Pentamers with Non-redundant Frames: Bias for Natural Circular Code Codons

The natural circular code consists of 20 codons (X0) overrepresented in the coding frame of protein-coding genes as compared to remaining noncoding frames, and X1 and X2 (N1N2N3 -> N3N1N2 and N1N2N3 -> N2N3N1 permutations of X0, overrepresented in + 1 and - 1 frames of protein-coding genes, not self-complementary). X0, X1 and X2 detect ribosomal, + 1 and - 1 frames. X0 spontaneously emerges in the 25 theoretical minimal RNA rings, 22-nucleotide-long circular RNAs designed to code once for each of the genetic code's coding signals (a start, a stop and each of the 20 amino acids) by three overlapping frames. RNA rings presumed ancient are biased for X1, and bias for X0 increases in presumed recent RNA rings, indicating an evolutionary X1-to-X0 switch. Here, analyses explore biases for X0, X1 and X2 in non-redundant nucleotide tetra- and pentamers, for different genetic codes. Biases for X0 occur in non-redundant nucleotide pentamers and seem stronger in nuclear than mitochondrial genetic codes; tendencies are opposite for X1. Strand-asymmetric replication presumably causes mitogenomes to escape Chargaff's rule which expects ratios A/T = G/C = 1 in single-stranded sequences. Hence, presumably X1 emerged in ancient genetic codes used in single-stranded protogenomes/coding RNAs; the self-complementary X0 presumably evolved secondarily with double-stranded genomes and strand-symmetric replication. Results indicate that selection for non-redundant overlap coding in short nucleotide sequences produced the natural circular code.