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

Braun, Wilhelm; Matthews, Paul C.; Thul, Ruediger

Authors

Wilhelm Braun pmxwb1@nottingham.ac.uk

Paul C. Matthews paul.matthews@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date May 7, 2015
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1539-3755
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 91
Article Number 052701
APA6 Citation Braun, W., Matthews, P. C., & Thul, R. (2015). First passage times in integrate-and-fire neurons with stochastic thresholds. Physical Review E, 91, https://doi.org/10.1103/PhysRevE.91.052701
DOI https://doi.org/10.1103/PhysRevE.91.052701
Keywords Neurons, Neural stochasticity
Publisher URL http://dx.doi.org/10.1103/PhysRevE.91.052701
Related Public URLs http://arxiv.org/abs/1504.03983
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
Additional Information Copyright 2015 American Physical Society

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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