Algebraic harmony and probabilities in genomes. Long-range coherence in quantum code biology

Universal dynamical function behind all genetic codes: P-adic attractor dynamical model

The genetic code is a map which gives the correspondence between codons in DNA and amino acids. In the attractor dynamical model (ADM), genetic codes can be described as the sets of the cyclic attractors of discrete dynamical systems - the iterations of functions acting in the ring of 2-adic integers Z2. This ring arises from representation of nucleotides by binary vectors and hence codons by triples of binary vectors. We construct a Universal Function B such that the dynamical functions for all known genetic codes can be obtained from B by simple transformations on the set of codon cycles - the "Addition" and "Division" operations. ADM can be employed for study of phylogenetic dynamics of genetic codes. One can speculate that the "common ancestor genetic code" was caused by B. We remark that this function has 24 cyclic attractors which distribution coincides with the distribution for the hypothetical pre-LUCA code. This coupling of the Universal Function with the pre-LUCA code assigns the genetic codes evolution perspective to ADM. All genetic codes are generated from B through the special chains of the "Addition" and "Division" operations. The challenging problem is to assign the biological meaning to these mathematical operations.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

The principle "like begets like" in algebra-matrix genetics and code biology

The article is devoted to analysis of emergent properties of the system of binary oppositions in the genetic code ensemble. The epochal model of the double helix of DNA by Watson and Crick showed that the multiple reproduction of genetic information on DNA strands uses the ancient principle "like begets like" based on the simple complementarity in pairs of nucleobases. Each of these pairs is built on the binary opposition "purine-pyrimidine". But the system of DNA n-plet alphabets and genetic coding is much richer in types of binary oppositions, which also have some coding meanings related to this principle. The article contains the results of the application of the author's "method of hierarchy binary stochastics" (HBS-method) to the analysis of the quasi-stochastic organization of binary sequences of hydrogen bonds in genomic single-stranded DNAs. This analysis revealed hidden probability rules related to dichotomous fractal-like probability trees. The relationship between inherited bodily dichotomies in living organisms and the discovered probability dichotomies in information sequences of genomic DNAs is discussed. The encoding properties of molecular binary oppositions in the DNA nucleotide system allows the algorithmic construction of (2n∗2n)-matrices of probabilities of n-plets in these binary sequences, which are matrix representations of 2n-dimensional hyperbolic numbers. Connections of these multidimensional numbers with some inherited physiological phenomena and deep neural networks are noted. A unified algebra-numeric certification of the DNAs of genomes and genes - based on these multidimensional numerical systems - is proposed.

The stochastic organization of genomes and the doctrine of energy-information evolution based on bio-antenna arrays

The article is devoted to the possibilities of considering the evolution of biological systems in connection with the unique emergent properties of antenna arrays, that is, systems of mutually matched antennas widely used in technology. Materials are presented in favor of the proposition that the evolution of biosystems can be formally considered as the evolution of systems of bio-antenna arrays and their energy-information wave activity, which participates in biological computation and contributes to the unification of body parts into a coherent whole. The use of digital antenna arrays in technology is based on their tensor-matrix theory. The author discovers a structural analogy of this theory with the tensor-matrix features of genetic coding systems, as well as algebraic modeling of the universal rules for the stochastic DNA organization of the genomes of higher and lower organisms. This analogy is just one of the facts presented in the article in favor of the usefulness of borrowing knowledge from modern antenna technology to consider the evolution of biosystems. The described new approach may exist along with other known approaches in evolutionary biology.