Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

Synaptic transmission is both history-dependent and stochastic, resulting in varying responses to presentations of the same presynaptic stimulus. This complicates attempts to infer synaptic parameters and has led to the proposal of a number of different strategies for their quantification. Recently Bayesian approaches have been applied to make more efficient use of the data collected in paired intracellular recordings. Methods have been developed that either provide a complete model of the distribution of amplitudes for isolated responses or approximate the amplitude distributions of a train of post-synaptic potentials, with correct short-term synaptic dynamics but neglecting correlations. In both cases the methods provided significantly improved inference of model parameters as compared to existing mean-variance fitting approaches. However, for synapses with high release probability, low vesicle number or relatively low restock rate and for data in which only one or few repeats of the same pattern are available, correlations between serial events can allow for the extraction of significantly more information from experiment: a more complete Bayesian approach would take this into account also. This has not been possible previously because of the technical difficulty in calculating the likelihood of amplitudes seen in correlated post-synaptic potential trains; however, recent theoretical advances have now rendered the likelihood calculation tractable for a broad class of synaptic dynamics models. Here we present a compact mathematical form for the likelihood in terms of a matrix product and demonstrate how marginals of the posterior provide information on covariance of parameter distributions. The associated computer code for Bayesian parameter inference for a variety of models of synaptic dynamics is provided in the supplementary material allowing for quantal and dynamical parameters to be readily inferred from experimental data sets

Statistical approaches for synaptic characterization

Synapses are fascinatingly complex transmission units. One of the fundamental features of synaptic transmission is its stochasticity, as neurotransmitter release exhibits variability and possible failures. It is also quantised: postsynaptic responses to presynaptic stimulations are built up of several and similar quanta of current, each of them arising from the release of one presynaptic vesicle. Moreover, they are dynamic transmission units, as their activity depends on the history of previous spikes and stimulations, a phenomenon known as synaptic plasticity. Finally, synapses exhibit a very broad range of dynamics, features, and connection strengths, depending on neuromodulators concentration [5], the age of the subject [6], their localization in the CNS or in the PNS, or the type of neurons [7]. Addressing the complexity of synaptic transmission is a relevant problem for both biologists and theoretical neuroscientists. From a biological perspective, a finer understanding of transmission mechanisms would allow to study possibly synapse-related diseases, or to determine the locus of plasticity and homeostasis. From a theoretical perspective, different normative explanations for synaptic stochasticity have been proposed, including its possible role in uncertainty encoding, energy-efficient computation, or generalization while learning. A precise description of synaptic transmission will be critical for the validation of these theories and for understanding the functional relevance of this probabilistic and dynamical release. A central issue, which is common to all these areas of research, is the problem of synaptic characterization. Synaptic characterization (also called synaptic interrogation [8]) refers to a set of methods for exploring synaptic functions, inferring the value of synaptic parameters, and assessing features such as plasticity and modes of release. This doctoral work sits at the crossroads of experimental and theoretical neuroscience: its main aim is to develop statistical tools and methods to improve synaptic characterization, and hence to bring quantitative solutions to biological questions. In this thesis, we focus on model-based approaches to quantify