pADIC APPROACH TO THE GENETIC CODE AND THE GENOME

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p-ADIC APPROACH TO THE GENETIC CODE AND THE
GENOME

• Branko Dragovich
• Institute of Physics, Belgrade, Serbia
• TAG, 20 24 Oct 2008, Annecy

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• Introduction
• p-Adic modeling of the genetic code
• p-Adic vertebral mitochondrial code
• p-Adic degeneracy of the genetic code
• p-Adic genomic spaces
• Evolution of the genetic code
• Conclusion

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INTRODUCTION

• Question p-adic ?
• Example 1, 2, 3, 4, 5, 6, 7, 8, 9,
• abs. value n n
• conventional distance a -b
• p-adic abs. value
• p-adic distance

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INTRODUCTION

• p-ADIC MATHEMATICAL PHYSICS
• p-Adic numbers
• discovered by K. Hansel in 1897.
• many applications in mathematics, e.g.
  representation theory, algebraic geometry and
  modern number theory
• many applications in mathematical physics since
  1987, e.g. string theory, QFT, quantum mechanics,
  dynamical systems, complex systems, ....
• Third International Conference on p-Adic
  Mathematical Physics from Planck scale physics
  to complex systems to biology. (Steklov Mathem.
  Institute, Moscow, 1-6 Oct. 2007).
• New intern. multidisciplinary journal p-Adic
  Numbers, Ultrametric Analysis, and Applications
• Any p-adic number has a unique canonical
  representation
• Real and p-adic numbers unify into adeles.

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DNA and RNA
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(No Transcript)
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Nucleotides (bases) and codons
Nucleotides C, A, U (T), G Codons ordered
trinucleotides 4 x 4 x 4 64 codons
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Amino acids
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(Universal) Genetic Code
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Modeling of the Genetic Code

• Gamov (1954), Crick (1957)
• Rumer (1966), Crick,
• Jukes, Woese, Swanson,
• 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 and Kozyrev, Bradley

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p-Adic Modeling of the Genetic Code

• p-adic codon space

C (cytosine) 1, A (adenine) 2, T
(thymine) U (uracil) 3, G (guanine) 4
( 0 absence of nucleotide )
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Our Table of Vertebral Mitochondrial Code
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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

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Evolution of the genetic code

• Modern assignment of codon doublets to particular
  amino acids may be a result of coevolution of
  the genetic code and amino acids single
  nucleotide code 4 amino acids, dinucleotide
  code 16 amino acids, trinucleotide code 202
  amino acids (selenocysteine, pyrrolysine).
• Other (15) codes may be regarded as slight
  modifications of the Vertebral Mitochondrial
  Code

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p-Adic Genomic Space

• Definition (p, q)-adic genomic space is a double

where
is a set of natural numbers, and
is q-adic distance.
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Examples of p-Adic Genomic Spaces

• 1-nucleotide codon space p5, m 1
• 2-nucleotide codon space p5, m 2
• 3-nucleotide codon space p5, m 3
• present space of amino acids p23, m1
• possible (Jukes) space of amino acids
• p29, m1
• first space of amino acids p5, m1
• second space of amino acids p17, m1

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p-Adic DNA, RNA and protein spaces

• cDNA and RNA space p 61
• ncDNA space p 5
• Protein space p 23
• (20 standard selenocysteine pyrrolysine)

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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!