Tuesday 15 Mar 2022: Noisy thresholds - casting neural dynamics in a new light
Rüdiger Thul - University of Nottingham
https://Universityofexeter.zoom.us/j/98128535238?pwd=b1NNR1MwV295VHRWWFh4b1NDTjJoZz09 Meeting ID: 981 2853 5238 Password: 561487 13:30-14:30
Neural dynamics epitomises excitability and hence is dramatically shaped by the interplay between molecular fluctuations and the firing threshold. The most common approach to modelling stochastic neural dynamics is via stochastic differential equations (SDEs) as exemplified by the stochastic version of the seminal integrate-and-fire (IF) model. Here, a stochastic subthreshold process is integrated until it reaches a pre-defined threshold, which signals the onset of a neuronal spike. Typically, the firing threshold is a deterministic function. However, experimental evidicene suggests that the firing threshold itself is random. We incorporate this finding into a novel class of stochastic IF models in which the subthreshold process is deterministic, but the dynamics of the firing threshold is governed by an SDE. We demonstrate that this model exhibits a nonlinear dependence of the firing rate as a function of the noise strength and explain this behaviour known as inverse stochastic resonance semi-analytically by computing the full first passage time (FPT) probability distribution. This setup also allows us to generalise the influential Rice series for FPT calculations to non-differentiable Gaussian processes. In the last part of my talk, I will apply the concept of noisy thresholds to neural fields and demonstrate its versatility by constructing travelling fronts, stationary bumps and multi-bumps and highlighting non-trivial linear stability properties of bumps.