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

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  • Rezania, Vahid
  • Tuszynski, Jack

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.

Suggested Citation

  • Rezania, Vahid & Tuszynski, Jack, 2008. "Modeling polymerization of microtubules: A semi-classical nonlinear field theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5795-5809.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:23:p:5795-5809
    DOI: 10.1016/j.physa.2008.06.023
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