Abstract
In our study, we represent the theoretical and numerical analysis of a stochastic version of the Hodgkin–Huxley model applied to a two-dimensional spatial cylindrical area simulating the neuronal somatic membrane. We characterized the spatiotemporal dynamics of the membrane potential by its local value V m (x, y, t) and the integral of this value with respect to time F(x, y, T) within an interval [0, T]. Analysis of the model showed that (i) there are nonzero gradients of F(x, y, T) at any distribution of ion channels; (ii) the maximum gradient F(x, y, T) decreases down to zero with the time T, if the channels are distributed homogeneously, and acquire some positive constant value, if the channels are distributed inhomogeneously; the gradient F(x, y, T) depends on the gradient of spatial distribution of the channels; and (iii) under conditions of spatial redistribution of the channels with preservation of their number, the dynamics of V m (x, y, t) does not change.
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Savchenko, L.P. Spatial Distribution of the Potential on a Cylindrical Surface Simulating the Somatic Membrane: Model Studies. Neurophysiology 32, 291–299 (2000). https://doi.org/10.1023/A:1010333820815
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DOI: https://doi.org/10.1023/A:1010333820815