Abnormal open states patterns in the ATXN2 DNA sequence depends on the CAG repeats length

Hereditary ataxias are one of the «anticipation diseases» types. Spinocerebral ataxia type 2 occurs when the number of CAG repeats in the coding region of the ATXN2 gene exceeds 34 or more. In healthy people, the CAG repeat region in the ATXN2 gene usually consists of 22-23 CAG trinucleotides. Mutations that increase the length of CAG repeats can cause severe neurodegenerative and neuromuscular disorders known as trinucleotide repeat expansion diseases. The mechanisms causing such diseases are associated with non-canonical configurations that can be formed in the CAG repeat region during replication, transcription or repair. This makes it relevant to study the zones of open states that arise in the region of CAG repeats under torque. The purpose of this work is to study, using mathematical modeling, zones of open states in the region of CAG repeats of the ATXN2 gene, caused by torque. It has been established that the torque effect on the 1st exon of the ATXN2 gene, in addition to the formation of open states in the promoter region, can lead to the formation of additional various sizes open states zones in the CAG repeats region. Moreover, the frequency of additional large zones genesis increases with increasing number of CAG repeats. The inverse of this frequency correlates with the dependence of the disease onset average age on the CAG repeats length. The obtained results will allow us to get closer to understanding the genetic mechanisms that cause trinucleotide repeat diseases.

Medium viscosity influence on the open states genesis in a DNA molecule

The studies were carried out by the mathematical modeling of DNA mechanical deformations. Numerical calculations done for the interferon alpha 17 gene, which consists of 980 base pairs. It has been established that the genesis and dynamics of open states in the DNA molecule depends on the magnitude of the external influence (torque) and on the viscosity of the environment. In addition, it is shown that the dynamics of open states zones can have a jump-like character with a small change in the magnitude of the torque. When torque is applied to all 980 base pairs of the gene, the following effect is observed: an increase in the viscosity of the medium leads to an increase in the value of the torque necessary for the occurrence of OS and DNA unwinding, i.e. viscosity plays an important stabilizing role in DNA dynamics. Under the influence of a localized torque on different (by the content of A-T and G-C pairs and location) regions of the interferon alpha 17 gene, it was found that the magnitude of the external torque necessary for the occurrence of open states at all calculated values of viscosity depends on the nucleotide composition. The dependence of the torque magnitude required for the open states occurrence on viscosity is observed when the torque is applied to areas close to the gene boundaries. At the same time, the significance of the end effect, which weakens DNA, decreased with increasing viscosity of the medium.Communicated by Ramaswamy H. Sarma.

Influence of a Single Deuterium Substitution for Protium on the Frequency Generation of Different-Size Bubbles in IFNA17

The influence of a single 2H/1H replacement on the frequency generation of different-size bubbles in the human interferon alpha-17 gene (IFNA17) under various energies was studied by a developed algorithm and mathematical modeling without simplifications or averaging. This new approach showed the efficacy of researching DNA bubbles and open states both when all hydrogen bonds in nitrogenous base pairs are protium and after an 2H-substitution. After a single deuterium substitution under specific energies, it was demonstrated that the non-coding region of IFNA17 had a more significant regulatory role in bubble generation in the whole gene than the promoter had. It was revealed that a single deuterium substitution for protium has an influence on the frequency generation of DNA bubbles, which also depends on their size and is always higher for the smaller bubbles under the largest number of the studied energies. Wherein, compared to the natural condition under the same critical value of energy, the bigger raises of the bubble frequency occurrence (maximums) were found for 11-30 base pair (bp) bubbles (higher by 319%), 2-4 bp bubbles (higher by 300%), and 31 bp and over ones (higher by 220%); whereas the most significant reductions of the indicators (minimums) were observed for 11-30 bp bubbles (lower by 43%) and bubbles size over 30 bp (lower by 82%). In this study, we also analyzed the impact of several circumstances on the AT/GC ratio in the formation of DNA bubbles, both under natural conditions and after a single hydrogen isotope exchange. Moreover, based on the obtained data, substantial positive and inverse correlations were revealed between the AT/GC ratio and some factors (energy values, size of DNA bubbles). So, this modeling and variant of the modified algorithm, adapted for researching DNA bubbles, can be useful to study the regulation of replication and transcription in the genes under different isotopic substitutions in the nucleobases.

Influence of Single Deuterium Replacement on Frequency of Hydrogen Bond Dissociation in IFNA17 under the Highest Critical Energy Range

The effect of single substitutions of protium for deuterium in hydrogen bonds between pairs of nitrogenous bases on the open states occurrence probability at high critical breaking energies of these bonds has been studied. The study was carried out using numerical methods based on the angular mathematical model of DNA. The IFNA17 gene was divided into three approximately equal parts. A comparison of the open states occurrence probability in these parts of the gene was done. To improve the accuracy of the results, a special data processing algorithm was developed. The developed methods have shown their suitability for taking into account the occurrence of open states in the entire range of high critical energies. It has been established that single ²H/¹H substitutions in certain nitrogenous bases can be a mechanism for maintaining the vital activity of IFNA17 under critical conditions. In general, the developed method of the mathematical modeling provide unprecedented insight into the DNA behavior under the highest critical energy range, which greatly expands scientific understanding of nucleobases interaction.

DNA Dynamics under Periodic Force Effects

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.

Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12551-021-00801-0.

Inequality in the Frequency of the Open States Occurrence Depends on Single 2H/1H Replacement in DNA

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.