A first principle (3+1) dimensional model for microtubule polymerization

TL;DR

This paper introduces a microscopic 3D model for microtubule polymerization, deriving a nonlinear Schrödinger equation that captures dynamic instability and matches experimental patterns.

Contribution

It presents a novel microscopic derivation of microtubule dynamics leading to a cubic-quintic nonlinear Schrödinger equation in 3D.

Findings

The model reproduces microtubule growth and shortening behaviors.

Numerical solutions show spatio-temporal patterns similar to experiments.

The dynamics exhibit fluctuations akin to observed instability.

Abstract

In this paper we propose a microscopic model to study the polymerization of microtubules (MTs). Starting from fundamental reactions during MT's assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in 3D. %coexistence with tubulin dimers in a solution. We found that the dynamics of a MT is mathematically expressed via a cubic-quintic nonlinear Schrodinger (NLS) equation. Interestingly, the generic 3D solution of the NLS equation exhibits linear growing and shortening in time as well as temporal fluctuations about a mean value which are qualitatively similar to the dynamic instability of MTs observed experimentally. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.