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 dynamical 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 dynamical 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 data sets and, most importantly, to the study of repetitive transmission under physiologically relevant patterns of synaptic activation.

Significance Statement: Transmission at chemical synapses is transiently adjusted on a spike-by-spike basis, which has been proposed to enhance information processing in neuronal networks. So far, however, dynamical properties of transmission have been characterized only for physiologically unrealistic patterns of activation. This is because current methods to estimate the parameters describing repetitive transmission are unable to deal with the responses’ fluctuations. These have either to be averaged out or estimated directly from the data, which requires a large number of repetitions of the same stimulation, severely constraining experimental protocols. We developed a novel method which allows one to estimate the parameters from a single, arbitrary pattern of activation. The method lays the groundwork for the characterization of transmission with in vivo-like patterns of activation.