Abstract
In 1957, Francis Crick et al. suggested an ingenious explanation for the process of frame maintenance. The idea was based on the notion of comma-free codes. Although Crick’s hypothesis proved to be wrong, in 1996, Arquès and Michel discovered the existence of a weaker version of such codes in eukaryote and prokaryote genomes, namely the so-called circular codes. Since then, circular code theory has invariably evoked great interest and made significant progress. In this article, the codon distributions in maximal comma-free, maximal self-complementary and maximal self-complementary circular codes are discussed, i.e., we investigate in how many of such codes a given codon participates. As the main (and surprising) result, it is shown that the codons can be separated into very few classes (three, or five, or six) with respect to their frequency. Moreover, the distribution classes can be hierarchically ordered as refinements from maximal comma-free codes via maximal self-complementary codes to maximal self-complementary circular codes.
Highlights
The genetic code as it is today is a product of a long evolutionary process
The degeneracy of the genetic code and clusters of similar amino acids corresponding to similar triplets should be explained [3]
We show that all of these ancient genetic codes that used only some of the 64 codons always contain a large comma-free code that codes for almost all of the amino acids involved
Summary
The genetic code as it is today is a product of a long evolutionary process. It can be seen as a kind of dictionary that translates information from the world of nucleic acids into the world of proteins. The fact that the frequency classes of the codons for maximal self-complementary C3 codes are refinements of the classes for maximal comma-free codes is a strong hint that the maximal self-complementary C3 codes used in the current genetic code could have evolved from the maximal comma-free codes, which were very likely used in earlier times, since these two classes of codes are disjoint. This means that there is no obvious mathematical reason for this refinement property.
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