Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model

TL;DR

This paper models the nonlinear electric field dynamics in microtubules using a classical pseudo-spin approach, deriving equations that reveal wave and soliton solutions, aiding understanding of microtubule functions.

Contribution

It introduces a realistic pseudo-spin model for microtubule dipole dynamics, deriving nonlinear equations and solutions that incorporate geometry and interactions.

Findings

Derivation of nonlinear equations of motion for microtubule dipoles

Identification of snoidal waves, solitons, kinks, and spikes as solutions

Insights into microtubule functions and potential quantum effects

Abstract

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.