Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Djekic, Milos

doi:10.5937/kgjsci1436059d

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Cited by 2 publications

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Kinks and bell-type solitons in microtubules

Zdravković

Gligorić

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In the present paper, we study the nonlinear dynamics of microtubules relying on the known u-model. As a mathematical procedure, we use the simplest equation method. We recover some solutions obtained earlier using less general methods. These are kink solitons. In addition, we show that the solution of the crucial differential equation, describing nonlinear dynamics of microtubules, can be a bell-type soliton. The discovery of this new solution is supported by numerical analysis.

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Kinks and bell-type solitons in microtubules

Zdravković

Gligorić

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mechanical Models of Microtubules

Zdravković¹

2018

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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Microtubules are the major part of the cytoskeleton. They are involved in nuclear and cell division and serve as a network for motor proteins. The first model that describes nonlinear dynamics of microtubules was introduced in 1993. Three nonlinear models are described in this chapter. They are longitudinal U-model, representing an improved version of the first model, radial φ-model and new general model. Also, two mathematical procedures are explained. These are continuum and semi-discrete approximations. Continuum approximation yields to either kink-type or bell-type solitons, while semidiscrete one predicts localized modulated waves moving along microtubules. Some possible improvements and suggestions for future research are discussed.

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Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Abstract: In the present paper we rely on the so called u-model of the dynamics of microtubules. We demonstrate how a crucial differential equation can be solved using the method of factorization. It was shown that the solutions match the ones obtained using the standard procedure.

Cited by 2 publications

References 10 publications

Kinks and bell-type solitons in microtubules

Kinks and bell-type solitons in microtubules

Mechanical Models of Microtubules

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