Adiabatic evolution of solitons embedded on lipid membranes

TL;DR

This paper investigates how solitons, representing nerve impulses, evolve within lipid membranes during phase transitions, using a perturbative approach to understand their behavior in viscous environments.

Contribution

It introduces a quasi-stationary method to analyze the adiabatic evolution of solitons in lipid bilayers considering viscous effects and phase transitions.

Findings

Dark and bright solitons emerge during liquid-gel phase transitions.

The adiabatic evolution of solitons is characterized under viscous conditions.

The model provides insights into nerve impulse dynamics in lipid membranes.

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.