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Symmetry 2018, 10(3), 53; doi:10.3390/sym10030053

Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher–KPP Model

1
Department of Theoretical Physics, Tomsk State University, 1 Novosobornaya Sq., 634050 Tomsk, Russia
2
Department of Physics and Mathematics, Tomsk State Pedagogical University, 60 Kievskaya St., 634041 Tomsk, Russia
3
Department of Higher Mathematics and Mathematical Physics, Tomsk Polytechnic University, 30 Lenin Ave., 634034 Tomsk, Russia
*
Author to whom correspondence should be addressed.
Received: 10 February 2018 / Revised: 10 February 2018 / Accepted: 24 February 2018 / Published: 27 February 2018
(This article belongs to the Special Issue Symmetry: Anniversary Feature Papers 2018)
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Abstract

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed. View Full-Text
Keywords: self-organization; solitons; DNA models; nonlocal Fisher–KPP model; released activity self-organization; solitons; DNA models; nonlocal Fisher–KPP model; released activity
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Shapovalov, A.V.; Obukhov, V.V. Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher–KPP Model. Symmetry 2018, 10, 53.

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