A simple model to explain three-base periodicity in coding DNA

A simple model is put forward to explain the long-known three-base periodicity in coding DNA. We propose the concept of same-phase triplet clustering, i.e. a condition wherein a triplet appears several times in one phase without interruption by the two other possible phases. For instance, in the sequence (i): NTT_GNN_NTT_GNN_NTT_GNN_NNN_NTT_GNN (where N is any nucleotide but combinations producing TTG are excluded) there would be clustering of same-phase TTG because this triplet appears uninterruptedly in phase 2. In contrast, in the sequence (ii): TTG_NTT_GNN_NNT_TGN_NNN_NTT_GNN there is no same-phase clustering because neighboring TTGs are all in different phases. Observe also that in sequence (i) TTG triplets are separated by 3, 3 and 6 nucleotides (3n distances), while in sequence (ii) they are separated by 1, 4 and 5 nucleotides (non-3n distances). In this work, we demonstrate that in coding DNA the 3n distances generated by (i)-type sequences proportionally outnumber the non-3n distances generated by (ii)-type sequences, this condition would be the basis of three-base periodicity. Randomized sequences had (i)- and (ii)-type sequences too but clustering was statistically different. To prove our model we generated (i)-type sequences in a randomized sequence by inducing clustering of same-phase triplets. In agreement with the model this sequence displayed three-base periodicity. Furthermore, two- and four-base periodicities could also be induced by artificially inducing clustering of duplets and tetraplets.