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

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.

Bright solitary waves as charge transport in DNA: A variational approximation

“…We consider in this work matrix elements ν n , n + 1 derived within the quantum chemical approach and further used in Lakhno et al The value of the effective coupling parameter ν ′ is taken from Shapovalov and Obukhov which is consistent with the experiment in Bertrand Tabi et al, while for α ′ , its value corresponds to the one calculated in Cadoni et al and is very close to the value used in Malomed, the latter one was used to explain the experiment in Cadoni et al It is well known that oscillation frequencies of base pairs are within the range of picoseconds . The oscillation frequencies adopted here are those used in Shapovalov and Obukhov . Hence, we set parameter values to be M = 10 −24 kg ≈ 602 amu, eV, ν ′ = 0.4 eV × Å −1 and α ′ = 0.13 eV × Å −1 .…”

Universal Complexity Science and Theory of Everything: Challenges and Prospects

“…Furthermore, it seems that scientists and philosophers consider the concept of "complexity" as particularly relevant in relation to "self-organization", "emergence", and "nonlinearity", all of which are typical features of complex systems [66]. While nonlinearity, which is essential to chaos theory, states that minor influences on the system can significantly change the state of the system on a large spatial scale [67,68], self-organization refers to an evolutionary process in which new, complex structures occur primarily within and by the system itself [69]. In other words, scientists recognize that self-organized systems exchange matter, energy, and information with their environment but achieve their organization without environmental instructions thanks to many components whose non-trivial interactions produce structural and dynamical order [12,70,71].…”

Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

“…The nonlocal generalizations of the FKPP equation are used to get insight in the study of such significant phenomena as the formation and evolution of spatial and temporal structures [3][4][5], of traveling and spiral waves [5,6], stability of steady-states [7], and some other features of reaction-diffusion systems. The FKPP model is used in studies of cell population dynamics [8][9][10] including its fractional versions [11,12]. Competitive interactions of microbial populations due to the diffusion of nutrients, the release of toxic substances, chemotaxis, and molecular communications between individuals lead to nonlocal effects that can be effectively described by the generalized nonlocal FKPP equation [9,[13][14][15][16].…”