Pietruszka M, Stolarek J, Pazurkiewicz-Kocot K
Faculty of Biology and Environmental Protection, University of Silesia, Katowice, Poland.
J Biol Phys. 1997 Dec;23(4):219-32. doi: 10.1023/A:1005020826000.
In this paper we extend and reconsider a solitonic model of the actionpotential in biological membranes for the case of plant cells. Aiming togive at least a qualitative description of the K(+),Cl(-) and Ca(2+) driven process of propagation ofthe action potential along plant cells we put forward the hypothesis ofthree scalar fields φ(i) (X), i = 1, 2, 3 which representK(+), Cl(-) and Ca(2+) ions,respectively. The modulus squared of these fields carries the usualquantum-mechanical (probabilistic) interpretation of the wave function. Onthe other hand, the fields are described themselves by the Lagrangiandensities ℒ[Formula: see text]. Moreover, the interaction and self-interaction term ℒ[Formula: see text] between thefields is considered. The Lagrangian densities ℒ[Formula: see text]include a double-well potential (which is proportional toσ(4) (i)) that leads to spontaneous symmetrybreaking which may produce structures with non-zero topological charge, e.g.longitudinal solitons. In order to describe the transversal motion of theions of concern we need to assume only non-uniform solutions of the system of equation of motion. Hence we seek for solutions (travelling waves) whichpreserve the shape and which move without dissipation and in this way wereconstruct the main dynamical features of the action potential in plants.
在本文中，我们针对植物细胞的情况扩展并重新考虑了生物膜中动作电位的孤子模型。旨在至少定性地描述钾离子（K⁺）、氯离子（Cl⁻）和钙离子（Ca²⁺）驱动的动作电位沿植物细胞传播的过程，我们提出了三个标量场φᵢ(X)，i = 1, 2, 3的假设，它们分别代表K⁺、Cl⁻和Ca²⁺离子。这些场的模平方具有波函数通常的量子力学（概率性）解释。另一方面，这些场本身由拉格朗日密度ℒ[公式：见正文]描述。此外，还考虑了场之间的相互作用和自相互作用项ℒ[公式：见正文]。拉格朗日密度ℒ[公式：见正文]包括一个双阱势（与σ⁴(i)成比例），它导致自发对称性破缺，这可能产生具有非零拓扑电荷的结构，例如纵向孤子。为了描述相关离子的横向运动，我们仅需假设运动方程系统的非均匀解。因此，我们寻找保持形状且无耗散地移动的解（行波），并以此方式重构植物中动作电位的主要动力学特征。
