Physics > Biological Physics
[Submitted on 26 Feb 2024 (v1), last revised 16 May 2024 (this version, v3)]
Title:Action potential propagation properties of 4D, 3D and 2D Hodgkin-Huxley type models
View PDF HTML (experimental)Abstract:We explore the relationship between the sodium and potassium gating variables in the Hodgkin-Huxley electrophysiology model, reducing the dimension of the original 4-dimensional (4D) HH model and decreasing the complexity of the model equations. New 3D and 2D model equations have been derived. The new 3D and 2D models result from the relationship $h\simeq c-n$, where $c$ is a constant, of the gate variables $h$ and $n$ of the 4D HH model, suggesting an interdependence between the dynamics of the Na$^+$ and K$^+$ transmembrane pumps. We have derived the main properties of the propagation speed and width of action potentials for axons with Na$^+$ and K$^+$ active channels as a function of the transmembrane capacity $C_m$ and resistivity $R$ of the conducting axon. For the three HH type models, we show that the action potential propagates along the axon with speed well described by $v(R, C_m)=\alpha /({C_m R^{\beta}})=\gamma D^{\beta}$, where $\alpha>0 $, $0<\beta <1$ and $\gamma$ are constants independent of the local intensity stimulus, and $D$ is the diffusion coefficient of the axon. The width $w$ of the action potential spikes depends on the resistivity of the axon with $w = \alpha_2 /R^{\beta_2}$, where $\alpha_2$ and $\beta_2$ are positive constants.
Submission history
From: Lízia Branco [view email][v1] Mon, 26 Feb 2024 16:30:23 UTC (7,351 KB)
[v2] Tue, 27 Feb 2024 10:15:21 UTC (7,355 KB)
[v3] Thu, 16 May 2024 10:39:03 UTC (11,593 KB)
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