Quantifying Repetitive Transmission at Chemical Synapses: A Generative-Model Approach

Abstract

The dependence of the synaptic responses on the history of activation and their large variability are both distinctive features of repetitive transmission at chemical synapses. Quantitative investigations have mostly focused on trial-averaged responses to characterize dynamic aspects of the transmission—thus disregarding variability—or on the fluctuations of the responses in steady conditions to characterize variability—thus disregarding dynamics. We present a statistically principled framework to quantify the dynamics of the probability distribution of synaptic responses under arbitrary patterns of activation. This is achieved by constructing a generative model of repetitive transmission, which includes an explicit description of the sources of stochasticity present in the process. The underlying parameters are then selected via an expectation-maximization algorithm that is exact for a large class of models of synaptic transmission, so as to maximize the likelihood of the observed responses. The method exploits the information contained in the correlation between responses to produce highly accurate estimates of both quantal and dynamic parameters from the same recordings. The method also provides important conceptual and technical advances over existing state-of-the-art techniques. In particular, the repetition of the same stimulation in identical conditions becomes unnecessary. This paves the way to the design of optimal protocols to estimate synaptic parameters, to the quantitative comparison of synaptic models over benchmark datasets, and, most importantly, to the study of repetitive transmission under physiologically relevant patterns of synaptic activation.

Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

“…The posterior distributions reflect the true parameters well for all synaptic parameters with the exception of the facilitation timescale τ F and quantal amplitude standard deviation σ a . These parameters have been observed to be hard to estimate in previous studies, with Costa et al (2013) finding broad distributions for τ F , and Bhumbra and Beato (2013) and Barri et al (2016) noting similar uncertainties in their estimates of quantal variability. The correlated Bayesian method does not qualitatively change these results, but makes the best use of available data to accurately estimate the uncertainty.…”

“…This method, presented earlier in Bird (2016) is equivalent to that simultaneously and independently discovered by Barri et al (2016) in their expectation-maximization approach, and represents a combination and extension of the recent work of Bhumbra and Beato (2013) on the exact likehood of isolated events and Costa et al (2013) on the approximated likelihood of serial events. By considering quantal and dynamic properties together, the method described accounts for information that is necessarily neglected when each component is examined in isolation.…”

“…Naively, this would appear to make the problem intractable. However, two independent studies (Barri et al, 2016; Bird, 2016) recently provided a solution to this problem by exploiting the underlying Markovian nature of the problem thereby allowing for the computation of the exact probability of a given set of observed amplitudes with a complexity that grows only linearly with PSP number. Here we develop the method, originally presented in Bird (2016), to show how the likelihood may be written in a compact mathematical form as a matrix product.…”

The readily releasable pool of synaptic vesicles

“…This approach can be used at synapses with prominent facilitation and a low probability of release. It is possible to either use averaged responses and traditional fitting methods, or to use the statistics of synaptic transmission [25–27]. It will be important to determine how well such methods estimate RRP size, and to determine if this approach can be adapted to synapses where release is mediated by multiple pools of vesicles with different properties.…”

Functional consequences of pre- and postsynaptic expression of synaptic plasticity

“…Recently, inference methods of short-term plasticity and quantal parameters have been introduced [55–57]. The sampling method of Costa et al .…”