Cortical neurons convert synaptic inputs arising from thousands of other neurons into a single output spike train. In order to better understand this basic computation, we have derived a simple repetitive firing model from the Hodgkin-Huxley equations. This novel model is related to the conventional integrate-and-fire model. but uses a time-varying time constant (whose value follows a stereotyped trajectory after each spike) in place of the usual fixed time constant. The model, whose parameters can be extracted from as few as two interspike intervals, provides an excellent fit to the respolnse of cortical neurons in vitro to both constant and time-varying inputs.
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