A Mathematical Proof of Double Helix DNA to Reverse Transcription RNA for Bioinformatics
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.
KeywordsDNA double helix RNA Kronecker product identity & hadamard matrix symmetry complementary
Unable to display preview. Download preview PDF.
- 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.H. M. Temin, “Nature of the provirus of rous sarcoma”, National Cancer Institute Monograph, vol. 17, pp. 557-570, 1964.Google Scholar
- 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.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.He M., Petoukhov S. Mathematics of Bioinformatics: Theory, Practice, and Applications. John Wiley & Sons, Inc., USA, 2011.Google Scholar
- 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.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.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.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.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