Three kinds of W-potentials in nonlinear biophysics of microtubules

Dragana Ranković, Vladimir Sivčević, Slobodan Zdravković, and Anna Batova Three kinds of W-potentials in nonlinear biophysics of microtubules. Chaos, Solitons & Fractals, Volume 170, May 2023, 113345.

DOI: 10.1016/j.chaos.2023.113345

Paper: https://www.sciencedirect.com/science/article/abs/pii/S0960077923002461

Abstract

In the present article we investigate the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton, relying on the known general model. We introduce the W-potential energy, describing a crucial interaction among constitutive particles within the microtubule. Three kinds of this potential are studied, one symmetrical and two non-symmetrical. We demonstrate an advantage of the latter ones. Solutions of crucial differential equations are solitary waves. The stability of the solutions having physical sense is studied. We show that only subsonic solitary waves are stable, while supersonic ones are not.

Non-Symmetrical W-potential in nonlinear biophysics of microtubules

Zdravković S. and Sivčević V. Non-Symmetrical W-potential in Nonlinear Biophysics of Microtubules - Nonlinear Phenomena In Complex Systems, 24 (2) 2021, pp. 198 - 202.

DOI: 10.33581/1561-4085-2021-24-2-198-202

Paper: http://www.j-npcs.org/abstracts/vol2021/v24no2/v24no2p198.html

Abstract

In this work, we study nonlinear dynamics of microtubules. An important interaction among constitutive particles is modeled using W-potential. We compare a symmetric potential with two kinds of non-symmetric ones. An advantage of the latter ones is demonstrated.

General model of microtubules

Zdravković S., Satarić M.V. and Sivčević V. General model of microtubules. Springer - Nonlinear Dynamics, 92(Issue2):479-486, 2018.

DOI: 10.1007/s11071-018-4069-5

Paper: https://link.springer.com/article/10.1007/s11071-018-4069-5

Abstract

In the present work, we deal with nonlinear dynamics of microtubules. A new model, describing nonlinear dynamics of microtubules, is introduced. Its advantages over two existing models are demonstrated. We show that dynamics of microtubules can be explained in terms of kink solitons. Also, circumstances yielding to either subsonic or supersonic solitons are discussed.