The sensitivity of DNA to electromagnetic radiation in different ranges differs depending on various factors. The aim of this study was to examine the molecular dynamics of DNA under the influence of external periodic influences with different frequencies. In the present paper, within the framework of a mechanical model without simplifications, we investigated the effect of various frequencies of external periodic action in the range from 10¹¹ s⁻¹ to 10⁸ s⁻¹ on the dynamics of a DNA molecule. It was shown that under the influence of an external periodic force, a DNA molecule can perform oscillatory movements with a specific frequency characteristic of this molecule, which differs from the frequency of the external influence ω. It was found that the frequency of such specific vibrations of a DNA molecule depends on the sequence of nucleotides. Using the developed mathematical model describing the rotational motion of the nitrogenous bases around the sugar–phosphate chain, it is possible to calculate the frequency and amplitude of the oscillations of an individual DNA area. Such calculations can find application in the field of molecular nanotechnology.

In the present study, the effect of ²H/¹H isotopic exchange in hydrogen bonds between nitrogenous base pairs on occurrence and open states zones dynamics is investigated. These processes are studied using mathematical modeling, taking into account the number of open states between base pairs. The calculations of the probability of occurrence of open states in different parts of the gene were done depending on the localization of the deuterium atom. The mathematical modeling study demonstrated significant inequality (dependent on single ²H/¹H replacement in DNA) among three parts of the gene similar in length of the frequency of occurrence of the open states. In this paper, the new convenient approach of the analysis of the abnormal frequency of open states in different parts of the gene encoding interferon alpha 17 was presented, which took into account both rising and decreasing of them that allowed to make a prediction of the functional instability of the specific DNA regions. One advantage of the new algorithm is diminishing the number of both false positive and false negative results in data filtered by this approach compared to the pure fractile methods, such as deciles or quartiles.

Fluctuations in viscosity within the cell nucleus have wide limits. When a DNA molecule passes from the region of high viscosity values to the region of low values, open states, denaturation bubbles, and unweaving of DNA strands can occur. Stabilization of the molecule is provided by energy dissipation—dissipation due to interaction with the environment. Separate sections of a DNA molecule in a twisted state can experience supercoiling stress, which, among other things, is due to complex entropic effects caused by interaction with a solvent. In this work, based on the numerical solution of a mechanical mathematical model for the interferon alpha 17 gene and a fragment of the Drosophila gene, an analysis of the external environment viscosity influence on the dynamics of the DNA molecule and its stability was carried out. It has been shown that an increase in viscosity leads to a rapid stabilization of the angular vibrations of nitrogenous bases, while a decrease in viscosity changes the dynamics of DNA: the rate of change in the angular deviations of nitrogenous bases increases and the angular deformations of the DNA strands increase at each moment of time. These processes lead to DNA instability, which increases with time. Thus, the paper considers the influence of the external environment viscosity on the dissipation of the DNA nitrogenous bases’ vibrational motion energy. Additionally, the study on the basis of the described model of the molecular dynamics of physiological processes at different indicators of the rheological behavior of nucleoplasm will allow a deeper understanding of the processes of nonequilibrium physics of an active substance in a living cell to be obtained.

The formation and dynamics of the open states in a double-stranded DNA molecule are largely determined by its mechanical parameters. The main one is the torque. However, the experimental study of DNA dynamics and the occurrence of open states is limited by the spatial resolution of available biophysical instruments. Therefore, in this work, on the basis of a mechanical mathematical model of DNA, calculations of the torque effect on the process of occurrence and dynamics of open states were carried out for the interferon alpha 17 gene. It was shown that torsion action leads to the occurrence of rotational movements of nitrogenous bases. This influence is nonlinear, and an increase in the amplitude of the torsion action does not lead to an automatic increase in the amplitude of rotational movements and an increase in the zones’ open states. Calculations with a constant torsion moment demonstrate that open states zones are more often formed at the boundaries of the gen and in regions with a predominance of A–T pairs. It is shown, that for the occurrence of open states in the part of the gene that contains a small number of A–T pairs, a large amount of torque is required. When the torque is applied to a certain region of the gene, the probability of the formation of the open state depends on the content of A–T pairs in this region, the size of this region, and on the exposure time. For this mathematical model, open states zones can be closed when the torsion action stops. The simulation results showed that the values of the torsion moment required for the appearance of open states zones, in some cases, are close to experimentally measured (13–15 pN·nm).

It is known that the presence of CAA codons in the CAG tract affects the nature and time of disease onset caused by the expansion of trinucleotide repeats. The mechanisms leading to the occurrence of these diseases should be sought not only at the level of the physiological role of the ATXN2 protein, but also at the DNA level. These mechanisms are associated with non-canonical configurations (hairpins) that can form in the CAG tract. The tendency of hairpins to slide along the corresponding threads is usually considered important to explain the expansion of the CAG tract. At the same time, hairpins occur in areas of open states. Previous studies on the role of CAA interruptions have suggested that, under certain conditions, they can stabilize the dynamics of the hairpin, preventing the expansion of the CAG tract. We calculated the probability of additional open state zones occurrence in the CAG tract using an angular mathematical model of DNA. The calculations made it possible to establish that CAA interruptions affect the stability of the CAG tract, and this influence, depending on the localization of the interruption, can both increase and decrease the stability of the CAG tract.

It is known that a number of neurodegenerative diseases, also called diseases of waiting, are associated with the expansion of the polyQ tract in the first exon of the ATXN2 gene. In the expanded polyQ tract, the probability of occurrence of non-canonical configurations (hairpins, G-quadruplexes, etc.) is significantly higher than in the normal one. Obviously, for their formation, the occurrence of open states (OSs) is necessary. Calculations were made for these processes using the angular mechanical model of DNA. It has been established that the probability of the large OS zones genesis in a DNA segment depends not only on the “strength” of the nucleotide sequence but also on the factors determining the dynamics of DNA; localization of the energy in the DNA molecule and the potential energy of interaction between pairs of nitrogenous bases also depend on environmental parameters. The potential energy of hydrogen bonds does not remain constant, and oscillatory movements lead to its redistribution and localization. In this case, OSs effectively dissipate the energy of oscillations. Thus, mathematical modeling makes it possible to calculate the localization of mechanical energy, which is necessary for the OSs formation, and to predict the places of their origin, taking into account the mechanical oscillations of the DNA molecule.