Microtubules: dynamics, soliton waves, some roles in the cell

TL;DR

This paper explores the nonlinear dynamics of microtubules, presenting models that describe soliton wave solutions such as kink solitons, breathers, and bell-type solitons, highlighting their potential roles in cellular functions.

Contribution

It introduces a mathematical model for microtubule dynamics and demonstrates the existence of various soliton wave solutions using continuum and semi-discrete approximations.

Findings

Identification of solitonic wave solutions in microtubule models

Classification of three types of solitons: kink, breather, bell-type

Discussion of the implications of solitons in cellular processes

Abstract

In the present paper we deal with nonlinear dynamics of microtubules (MTs). The structure and role of MTs in cells are explained. One model explaining MT dynamics is explained. Solutions of the crucial nonlinear differential equation depend on used mathematical procedures. Two of them, continuum and semi-discrete approximations, are explained. Finally, these solutions are shown and discussed. They are solitonic waves. Three different kinds of them are known in the moment. They are kink solitons, breathers and bell-type solitons.