title: Codon Distribution in Error-Detecting Circular Codes.
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 C³ 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 C(3) codes to maximal self-complementary circular codes.
authors.affiliation: Institute for Mathematical Biology, Faculty of Computer Science, Mannheim University of Applied Sciences, Paul-Wittsack Str. 10, 68163 Mannheim, Germany. e.fimmel@hs-mannheim.de.
authors.forename: Elena
authors.initials: E
authors.lastname: Fimmel
authors.affiliation: Institute for Mathematical Biology, Faculty of Computer Science, Mannheim University of Applied Sciences, Paul-Wittsack Str. 10, 68163 Mannheim, Germany. l.struengmann@hs-mannheim.de.
authors.forename: Lutz
authors.initials: L
authors.lastname: Strüngmann
keywords: circular codes; codon usage; comma-free codes; evolution of the genetic code; genetic code