Maximal dinucleotide comma-free codes. (21st January 2016)

• Record Type: Journal Article
• Authors: Fimmel, Elena; Strüngmann, Lutz
• Is Part Of: Journal of theoretical biology. Volume 389(2016)
• Page Start: 206
• Page End: 213
• Publication Date: 2016-01-21
• Subjects: Genetic code -- Circular code -- Comma-free code -- Dinucleotides; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2015.10.022
• Languages: English
• ISSNs: 0022-5193

Abstract

Abstract: The problem of retrieval and maintenance of the correct reading frame plays a significant role in RNA transcription. Circular codes, and especially comma-free codes, can help to understand the underlying mechanisms of error-detection in this process. In recent years much attention has been paid to the investigation of trinucleotide circular codes (see, for instance, Fimmel et al., 2014; Fimmel and Strüngmann, 2015a; Michel and Pirillo, 2012; Michel et al., 2012, 2008 ), while dinucleotide codes had been touched on only marginally, even though dinucleotides are associated to important biological functions. Recently, all maximal dinucleotide circular codes were classified (Fimmel et al., 2015; Michel and Pirillo, 2013 ). The present paper studies maximal dinucleotide comma-free codes and their close connection to maximal dinucleotide circular codes. We give a construction principle for such codes and provide a graphical representation that allows them to be visualized geometrically. Moreover, we compare the results for dinucleotide codes with the corresponding situation for trinucleotide maximal self-complementary C 3 -codes. Finally, the results obtained are discussed with respect to Crick׳s hypothesis about frame-shift-detecting codes without commas. Abstract : Highlights: Complete classification of all maximal dinucleotide comma-free codes. Any max. dinucleotide comma-free code is induced by a max. dinucleotide circular code. Any max. dinucleotide circular code contains exactly 3 max. dinucleotide comma-free codes. Comparison with the situation for trinucleotide codes. The results discussed with respect to the Crick׳s hypothesis on comma-free codes.