synaptic transmission, for which different methods are reviewed in Chapter 3. By fitting a generative model of postsynaptic currents to experimental data, it is possible to infer the value of the synapse’s parameters. By performing model selection, we can compare different modelizations of a synapse and thus quantify its features. The main goal of this thesis is thus to develop theoretical and statistical tools to improve the efficiency of both model fitting and model selection. A first question that often arises when recording synaptic currents is how to precisely observe and measure a quantal transmission. As mentioned above, synaptic transmission has been observed to be quantised. Indeed, the opening of a single presynaptic vesicle (and the release of the neurotransmitters it contains) will create a stereotypical postsynaptic current q, which is called the quantal amplitude. As the number of activated presynaptic vesicles increases, the total postsynaptic current will increase in step-like increments of amplitude q. Hence, at chemical synapses, the postsynaptic responses to presynaptic stimulations are built up of k quanta of current, where k is a random variable corresponding to the number of open vesicles. Excitatory postsynaptic current (EPSC) thus follows a multimodal distribution, where each component has its mean located to a multiple kq with k 2 N and has a width corresponding to the recording noise σ. If σ is large with respect to q, these components will fuse into a unimodal distribution, impeding the possibility to identify quantal transmission and to compute q. How to characterize the regime of parameters in which quantal transmission can be identified? This question led us to define a practical identifiability criterion for statistical model, which is presented in Chapter 4. In doing so, we also derive a mean-field approach for fast likelihood computation (Appendix A) and discuss the possibility to use the Bayesian Information Criterion (a classically used model selection criterion) with correlated observations (Appendix B). A second question that is especially relevant for experimentalists is how to optimally stimulate the presynaptic cell in order to maximize the informativeness of the recordings. The parameters of a chemical synapse (namely, the number of presynaptic vesicles N, their release probability p, the quantal amplitude q, the short-term depression time constant τD, etc.) cannot be measured directly, but can be estimated from the synapse’s postsynaptic responses to evoked stimuli. However, these estimates critically depend on the stimulation protocol being used. For instance, if inter-spike intervals are too large, no short-term plasticity will appear in the recordings; conversely, a too high stimulation frequency will lead to a depletion of the presynaptic vesicles and to a poor informativeness of the postsynaptic currents. How to perform Optimal Experiment Design (OED) for synaptic characterization? We developed an Efficient Sampling-Based Bayesian Active Learning (ESB-BAL) framework, which is efficient enough to be used in real-time biological experiments (Chapter 5), and propose a link between our proposed definition of practical identifiability and Optimal Experiment Design for model selection (Chapter 6). Finally, a third biological question to which we ought to bring a theoretical answer is how to make sense of the observed organization of synaptic proteins. Microscopy observations have shown that presynaptic release sites and postsynaptic receptors are organized in ring-like patterns, which are disrupted upon genetic mutations. In Chapter 7, we propose a normative approach to this protein organization, and suggest that it might optimize a certain biological cost function (e.g. the mean current or SNR after vesicle release). The different theoretical tools and methods developed in this thesis are general enough to be applicable not only to synaptic characterization, but also to different experimental settings and systems studied in physiology. Overall, we expect to democratize and simplify the use of quantitative and normative approaches in biology, thus reducing the cost of experimentation in physiology, and paving the way to more systematic and automated experimental designs

