Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

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.

Computational roles of plastic probabilistic synapses

“…Recent technical developments on the measurement of presynaptic and postsynaptic terminals both in vitro and in vivo is reaching the point at which it will soon be possible to monitor the synaptic response statistics as an animal learns with high spatial and temporal resolution (Rey et al, 2015;Tang et al, 2016). In particular, recent advances in ultrafast glutamate imaging (Helassa et al, 2018) and statistical inference methods (Costa et al, 2013;Bird et al, 2016;Ghanbari et al, 2017) will enable accurate and optical measurements of synaptic transmission statistics. However, despite such fast developments in experimental neuroscience, theoretical neuroscience, with some exceptions (e.g.…”

Modeling the short-term dynamics of in vivo excitatory spike transmission

“…can also increase or decrease depending on the recent history of pre-and postsynaptic activity 48 (Usrey et al, 2000;Swadlow and Gusev, 2001). Although many models exist to describe 49 intracellular observations of short-term synaptic plasticity (Costa et al, 2013;Hennig, 2013; Barri 50 et al, 2016; Bird et al, 2016), most models of functional connections between neurons based on 51 extracellular spike observations assume that connections are fixed over time (Truccolo et al, 2005; 52 Pillow et al, 2008). Unlike intracellular PSP observations, where the amplitude of each individual 53 presynaptic spike can be measured (subject to noise), extracellular spike observations are sparse, 54 typically all-or-none binary events.…”

Estimating short-term synaptic plasticity from pre- and postsynaptic spiking

“…Although this posterior is not guaranteed to be convex, in many cases, the non-convexity of GLM-like models does not lead to optimization problems [60][61][62]. Previous work estimating STP parameters from intracellular recordings suggests that, rather than point estimates, a fully Bayesian approach may provide a more accurate understanding of the parameters [17,40]. Although it is possible to use MCMC to sample from the posterior, the large number of function evaluations (compared to optimization) makes it less attractive for our model with spike observations.…”