Neuronal network inference and membrane potential model using multivariate Hawkes processes.

ABSTRACT

BACKGROUND: 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. NEW METHOD: We provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. To the best of our knowledge, this is the first time that a Hawkes-diffusion model is investigated on such complex data. The first step of the proposed procedure is to select a subnetwork of neurons impacting the central neuron using a multivariate Hawkes process. 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. RESULTS: From the Hawkes estimation step we recover a small connectivity graph which contains the central neuron, and we show that taking into account this information improves the inference of membrane potential through the proposed jump-diffusion model. A goodness of fit test is applied to validate the relevance of the Hawkes model in such context. COMPARISON WITH EXISTING METHODS: We compare an empirical inference method and two sparse estimation procedures based on the Hawkes assumption for the reconstruction of the connectivity graph using the spike-trains. Then, the Hawkes-diffusion model is competed with the simple diffusion in terms of best fit to describe the behavior of the membrane potential of a central neuron surrounded by a network. CONCLUSIONS: The present method takes advantage of both spike trains and membrane potential to understand the behavior of a fixed neuron. The entire code has been developed and is freely available on GitHub.