Derivation of an Improved Hodgkin-Huxley Model for Potassium Channel by Means of the Fokker-Planck Equation

Details Derivation of an Improved Hodgkin-Huxley Model for Potassium Channel by Means of the Fokker-Planck Equation Derivation of an Improved Hodgkin-Huxley Model for Potassium Channel by Means of the Fokker-Planck Equation

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jsp....89..997l&link_type=abstract

Journal of Statistical Physics, Volume 89, Issue 5-6, pp. 997-1016

Physics

2

Fokker-Planck Equation, Gaussian Distribution, Hodgkin, Huxley Model, Cole, Moore Shift

Scientific paper

This paper demonstrates the derivation of Hodgkin-Huxley-like equations from the Fokker-Planck equation. The primary result is that instead of the familiarg_K = hat g_K n^4 equation expressing the potassium conductance as a function of the variable n which obeys a first order differential equation, the expressiong_K = g_o exp[L^2 - (n - L)^2 ], where L = 2.7, is to be used. This form is obtained by solving analytically an approximate solution to a Fokker-Planck partial difference equation. Instead of the Hodgkin-Huxley interpretation as the probability of occupying the conducting state, the parameter n( t) is now interpreted as the position of the “peak” of the population distribution function P( N, t), which changes in time described by the Fokker-Planck equation. This new approach enables close fitting of the experimental voltage clamp data for potassium conductance. In addition, the Cole-Moore shift paradox can be quantitatively explained in terms of the shift of the distribution function P( N,t) by the initial clamped transmembrane potential V i before the final clamped transmembrane potential V f is applied, thus increasing the time necessary for the establishment of equilibrium.

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