Mixed circular codes
Elena Fimmel,Christian J. Michel,François Pirot,François Pirot,Jean-Sébastien Sereni,Lutz Strüngmann +5 more
TL;DR: Any maximal dinucleotides circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C3-comma-free code.
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Abstract: By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C3-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes were investigated. By using a graph-theoretical approach of circular codes recently developed, we study mixed circular codes, which are the union of a dinucleotide circular code, a trinucleotide circular code and a tetranucleotide circular code. Maximal mixed circular codes of (di,tri)-nucleotides, (tri,tetra)-nucleotides and (di,tri,tetra)-nucleotides are constructed, respectively. In particular, we show that any maximal dinucleotide circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C3-comma-free code. The growth function of self-complementary mixed circular codes of dinucleotides and trinucleotides is given. Self-complementary mixed circular codes could have been involved in primitive genetic processes.
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Citations
Infinite combinatorics in mathematical biology.
TL;DR: In this article, the authors introduce the theory of forcing and an algebraic construction technique based on trees and forests using infinite binary sequences for proving existence results and independence theorems in algebra.
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Potential role of the X circular code in the regulation of gene expression.
Julie Dawn Thompson,Raymond Ripp,Claudine Mayer,Claudine Mayer,Claudine Mayer,Olivier Poch,Christian J. Michel +6 more
TL;DR: In this paper, the authors investigated the role of X motifs as functional elements of protein-coding genes and found that the motifs may represent a genetic signal contributing to the maintenance of the correct reading frame and the optimization and regulation of gene expression.
6
Genes on the circular code alphabet
TL;DR: In this paper, a new occurrence relation of the circular code X under the hypothesis of an equiprobable (balanced) strand pairing is given, but not on the DNA alphabet.
3
Potential role of the X circular code in the regulation of gene expression
Julie Dawn Thompson,Raymond Ripp,Claudine Mayer,Claudine Mayer,Claudine Mayer,Olivier Poch,Christian J. Michel +6 more
TL;DR: The hypothesis that the X circular code represents an ancestor of the standard genetic code, that was used in primordial systems to simultaneously decode a smaller set of amino acids and synchronize the reading frame is proposed.
Reading Frame Retrieval of Genes: A New Parameter of Codon Usage Based on the Circular Code Theory
TL;DR: Based on the circular code theory, a new function f that quantifies the property of reading frame retrieval (RFR) of genes from their codon usage is defined in this paper , which is computed on a massive scale in genes of genomes of bacteria, eukaryotes and archaea.
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