On comparing composition principles of long DNA sequences with those of random ones

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.

Computational Analysis of Genetic Code Variations Optimized for the Robustness against Point Mutations with Wobble-like Effects

It is believed that the codon-amino acid assignments of the standard genetic code (SGC) help to minimize the negative effects caused by point mutations. All possible point mutations of the genetic code can be represented as a weighted graph with weights that correspond to the probabilities of these mutations. The robustness of a code against point mutations can be described then by means of the so-called conductance measure. This paper quantifies the wobble effect, which was investigated previously by applying the weighted graph approach, and seeks optimal weights using an evolutionary optimization algorithm to maximize the code's robustness. One result of our study is that the robustness of the genetic code is least influenced by mutations in the third position-like with the wobble effect. Moreover, the results clearly demonstrate that point mutations in the first, and even more importantly, in the second base of a codon have a very large influence on the robustness of the genetic code. These results were compared to single nucleotide variants (SNV) in coding sequences which support our findings. Additionally, it was analyzed which structure of a genetic code evolves from random code tables when the robustness is maximized. Our calculations show that the resulting code tables are very close to the standard genetic code. In conclusion, the results illustrate that the robustness against point mutations seems to be an important factor in the evolution of the standard genetic code.

Motif lengths of circular codes in coding sequences

Protein synthesis is a crucial process in any cell. Translation, in which mRNA is translated into proteins, can lead to several errors, notably frame shifts where the ribosome accidentally skips or re-reads one or more nucleotides. So-called circular codes are capable of discovering frame shifts and their codons can be found disproportionately often in coding sequences. Here, we analyzed motifs of circular codes, i.e. sequences only containing codons of circular codes, in biological and artificial sequences. The lengths of these motifs were compared to a statistical model in order to elucidate if coding sequences contain significantly longer motifs than non-coding sequences. Our findings show that coding sequences indeed show on average greater motif lengths than expected by chance. On the other hand, the motifs are too short for a possible frame shift recognition to take place within an entire coding sequence. This suggests that as much as circular codes might have been used in ancient life forms in order to prevent frame shift errors, it remains to be seen whether they are still functional in current organisms.

Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for the cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The results concerns additionally the problem of the origin of life. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method is shown to the analysis of amino acid sequences in long proteins like the protein Titin. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.