A model of neurons with pacemaker behavior receiving strong synaptic input

A “pacemaker” neuron with the following properties is considered: after a firing, the membrane potential is reset to a constant value from which it increases to the firing threshold during a time t
0
. The neuron receives strong synaptic input producing postsynaptic potentials (PSP's) which change the membrane potential to the reversal potential of the synapse, from which level the potential increases to the firing threshold during a time t
1
Provided that interarrival times for the PSP's are independent and identically distributed, successive interspike intervals in this class of model neurons can be described by a regenerative stochastic process simple enough to allow the derivation of tractable expressions for the limiting distribution of the interspike intervals, including a simple expression for the mean firing rate. A central limit theorem for the partial sums of interspike intervals can also be proved. This class of models is a generalization of a model of the crayfish's stretch receptors, a commonly used neurophysiological system. In two examples the model is studied under varying temporal patterns for the PSP's to illustrate, respectively, phase locking and certain principles of summation of excitation and inhibition.