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arXiv 1809.05960physics.bio-ph
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基于Action电势和轴突电场的膜性质的单一微分方程描述

A Single Differential Equation Description of Membrane Properties Underlying the Action Potential and the Axon Electric Field

Robert F. Melendy, Ph. D

摘要:

在65年前发表的一系列文章中,艾伦·劳埃德·霍奇金爵士和安德鲁·菲尔丁·赫胥黎爵士建立了我们现在对神经兴奋的物理理解,以及轴突如何传导动作电位。他们独特地量化了动作电位过程中神经细胞中离子的运动,并证明了动作电位是跨细胞膜去极化事件的结果。他们证实,一个完整的去极化事件之后是一个突然增加的电压,沿着轴突纵向传播,伴随着膜电导的显着增加。在一个优雅的理论框架中,他们严格描述了动作电位固有的Na+和K+电导的基本性质。尽管霍奇金和赫胥黎的一系列发现精辟而解释性强,但他们的模型在数学上很复杂,依赖于大量的随机因素,而且没有解析解。求解膜动作电位和离子电流需要使用数值方法近似积分。在这篇文章中,我提出了一个分析的形式主义的神经动作电位,Vm和伴随的细胞膜电场,EM。最后,我提出了一个新的描述Vm在一个单一的,非线性微分方程。这是一篇独立的原创文章:主要贡献是后者,以及这种描述如何与细胞膜电场相吻合。这项工作有必要统一的信息,从两个以前的文件,每一个被关注的发展封闭形式的描述神经动作电位。

英文摘要:

In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential. They uniquely quantified the movement of ions in the nerve cell during the action potential, and demonstrated that the action potential is the result of a depolarizing event across the cell membrane. They confirmed that a complete depolarization event is followed by an abrupt increase in voltage that propagates longitudinally along the axon, accompanied by considerable increases in membrane conductance. In an elegant theoretical framework, they rigorously described fundamental properties of the Na+ and K+ conductances intrinsic to the action potential. Notwithstanding the elegance of Hodgkin and Huxley's incisive and explicative series of discoveries, their model is mathematically complex, relies on no small number of stochastic factors, and has no analytical solution. Solving for the membrane action potential and the ionic currents requires integrations approximated using numerical methods. In this article I present an analytical formalism of the nerve action potential, Vm and that of the accompanying cell membrane electric field, Em. To conclude, I present a novel description of Vm in terms of a single, nonlinear differential equation. This is an original stand-alone article: the major contribution is the latter, and how this description coincides with the cell membrane electric field. This work has necessitated unifying information from two preceding papers, each being concerned with the development of closed-form descriptions of the nerve action potential.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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