TOWARDS p-ADIC GENOMICS Branko Dragovich Institute of Physics, Belgrade Alexandra Dragovich Vavilov Institute of General Genetics, Moscow 3rd International Conference on p-Adic Mathematical Physics 1-6. 10.2007, Moscow
DNA (Deoxyribonucleic acid) Crick and Watson (1953)
Genomics is the study of the genome, which is whole information encoded in DNA.
Nucleotides (bases) and codons Nucleotides: C, A, U (T), G Codons: ordered trinucleotides 4 x 4 x 4 = 64 codons
Modeling of the Genetic Code • Gamov (1954), Crick (1957), Rumer (1966), … • Swanson (1984), … • J. Hornos and Y. Hornos (1993), Forger and Sachse (2000) • Frappat, Sciarrino and Sorba (1998) • p-Adic approach: B. Dragovich and A. Dragovich (2006), Khrennikov (2006) and Kozyrev (2007), Bradley (2007)
p-adic codon space: p-Adic Modeling of the Genetic Code C (cytosine) = 1, A (adenine) = 2, T (thymine) = U (uracil) = 3, G (guanine) = 4 ( 0 = absence of nucleotide )
p-Adic Properties of the Vertebral Mitochondrial Code • T-symmetry: doublets-doublets and quadruplets-quadruplets invariance • 5-Adic distance gives quadruplets • 2-Adic distance inside quadruplets gives doublets • Degeneration of the genetic code has p-adic structure • p-Adic degeneracy principle: Codons code amino acids and stop signals by doublets which are result of combined 5-adic and 2-adic distances • Modern assignment of codon doublets to particular amino acids is a result of coevolution of the genetic code and amino acids: single nucleotide code – 4 amino acids, dinucleotide code – 16 amino acids, trinucleotide code 20 amino acids. • Other (15) codes may be regarded as slight modifications of the Vertebral Mitochondrial Code
P-Adic Genomic Space where Definition: (p, q)-adic genomic space is a double is a set of natural numbers, and is q-adic distance.
Examples of p-Adic Genomic Spaces • 1-nucleotide codon space: p=5, m =1 • 2-nucleotide codon space: p=5, m =2 • 3-nucleotide codon space: p=5, m =3 • present space of amino acids: p=23, m=1 • future space of amino acids: p=29, m=1 • first space of amino acids: p=5, m=1 • second space of amino acids: p=17, m=1
Conclusion • Space of nucleotides is p-adic • Space of codons is p-adic • Genetic code has p-adic degeneration • Genomic spaces (spaces of nucleotides, codons, DNA, RNA, amino acids, proteins) have p-1 structural units, where p = prime number. There is p-adics in genomics!