A note on neuronal firing and input variability.
The Ornstein-Uhlenbeck process with a constant forcing function has often been used as a model for the subthreshold membrane potential of a neuron. The mean, variance and coefficient of variation of the first passage time to a constant threshold are examined for this model in the limit of small synaptic noise and low thresholds. A comparison is made between the asymptotic results of Wan & Tuckwell, who used perturbation analysis, and several computationally simpler approximation methods. A generalization of Stein's method gives an overestimate of the mean interval while an approximation by a Wiener process with linear drift gives an underestimate of the mean interval. These bounds are simple to calculate and can be used as a prelude to a more detailed perturbation analysis.
Smith
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CE
Department of Statistics, North Carolina State University, Raleigh 27695-8203.
D000818:Animals; D008433:Mathematics; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology