Upcrossing-rate dynamics for a minimal neuron model receiving spatially distributed synaptic drive

Abstract

This article is part of the Physical Review Research collection titled Physics of Neuroscience. The spatiotemporal stochastic dynamics of the voltage, as well as the upcrossing rate, are derived for a model neuron comprising a long dendrite with uniformly distributed filtered excitatory and inhibitory synaptic drive. A cascade of ordinary and partial differential equations is obtained describing the evolution of first-order means and second-order spatial covariances of the voltage and its rate of change. These quantities provide an analytical form for the general, steady-state, and linear response of the upcrossing rate to dynamic synaptic input. It is demonstrated that this minimal dendritic model has an unexpectedly sustained high-frequency response despite synaptic, membrane, and spatial filtering.