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∈T={AAA,…,TTT}) in the prokaryotic protein coding genes (words of large sizes) is studied with autocorrelation functions. The trinucleotides wp can be read in 3 frames p (p=0: reference frame, p=l: reference frame shifted by 1 letter, p=2: reference frame shifted by 2 letters) in coding genes. Then, the autocorrelation function wP(N)iw’ analyses the occurrence probability of the i-motif wP(N)iw’, i.e. 2 trinucleotides wp in frame p and w’ in any frame (w,w’∈T) 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 wP(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 T0={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 T1 and T2 respectively. Except for AAA, CCC, GGG and TTT, the sub-sets T1 and T2 are generated by a circular permutation P of T0: P(T0)=T1 and P(T1)=T2. Furthermore, the complementarity property C of the DNA double helix (i.e. C(A)=T, C(C)=G, C(G)=C, C(T)=A and if w=lll213 then C(w)=C(l3)C(12)C(ll). with l1,12,13∈ {A,C,G,T}) is observed in these 3 sub-sets: C(T0)=T0, C(T1)=T2 and C(T2)=T1.