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.

Background: Trinucleotide repeats are the cause of many neurodegenerative diseases that are currently incurable. In this regard, the question of the causes of occurrence and methods of prevention or treatment of diseases caused by the expansion of repeats in the CAG tract of the ATXN2 gene remains relevant. Previously, it was shown that the frequency of occurrence of additional OS (open states) zones increases with increasing length of the CAG tract, and the value inverse to the frequency correlates with the age of disease onset. Methods: In this work, the influence of the viscosity of the medium and the external torque on the stability of the CAG tract in the ATXN2 gene was studied using mathematical modeling methods. Results: It has been established that the probability of the appearance of additional OS zones of significant size increases with an increase in the CAG of the tract (k > 40 CAG repeats) for all viscosity values, however, at k ≤ 40, the change in viscosity does not significantly affect the probability of additional OS zones in the tract. Conclusions: It was found that under normal conditions (absence of pathology), viscosity does not have a reliable effect on the stability of the DNA molecule, but when pathology appears, an increase in viscosity contributes to an increase in DNA stability, and, accordingly, a decrease has a negative effect on the stabilization of the DNA molecule. In the zone of close to incomplete penetrance of the disease, viscosity does not have a reliable effect on the stability of the CAG tract.

Background: The isotopic composition of the body’s internal environment can affect its functional state. Such effects are realized, among other things, by inserting deuterium atoms into hydrogen bonds between pairs of nitrogenous bases of DNA molecules and modifying their mechanical properties. Methods: This study uses a coarse-grained mathematical model of DNA. Results: It has been established that in a certain range of the magnitude of the torque, with the presence of a deuterium atom within it, stabilization of the CAG repeat tract is observed. In addition, it was found that, regardless of which base pair the deuterium atom falls into in the CAG repeat tract, its stability increases and the probability of hairpin formation decreases, which may interfere with the reading of genetic information from the site encoding glutamine. Conclusions: Single H/D substitutions in the CAG repeat tract of the ATXN2 gene increase its stability by reducing the formation of open states, regardless of the position of deuterium.