Balanced neurons: analysis of leaky integrate-and-fire neurons with reversal potentials

A new technique is presented for analyzing leaky integrate-and-fire neurons that incorporates reversal potentials, which impose a biologically realistic lower bound to the membrane potential. The time distribution of the synaptic inputs is modeled as a Poisson process. The analysis is carried out in the Gaussian approximation, which comparison with numerical simulations confirms is most accurate in the limit of a large number of inputs. The hypothesis that the observed variability in the spike times of cortical neurons is caused by a balance of excitatory and inhibitory synaptic inputs is supported by the results for the coefficient of variation of the interspike intervals. Its value decreases with both increasing numbers and amplitude of inputs, and is consistently lower than 1.0 over a wide range of realistic parameter values. The dependence of the output spike rate upon the rate, number, and amplitude of the synaptic inputs, as well as upon the value of the inhibitory reversal potential, is given.