Bimodality of the interspike interval distributions for subordinated diffusion models of integrate-and-fire neurons

Abstract

A subordinated Langevin process, with a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, is considered as a generalization of the conventional perfect and leaky integrate-and-fire neuron models. The parent process is given by standard Brownian motion. The effect of the random activity of synaptic inputs, which arises from other neurons forming local and distant networks, is modeled via a Lévy exponent of the subordinator. Using a first-passage-time formulation in an external force field, we find exact expressions for the Laplace transform of the output interspike interval (ISI) density. More detailed analysis is presented on the properties of the ISI distribution in the case of the Lévy exponent which corresponds to the truncated double-order time-fractional diffusion equation for the probability density of the membrane potential. Particularly, it is shown that at some parameter regimes the ISI density exhibits a bimodal structure. Moreover, it is demonstrated that the ISIs regularity is maximized at an intermediate value of the mean input current.