Modeling polymerization of microtubules: a quantum mechanical approach

TL;DR

This paper presents a quantum mechanical model of microtubule dynamics, deriving equations that describe their assembly and disassembly, and linking these to nonlinear Schrödinger equations to explain their instability behavior.

Contribution

It introduces a novel quantum field theoretical framework for microtubule dynamics, connecting quantum operators to classical nonlinear equations.

Findings

Microtubule dynamics modeled by a cubic-quintic nonlinear Schrödinger equation.

Vortex filament solutions exhibit growth/shrinkage similar to microtubule instability.

Quantum approach provides new insights into microtubule behavior.

Abstract

In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion for the quantum fields are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. We find that the dynamics of a microtubule can be mathematically expressed via a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation. We show that a vortex filament, a generic solution of the NLS equation, exhibits linear growth/shrinkage in time as well as temporal fluctuations about some mean value which is qualitatively similar to the dynamic instability of microtubules.