To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?

TL;DR

This study investigates whether the membrane potential of neurons between spikes can be modeled as a semimartingale, finding it generally applies in non-spiking cases but fails during spiking activity.

Contribution

It provides a novel analysis of membrane potential data using p-variations and compares it with semimartingale models, highlighting their limitations during spikes.

Findings

Membrane potential behaves as a semimartingale in non-spiking cases.

Semimartingale models are inadequate during spiking activity.

In some cases, the potential behaves as a semimartingale with jumps.

Abstract

We consider $p$-variations in some membrane potential data --viewed as a function of the step size in case where $p$ is fixed, or viewed as a function of $p$ in case where the step size is fixed-- and compare their shape with results in Ait-Sahalia and Jacod (2009) which do hold for general semimartingales. We obtain the following conclusion: in non- or very rarely spiking cases the membrane potential behaves as a semimartingale, in some cases as a semimartingale with jumps. Once the neuron is spiking, a semimartingale modelization is no longer adequate for the membrane potential between successive spikes, even if interspike intervals are relatively long.