Fuchikami N, Sawashima N, Naito M, Kambara T
Department of Physics, Faculty of Science, Tokyo Metropolitan University, Japan.
Biophys Chem. 1993 May;46(3):249-59. doi: 10.1016/0301-4622(93)80018-e.
A simple mathematical model of the chemically excitable membranes leading to autonomous chaotic oscillations is presented. The model assumes two kinds of autocatalytic ion channels, one is for cations and the other is for anions. Self-consistency between the ion distributions and the electric potentials is taken into account by including the counter ions explicitly. Cations and anions pass through their own channels with their permeabilities changing nonlinearly with the densities of ions at the surfaces of the membrane. Cation and anion transport systems then form two subsystems that oscillate and interact with each other through the membrane potential. When the coupling strength between the two ion systems and adsorption rate of ions to channels are varied, various types of chaotic oscillations are generated autonomously, i.e., without a stimulating periodic force. Experimental evidence to the present model is discussed. It is suggested that endogenous chaos in biological systems may appear from the electric coupling among different kinds of ion transport systems.
本文提出了一个导致自主混沌振荡的化学可激发膜的简单数学模型。该模型假设存在两种自催化离子通道，一种用于阳离子，另一种用于阴离子。通过明确包含抗衡离子来考虑离子分布和电势之间的自洽性。阳离子和阴离子通过各自的通道，其渗透率随膜表面离子密度非线性变化。阳离子和阴离子传输系统随后形成两个子系统，它们通过膜电位相互振荡并相互作用。当两个离子系统之间的耦合强度和离子对通道的吸附速率发生变化时，会自主产生各种类型的混沌振荡，即无需周期性刺激力。讨论了针对本模型的实验证据。有人提出，生物系统中的内源性混沌可能源于不同种类离子传输系统之间的电耦合。
