Leaky Integrate and Fire Models Coupled through Copulas: Association Properties of the Interspike Intervals

Abstract

We propose a model able to describe the Interspike Intervals of two or more neurons subject to common inputs from the network. The single neuron dynamic is described through a classical Leaky Integrate and Fire model, but the model also catches the joint behavior of two neurons resorting to the use of copulas. Copulas are mathematical objects largely used to describe dependencies laws. Synchronous and delayed dependencies are considered by means of a set of examples. Results are discussed making use of crosscorrelograms.

Detecting dependencies between spike trains of pairs of neurons through copulas

“…Indeed, oscillations in the crosscorrelogram might be due to marginal behaviors, as described by Sacerdote and Tamborrino (2010) and Tetzlaff et al (2008). Thus, it is not always possible to distinguish between the two cases.…”

“…In particular, they provide a method to estimate the parameters of the prescribed copula. Sacerdote and Sirovich (2010) propose to use copulas to model the coupling of two or more neurons, while Sacerdote and Tamborrino (2010) investigate the reliability of crosscorrelograms analysis to detect dependencies in spike trains with known connections, being simulated through copula models.…”

“…Unfortunately, crosscorrelation de-scribes linear dependencies and it might fail to detect nonlinearities (Sacerdote and Tamborrino, 2010).…”