Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times

Abstract

We analytically investigate the interspike interval (ISI) density, the Fano factor, and the coefficient of variation of a leaky integrate-and-fire neuron model driven by exponentially correlated Gaussian noise with a large correlation time tau . We find a burstinglike behavior of the spike train, which is revealed by a dominant peak of the ISI density at small intraburst intervals and a slow power-law decay of long interburst intervals. The large, power-law distributed ISIs give rise to a coefficient of variation which diverges as square root [tau] . This leads to the paradoxical effect that ISI correlations, as expressed by the serial correlation coefficient, vanish for large correlation times. This is in contrast to findings of previous works on a simpler neuron model where the effect of noise correlations appeared in higher-order statistical measures.