Coarse-grained mathematical models for studying mechanical properties of the DNA

The paper describes approaches to coarse-grained modeling of mechanical movements of DNA. The theoretical results of applying the angular model to calculations of the natural oscillation frequency, the effect of medium viscosity on the probability of open states, and the distribution of mechanical energy in a DNA molecule under external influence are considered. Examples of the practical application of model calculations to assess the effect of disorders in the ATXN2 gene on the occurrence of additional zones of open states in the region of trinucleotide repeats are given. The practical application of coarse-grained models covers many areas: from fundamental studies of the mechanisms of DNA interaction with proteins to the development of new methods of genetic engineering and the creation of functional DNA nanomaterials. Coarse-grained DNA models demonstrate high versatility as a research tool in modern molecular biology and biophysics. Their fundamental advantage lies in the ability to effectively reproduce the key characteristics of molecular dynamics with significant savings in computing resources compared to full-atom modeling. The versatility of these models is manifested in their adaptability to the study of a wide range of biological phenomena. They allow one to adequately describe both local conformational changes in individual sections of a molecule and global mechanical properties of extended DNA structures. At the same time, the possibility of a detailed study of the interaction of a molecule with the environment, including the effect of solvent viscosity, is preserved. Of particular value is the ability to study both equilibrium and nonequilibrium processes over a wide range of time scales.