Abstract
Time-varying excitatory and inhibitory synaptic inputs govern activity of neurons and process information in the brain. The importance of trial-to-trial fluctuations of synaptic inputs has recently been investigated in neuroscience. Such fluctuations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering (GMKF) for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential in current clamp recordings. The KF is followed by an expectation maximization (EM) algorithm to infer the statistical parameters (time-varying mean and variance) of the synaptic inputs in a non-parametric manner. As our proposed algorithm is repeated recursively, the inferred parameters of the mixtures are used to initiate the next iteration. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model (GMM). The performance of the proposed algorithms is compared to a previously proposed PF-based algorithm (Paninski et al., 2012) with several illustrative examples, assuming that the distribution of synaptic input is unknown. If noise is small, the performance of our algorithms is similar to that of the previous one. However, if noise is large, they can significantly outperform the previous proposal. These promising results suggest that our algorithm is a robust and efficient technique for estimating time varying excitatory and inhibitory synaptic conductances from single trials of membrane potential recordings.
Highlights
Interaction of the excitatory and inhibitory synaptic inputs constructs the shape of the receptive fields and can elucidate the synaptic mechanism underlying the functional activities of neurons
We propose a robust recursive algorithm, based on Gaussian mixture Kalman filtering (GMKF), for filtering/smoothing the dynamics of a compact neuronal model followed by an expectation maximization (EM) algorithm to infer the statistical parameters of such synaptic inputs
We have considered two conditions to analyze the performance of the proposed KF- and GMKF-based algorithms, i.e., the conditions with large and small signal-to-noise ratios (SNRs)
Summary
Interaction of the excitatory and inhibitory synaptic inputs constructs the shape of the receptive fields and can elucidate the synaptic mechanism underlying the functional activities of neurons. Estimating synaptic inputs based on averaging over many trials and linear regression fitting, which is commonly used, is not always the best methodology because the trial-to-trial variations of synaptic inputs are ignored The significance of such variations in understanding the neuronal mechanisms of the brain activity (especially spontaneous) and their key roles in information processing is well reviewed in (Destexhe and Contreras, 2006). We point out two recent studies (Kobayashi et al, 2011; Paninski et al, 2012) that have used the well-known Bayesian approach to infer synaptic inputs in single trials. In both studies, promising results were reported under low observation noise. This is the major theoretical drawback of these methods because synaptic distributions
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