K E Plokhotnikov (Lomonosov Moscow State University) :
Articles:
519.6 + 539.182 Numerical modeling of the shape matrix of a DNA molecule
Plokhotnikov K. E. (Lomonosov Moscow State University)
doi: 10.18698/2309-3684-2026-1-99118
The concept of a shape matrix or morph to describe an arbitrary molecular system (cluster) was introduced by the author earlier in a previous paper. The shape matrix can always be constructed according to the available configuration of cluster atoms. In general, a morph is a symmetric matrix with N x N non—negative elements, where Nis the number of atoms in the cluster. The variation of the cluster shape matrix made it possible to regulate the number of locally equilibrium configurations of the affiliated potential energy function and, thus, within known limits, solve the problem of choosing an equilibrium cluster configuration from a set of possible ones. An example of constructing the primary structure of a small fragment of a DNA molecule, also called an oligonucleotide, as a locally equilibrium configuration of a suitable potential energy function is considered. The oligonucleotide shape matrix is constructed sequentially by constructing the shape matrices of all the constituent components, including the four nitrogenous bases of DNA: adenine, guanine, cytosine and thymine. The matrices of the form of the carbohydrate component of nucleic acid — deoxyribose, as well as combinations of the carbohydrate component and the phosphate group of nucleic acid — deoxyribose-phosphate were determined. Finally, matrices of the form of nucleoside monophosphates (nucleotides) were constructed: deoxyadenosine, deoxyguanosine, deoxycytidine, thymidine. The desired matrix of the oligonucleotide shape (DNA molecule) is defined as a block-diagonal matrix, in which the blocks are the matrices of the shapes of individual nucleotides. The constructed DNA shape matrix has the prospect of generalizing this description format to the case of secondary and subsequent structures of the DNA molecule.
Плохотников К.Э. Численное моделирование матрицы формы молекулы ДНК. Математическое моделирование и численные методы, 2026, № 1, с. 99–118.