Serial Dependency in Neural Point Processes Due to Cumulative Afterhyperpolarization

The effects of cumulative vs noncumulative afterhyperpolarization (AHP) are examined through simulations of a stochastic neural model (Smith and Goldberg, 1986). The afterhyperpolarization in the model is due to a timevarying potassium conductance. Cumulative effects result from summing the residual activity of the potassium conductance in the preceding interspike interval. The variablity in the model is due to random quantal transmitter release. The statistical properties of the steady state discharge patterns that are independent of the serial ordering of interspike intervals show only slight differences between the two cases. Sever~forder dependent statistical measures are used to show that a negative serial dependency results from cumulative AHP at moderate to high discharge rates. The discussion considers the robustness of the model and its relation to a generalized Poisson process description of spike trains. Possible applications of the results to neurons in the auditory and vestibular systems are also examined.