Adiabatic evolution of solitons embedded on lipid membranes

O. Pavón-Torres, M. A. Agüero-Granados, R. Valencia-Torres
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Abstract

The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve impulses can be represented as nonlinear excitations of low amplitude depicted by the damped nonlinear Schr\"odinger equation and their adiabatic evolution can be analyzed using direct perturbative methods. Based on the foregoing, we carry out the current study using the quasi-stationary approach to obtain the adiabatic evolution of solitons embedded in lipid bilayers under the influence of a viscous elastic fluid. This analysis encompasses liquid-to-gel transition of the lipid bilayers, for whose dark and bright solitons arise, respectively.
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嵌入脂膜的孤子的绝热演化
海姆伯格-杰克逊模型,即神经脉冲的热力学孤子理论,作为研究神经脉冲和脂质双层膜动力学的一种替代模型,有着良好的记录。在这一框架内,神经脉冲可以表示为阻尼非线性薛定谔方程所描述的低振幅非线性激励,其绝热演化可以用直接扰动方法进行分析。在此基础上,我们采用准稳态方法进行了本研究,以获得在粘性弹性流体影响下嵌入脂质双层膜的孤子的绝热演化。该分析包括脂质双层膜从液态到凝胶态的转变,分别产生了暗孤子和亮孤子。
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