Time discrete model of recurrent inhibition in hippocampal dentate gyrus

A time discrete model of recurrent inhibition in the hippocampal dentate gyrus is made and analyzed. This model assumes that (1) each granule cell can generate only one action potential in response to a single stimulation of the perforant path, (2) each interneuron receives synaptic inputs from many granule cells, and (3) an output of the interneuron is inhibitory for granule cells. Although each granule cell generates an action potential in the all-or-none fashion, the population spike is shown to be approximated by a piecewise linear function of the population excitatory post-synaptic potential (EPSP). From this model six patterns in the population spike responses to the paired-pulse stimulation are deduced. Each pattern is composed of some broken lines whose slopes and intercepts are explicitly expressed by the average and variance of the microscopic parameters and the population size of the cells. This model clarifies the relation between the measured quantity in the field potential experiment and the microscopic quantities peculiar to the granule cell and to the interneuron.