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Stability Analysis of Jacobi Elliptic Solutions of Microtubule

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A nonlinear dynamic model which elucidate the mechanism of the internal motion occuring during the assembly of microtubules (MTs) is considered. The nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. MTs is assumed to be a single longitudinal degree of freedom per tubulin dimer, and the motion equation is reduced to the discrete nonlinear Schrödinger equation. Exact solutions are investigated using the Jacobian elliptic fonctions approach. It is shown that such a nonlinear model can lead to the existence of kink solitons, breather as well as Jacobi solutions which can propagate along the microtubule outer surface, and the tubulin tail soliton collisions could serve as elementary computational gates that control cytoskeletal processes. We examine the stability of these solutions and found that the kink solution is stable with respect to small-amplitude fluctuations.
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Keywords: IONIC WAVE; JACOBIAN ELLIPTIC FUNCTIONS; MICROTUBULE DYNAMIC; SOLITONS

Document Type: Research Article

Publication date: November 1, 2014

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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