Modeling polymerization of microtubules: A semi-classical nonlinear field theory approach

Vahid Rezania and Jack Tuszynski

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 23, 5795-5809

Abstract: In this paper, for the first time, a three-dimensional treatment of microtubules’ polymerization is presented. Starting from fundamental biochemical reactions during microtubule’s assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in three dimensions. We found that the dynamics of a microtubule is mathematically expressed via a cubic-quintic nonlinear Schrödinger (NLS) equation. We show that in 3D 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. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.

Keywords: Microtubule; Polymerization; Dynamic instability; Quantum theory (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:23:p:5795-5809

DOI: 10.1016/j.physa.2008.06.023

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