Identification of several types of periodicities in the collagens and their simulation

The collagens constitute an important population of proteins providing the structural support in vertebrate tissues A collagen is mainly based on a series of tripeptides of the type GX1X2 (G = Glycine, X1 and X2 being any residues). The nine amino acids occurring with significant frequencies in the X1 and X2 residue sites and G form the reduced protein alphabet Q = [A,D,E,G,K,L,P,Q,R,S] (A = Alanine, D = Aspartic acid, E = Glutamic acid, K = Lysine, L = Leucine, P = Proline, Q = Glutamine, R = Arginine, S = Serine). Surprisingly, the method based on the autocorrelation function w(X)iw' analysing the probability that an amino acid w' in Q occurs any i residues X after an amino acid w in Q (called i-motif w(X)iw'), identifies six types of modulo 3 periodicities in collagens: three basic types 0, 1 and 2 modulo 3 and three combined types 0,1, 0,2 and 1,2 modulo 3. Furthermore, the classification of these 100 i-motifs according to the types of periodicities shows several strong relations between four sub-sets of Q [G], [A,D,P,S], [E,L] and [K,Q,R]. Then, these relations allow the construction of a simple automaton for the generation of model collagen sequences. Indeed, this automaton can simulate the six types of periodicities and it retrieves the types of periodicities for almost all i-motifs. Finally, the autocorrelation function based on the sub-set [K,Q,R] identifies segments of 18 amino acids in collagens which may correspond to the exons (segments of genes of 54 nucleotides) coding for those collagens.