Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

TL;DR

This paper introduces a comprehensive framework combining multivariate Hawkes processes and jump-diffusion models to analyze neuronal membrane potential dynamics influenced by interconnected spike trains, validated through goodness-of-fit tests.

Contribution

It presents a novel unified pipeline for neuronal activity analysis, integrating spike train modeling, connectivity inference, and membrane potential dynamics, with publicly available code.

Findings

Hawkes process effectively models spike train connectivity.

Incorporating connectivity improves membrane potential inference.

The framework is validated with goodness-of-fit tests.

Abstract

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. Our main contribution is to provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. The first step of the procedure is to select a subnetwork of neurons impacting the central neuron: we use a multivariate Hawkes process to model the spike trains of all neurons and compare two sparse inference procedures to identify the connectivity graph. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron. We validate the Hawkes model with a goodness-of-fit test and we show that taking into account the information from the connectivity graph improves the inference of the jump-diffusion process. The entire code has been developed and is freely available on GitHub.