Nonlinear dynamics of microtubules - A new model

TL;DR

This paper introduces a nonlinear model for microtubule dynamics that predicts kink solitons and calculates electrical and energetic properties using analytical and numerical methods.

Contribution

It presents a novel nonlinear PDE model for microtubules with analytical solutions and a theorem simplifying energy calculations.

Findings

Existence of kink solitons in microtubules.

Agreement between two methods for electrical field strength calculation.

Estimation of energy, velocity, and width of solitons.

Abstract

In the present paper we describe a model of nonlinear dynamics of microtubules (MT) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimer`s dynamics within MT, is solved both analytically and numerically. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. Internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled estimation of total energy, kink velocity and kink width. To simplify the calculation of the total energy we proved a useful theorem.