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In this work, we propose to catch the complexity of the membrane potential'sdynamic of a motoneuron between its spikes, taking into account the spikes fromother neurons around. Our approach relies on two types of data: extracellularrecordings of multiple spikes trains and intracellular recordings of themembrane potential of a central neuron. Our main contribution is to provide aunified framework and a complete pipeline to analyze neuronal activity fromdata extraction to statistical inference. The first step of the procedure is toselect a subnetwork of neurons impacting the central neuron: we use amultivariate Hawkes process to model the spike trains of all neurons andcompare two sparse inference procedures to identify the connectivity graph.Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkesprocess, the occurrences of which correspond to the spike trains of theaforementioned subset of neurons that interact with the central neuron. Wevalidate the Hawkes model with a goodness-of-fit test and we show that takinginto account the information from the connectivity graph improves the inferenceof the jump-diffusion process. The entire code has been developed and is freelyavailable on GitHub.

Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes