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  • 1Institute of Physics, University of Belgrade, Belgrade, Serbia; Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia.

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Summary

This study introduces p-adic modeling to analyze genetic codes, revealing that codons with minimal 5-adic and 2-adic distances often code similar amino acids. This mathematical approach models the genetic code as a fractal network.

Keywords:
Amino acidsBioinformationGenetic codeGenetic languageUltrametric codon treep-Adic distancep-Adic network

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Area of Science:

  • Bioinformatics
  • Number Theory
  • Genetics

Background:

  • The genetic code translates nucleotide sequences into amino acids.
  • Understanding codon relationships is crucial for molecular biology.
  • Existing models may not fully capture the structural properties of genetic information.

Purpose of the Study:

  • To apply p-adic modeling to analyze the standard and vertebrate mitochondrial genetic codes.
  • To investigate the use of p-adic distances for quantifying codon similarity.
  • To represent the codon set as a mathematical structure like an ultrametric tree or fractal network.

Main Methods:

  • Utilizing 5-adic and 2-adic distances as mathematical tools.
  • Analyzing codon relationships within a bioinformation space.
  • Representing the set of codons as an ultrametric tree, fractal, and p-adic network.

Main Results:

  • Codons with the smallest 5-adic and 2-adic distances frequently code for the same or similar amino acids/stop signals.
  • The genetic code can be conceptualized as sequential translations between genetic languages.
  • The p-adic approach is applicable to nucleotide sequences of any finite length.

Conclusions:

  • P-adic modeling offers a novel mathematical framework for understanding genetic code structure.
  • This approach reveals inherent mathematical properties and relationships within genetic sequences.
  • The study provides new insights into the organization and potential translation mechanisms of genetic information.