Modeling polymerization of microtubules: a quantum mechanical approach

Details Modeling polymerization of microtubules: a quantum mechanical approach Modeling polymerization of microtubules: a quantum mechanical approach

2007-08-27

arxiv.org/abs/0708.3509v2

Physica A, Vol. 387, 5795 - 5809 (2008)

Biology

Quantitative Biology

Biomolecules

19 pages, 1 figure

Scientific paper

In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion for the quantum fields are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. We find that the dynamics of a microtubule can be mathematically expressed via a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation. We show that 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.

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