ISSN:
1573-0689
Keywords:
Action potentials
;
Plants
;
Ion fluxes
;
Longitudinal solitons
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Physics
Notes:
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 ℒ $$_{\emptyset i} $$ . Moreover, the interaction and self-interaction term ℒ $$_{(\emptyset i,\emptyset j)} $$ between thefields is considered. The Lagrangian densities ℒ $$_{\emptyset i} $$ include a double-well potential (which is proportional toσ4 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005020826000
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