Modified extended tanh-function method and nonlinear dynamics of microtubules

TL;DR

This paper introduces a modified extended tanh-function method to analyze nonlinear microtubule dynamics, revealing kink solitons' role in cellular signaling and traffic regulation, supported by analytical and numerical solutions.

Contribution

It presents a novel application of the METHF method to a ferroelectric microtubule model, demonstrating the existence of kink solitons and their potential biological functions.

Findings

Analytical and numerical solutions of MT dynamics agree perfectly.

Parameter variations affect the behavior of kink solitons.

Kinks may serve as signaling tools in cellular processes.

Abstract

We here present a model of nonlinear dynamics of microtubules (MT) in the context of modified extended tanh-function (METHF) method. We rely on the ferroelectric model of MTs published earlier by Satari\'c et al [1] where the motion of MT subunits is reduced to a single longitudinal degree of freedom per dimer. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. An analytical solution of the basic equation, describing MT dynamics, was compared with the numerical one and a perfect agreement was demonstrated. It is now clearer how the values of the basic parameters of the model, proportional to viscosity and internal electric field, impact MT dynamics. Finally, we offer a possible scenario of how living cells utilize these kinks as signaling tools for regulation of cellular traffic as well as MT depolymerisation.