Temporal processing in the exponential integrate-and-fire model is nonlinear

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocmé et al. [How spike generation mechanisms determine the neuronal response to fluctuating inputs, J. Neurosci. 23 (2003) 11628-11640] as an extension of the standard leaky integrate-and-fire model. Here, the nonlinearity in the EIF model's temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for square-wave inputs indicates that at frequencies above ∼40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in isolation.