Identifiability of a Binomial Synapse

Abstract

Synapses are highly stochastic transmission units. A classical model describing this stochastic transmission is called the binomial model, and its underlying parameters can be estimated from postsynaptic responses to evoked stimuli. The accuracy of parameter estimates obtained via such a model-based approach depends on the identifiability of the model. A model is said to be structurally identifiable if its parameters can be uniquely inferred from the distribution of its outputs. However, this theoretical property does not necessarily imply practical identifiability. For instance, if the number of observations is low or if the recording noise is high, the model's parameters can only be loosely estimated. Structural identifiability, which is an intrinsic property of a model, has been widely characterized; but practical identifiability, which is a property of both the model and the experimental protocol, is usually only qualitatively assessed. Here, we propose a formal definition for the practical identifiability domain of a statistical model. For a given experimental protocol, this domain corresponds to the set of parameters for which the model is correctly identified as the ground truth compared to a simpler alternative model. Considering a model selection problem instead of a parameter inference problem allows to derive a non-arbitrary criterion for practical identifiability. We apply our definition to the study of neurotransmitter release at a chemical synapse. Our contribution to the analysis of synaptic stochasticity is threefold: firstly, we propose a quantitative criterion for the practical identifiability of a statistical model, and compute the identifiability domains of different variants of the binomial release model (uni or multi-quantal, with or without short-term plasticity); secondly, we extend the Bayesian Information Criterion (BIC), a classically used tool for model selection, to models with correlated data (which is the case for most models of chemical synapses); finally, we show that our approach allows to perform data free model selection, i.e., to verify if a model used to fit data was indeed identifiable even without access to the data, but having only access to the fitted parameters.

Local Connectivity and Synaptic Dynamics in Mouse and Human Neocortex

“…Most prior methods use a metric similar to the likelihood defined above along with an optimization method to efficiently find a single point in the parameter space that is most consistent with the recorded data. However, minimization is notoriously difficult in this domain because the model parameters are underconstrained--there exist many solutions that adequately explain the recorded data, and thus large differences in the optimal parameters may simply result from noise or experimental artifacts, rather than physiological differences between synapses (Bykowska et al, 2019;Gontier and Pfister, 2020). To avoid this outcome, we measure the model performance at every point in a large parameter space, thereby identifying the region of the parameter space consistent with the responses recorded from each synapse (Figure S11D).…”

Modeling the spread of fake news on Twitter

“…While the first cascade parameters are estimated from the entire data, the second cascade parameters are estimated from the observation data after the correction time t c . Moreover, the model parameters are not identifiable [37,38] in the case of a 1 ¼ a 2 e À t c =t 2 and τ 1 = τ 2 . Because the proposed model is equivalent to TiDeH (a 2 = 0, t c � T obs ) in this case, other parameter sets can also reproduce the observed data.…”

Efficient Sampling-Based Bayesian Active Learning for synaptic characterization

“…A classically used model to describe the release of neurotransmitters at chemical synapses is called the binomial model [2,4,5,6,22,23]. Under this model, a synapse is described as a Hidden Markov Model (HMM) with the following parameters (units are given in square brackets, see also Figure 2 (a)): N (the number of independent release sites [-]); p (their release probability [-]); σ (the recording noise [A]); q (the quantum of current elicited by one release event [A]); τ D (the time constant of vesicles refilling [s]).…”

“…Computing the posterior distribution of θ also implies to specify a prior p(θ) from which the initial particles {θ i 0 } 1≤i≤Mout will be drawn. For simplicity, we consider here uniform priors (as in [5,6]), although the algorithm readily extends to different choices of prior.…”

“…estimates critically depends on the experimental protocol used for stimulating the presynaptic cell. If observations are noisy or scarce, parameter estimates will be unreliable, leading to identifiability issues [6,7]. If ISI are longer than the depression time constant τ D , STD will not be precisely quantified.…”