Analytical firing rate from leaky integrate-and-fire models receiving non-normal inputs

Abstract The leaky integrate-and-fire (LIF) model is one of the most widely used models in characterizing neuronal dynamics. The simplicity and brevity of LIF models allow for analytical solutions that could quickly navigate the parameter space and provide insights of the neuronal computational properties. In this work, we developed analytical methods for computing neuronal dynamics of an LIF model receiving non-normal inputs, which have not been effectively characterized in existing works. We first characterize the distribution of a general input using the kernel density estimation (KDE), which accurately tracks varying non-normal features. Based on the KDE-distribution, we analytically derive the steady-state firing rates and inter-spike-interval distributions of the LIF model. As an example, we specify the input as consisting of two coupled stochastic Ornstein–Uhlenbeck processes and a sinusoidal drive; such total input is significantly non-normal in general. The analytical firing rate is highly consistent with direct model simulations, in response to wide ranges of different parameters. The analytical method developed in this work could be potentially implemented to general input current like experimental recordings, and help in facilitating neuromorphic computation of spiking network models, navigating parameter spaces for model fitting, increasing neuronal mechanistic understandings in terms of computational properties.