Single-Frame, Multiple-Frame and Framing Motifs in Genes

We study the distribution of new classes of motifs in genes, a research field that has not been investigated to date. A single-frame motif SF has no trinucleotide in reading frame (frame 0) that occurs in a shifted frame (frame 1 or 2), e.g., the dicodon AAACAA is [Formula: see text] as the trinucleotides AAA and CAA do not occur in a shifted frame. A motif which is not single-frame [Formula: see text] is multiple-frame [Formula: see text]. Several classes of [Formula: see text] motifs are defined and analysed. The distributions of single-frame [Formula: see text] motifs (associated with an unambiguous trinucleotide decoding in the two [Formula: see text] and [Formula: see text] directions) and 5′ unambiguous motifs [Formula: see text] (associated with an unambiguous trinucleotide decoding in the [Formula: see text] direction only) are analysed without and with constraints. The constraints studied are: initiation and stop codons, periodic codons [Formula: see text] , antiparallel complementarity and parallel complementarity. Taken together, these results suggest that the complementarity property involved in the antiparallel (DNA double helix, RNA stem) and parallel sequences could also be fundamental for coding genes with an unambiguous trinucleotide decoding in the two [Formula: see text] and [Formula: see text] directions or the [Formula: see text] direction only. Furthermore, the single-frame motifs [Formula: see text] with a property of trinucleotide decoding and the framing motifs [Formula: see text] (also called circular code motifs; first introduced by Michel (2012)) with a property of reading frame decoding may have been involved in the early life genes to build the modern genetic code and the extant genes. They could have been involved in the stage without anticodon-amino acid interactions or in the Implicated Site Nucleotides (ISN) of RNA interacting with the amino acids. Finally, the [Formula: see text] and [Formula: see text] dipeptides associated with the [Formula: see text] and [Formula: see text] dicodons, respectively, are studied and their importance for biology and the origin of life discussed.