Alla Eduardovna Sidorova

A new algorithm is proposed for calculating a functional that characterizes the empirical chirality of an examined object. Empirical chirality is calculated as the normalized scalar product of a vector connecting the first and last reference points with the sum of the vector products of vectors connecting adjacent reference points. The system of reference points is constructed based on experimental data and characterizes the object with the given precision. The sign of the empirical chirality indicates the object’s twist direction (positive for right-handed, negative for left-handed). The chirality modulus, equal to zero, corresponds to an achiral object, while a modulus of one represents a maximally twisted object. Using the elongation of the object as a secondary coordinate allows for its representation as a point on a two-dimensional chirality map. The empirical chirality of biological macromolecules shows good agreement with the existing structural representations. The proposed algorithm is used to study the chirality of technical objects, and the found estimates of the chirality of the two stairs of the Leaning Tower of Pisa correspond to their design. Analyzing the Orion Arm in the vicinity of the Solar System required calculating reference points based on the averaged coordinates of multiple stars. It is found that the Orion Arm has a left-handed twist. The proposed method enables the calculation of empirical chirality, characterizing the geometric properties of objects across a wide range of scales, and facilitates their representation on a general map of chirality.

A space–time trigger model of tumor growth is considered depending on the concentration of hydrogen ions, oxygen, and tumor cell density at the initial stage of the tumor spheroid development. A system of parabolic equations with a piecewise linear right-hand side of modular type is used to solve this problem. Numerical implementation is carried out in a three-dimensional domain shaped as a cube with an edge of 0.1 mm on a uniform grid using the method of lines, the Rosenbrock scheme, and the factorization method in the spatial coordinates. The presented model quite well describes the dynamics of variation in the spheroid area at the initial stage of the tumor development depending on time. A distinctive feature of the model is that it reflects both the process of tumor growth into the external environment and the formation of a necrotic core at the tumor center. Based on the presented system of equations, it is possible to design a model that takes both the heterogeneity of the environment and more complex mechanisms of tumorigenesis into account.

The model of spatio-temporal self-organization of megacities as conjugate active environments – anthropogenic and natural subsystems – is considered. An analytical and numerical study of stationary solutions of the system is presented. The model allows us to identify threshold values of control (anthropogenic and natural) parameters and the basic principles of the development of autowave processes that form the spatiotemporal structures of megacities. The model is confirmed by statistical and cartographic data on the development of Moscow from 1952 to 1968. Forecast models for the development of New Moscow and Shanghai from 2017 to 2030 are considered. Numerical studies were carried out using the author’s program in C++, which allows you to create text files based on cartographic data. The code was created in the OpenCL environment and implemented using AMD FIREPRO GPUs. Graphic interpretation was carried out using the “Surfer” program.

Chirality plays an important role in studies of natural protein structures. Therefore, much attention is paid to solving the problems associated with the development of criteria and methods for assessing the chirality of biomolecules. In this paper, a new method for calculating the sign and degree of chirality of superhelices is proposed. The method makes it possible to characterize the chirality sign and to quantify coiled-coils and collagen superhelices. The degree of chirality is understood as a value indicating the intensity of twisting of individual helices around the axis of the superhelix. The calculation requires information about the relative spatial arrangement of the alpha carbon of the amino acid residues of the helices that make up the superhelix. The use of a small amount of raw data makes the method easy to apply, and the validity of the results of this study is confirmed through the analysis of real protein structures.

This paper considers a model for the accumulation of mutations in a population of mice with a weakened function of polymerases responsible for correcting DNA copying errors during cell division. The model uses the results of the experiment published by Japanese scientists, which contain data on the accumulation of phenotypic differences in three isolated groups of laboratory mice. We have developed a model for the accumulation of negative mutations. Since the accumulation of phenotypic differences in each of the three groups of mice occurred in its own way, we assumed that these differences were associated with genotypic differences in the zeroth generation and set the inverse problem of determining the initial distribution of these differences. Additional information for solving the inverse problem was a set of experimental data on the number of mutant lines and the number of individuals in each group of mice. The results obtained confirmed our assumption.

A review of materials within the concept of chirality as a symmetric basis of self-organization in biomacromolecules is presented. The following topics are considered: methods for determining the chirality of regular and irregular protein structures, the distribution of helical and superhelical structures in polypeptide chains, a model for the formation of a three-dimensional structure of the right-handed α-helix from a chain of L-amino acid residues, and a model for the formation of the right-handed α-helix based on a two-particle model of movement in the Lennard-Jones potential. The applied aspects of the concept of chirality in pharmacology and bioengineering, the chirality of drugs with bioactive enantiomers and the mechanisms of self-assembly of helical structures of phenylalanine and diphenylalanine nanotubes of different chirality are discussed. The basic concepts of molecular machines as chiral hierarchical structures are presented.

Работа посвящена рассмотрению закономерностей пространственного структурообразования в белках и их применению в нанобиоинженерии. Представлены методы оценки хиральности регулярных и нерегулярных структур белка, а также спиральных нанотрубок на основе фенилаланина. Рассчитаны величина и знак хиральности α-, 310- и π-спиралей, β- и α-поворотов, Ω-петель, а также правых и левых фенилаланиновых нанотрубок. Полученные результаты могут быть использованы в управлении сборкой природных и искусственных белков.

In this paper, we propose and use a new approach for a relatively simple technique for conducting MD simulation (MDS) of various molecular nanostructures, determining the trajectory of the MD run and forming the final structure using external force actions. A molecular dynamics manipulator (MD manipulator) is a controlled MDS type. As an example, the applicability of the developed algorithm for assembling peptide nanotubes (PNT) from linear phenylalanine (F or Phe) chains of different chirality is presented. The most adequate regimes for the formation of nanotubes of right chirality D from the initial L-F and nanotubes of left chirality L of their initial dipeptides D-F modes were determined. We use the method of a mixed (vector–scalar) product of the vectors of the sequence of dipole moments of phenylalanine molecules located along the nanotube helix to calculate the magnitude and sign of chirality of self-assembled helical phenylalanine nanotubes, which shows the validity of the proposed approach. As result, all data obtained correspond to the regularity of the chirality sign change of the molecular structures with a hierarchical complication of their organization.