrium Ca2+ concentration near a point source in the presence of a mobile Ca2+ buffer, which achieve great accuracy over a wide range of model parameters. Such approximations provide an efficient method for estimating Ca2+ and buffer concentrations without resorting to numerical simulations and allow to study the qualitative dependence of nanodomain Ca2+ distribution on the buffer’s Ca2+ binding properties and its diffusivity. The new approximants presented here for the case of a simple, one-to-one Ca2+ buffer have a functional form that combines rational and exponential functions, which is similar to that of the well-known Excess Buffer Approximation and the linear approximation, but with parameters estimated using two novel methods. One of the methods involves interpolation between the short-range Taylor series of the buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. A second method is based on the variational approach and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. Extensive parameter sensitivity analysis is presented, comparing approximants found using these two methods with the previously developed approximants. Apart from increased accuracy, the strength of the new approximants is that they can be extended to more realistic buffers with multiple Ca2+ binding sites, such as calmodulin and calretinin. In the second part of the dissertation, the series interpolation method is extended to buffers with two Ca2+ binding sites, yielding closed-form interpolants combining exponential and rational functions that achieve reasonable accuracy even in the case of buffers characterized by significant Ca2+ binding cooperativity. Finally, open challenges and potential future extensions of this work are discussed in detail

Multi-Scale Modeling and Simulation of Cell Signaling and Transport in Renal Collecting Duct Principal Cells

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell is regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, I aggregated pathways and mechanisms from literature and derived models in a hypothesis-driven approach. Furthermore, I combined the models to a single multi-scale model to gain insight into key regulatory mechanisms of aquaporin 2 recycling. To achieve this, I developed a computational framework for the modeling and simulation of cellular signaling systems. The framework integrates reaction and difusion of biochemical entities on a microscopic scale with mobile vesicles, membranes, and compartments on a cellular level. The simulation uses an adaptive step-width approach that e ciently regulates the agent-based simulation of macroscopic components with the numerical integration of mass action kinetics and grid-based nite diference methods. A reaction network generation algorithm was designed, that, in combination with a highly-modular modeling approach, allows for fast model prototyping. The analysis of the aquaporin 2 model system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if speci c cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.:Abstract 1. Introduction 1.1. Eukaryotic Signaling 1.2. Modeling and Simulation of Cellular Processes 1.3. Aquaporin 2 recycling 1.4. Motivation and Aims 1.5. Outline I. Background 2. Modeling and Simulation of Complex Signaling Pathways 2.1. Multi-scale Modeling 2.1.1. Approaches to Multi-scale Modeling 2.1.2. Reduction of Computational Complexity 2.2. Models of Chemical Reaction Networks 2.2.1. Reactions and Reaction Rates 2.2.2. Numerical Solutions 2.2.3. Reaction Network Generation 2.3. Models of Intracellular Transport 2.3.1. Undirected Transport 2.3.2. Directed Transport 3. Aquaporin 2 Recycling in Renal Principal Cells 3.1. The Physiology of Water Homeostasis 3.2. Molecular Mechanisms of the Vasopressin Response 3.2.1. The Vasopressin Receptor 3.2.2. cAMP Regulation of Protein Kinase A 3.2.3. Endo- and Exocytosis 3.3. Models of Water Transport in Renal Principal Cells II. Results & Discussion 4. Multi-scale Simulation of Cellular Signaling Pathways 4.1. Scale Separation and Bridging 4.2. Micro-scale Simulation Approach 4.2.1. Difusion and Discretization of the Simulation Space 4.2.2. Reaction Kinetics 4.3. Rule-based Reaction Network Generation 4.3.1. Definition of the Data Model 4.3.2. Design of Rule Based Reactions 4.3.3. Automated Generation of Reaction Networks 4.4. Macro-scale Simulation Approach 4.4.1. Agent-based Simulation of Discrete Entities 4.4.2. Modules for Displacement-based Behavior 4.5. Modularization and Error Estimation 4.5.1. Determination of the Numerical Error 4.5.2. Modularization of Concentration-based Events 4.5.3. Determination of the Displacement-based Error 5. Aquaporin 2 Recycling Model and Simulation 5.1. Model of Allosteric PKA Phosphorylation 5.1.1. Model Design 5.1.2. Simulation Results and Discussion 5.1.3. Conclusions 5.2. cAMP Compartmentalization in the Vesicle Storage Region 5.2.1. Model Design 5.2.2. Simulation Results and Discussion 5.2.3. Conclusions 5.3. Clathrin-mediated Endocytosis 5.3.1. Model Design 5.3.2. Simulation Results and Discussion 5.3.3. Conclusions 5.4. Intracellular Transport and Recycling 5.4.1. Model Design 5.4.2. Simulation Results and Discussion 6. Conclusion 6.1. Modeling and simulation approach 6.2. Insights into the AQP2 recycling model III. Appendix A. Code Availability B. Module Overview Bibliograph

