Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

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.