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.

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.

Ген ATXN2 играет ключевую роль в патогенезе нейродегенеративных заболеваний, таких как спиноцеребеллярная атаксия 2-го типа (СЦА2). Экспансия тринуклеотидных повторов в гене приводит к образованию аномального белка с удлиненным участком полиглутамина, который оказывает токсическое действие на нейроны и приводит к их гибели. В результате нарушается функционирование мозжечка и других структур центральной нервной системы, что проявляется прогрессирующим ухудшением координации движений и другими неврологическими симптомами. Открытым вопросом остается понимание молекулярных основ нейродегенеративных процессов, вызываемых мутациями в гене ATXN2, а также влияние внешних факторов на развитие заболеваний. В связи с этим, целью исследования являлось изучение влияния внешней среды на стабильность полиглутаминового тракта (polyQ) в гене ATXN2 при наличии CAA-прерывания. Для расчетов использовали угловую модель ДНК, которая рассматривает молекулу как систему взаимосвязанных маятников, что позволяет учитывать влияние вязкости среды на динамику открытых состояний (ОС) в ДНК. Исследование проводили при значениях вязкости (λ = 0,9; 1,0; 1,1) и длинах CAG-тракта (от 35 до 55 повторов). Результаты показали, что вязкость среды оказывает значительное влияние на стабильность polyQ-тракта, особенно при длине CAG-повторов более 40. Увеличение вязкости (λ = 1,1) способствовало снижению количества дополнительных зон ОС, что указывает на её стабилизирующую роль. Напротив, снижение вязкости (λ = 0,9) увеличивало вероятность образования ОС, усугубляя нестабильность тракта.

The ATXN2 gene plays a key role in the pathogenesis of neurodegenerative diseas-es such as spinocerebellar ataxia type 2 (SCA2). Expansion of trinucleotide repeats in the gene results in the formation of an abnormal protein with an extended polyglutamine strand, which is toxic to neurons and leads to their death. This disrupts the functioning of the cerebellum and other central nervous system structures, resulting in progressive deterioration of motor coordination and other neurological symptoms. Understanding the molecular basis of neurodegenerative processes caused by mutations in the ATXN2 gene, as well as the influence of environmental factors on disease development, remains an open question. Therefore, the aim of this study was to investigate the influence of the environment on the stability of the polyglutamine tract (polyQ) in the ATXN2 gene in the presence of a CAA interruption. The calculations were performed using an angular model of DNA, which considers the molecule as a system of interconnected pendulums, allow-ing for the influence of environmental viscosity on the dynamics of open states (OS) in DNA. The study was conducted at various viscosity values (λ = 0.9; 1.0; 1.1) and CAG tract lengths (from 35 to 55 repeats). The results showed that medium viscosity has a significant impact on polyQ tract stability, especially for CAG repeat lengths greater than 40. An increase in viscosity (λ = 1.1) contributed to a decrease in the number of additional OS zones, indicating its stabilizing role. Conversely, a decrease in viscosity (λ = 0.9) increased the likelihood of OS formation, exacerbating tract instability. It was established that CAA insertions in the polyQ tract influence the formation of additional OS zones and CAG tract stability depending on their location. The results of this study provide a pre-requisite for understanding the mechanisms regulating the structural stability of proteins associated with neurodegenerative diseases. The findings may lead to the development of more effective therapeutic strategies aimed at stabilizing abnormal polyQ tracts, poten-tially slowing the progression of diseases such as spinocerebellar ataxia and other pol-yglutamine pathologies.