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 GX(1)X(2) (G=Glycine, X(1) and X(2) being any residues). The nine amino acids occurring with significant frequencies in the X, and X, 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)(i)w' 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)(i)w'), identifies six types of module 3 periodicities in collagens: three basic types 0, 1 and 2 module 3 and three combined types 0, 1, 0,2 and 1,2 module 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 I 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.