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. 1997 Dec;23(4):219–232. doi: 10.1023/A:1005020826000

Time Evolution of the Action Potential in Plant Cells

Mariusz Pietruszka 1, Jan Stolarek 1, Krystyna Pazurkiewicz-Kocot 1
PMCID: PMC3456497  PMID: 23345663

Abstract

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 Ca2+ driven process of propagation ofthe action potential along plant cells we put forward the hypothesis ofthree scalar fields φi (X), i = 1, 2, 3 which representK+, Cl- and Ca2+ 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 ℒInline graphic. Moreover, the interaction and self-interaction term ℒInline graphic between thefields is considered. The Lagrangian densities ℒInline graphicinclude a double-well potential (which is proportional toσ4i) 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.

Keywords: Action potentials, Plants, Ion fluxes, Longitudinal solitons

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