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Model of spiking


We use an integrate-and-fire mechanism to model the transformation of synaptic inputs into spike trains in cortical neurons. Let tex2html_wrap_inline1109 be the synaptic current driving a leaky integrator with a time constant tex2html_wrap_inline1111 and a threshold tex2html_wrap_inline1113. As long as the voltage is subthreshold, tex2html_wrap_inline1115, the voltage is given by
where tex2html_wrap_inline1117 is the input resistance and tex2html_wrap_inline1119 is the resting potential. At the instant the voltage reaches the threshold tex2html_wrap_inline1113, the neuron emits a spike, and resets to some level tex2html_wrap_inline1123. The five parameters of this model, tex2html_wrap_inline1113, tex2html_wrap_inline1127, tex2html_wrap_inline1119, tex2html_wrap_inline1111 and tex2html_wrap_inline1117, determine its response to a given input current.

The output of the model is a spike train i.e. a sequence of times at which v(t) exceeded threshold. If time is finely discretized into bins shorter than the shortest interspike interval, so that the number of spikes in each bin is either zero or one (but not greater than one), then the spike train can be represented as a binary string tex2html_wrap_inline1137, with ones at times when the neuron fired and zeros at other times.

Tony Zador
Fri Nov 28 10:17:14 PST 1997