Noise and the PSTH response to current transients: II. Integrate-and-fire model with slow recovery and application to motoneuron data.

A generalized version of the integrate-and-fire model is presented that qualitatively reproduces firing rates and membrane trajectories of motoneurons. The description is based on the spike-response model and includes three different time constants: the passive membrane time constant, a recovery time of the input conductance after each spike, and a time constant of the spike afterpotential. The effect of stochastic background input on the peristimulus time histogram (PSTH) response to spike input is calculated analytically. Model results are compared with the experimental data of Poliakov et al. (1996). The linearized theory shows that the PSTH response to an input spike is proportional to a filtered version of the postsynaptic potential generated by the input spike. The shape of the filter depends on the background activity. The full nonlinear theory is in close agreement with simulated PSTH data.