Emergent Time Windows in Nonlinear Neural Models

In order to study how n to 1 convergence sharpens timing information, we have used a simple time-window (TW) model in which the target neuron fires the first time it has received m action potentials in the previous εmilleseconds. Although the TW is convenient for proving theorems and Monte-Carlo simulations, it is a natural question whether it represents well the physiological reality. We first present simulations that show, in the case n = 3, m = 3, that the Hodgkin-Huxley model has a very sharp time window but the leaky integrate-and-fire model (LIF) does not. Simulations also show that other non-linear models including quadratic-integrate-and-fire (QIF), the theta model, and the Fitzhugh-Nagumo model also have sharp time window behavior. We then give a complete analytical treatment of the LIF and QIF models to explain why the first does not have a sharp time window but the second does. This suggests that TW neurons may give a better approximation to physiological reality than LIF neurons.