Estimating Excitatory and Inhibitory Synaptic Conductances from Spike Trains using a Recursive Bayesian Approach

Abstract

Inference of excitatory and inhibitory synaptic conductances (SCs) from the spike trains is poorly addressed in the literature due to the complexity of the problem. As recent technological advancements make recording spikes from multiple (neighbor) neurons of a behaving animal (in some rare cases from humans) possible, this paper tackles the problem of estimating SCs solely from the recorded spike trains. Given an ensemble of spikes corresponding to population of neighbor neurons, we aim to infer the average excitatory and inhibitory SCs underlying the shared neural activity. In this paper, we extended our previously established Kalman filtering (KF) based algorithm to incorporate the voltage-to-spike nonlinearity (mapping from membrane potential to spike rate). Having estimated the instantaneous spike rate using optimal linear filtering (Gaussian kernel), our proposed algorithm uses KF followed by expectation maximization (EM) algorithm in a recursive fashion to infer the average SCs. As the dynamics of SCs and membrane potential is included in our model, the proposed algorithm, unlike other related works, considers different sources of stochasticity, i.e., the variabilities of SCs, membrane potential, and spikes. Moreover, it is worth mentioning that our algorithm is blind to the external stimulus, and it performs only based on observed spikes. We validate the accuracy and practicality of our technique through simulation studies where leaky integrate and fire (LIF) model is used to generate spikes. We show that the estimated SCs can precisely track the original ones. Moreover, we show that the performance of our algorithm can be further improved given enough number of trials (spikes). As a rule of thumb, 50 trials of neurons with the average firing rate of 5 Hz can guarantee the accuracy of our proposed algorithm.