Adiabatic evolution of solitons embedded on lipid membranes

2024/06/30 by O. Pavón-Torres, Pavón-Torres, O., M. A. Agüero-Granados +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · #FOS: Physical sciences #Lipid Membrane Structure and Behavior #Pattern Formation and Solitons (nlin.PS) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2407.00601

openalex publication_date 2024/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger 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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