A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Abstract

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L${}_1$ penalization methods.

Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity
• The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation
• Reconstructing networks of pulse-coupled oscillators from spike trains
• netrd: A library for network reconstruction and graph distances
• Scalable Inference for Neuronal Connectivity from Calcium Imaging
• Efficient methods for sampling spike trains in networks of coupled neurons
• A shotgun sampling solution for the common input problem in neural connectivity inference