Allosteric regulation of synaptic processes

Glutamatergic neurotransmission is of key importance for short-term and long-term plasticity in the hippocampus, a part of the medial temporal lobe which is responsible for processes of explicit semantic and spatial memory. Short-term plasticity is mainly regulated by the presynaptic neuron and long-term plasticity is to large parts regulated by the post-synaptic neuron. In this thesis we have looked into cellular and molecular biophysical mechanisms in glutamatergic neurons mainly in the hippocampus. We first reviewed the presynaptic mechanisms underlying short-term plasticity like assembly of the release machinery, positional and molecular priming, site preparation, calcium dynamics regulation, intrinsic vesicular fusogenicity, endocytosis, acidification and filling. In study 1 we looked into the role of intrinsic vesicle fusogenicity on short-term plasticity by formulating a deterministic vesicular release model based on ordinary differential equations. Intrinsic vesicular fusogenicity was an allosteric property we invented in order to test the hypothesis of calcium independence. The model was able to simulate properties of resting neurons, by reproducing the spontaneous release rates and the size of the readily releasable pool. Furthermore, assuming that the heterogeneity in vesicular release probability arises due to differences in intrinsic vesicular fusogenicity, the model was able to explain depression by an imbalance between fusion and vesicular priming. It also predicted that facilitation could be due to an increase in intrinsic vesicular fusogenicity, which together with build-up of calcium gave rise to initial increase in vesicular release. Finally, we investigated the effect of three different modes of regulation of release probability on short-term plasticity. It was seen that differences in intrinsic vesicular fusogenicity gave rise to a more significant change in shortterm plasticity than change in calcium sensitivity of release. All in all the results tell us that intrinsic vesicular fusogenicity has an important role in tuning short-term plasticity. In study 2 we investigated the regulation of the postsynaptic allosteric AMPA receptor. To do this we developed a model based on the Monod Wyman Changeux framework which described the ligand concentration dependence of the conductance states by increasing affinity to conductance states. The model was able to explain thermodynamic behaviours of native and recombinant receptors when stimulated with full agonists like glutamate and quisqualate as well as partial agonists like willardiines. It was also predicted that the receptor stabilizes its large conductance state within the rise time of a so-called 'mini' post-synaptic current, providing a possible underlying mechanism for the peak of the current. In study 3 we investigated the high-dose hook effect in allosteric proteins by first developing a combinatorical theory for how linker proteins behave under conditions of perfect binding. The theory predicted that the steady-state concentration of fully bound linker-proteins decreases at a critical concentration of initial free linker protein as the free linker protein concentration is increased. This effect is however decreased in proteins where binding of ligand occurs in a cooperative fashion. The outcome was validated by simulations of dimeric and tetrameric linker proteins under imperfect binding. We also simulated the cooperative synaptic protein calmodulin, and it was seen to be subject to the hook effect. The hook effect was stronger in the presence of the allosteric activator Ca2+/calmodulin kinase II (CamKII). We show that increased amounts of the allosteric activator can decrease the activity of calmodulin. At 140 uM calmodulin behaved only as if the molecule only appeared in the relaxed (R) state. The relaxed state has no cooperativity, but has higher ligand affinity than the wild-type calmodulin. Even though this phenomenon may be present in many different biochemical systems, synapses contain several linker proteins that are pivotal for synaptic plasticity for instance AMPA receptors, synaptotagmin, calbinding and calmodulin. In summary, this thesis gives insight into allosteric mechanisms in glutamatergic hippocampal neurons by using whole-cell voltage clamp and algebraic modelling. Specifically, it suggests an explanation for the important role of allosteric mechanisms in vesicular release probability and short-term plasticity. It also provides an explanation for the ligand concentration dependence of AMPA receptors and puts forward a theory for how complexes and active forms of linker proteins behave under increase of free linker protein concentration, a behaviour might contribute to pre-and postsynaptic processes