LETTER Communicated by Emilio Salinas The Dynamics of Integrate-and-Fire: Mean Versus Variance Modulations and Dependence on Baseline Parameters

The leaky integrate-and-fire (LIF) is the simplest neuron model that cap-tures the essential properties of neuronal signaling. Yet common intu-itions are inadequate to explain basic properties of LIF responses to si-nusoidal modulations of the input. Here we examine responses to low-and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. However, the cutoff shows a rapid, supralinear increase with firing rate, with a steeper increase in the case of lower noise. For modulations of the input variance, the gain at high frequency remains finite. Here, we show that the low-frequency re-sponses depend strongly on baseline parameters and derive an analytic condition specifying the parameters at which responses switch from be-ing dominated by low versus high frequencies. Additionally, we show that the resonant responses for variance modulations have properties not expected for common oscillatory resonances: they peak at frequencies higher than the baseline firing rate and persist when oscillatory spiking is disrupted by high noise. Finally, the responses to mean and variance modulations are shown tohave a complementarydependence onbaseline parameters at higher frequencies, resulting in responses to modulations of Poisson input rates that are independent of baseline input statistics.