$p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

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Branko Dragovich and Nataša Ž. Mišić

Ultrametricity in the Genetic Code and Bioinformatics


The genetic code (GC) is a mapping from the set of $64$ codons onto set of $21$ elements, which consists of $20$ amino acids and $1$ stop signal. Codons are ordered triples of four nucleotides (C, A, T (U), G) and they are building blocks of the genes. Canonical amino acids are building blocks of the proteins, and stop signal terminates synthesis of proteins. One of the main reasons for modeling the GC is a huge number (about $10^{84}$) of possible connections between $64$ codons and $20$ amino acids with one stop signal, while in living organisms there is practically one GC with about thirty its slight variations. So far there is no model which contains complete GC description. Some of existing models are rather complex. In this talk we present an ultrametric model of the GC, which is mathematically simple and conceptually natural, where ultrametricity is quantified by the $p$-adic distance. Ultrametric approach describes similarity and nearness not only in the genetic code but also in some other bioinformation systems. $p$-Adic approach to the genetic code was introduced in [1] and then discussed is some papers (see, e.g. [2] and references therein). Codons are presented with three-digit $5$-adic numbers by identifying nucleotides with digits $(C=1, A =2, T=U =3, G=4).$ To differ purines and pyrimidines, $2$-adic distance is used. Each doublet of codons codes either one of $20$ amino acids or stop signal in the GC of the vertebrate mitochondria. \medskip [1] B. Dragovich and A. Dragovich, ``A $p$-adic model of DNA sequence and genetic code,'' {\em $p$-Adic Numbers, Ultrametric Analysis and Applications} \textbf{1} (1), 34--41 (2009), [arXiv:q-bio.GN/0607018v1]. [2] B. Dragovich and A. Dragovich, ``$p$-Adic modelling of the genome and the genetic code,'' {\em Computer Journal} \textbf{53} (4), 432--442 (2010), [arXiv:0707.3043[]].