Binary oppositions, algebraic holography and stochastic rules in genetic informatics

Abstract

The article is devoted to the author's results of the algebraic analysis of molecular genetic systems, including a set of structured DNA alphabets and long nucleotide sequences in single-stranded DNA of eukaryotic and prokaryotic genomes. A connection of the system of DNA n-plets alphabets with principles of algebraic holography is shown, which concerns a popular theme of holography principles in genetically inherited physiology. In addition, a relation between DNA n-plets alphabets and the Poincaré disk model of Lobachevski hyperbolic geometry is revealed. This relation can explain known facts of the relationship of physiological phenomena with hyperbolic geometry. Considering long DNA sequences as a bunch of many parallel texts written in different n-plets alphabets led to the discovery of some universal rules of the stochastic organization of genomic DNAs. These rules are discussed concerning the general problem of the biological dualism "probability-vs-determinism". In general, the presented results give pieces of evidence in favor of the efficiency of a model approach to living organisms as quantum-informational algebraic-harmonic essences.

Keywords: Algebraic holography; Binary oppositions; DNA alphabets; Genomic sequences; Matrices; Poincaré disk model; Tensor product.