GENETIC BASIS OF ALGEBRAIC BIOLOGY, GESTALT GENETICS AND TETRA-EIDOSES BY Yu. I. KULAKOV

The article is devoted to the universal algebraic rules of nucleotide sequences in the DNA of genomes of higher and lower organisms. The patterns identified by the author are related to the known binary nature of genetic structures and are expressed in genomic gestalt phenomena, which are similar to genetically inherited phenomena of gestalt psychology. This allows the author to develop the ideas of gestalt genetics and algebraic biology. Many genetic phenomena of tetrastructurization evoke associations with Kulakov’s concept of tetra-eidoses.

Tensor Rules in the Stochastic Organization of Genomes and Genetic Stochastic Resonance in Algebraic Biology

The article is devoted to the new results of the author, which add his previously published ones, of studying hidden rules and symmetries in structures of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes. The author uses the existence of different alphabets of n-plets in DNA: the alphabet of 4 nucleotides, the alphabet of 16 douplets, the alphabet of 64 triplets, etc. Each of such DNA alphabets of n-plets can serve for constructing a text as a chain of these n-plets. Using this possibility, the author represents any long DNA nucleotide sequence as a bunch of many so-called n-texts, each of which is written on the basis of one of these alphabets of n-plets. Each of such n-texts has its individual percents of different n-plets in its genomic DNA. But it turns out that in such multi-alphabetical or multilayer presentation of each of many genomic DNA, analyzed by the author, universal rules of probabilities and symmetry exist in interrelations of its different n-texts regarding their percents of n-plets. In this study, the tensor product of matrices and vectors is used as an effective analytical tool borrowed from the arsenal of quantum mechanics. Some additions to the topic of algebra-holographic principles in genetics are also presented. Taking into account the described genomic rules of probability, the author puts also forward a concept of the important role of stochastic resonances in genetic informatics.

Modelling Biomolecular Structures in Categorical Systems Theory

In the systemic movement there exist numerous approaches to systems, the most profound of which is the theory of functional systems by Anokhin, which remained largely intuitive science until his pioneering works. The basic principles of functional systems are formalized with the help of the convolutional polycategories in the form of categorical systems theory, which embraced the main systemic approaches, including the traditional mathematical theory of systems. Convolutional polycategories can be built using categorical splices that directly model the external and internal parts of systems. For an algebraic biology using the categorical theory of systems in relation to systemic constructions, the main task of which is to predict the properties of organisms from the genome using strict algebraic methods, new categorical methods are proposed that are widely used in categorical systems theory. These methods are based on the theory of categorical splices, with the help of which the behaviour of quantum-mechanical particles is modelled, in particular, within the framework of the proposed representation of molecules, including RNA and DNA, as categorical systems. Thus, new algebraic and categorical methods (associative algebras with identities, PROP, categorical splices) are involved in the analysis of the genome. The paper presents new results on these matters.

Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.