Minimal time spiking in various ChR2-controlled neuron models

TL;DR

This paper investigates the minimal time required to induce a neuron spike using optogenetic control in conductance-based neuron models, applying geometric optimal control theory and numerical methods.

Contribution

It introduces a framework combining mathematical modeling of optogenetics with optimal control techniques to analyze neuron spiking timing.

Findings

Identification of conditions for minimal spike timing

Numerical observation of bang-bang control strategies

Application of geometric control theory to neuron models

Abstract

We use conductance based neuron models and the mathematical modeling of Optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls.