Identification and simulation of shifted periodicities common to protein coding genes of eukaryotes, prokaryotes and viruses

The distribution of nucleotides in protein coding genes is studied with autocorrelation functions. The autocorrelation functionYRY (N)iYRY,analysing the occurrence probability of thei-motifYRY(N)iYRY(two motifsYRYseparated by anyibasesN, R= purine = Adenine or Guanine,Y= pyrimidine = Cytosine or Thymine,N = RorY) in the protein coding genes of eukaryotes, prokaryotes and viruses, reveals the classical periodicity 0 modulo 3 associated with the normal frame 0 (maximal values of the function ati= 0, 3, 6, etc). The specification ofYRY(N)iYRYon the alphabet {A, C, G, T} leads to 64i-motifs: CAC(N)iCAC, CAC(N)iCAT, . . ., TGT(N)iTGT. The 64 auto-correlation functions associated with these 64i-motifs in protein coding genes have all the periodicity modulo 3, but, surprisingly, not always the expected periodicity 0 modulo 3. Two new types of periodicities are identified: a periodicity 1 modulo 3 associated with the shifted frame + 1 (maximal values of the function ati= 1, 4, 7, etc) and a periodicity 2 modulo 3 associated with the shifted frame - 1 (maximal values of the function ati= 2, 5, 8 etc). Furthermore, the classification ofi-motifs according to the type of periodicity demonstrates a strong coherence relation between the 64i-motifs, which is, in addition, common to the three gene populations, as the samei-motifs in the three gene populations have the same periodicities. ree periodicities 0, 1 and 2 modulo 3 can be simulated by an evolutionary model at two successive processes. The simulated genes are generated by a process of gene construction, with a stochastic automaton followed by a process of gene evolution with random insertions and deletions of trinucleotides simulating RNA editing. For almost alli-motifs, the autocorrelation functions in these simulated genes are strongly correlated with those in protein coding genes, for both the type and the probability level of periodicities. aper describes the process of ribosomal frameshifting leading to the shifted periodicities, which may reveal overlapping genes or concatenated genes from different frames. It also presents the evolutionary aspects of the shifted periodicities. The shifted periodicities cannot be associated with theRNYmodel (Eigen & Schuster, 1978,Naturwissenschaften65,341-369) or theRRYmodel (Cricket al.,1976, Origins of Life7,389-397), but are compatible with the oligonucleotide mixing model (Arquès & Michel, 1990,Bull. math. Biol.52,741-772). Finally, a variant of the primitive translation model of Cricket al.(1976) is proposed to explain the shifted periodicities.