A possible code in the genetic code

Abstract

In order to analyse the genetic code, the distribution of the 64 trinucleotides w (words of 3 letters on the gene alphabet {A,C,G,T}, w∈τ={AAA,⋯,TTT}) in the prokaryotic protein coding genes (words of large sizes) is studied with autocorrelation functions. The trinucleotides w^p can be read in 3 frames p (p=0: reference frame, p=1: reference frame shifted by 1 letter, p=2: reference frame shifted by 2 letters) in coding genes. Then, the autocorrelation function w^p(N)_iw′ analyses the occurrence probability of the i-motif w^p(N)_iw′, i.e. 2 trinucleotides w^p in frame p and w′ in any frame (w,w′∈ τ) which are separated by any i bases N (N=A, C, G or T). The 64²×3=12288 autocorrelation functions applied to the prokaryotic protein coding genes are almost all non-random and have a modulo 3 periodicity among the 3 following types: 0 modulo 3, 1 modulo 3 and 2 modulo 3. The classification of 12288 i-motifs w^p(N)_iw′ according to the type of periodicity implies a constant preferential occurrence frame for w′ independent of w and p. Three sub-sets of trinucleotides are identified: 22 trinucleotides in frame 0 forming the subset τ ₀={AAA, AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC, TTT} and 21 trinucleotides in each of the frames 1 and 2 forming the sub-sets τ ₁ and τ ₂ respectively. Except for AAA, CCC, GGG and TTT, the sub-sets τ ₁ and τ ₂ are generated by a circular permutation P of τ ₀: P(τ ₀)=τ ₁ and P(τ ₁)=τ ₂. Furthermore, the complementarity property ∁ of the DNA double helix (i.e. ∁(A)=T, ∁(C)=G, ∁(G)=C, ∁(T)=A and if w=l₁l₂l₃ then ∁(w)=∁(l₃)∁(l₂)∁(l₁) with l₁, l₂, l₃∈{A,C,G,T}) is observed in these 3 sub-sets: ∁(τ ₀)=τ ₀, ∁(τ ₁)=τ ₂ and ∁(τ ₂)=τ ₁.