Signatures of Bayesian inference emerge from energy efficient synapses

Biological synaptic transmission is unreliable, and this unreliability likely degrades neural circuit performance. While there are biophysical mechanisms that can increase reliability, for instance by increasing vesicle release probability, these mechanisms cost energy. We examined four such mechanisms along with the associated scaling of the energetic costs. We then embedded these energetic costs for reliability in artificial neural networks (ANN) with trainable stochastic synapses, and trained these networks on standard image classification tasks. The resulting networks revealed a tradeoff between circuit performance and the energetic cost of synaptic reliability. Additionally, the optimised networks exhibited two testable predictions consistent with pre-existing experimental data. Specifically, synapses with lower variability tended to have 1) higher input firing rates and 2) lower learning rates. Surprisingly, these predictions also arise when synapse statistics are inferred through Bayesian inference. Indeed, we were able to find a formal, theoretical link between the performance-reliability cost tradeoff and Bayesian inference. This connection suggests two incompatible possibilities: evolution may have chanced upon a scheme for implementing Bayesian inference by optimising energy efficiency, or alternatively, energy efficient synapses may display signatures of Bayesian inference without actually using Bayes to reason about uncertainty.Comment: 29 pages, 11 figure

Temporal and spatial factors affecting synaptic transmission in cortex

Synaptic transmission in cortex depends on both the history of synaptic activity and the location of individual anatomical contacts within the dendritic tree. This thesis analyses key aspects of the roles of both these factors and, in particular, extends many of the results for deterministic synaptic transmission to a more naturalistic stochastic framework. Firstly, I consider how correlations in neurotransmitter vesicle occupancy arising from synchronous activity in a presynaptic population interact with the number of independent release sites, a parameter recently shown to be modified during long-term plasticity. I study a model of multiple-release-site short-term plasticity and derive exact results for the postsynaptic voltage variance. Using approximate results for the postsynaptic firing rate in the limits of low and high correlations, I demonstrate that short-term depression leads to a maximum response for an intermediate number of presynaptic release sites, and that this in turn leads to a tuning-curve response peaked at an optimal presynaptic synchrony set by the number of neurotransmitter release sites per presynaptic neuron. As the nervous system operates under constraints of efficient metabolism it is likely that this phenomenon provides an activity-dependent constraint on network architecture. Secondly, I consider how synapses exhibiting short-term plasticity transmit spike trains when spike times are autocorrelated. I derive exact results for vesicle occupancy and postsynaptic voltage variance in the case that spiking is a renewal process, with uncorrelated interspike intervals (ISIs). The vesicle occupancy predictions are tested experimentally and shown to be in good agreement with the theory. I demonstrate that neurotransmitter is released at a higher rate when the presynaptic spike train is more regular, but that positively autocorrelated spike trains are better drivers of the postsynaptic voltage when the vesicle release probability is low. I provide accurate approximations to the postsynaptic firing rate, allowing future studies of neuronal circuits and networks with dynamic synapses to incorporate physiologically relevant spiking statistics. Thirdly, I develop a Bayesian inference method for synaptic parameters. This expands on recent Bayesian approaches in that the likelihood function is exact for both the quantal and dynamic synaptic parameters. This means that it can be used to directly estimate parameters for common synaptic models with few release sites. I apply the method to simulated and real data; demonstrating a substantial improvement over analysis techniques that are based around the mean and variance. Finally, I consider a spatially extended neuron model where the dendrites taper away from the soma. I derive an accurate asymptotic solution for the voltage profile in a dendritic cable of arbitrary radius profile and use this to determine the profile that optimally transfers voltages to the soma. I find a precise quadratic form that matches results from non-parametric numerical optimisation. The equation predicts diameter profiles from reconstructed cells, suggesting that dendritic diameters optimise passive transfer of synaptic currents

Assessment of Synaptic Function During Short-Term Facilitation in Motor Nerve Terminals in the Crayfish

An enhanced buildup of [Ca2+]i occurs during short-term facilitation (STF) at the crayfish neuromuscular junction (NMJ). As a model system, this NMJ allows discrete postsynaptic quantal events to be counted and characterized in relation to STF. Providing 10 pulses, at 20 and 40Hz, we monitored postsynaptic quantal events over a discrete region of a nerve terminal with a focal macropatch electrode. Characteristics of quantal events were clustered into groups by peak amplitude and time to the peak amplitude. Since the synapses at this NMJ have varied spacing of active zones, number of active zones and synaptic size, the graded nature of synaptic recruitment is likely one means of titrating synaptic efficacy for the graded depolarization on the non-spiking muscle fiber. Synapses in this preparation would appear to have a quantal signature that can be used for quantifying their activity which is useful in estimating the overall number of active sites. We use mixture modeling to estimate n (number of active sites) and p (probability of vesicle fusion) from the quantal characteristics. In a preparation that was stimulated at 40Hz, synapses were recruited (increase in n) and the number active synapses increased in p. In a different preparation, p increased as the stimulation was changed from 20 to 40Hz, but n did not show a substantial increase; however, during the STF train, p increases slightly. This study provides a novel approach in determining subsets of the single evoked quanta to better estimate n and p which describe synaptic function

THE INFLUENCE OF Ca2+ REGULATION IN SYNAPTIC FACILITATION OF MOTOR NERVE TERMINALS IN CRAYFISH AND \u3ci\u3eDROSOPHILA\u3c/i\u3e AS WELL AS IN THE PHYSIOLOGICAL REGULATION OF LARVAL \u3ci\u3eDROSOPHILA\u3c/i\u3e HEART

