Estimation and Verification of a Stochastic Neuron Model

The treatment of a neuron as an information processor is complicated by the nonlinear, time-varying, and distributed parameter attributes of the classical Hodgkin-Huxley neuron model. In this paper, we fit data from experiments on spontaneously firing snail neurons to a much simpler integrate and fire model featuring random process descriptions of the input current density, threshold, and reset potentials. The method of generalized least squares is used to show that the integrate and fire model explains 99.6 percent of the variation in the data used to describe the population behavior of neurons on the visceral ganglion of the Helix Aspersa snail. Experimental histograms suggest that most of the random variation in the interspike interval is caused by the randomness in the input current density and comparatively little by the random fluctuations in threshold and reset potentials, although the latter are still significant from an information processing viewpoint. Residuals from the regression are used to estimate the range of the input current density random process. The residuals also show that slight, but significant, autocorrelation exists in the input current densities. This suggests that information in addition to the mean input current density is being transmitted in the interspike interval code.