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 SF as the trinucleotides AAA and CAA do not occur in a shifted frame. A motif which is not single-frame SF is multiple-frame MF. Several classes of MF motifs are defined and analysed. The distributions of single-frame SF motifs (associated with an unambiguous trinucleotide decoding in the two 5'–3' and 3'–5' directions) and 5′ unambiguous motifs 5'U (associated with an unambiguous trinucleotide decoding in the 5'–3' direction only) are analysed without and with constraints. The constraints studied are: initiation and stop codons, periodic codons AAA,CCC,GGG,TTT, 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 5'–3' and 3'–5' directions or the 5'–3' direction only. Furthermore, the single-frame motifs SF with a property of trinucleotide decoding and the framing motifs F (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 SF and MF dipeptides associated with the SF and MF dicodons, respectively, are studied and their importance for biology and the origin of life discussed.
Photonic approach to microwave frequency measurement with digital circular-code results
