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.