A Mathematical Proof of Double Helix DNA to Reverse Transcription RNA for Bioinformatics

  • Moon Ho Lee
  • Han Hai
  • Sung Kook Lee
  • Sergey V. Petoukhov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 658)

Abstract

This paper presents a mathematical proof of deoxyribose nucleic acid (DNA) to ribonucleic acid (RNA) based on the block circulant Jacket matrix (BCJM) characteristics, which is used to develop a bioinformatics for the molecular communications. The DNA matrix decomposition is the form of the Kronecker product of identity and Hadamard matrices with pair complementarity. The RNA 4 by 4 genetic matrix is the anti-symmetric pair complementary of the core kernel. The variants of kernel of the Kronecker families are produced by permutations of the four letters C, A, U, G on positions in the matrix. Thus, we get 6 subset pattern of block circulant matrix, 6 upper-lower block symmetric matrix and 6 left-right block symmetric matrix. This decomposition of DNA to RNA leads very clearly to the Kronecker product of the symmetrical genetic matrices.

Keywords

DNA double helix RNA Kronecker product identity & hadamard matrix symmetry complementary 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. D. Watson, F. H. C. Crick, “Molecular structure of nucleic acids”, Nature, vol. 171, no. 4356, pp. 737-738, April 1953.Google Scholar
  2. 2.
    H. M. Temin, “Nature of the provirus of rous sarcoma”, National Cancer Institute Monograph, vol. 17, pp. 557-570, 1964.Google Scholar
  3. 3.
    Z. Chen, M. H. Lee, G. Zeng, “Fastcocyclic Jacket transform”, IEEE trans. on Signal Processing, vol. 56, no. 5, May 2008.Google Scholar
  4. 4.
    M. H. Lee,H. Hai, X. D.Zhang, MIMO Communication Method and System using the Block Circulant Jacket Matrix, USA Patent 9,356,671, 05/31/2016.Google Scholar
  5. 5.
    He M., Petoukhov S. Mathematics of Bioinformatics: Theory, Practice, and Applications. John Wiley & Sons, Inc., USA, 2011.Google Scholar
  6. 6.
    S. K. Lee, D. C. Park, M. H. Lee,“RNA genetic 8 by 8 matrix construction from the block circulant Jacket matrix”, Symmetric Festival 2016, 18-22 July 2016, Vienna, Austria.Google Scholar
  7. 7.
    K. V. Srinivas, A. W. Eckford, R. S. Adve, “Molecular communication in fluid media: The additive inverse Gaussian noise channel”, IEEE Trans. on Information Theory, Vol. 58, no. 7, July 2012.Google Scholar
  8. 8.
    J. Hou, M. H. Lee, Ju Yong Park, “Matrices analysis of quasi-orthogonal space time block codes”, IEEE Comm. Letters, vol. 7, no. 8, 2003.Google Scholar
  9. 9.
    E. R. Miranda, E. Braund, “Interactive musical biocomputer: an unconventional approach to research in unconventional computing”, Symmetry: Culture and Science, vol. 28, no. 2, 7-20, 2017.Google Scholar
  10. 10.
    Petoukhov S.V., He M. Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. - IGI Global, Hershey, USA, 2010, 271 p.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Moon Ho Lee
    • 1
  • Han Hai
    • 1
  • Sung Kook Lee
    • 2
  • Sergey V. Petoukhov
    • 3
  1. 1.Division of Electronics and Information EngineeringChonbuk National UniversityJeonjuKorea
  2. 2.Dept. of EconomicsIndiana University-BloomingtonBloomingtonUSA
  3. 3.Institute of Machines StudiesRussian Academy of SciencesMoscowRussia

Personalised recommendations