What causes a neuron to spike?

The computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output. White noise stimulus and reverse correlation (the spike-triggered average and spike-triggered covariance) are often used in experimental neuroscience to `ask' neurons which dimensions in stimulus space they are sensitive to, and to characterize the nonlinearity of the response. In this paper, we apply reverse correlation to the simplest model neuron with temporal dynamics--the leaky integrate-and-fire model--and find that even for this simple case standard techniques do not recover the known neural computation. To overcome this, we develop novel reverse correlation techniques by selectively analyzing only `isolated' spikes, and taking explicit account of the extended silences that precede these isolated spikes. We discuss the implications of our methods to the characterization of neural adaptation. Although these methods are developed in the context of the leaky integrate-and-fire model, our findings are relevant for the analysis of spike trains from real neurons.