Ultrametrics in the genetic code and the genome

Ultrametric approach to the genetic code and the genome is considered and developed. p-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be treated as p-adic ultrametric networks. Ultrametric modification of the Hamming distance is defined and noted how it can be useful. Ultrametric approach with p-adic distance is an attractive and promising trend towards investigation of bioinformation.

[1]  K. Hirsch,et al.  Representation theory and automorphic functions , 1969 .

[2]  S. V. Kozyrev,et al.  Genetic code on the diadic plane , 2007, q-bio/0701007.

[3]  Branko Dragovich,et al.  p-Adic Structure of the Genetic Code , 2011, 1202.2353.

[4]  F. Murtagh,et al.  Formal foundations for the origins of human consciousness , 2016 .

[5]  Branko Dragovich,et al.  p-Adic Modelling of the Genome and the Genetic Code , 2007, Comput. J..

[6]  Andrei Khrennikov,et al.  Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models , 2011 .

[7]  V. S. Vladimirov,et al.  P-adic analysis and mathematical physics , 1994 .

[8]  M. Rakocevic,et al.  A harmonic structure of the genetic code. , 2004, Journal of theoretical biology.

[9]  Rumer IuB Systematization of codons in the genetic code , 1969 .

[10]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .

[11]  S. Osawa,et al.  Recent evidence for evolution of the genetic code , 1992, Microbiological reviews.

[12]  J. Wong A co-evolution theory of the genetic code. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Jayanth R Banavar,et al.  Physics of proteins. , 2007, Annual review of biophysics and biomolecular structure.

[14]  Brian Hayes,et al.  THE INVENTION OF THE GENETIC CODE , 1998 .

[15]  P. Freund,et al.  p-adic numbers in physics , 1993 .

[16]  R. Swanson A unifying concept for the amino acid code. , 1984, Bulletin of mathematical biology.

[17]  Eugene V Koonin,et al.  Origin and evolution of the genetic code: The universal enigma , 2008, IUBMB life.

[18]  B. Dragovich p‐Adic and Adelic Cosmology: p‐Adic Origin of Dark Energy and Dark Matter , 2006, hep-th/0602044.

[19]  Hornos Algebraic model for the evolution of the genetic code. , 1993, Physical review letters.

[20]  A. Khrennikov Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena , 2004 .

[21]  M. Forger,et al.  Lie superalgebras and the multiplet structure of the genetic code. I. Codon representations , 2000 .

[22]  V. I. Shcherbak,et al.  Arithmetic inside the universal genetic code. , 2003, Bio Systems.

[23]  S. V. Kozyrev,et al.  On p-adic mathematical physics , 2006, 0904.4205.

[24]  Branko Dragovich,et al.  A p-adic model of DNA sequence and genetic code , 2006, ArXiv.

[25]  Branko Dragovich,et al.  Genetic Code and Number Theory , 2009, 0911.4014.

[26]  Yu. N. Zhuravlev,et al.  An evolutionary interpretation of the p-adic ultrametric diffusion equation , 2007 .

[27]  Andrei Khrennikov,et al.  Gene expression from polynomial dynamics in the 2-adic information space , 2006, q-bio/0611068.

[28]  F. H. C. CRICK,et al.  Origin of the Genetic Code , 1967, Nature.

[29]  A Yu Khrennikov,et al.  2-Adic clustering of the PAM matrix. , 2009, Journal of theoretical biology.

[30]  Ivan Dimitrijevic,et al.  Cosmological solutions in modified gravity with monomial nonlocality , 2016, Appl. Math. Comput..

[31]  W. H. Schikhof Ultrametric Calculus: An Introduction to p-Adic Analysis , 1984 .