Abstract
The Hodgkin and Huxley equations have served as the benchmark model in electrophysiology since 1950s. But it suffers from four major drawbacks. Firstly, it is only phenomenological not mechanistic. Secondly, it fails to exhibit the all-or-nothing firing mechanism for action potential generation. Thirdly, it lacks a theory for ion channel opening and closing activation across the cell membrane. Fourthly, it does not count for the phenomenon of voltage-gating which is vitally important for action potential generation. In this paper, a mathematical model for excitable membranes is constructed by introducing circuit characteristics for ion pump exchange, ion channel activation, and voltage-gating. It is demonstrated that the model is capable of re-establishing the Nernst resting potentials, explicitly exhibiting the all-or-nothing firing mechanism, and most important of all, filling the long-lasting theoretical gap by a unified theory on ion channel activation and voltage-gating. It is also demonstrated that the new model has one half fewer parameters but fits significantly better to experiment than the HH model does. The new model can be considered as an alternative template for neurons and excitable membranes when one looks for simpler models for mathematical studies and for forming large networks with fewer parameters.
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Deng, B. Alternative Models to Hodgkin–Huxley Equations. Bull Math Biol 79, 1390–1411 (2017). https://doi.org/10.1007/s11538-017-0289-y
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DOI: https://doi.org/10.1007/s11538-017-0289-y