¹Institute of Continuous Media Mechanics Ural Branch of RAS, Perm, Russia
²Institute for Metals Superplasticity Problems RAS, Ufa, Russia
³National Research Tomsk State University, Tomsk, Russia

Abstract. 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.

Key words: DNA, Peyrard–Bishop, helicoidal model, open states, modulation interference microscopy.