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Codon Distribution in Error-Detecting Circular Codes

Institute for Mathematical Biology, Faculty of Computer Science, Mannheim University of Applied Sciences, Paul-Wittsack Str. 10, 68163 Mannheim, Germany
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Helga Stan-Lotter and David Deamer
Received: 15 December 2015 / Revised: 24 February 2016 / Accepted: 10 March 2016 / Published: 15 March 2016
(This article belongs to the Section Life Sciences)
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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 C3 codes to maximal self-complementary circular codes. View Full-Text
Keywords: genetic code; comma-free codes; circular codes; codon usage; evolution of the genetic code genetic code; comma-free codes; circular codes; codon usage; evolution of the genetic code

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Fimmel, E.; Strüngmann, L. Codon Distribution in Error-Detecting Circular Codes. Life 2016, 6, 14.

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