Stochastic model of the overdispersion in the place cell discharge

The spontaneous firing activity of the place cells reflects the position of an experimental animal in its arena. The firing rate is high inside a part of the arena, called the firing field, and low outside. It is generally accepted concept that this is the way in which the hippocampus stores a map of the environment. This well known fact was recently reinvestigated [Fenton, A.A., Muller, R.U., 1998. Proc. Natl. Acad. Sci. USA 95, 3182-3187] and it was found that while the activity was highly reliable in position, it did not retain the same reliability in time. The number of action potentials fired during different passes through the firing field were substantially different (overdispersion). We present a mathematical model based on a doubly stochastic Poisson process which is able to reproduce the experimental findings. Further, it enables us to propose specific statistical inference on the experiments in aim to verify data and model compatibility. The model permits to speculate about the neural mechanisms leading to the overdispersion in the activity of the hippocampal place cells. Namely, the statistical variation of the intensity of firing can be achieved, for example, by introducing a hierarchical structure into the local neural network.