Two-component model of a microtubule in a semi-discrete approximation

TL;DR

This paper models microtubule dynamics using a two-component system and semi-discrete approximation, revealing that localized breather waves are stable only when carrier velocity exceeds envelope velocity, challenging prior assumptions.

Contribution

Introduces a novel two-component model for microtubules and demonstrates the stability conditions of breather waves using semi-discrete approximation.

Findings

Breather solutions are stable only if carrier velocity > envelope velocity.

Disproves previous models assuming equal carrier and envelope velocities.

Provides detailed parameter estimation for microtubule dynamics.

Abstract

In the present work, we study the nonlinear dynamics of a microtubule, an important part of the cytoskeleton. We use a two-component model of the relevant system. A crucial nonlinear differential equation is solved with semi-discrete approximation, yielding some localised modulated solitary waves called the breathers. A detailed estimation of the existing parameters is provided. The numerical investigation shows that the solutions are robust only if the carrier velocity of the breather wave is higher than its envelope velocity. That disproves the previously accepted solutions based on the equality of these velocities.