Spontaneous evolution of circular codes in theoretical minimal RNA rings

Small circular RNAs occur in many cells. Theoretical considerations designed to mimick primordial RNAs designed 25 theoretical, minimal 22-nucleotide long circular RNAs (RNA rings) forming stem-loop hairpins, including one codon per amino acid, a start and a stop codon. These RNA rings resemble consensus tRNAs, whose predicted anticodons assign to each RNA ring a potential cognate amino acid. Assuming dual translator and messenger roles, three consecutive translation rounds produce 21-residue-long peptides, seven codons at each round. In these conditions, steric hindrances between tRNA(-like) translators competing for partially overlapping nucleotide triplets can be reduced if none of the seven codons produces by circular permutation (position 1 → 3, or position 3 → 1) any of the six others. This non-permutability of codon sets is one of the conditions that define potential circular codes regulating translational frame. A near-universal maximal self-complementary circular code exists in reading frames of natural genes, and permutations of this circular code define maximal circular codes in each +1, +2 gene frames. Chronologically scaling RNA rings according to the genetic code inclusion order of their cognate amino acid, codon numbers belonging to the natural frame +1 circular code X1 decrease with cognate amino acid inclusion order, those belonging to the natural frame 0 circular code X0 increase. RNA rings with early cognates apparently reflect pre-(tRNA-like)-adaptor translation by direct codon-amino acid affinity with partially overlapping consecutive codons where X1 regulated translation. Translation of non-overlapping consecutive codons evolved in parallel with RNA rings' cognate inclusion in the genetic code and with X0. Hence the complex "multi-frame" natural circular codes potentially evolved spontaneously from small coding circular RNAs mimicked by theoretical minimal RNA rings. Modern reading frames evolved from earlier reading frames corresponding to modern +1 frames.