DNA transformation, cell epigenetic landscape and open complex dynamics in cancer development

O. B. Neumark ; Yu. V. Bayandin ; Yu. A. Beloglazova ; O. N. Gagarskich ; V. V. Grishko ; A. S. Nikityuk ; A. O. Voronina

Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020) no. 2, pp. 251-267.

Résumé

Statistical thermodynamics allowed the formulation of mesoscopic approach of DNA transformation in course of the excitation of collective distortion modes (denaturation bubbles) associated with hydrogen bond breaking between the base pairs. Intermediate (non-continual limit) of DNA modeling (the Peyrard –Bishop model) is combined with the field description (generalized Ginzburg –Landau approach) to analyze the dynamics of collective open complex modes associated with mesodefects in the DNA ensemble. Collective modes dynamics describes different scenario of gene expression according to statistically predicted form of out-of-equilibrium potential (epigenetic landscape) reflecting specific type criticality of “soft matter” with mesodefects (open complexes) – the structural-scaling transition. Principal difference of thermodynamics of non-continual and continual models is thermalization conditions related to thermal fluctuations responsible for the DNA breathing (localized excitation with breather dynamics) and structural-scaling parameter responsible for spinodal decomposition of out-of-equilibrium potential metastability due to generation of open complex collective modes. Open complex collective modes have the nature of self-similar solutions (breathers, auto-solitary and blow-up modes) of open complex evolution equation accounting qualitative different types of potential metastabilities. Sub-sets of collective modes represent the phase variables of attractors associated with different scenario of expression dynamics, which allows the interpretation of multistability of the epigenetic landscape and the Huang diagram of gene expression. It was shown different epigenetic pathway in attractors phase space corresponding to normal and cancer expression scenario. These scenarios were supported by laser interference microscopy of living normal and cancer cells illustrating multi- and monofractal dynamics.

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