Phase Response Curves Determine the Responses of Neurons to Transient Inputs

Neuronal firing is determined largely by incoming barrages of ex-citatory postsynaptic potentials (EPSPs), each of which produce a transient increase in firing probability. To measure the effects of weak transient inputs on firing probability of cortical neurons, we compute Phase-Response Curves (PRC). PRCs, whose shape can be related to the dynamics of spike generation, document the changes in timing of spikes caused by an EPSP in a repetitively firing neuron as a function of when it arrives in the interspike interval (ISI). The PRC can be exactly related to the post-stimulus time histogram (PSTH) so that knowledge of one uniquely determines the other. Typically, PRCs have zero values at the start and end of the ISI, where EPSPs have minimal effects and a peak in the middle. Where the peak occurs depends in part on the firing properties of neurons. The PRC can have regions of positivity and negativity corresponding respectively to speeding up and slowing down the time of the next spike. A simple canonical model for spike generation is introduced which shows how both the background firing rate and the degree of post-spike afterhyperpolar