A first principle (3+1) dimensional model for microtubule polymerization
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.
Cite
@article{arxiv.0810.4099,
title = {A first principle (3+1) dimensional model for microtubule polymerization},
author = {Vahid Rezania and Jack Tuszynski},
journal= {arXiv preprint arXiv:0810.4099},
year = {2009}
}
Comments
12 pages, 2 figures. Accepted in Physics Letters A