Dynamics of populations and networks of neurons with voltage-activated and calcium-activated currents

The profile of transmembrane-channel expression in neurons is class dependent and a crucial determinant of neuronal dynamics. Here, a generalization of the experimentally verified exponential integrate-and-fire model is introduced that includes biophysical, nonlinear gated conductance-based currents, and a spike shape. A Fokker-Planck-based method is developed that allows for the rapid numerical calculation of steady-state and linear-response properties for recurrent networks of neurons with gating-variable dynamics slower than that of the voltage. This limit includes many cases of biological interest, particularly under in vivo conditions of high synaptic conductance. The utility of the method is illustrated by applying it to two biophysically detailed models adapted from the literature: an entorhinal layer-II cortical neuron and a neuron featuring both calcium-activated and voltage-activated spike-frequency-adaptation currents. The framework generalizes to networks comprised of different neuronal classes and so will allow for the modeling of emergent states in neural tissue at significantly increased levels of biological detail.