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      Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

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          Abstract

          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.

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          Most cited references47

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          Short-term synaptic plasticity.

          Synaptic transmission is a dynamic process. Postsynaptic responses wax and wane as presynaptic activity evolves. This prominent characteristic of chemical synaptic transmission is a crucial determinant of the response properties of synapses and, in turn, of the stimulus properties selected by neural networks and of the patterns of activity generated by those networks. This review focuses on synaptic changes that result from prior activity in the synapse under study, and is restricted to short-term effects that last for at most a few minutes. Forms of synaptic enhancement, such as facilitation, augmentation, and post-tetanic potentiation, are usually attributed to effects of a residual elevation in presynaptic [Ca(2+)]i, acting on one or more molecular targets that appear to be distinct from the secretory trigger responsible for fast exocytosis and phasic release of transmitter to single action potentials. We discuss the evidence for this hypothesis, and the origins of the different kinetic phases of synaptic enhancement, as well as the interpretation of statistical changes in transmitter release and roles played by other factors such as alterations in presynaptic Ca(2+) influx or postsynaptic levels of [Ca(2+)]i. Synaptic depression dominates enhancement at many synapses. Depression is usually attributed to depletion of some pool of readily releasable vesicles, and various forms of the depletion model are discussed. Depression can also arise from feedback activation of presynaptic receptors and from postsynaptic processes such as receptor desensitization. In addition, glial-neuronal interactions can contribute to short-term synaptic plasticity. Finally, we summarize the recent literature on putative molecular players in synaptic plasticity and the effects of genetic manipulations and other modulatory influences.
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            Synaptic computation.

            Neurons are often considered to be the computational engines of the brain, with synapses acting solely as conveyers of information. But the diverse types of synaptic plasticity and the range of timescales over which they operate suggest that synapses have a more active role in information processing. Long-term changes in the transmission properties of synapses provide a physiological substrate for learning and memory, whereas short-term changes support a variety of computations. By expressing several forms of synaptic plasticity, a single neuron can convey an array of different signals to the neural circuit in which it operates.
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              Synaptic theory of working memory.

              It is usually assumed that enhanced spiking activity in the form of persistent reverberation for several seconds is the neural correlate of working memory. Here, we propose that working memory is sustained by calcium-mediated synaptic facilitation in the recurrent connections of neocortical networks. In this account, the presynaptic residual calcium is used as a buffer that is loaded, refreshed, and read out by spiking activity. Because of the long time constants of calcium kinetics, the refresh rate can be low, resulting in a mechanism that is metabolically efficient and robust. The duration and stability of working memory can be regulated by modulating the spontaneous activity in the network.
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                Author and article information

                Contributors
                Journal
                Front Comput Neurosci
                Front Comput Neurosci
                Front. Comput. Neurosci.
                Frontiers in Computational Neuroscience
                Frontiers Media S.A.
                1662-5188
                25 November 2016
                2016
                : 10
                : 116
                Affiliations
                [1] 1Theoretical Neuroscience Group, Warwick Systems Biology Centre, University of Warwick Coventry, UK
                [2] 2Ernst Strüngmann Institute for Neuroscience, Max Planck Society Frankfurt, Germany
                [3] 3Frankfurt Institute for Advanced Studies Frankfurt, Germany
                [4] 4School of Life Sciences, University of Warwick Coventry, UK
                [5] 5Warwick Mathematics Institute, University of Warwick Coventry, UK
                Author notes

                Edited by: David Holcman, École Normale Supérieure, France

                Reviewed by: Gianluigi Mongillo, Paris Descartes University, France; Mark C. W. Van Rossum, University of Edinburgh, UK

                *Correspondence: Alex D. Bird a.d.bird@ 123456warwick.ac.uk
                Article
                10.3389/fncom.2016.00116
                5122579
                27932970
                7a79419e-4445-4187-8323-257a1615c1c8
                Copyright © 2016 Bird, Wall and Richardson.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 26 August 2016
                : 28 October 2016
                Page count
                Figures: 4, Tables: 2, Equations: 34, References: 55, Pages: 14, Words: 8909
                Funding
                Funded by: Biotechnology and Biological Sciences Research Council 10.13039/501100000268
                Award ID: BB/J015369/1
                Award ID: BB/G530233/1
                Categories
                Neuroscience
                Methods

                Neurosciences
                correlation,bayesian,epsp,synapse,quantal,stochastic,plasticity
                Neurosciences
                correlation, bayesian, epsp, synapse, quantal, stochastic, plasticity

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