We use an integrate-and-fire mechanism to model the transformation of
synaptic inputs into spike trains in cortical neurons. Let
be the synaptic current driving a leaky integrator with a time
constant and a threshold . As long as the voltage is
subthreshold, , the voltage is given by
where is the input resistance and is the resting potential. At the instant the voltage reaches the threshold , the neuron emits a spike, and resets to some level . The five parameters of this model, , , , and , 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 , with ones at times when the neuron fired and zeros at other times.