Behavior of integrate-and-fire and Hodgkin-Huxley models with correlated inputs

We assess, both numerically and theoretically, how positively correlated Poisson inputs affect the output of the integrate-and-fire and Hodgkin-Huxley models. For the integrate-and-fire model the variability of efferent spike trains is an increasing function of input correlation, and of the ratio between inhibitory and excitatory inputs. Interestingly for the Hodgkin-Huxley model the variability of efferent spike trains is a decreasing function of input correlation, and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs. In terms of the signal to noise ratio of efferent spike trains the integrate-and-fire model works better in an environment of asynchronous inputs, but the Hodgkin-Huxley model has an advantage for more synchronous (correlated) inputs. In conclusion the integrate-and-fire and Hodgkin-Huxley models respond to correlated inputs in totally opposite ways.