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An evolutionary analytical model of a complementary circular code

Abstract : The subset X-0,={AAC,AAT,ACC,ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG,GAT,GCC,GGC,GGT,GTA, GTC,GTT,TAC,TTC} of 20 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. This subset X-0 is a complementary maximal circular code with two permutated maximal circular codes X-1 and X-2 in the frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5'-3' direction). X-0 is called a C-3 code (Arquis and Michel, 1997, J. Biosyst 44, 107-134). A quantitative study of these three subsets, X-0, X-1, and X-2 in the three frames 0, 1 and 2 of eukaryotic protein genes shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of X-0, X-1 and X-2 in the frame 0 of eukaryotic protein genes are 48.5%, 29% and 22.5% respectively. These properties are not observed in the 5' and 3' regions of eukaryotes where X-0, X-1 and X-2 occur with variable frequencies around the random value (1/3). Several frequency asymmetries unexpectedly observed, e.g. the frequency difference between X-1 and X-2 in the frame 0, are related to a new property of the C-3 code X-0 involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 20 codons (trinucleotides in the frame 0) of X-0 with equiprobability (1/20) followed by t approximate to 4 substitutions per codon according to the proportions p approximate to 0.1, q approximate to 0.1 and r = 1 - p - q approximate to 0.8 in the three codon sites respectively, retrieves the frequencies of X-0, X-1 and X-2 observed in the three frames of protein genes and explains these asymmetries. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine. Finally, the evolutionary analytical method developed could be applied to the phylogenetic tree reconstruction and the DNA. sequence alignment. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.
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Didier Arquès, Jp Fallot, L Marsan, Cj Michel. An evolutionary analytical model of a complementary circular code. BioSystems, Elsevier, 1999, 49 (2), pp.83--103. ⟨10.1016/S0303-2647(98)00038-0⟩. ⟨hal-00694250⟩

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