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.
Molecular-morphological signs of oncogenesis can be linked to multiscale collective effects in molecular and cell ensembles. It was shown that nonlinear behavior of biological systems can be associated with the generation of characteristic collective modes representing the open states in molecular and cell organization as the mechanism of the coherent expression dynamics. The mechanical DNA model is developed to study the nonlinear dynamics of the helicoidal geometry DNA molecule. To construct the model of DNA the Peyrard-Bishop-Barbi approach has been applied. The analytical small localized solutions as the discrete breather and the antikink have been obtained by multiple scale expansion method for multicomponent lattices. The set of collective open states (breathers) in the molecular ensembles provides the collective expression dynamics to attract cells toward a few preferred global states. This result allows the formulation of the experimental strategy to analyze the qualitative changes in cell dynamics induced by mentioned collective modes. The biomechanical changes have been shown experimentally using the original data of Coherent Phase Microscopy analyzing the time series of phase thickness fluctuations. Study of the mechanical aspects of the behavior of single cells is a prerequisite for the understanding of cell functions in the case of qualitative changes in diseases affecting the properties of cells and tissues morphology to develop diagnostic and treatment design methodology.
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