Intracellular Ca2+ ions are highly regulated in animal cells for them to function normally. Since the tight regulation of [Ca2+]i is so ubiquitous among cells, it is not surprising that altered function in [Ca2+]i regulation is associated with a myriad of disease states in humans. This is particularly evident in pacing myocytes and nerve terminals related to synaptic transmission. A common thread through this dissertation is on the role of three regulators proteins that are common to many cell types. These are the plasmalemmal Na+/Ca2+ exchanger (NCX), the Ca2+-ATPase (PMCA) and the SERCA on the endoplasmic reticulum. In chapter 1 a historical overview is provided on how the understanding in the importance of Ca2+ came about. In Chapter 2, I address indirectly the function of residual [Ca2+]i on the efficacy of synaptic transmission by quantal analysis but also develop novel means of assessing quantal analysis to assign a n and p value to particular synapses. Chapters 3 and 4 address the role of the three Ca2+ regulator proteins in short bursts of synaptic transmission related to short-term facilitation or depression depending on the type of neuromuscular junction (NMJ). Two key model NMJs I used were the crayfish (Chapter 3) and the larval Drosophila (Chapter 4). For comparative purposes in investigating the role of the three proteins in [Ca2+]i regulation, I used the Drosophila larval heart preparation (Chapter 5). Throughout these studies, I used various pharmacological and ionic approaches to compromise the function of these Ca2+ channels. The results were unexpected in some cases due to non-specific effects of the pharmacological agent or ionic manipulations. In addition, a mutational line of Drosophila was used to asses SERCA function, but the results at the NMJ were not as expected. However, results with the mutation on the function of the heart were promising. The significance of these studies stresses that multiple approaches to compromise channels is warranted and the findings should be beneficial for future investigators to advance in mechanistic studies

Experimental and theoretical analysis of multivesicular release at a sensory synapse

Traditionally, neurons were believed to transmit information between one another by action potentials and the release of synaptic vesicles, both of which thought to be binary processes. In this framework, an action potential (or change in membrane potential for graded neurons) elicits the release of at most a single vesicle per active zone (AZ), the site of vesicular release. Information, then, is conveyed in this system simply be altering the probability of a single vesicle being released, and thus altering the total rate of release. In recent years, however, evidence has demonstrated that many cells, particularly those in the early sensory systems, are capable of multivesicular release (MVR), wherein multiple synaptic vesicles are released nearly simultaneously, with precision of up to 10 microseconds. As most neurons have a temporal integration window on the millisecond range, it is thus likely the postsynaptic cell could represent these events as distinct symbols in a non-binary digital system, allowing for information transmission not only in the rate of vesicular events, but also their amplitude. While evidence for MVR has existed for decades, considerably less attention has been paid to its functional significance – how does MVR affect processing in intact circuits? Is it utilized to transmit information? How efficiently does it operate? In this work I attempt to answer these questions, first by developing a method with which one can decompose 2p glutamate recordings from intact zebrafish BC terminals into units of individual vesicles – essentially ‘counting’ vesicles. In doing so, I show that MVR is used in the early visual system to transmit temporal contrast information, one of the most basic aspects of the visual scene. Finally, I create a model of vesicle release and postsynaptic activity that allows for directly comparing how information transmission can be influenced by either rate or amplitude coding. Here, by systematically altering the parameters of the postsynaptic cell, I demonstrate in which circumstances either rate coding or amplitude coding are beneficial for transmission. MVR, rather than being some obscure phenomenon, plays a fundamental part in processing and transmitting information in early sensory systems

Probabilistic inference of short-term synaptic plasticity in neocortical microcircuits

Short-term synaptic plasticity is highly diverse across brain area, cortical layer, cell type, and developmental stage. Since short-term plasticity (STP) strongly shapes neural dynamics, this diversity suggests a specific and essential role in neural information processing. Therefore, a correct characterization of short-term synaptic plasticity is an important step towards understanding and modeling neural systems. Phenomenological models have been developed, but they are usually fitted to experimental data using least-mean-square methods. We demonstrate that for typical synaptic dynamics such fitting may give unreliable results. As a solution, we introduce a Bayesian formulation, which yields the posterior distribution over the model parameters given the data. First, we show that common STP protocols yield broad distributions over some model parameters. Using our result we propose a experimental protocol to more accurately determine synaptic dynamics parameters. Next, we infer the model parameters using experimental data from three different neocortical excitatory connection types. This reveals connection-specific distributions, which we use to classify synaptic dynamics. Our approach to demarcate connection-specific synaptic dynamics is an important improvement on the state of the art and reveals novel features from existing data