Abstract
The expected time to firing of a nerve impulse when there is Poisson excitation is calculated exactly in Stein's model. This is done at various input frequencies and various ratios of threshold to epsp magnitude, extending some previous calculations. The appropriate conditions for the validity of the model are discussed. Details of a particular calculation are given which involves the solution of a differential-difference equation. The results are presented as variation of expected time to firing as a function of input frequency for a given threshold to epsp ratio. The experimental results of Redman et al. for Poisson monosynaptic excitation of cat spinal motoneurons lead to the estimation of the epsp size which was not measured. The magnitude of the epsps predicted is in good agreement with that expected under the given conditions of stimulation. The predicted variation of epsp magnitude with input frequency is in accordance with that obtained in other experiments. When the finite rise time of epsps is taken into account the predicted epsp sizes are in better agreement with their expected amplitudes.
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Tuckwell, H.C. Firing rates of motoneurons with strong random synaptic excitation. Biol. Cybernetics 24, 147–152 (1976). https://doi.org/10.1007/BF00364117
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DOI: https://doi.org/10.1007/BF00364117