title: First-passage times in integrate-and-fire neurons with stochastic thresholds.
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 nonmonotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first-passage time is maximal for nonvanishing 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 nonmonotonic behavior 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.
authors.affiliation: School of Mathematical Sciences and Centre for Mathematical Medicine and Biology, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
authors.forename: Wilhelm
authors.initials: W
authors.lastname: Braun
authors.affiliation: School of Mathematical Sciences and Centre for Mathematical Medicine and Biology, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
authors.forename: Paul C
authors.initials: PC
authors.lastname: Matthews
authors.affiliation: School of Mathematical Sciences and Centre for Mathematical Medicine and Biology, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
authors.forename: Rüdiger
authors.initials: R
authors.lastname: Thul
mesh_terms: D008959:Models, Neurological; D009474:Neurons / Q000166:cytology*; D013269:Stochastic Processes; D013997:Time Factors