Decoding spike timing: the differential reverse-correlation method.

It is widely acknowledged that detailed timing of action potentials is used to encode information, for example, in auditory pathways; however, the computational tools required to analyze encoding through timing are still in their infancy. We present a simple example of encoding, based on a recent model of time-frequency analysis, in which units fire action potentials when a certain condition is met, but the timing of the action potential depends also on other features of the stimulus. We show that, as a result, spike-triggered averages are smoothed so much that they do not represent the true features of the encoding. Inspired by this example, we present a simple method, differential reverse correlations, that can separate an analysis of what causes a neuron to spike, and what controls its timing. We analyze with this method the leaky integrate-and-fire neuron and show the method accurately reconstructs the model's kernel.