First passage times in integrate-and-fire neurons with stochastic thresholds

TL;DR

This paper investigates how stochastic, Ornstein-Uhlenbeck process-driven thresholds affect the first passage times in integrate-and-fire neuron models, revealing non-monotonic dependencies on noise amplitude and providing analytical tools for understanding these effects.

Contribution

It introduces a novel analytical framework transforming the neuron threshold problem into a Brownian motion first passage time problem, applicable to various subthreshold dynamics and threshold processes.

Findings

Mean first passage time depends non-monotonically on noise amplitude.

Large correlation times maximize the mean first passage time at non-zero noise levels.

Analytical perturbation matches numerical simulations accurately.

Abstract

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first passage time can depend non-monotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first passage time is maximal for non-vanishing noise. We provide an explanation for this effect by analytically transforming the original model into a first passage time problem for Brownian motion. This transformation also allows for a perturbative calculation of the first passage time histograms. In turn this provides quantitative insights into the mechanisms that lead to the non-monotonic behaviour of the mean first passage time. The perturbation expansion is in excellent agreement with direct numerical simulations. The approach developed here can be applied to any deterministic subthreshold dynamics and any Gauss-Markov processes for the firing threshold. This opens up the possibility to incorporate biophysically detailed components into the subthreshold dynamics, rendering our approach a powerful framework that sits between traditional integrate-and-fire models and complex mechanistic descriptions of neural dynamics.