The rules of long DNA-sequences and tetra-groups of oligonucleotides

Sergey V. Petoukhov Head of Laboratory of Biomechanical System, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow
spetoukhov@gmail.com, http://petoukhov.com/ Comment: Some materials of this article were presented by the author in the keynote speeches at the following conferences: the International Belgrade Bioinformatics Conference 2018 (Belgrade, Serbia, 18-22 June 2018, http://belbi.bg.ac.rs/); the 2nd International Conference Artificial Intelligence, Medical Engineering, Education (Moscow, Russia, 1-3 October 2019); the 3rd International Conference on Computer Science, Engineering and Education Applications (Kiev, Ukraine, 21-22 January 2020). Also an author’s presentation with elements of this article was done at the 6th International Conference in Code Biology (Friedrichsdorf, Germany, 3-7 June 2019, http://www.codebiology.org/conferences/Friedrichsdorf2019/) .

Abstract. The article represents a new class of hidden symmetries in long sequences of oligonucleotides of single stranded DNA from their representative set. These symmetries are an addition to symmetries described by the second Chargaff’s parity rule (%A ≅ %T and %G ≅ %C). These new symmetries and their rules concern the cooperative oligomer organization of long DNA sequences including complete sets of chromosomes of human and some model organisms. The rules on the equality of collective probabilities and the associated hyperbolic rules for the total sums of oligomers of length n were identified in long DNA sequences due to using the author’s method of oligomer sums, which is also described in the article. These rules are considered as possible candidacies for the role of the universal rules of long DNA-sequences. A quantum- informational model of the described genetic symmetries is proposed on the basis of the known quantum-mechanic statement that quantum state of a multicomponent system is defined by the tensor product of quantum states of its subsystems. In this model, nitrogenous bases C, T, G, A of DNA are represented as computational basis states of 2-qubit quantum CTGA-systems. An important role of resonances, photons and photonic crystals in quantum-information genetics is noted.

Key words. Chargaff’s rules, symmetry, tetra-group of oligonucleotides, probabilities, total sums, hyperbolic rules, tensor product, quantum informatics, qubit, resonance, photon

CONTENT

1. Introduction
2. Tetra-groups of oligonucleotides and collective probabilities of tetra- groups in long DNA-texts
3. The first, second and third rules of symmetries of collective probabilities of tetra-groups in long DNA-texts
4. DNA-alphabets, genetic binary oppositions and the tensor product of matrices
5. The quantum-information model to explain and predict symmetries of collective probabilities in tetra-groups of long DNA-texts
6. The explanation of the second Chargaff’s parity rule on the basis of the quantum-information approach.
7. About short DNA-texts
8. Resonances, photons and quantum-information genetics
9. The rules of symmetries of collective probabilities in tetra-groups in the complete set of human chromosomes. The fourth rule of symmetries of tetra-group probabilities (for complete sets of chromosomes)
10. Tetra-group rules in complete sets of chromosomes of model organisms: Caenorhabditis elegans, Drosophila melanogaster, Arabidopsis thaliana,
    Mus musculus
11. Fractal genetic nets and the fifth and sixth rules of symmetries of collective probabilities of tetra-groups. On a fractal grammar of long
    DNA-texts
12. About letter-ordered representations of long DNA-texts conserving their
    collective probabilities in tetra-groups.
13. On the biological sense of the symmetries of collective probabilities of
    tetra-groups in long DNA texts.
14. Hyperbolic rules of the oligomer collective organization of genomes.
15. Applications of the oligomer sums method to analysis of long genes. 16. Some concluding remarks Appendix 1. Additional data about tetra-group rules and tetra-group
    symmetries in long DNA-texts Appendix 2. Symmetries of tetra-group probabilities in the compete set of
    human chromosomes Appendix 3. Symmetries of tetra-group probabilities in the complete set of
    chromosomes of a nematode Caenorhabditis elegans Appendix 4. Symmetries of tetra-group probabilities in the complete set of
    chromosomes of Drosophila melanogaster Appendix 5. Symmetries of tetra-group probabilities in the complete set of
    chromosomes of Arabidopsis thaliana Appendix 6. Symmetries of tetra-group probabilities in the complete set of
    chrom

…(Full text truncated)…