Laser interference microscopy (LIM) is a promising label-free method for single-cell research applicable to cell viability assessment in the studies of mammalian cells. This paper describes the development of a sensitive and reproducible method for assessing cell viability using LIM. The method, based on associated signal processing techniques, has been developed as a result of real-time investigation in phase thickness fluctuations of viable and non-viable MCF-7 cells, reflecting the presence and absence of their metabolic activity. As evinced by the values of the variable v_c, this variable determines the viability of a cell only in the attached state (v_c exceeds 20 nm² for viable attached cells). The critical value of the power spectrum slope β_c of the phase thickness fluctuations equals 1.00 for attached MCF-7 cells and 0.71 for suspended cells. The slope of the phase fluctuations’ power spectrum for MCF-7 cells was determined to exceed the threshold value of β_c for a living cell, otherwise the cell is dead. The results evince the power spectrum slope as the most appropriate indicator of cell viability, while the integrated evaluation criterion (v_c and β_c values) can be used to assay the viability of attached cells.

One of the main problems in the nonlinear dynamics of DNA is the identification of physical mechanisms responsible for the mechanical features of its behaviour. The formation and interaction of open states in the DNA structure may be one such mechanism. In this paper we propose a mathematical model of native DNA, which allows us to describe its thermodynamic and kinetic properties taking into account the collective behaviour of the ensemble of open states. The concept of a microscopic open state in DNA and its associated parameter, the displacement vector of nitrogenous bases, are introduced. By averaging the base displacement vectors over the ensemble of states, the thermodynamic variable is determined. According to the statistical model of DNA in the self-consistent field approximation, the structural parameter of the system thermalization is derived. This parameter reflects the statistical self-similarity in the behaviour of the ensemble of open states. Regularities of "criticality" for different ranges of the structural parameter are established and phenomenological representations of the free energy in the framework of the Ginzburg-Landau approach are proposed. Numerical modelling of the dynamics of native DNA is carried out for different ranges of the structural parameter, which has allowed us to establish the types of self-similar solutions and the corresponding open-state collective modes. It is shown that the latter have the nature of finite-amplitude fluctuations in the form of breahters and autosoliton modes, as well as blow-up dissipative structures. The sensitivity of the model to initial conditions is investigated, and the influence of nonlinearity inherent in the model on the modelling results is established. The limitations and prospects of using the approach proposed in this work for mathematical modelling of native DNA are discussed.

The mechanical DNA model is developed to study the nonlinear dynamics, topological constrains of the helicoidal geometry DNA molecule, dissipation effects and influence of the external force.

The aim of this work is to study of the phase transition during thermal denaturation of DNA by the method of recurrence quantification analysis, which is the most modern and efficient approach for the analysis of complex systems. To achieve the goal, the nonlinear dynamics model of the DNA denaturation is implemented, based on the Pey-rard – Bishop – Dauxois approach, which allows determining the state of DNA base pairs at an arbitrary point in time. Next, the dynamics of DNA is simulated at different tempera-tures, and the evolution of hydrogen bond stretching during DNA heating is studied. To analyze the results obtained, the method of recurrence quantification analysis is used, which makes it possible to judge the nature of the processes which occur in the system and are of particular interest in relation to the study of nonlinear DNA dynamics. In par-ticular, those are phase transitions, since on the basis of their analysis it is possible to identify states of repetition and fading (laminarity), the occurrence of extreme events, the presence of hidden periodicity and cyclicity. Using this method of analysis, quantitative measures are calculated in a window shifted along the main diagonal of the recurrent plot (RP). These measures quantify fine-scale RP structures. The calculations reveal the most sensitive measures to the analysis of the process under study, with the help of which the precursors of the phase transition are determined.