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

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

2008-10-22

arxiv.org/abs/0810.4099v1

Physics Letters A 372 (2008) 7051--7056

Biology

Quantitative Biology

Quantitative Methods

12 pages, 2 figures. Accepted in Physics Letters A

Scientific paper

10.1016/j.physleta.2008.10.038

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.

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