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circular code motifs in genomes of eukaryotes

JOURNAL OF THEORETICAL BIOLOGY 2016年第0期408卷 198-212页

作者： El Soufi, Karim Michel, Christian J. Univ Strasbourg ICube Theoret Bioinformat CNRS 300 Blvd Sebastien Brant F-67400 Illkirch Graffenstaden France

A set X of 20 trinucleotides was identified in genes of bacteria, eukaryotes, plasmids and viruses, which has in average the highest occurrence in reading frame compared to its two shifted frames (Michel, 2015;Argues and Michel, 1996). This set X has an interesting mathematical property as X is a circular code (Argues and Michel, 1996). Thus, the motifs from this circular code X, called X motifs, have the property to always retrieve, synchronize and maintain the reading frame in genes. In this paper, we develop several statistical analyzes of X motifs in 138 available complete genomes of eukaryotes in which genes as well as non-gene regions are examined. Large X motifs (with lengths of at least 15 consecutive trinucleotides of X and compositions of at least 10 different trinucleotides of X among 20) have the highest occurrence in genomes of eukaryotes compared to its 23 large bijective motifs, its two large permuted motifs and large random motifs. The largest X motifs identified in eukaryotic genomes are presented, e.g. an X motif in a non-gene region of the genome Solarium pennellii with a length of 155 trinucleotides (465 nucleotides) and an expectation E = 10(-71). In the human genome, the largest X motif occurs in a non gene region of the chromosome 13 with a length of 36 trinucleotides and an expectation E = 10(-11). X motifs in non-gene regions of genomes could be evolutionary relics of primitive genes using the circular code for translation. However, the proportion of X motifs (with lengths of at least 10 consecutive trinucleotides of X and compositions of at least 5 different trinucleotides of X among 20) in genes/non-genes of the 138 complete eukaryotic genomes is about 8. Thus, the X motifs occur preferentially in genes, as expected from the previous works of 20 years. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： circular code motifs circular code Bijective transformation circular code Permuted circular code Genomes of eukaryotes

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Plant microRNA detection using the circular code information

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2008年第6期32卷 400-405页

作者： Ahmed, Ahmed Michel, Christian J. Univ Louis Pasteur Strasbourg 1 CNRSPole API LSIITULP Equipe Bioinformat TheorUMR 7005 F-67400 Illkirch Graffenstaden France

In this paper we present a new computational method leading to the identification of a new property in the plant microRNAs. This property which is based on the circular code information is then used to detect microRNAs in plants. The common C-3 circular code X is a set of 20 trinucleotides identified in the reading frames of both eukaryotic and prokaryotic genes allowing retrieval of any frame in genes, locally anywhere in the three frames (reading frame and its two shifted frames) and automatically with the same window length of 13 nucleotides in each frame. This code X is detected around the beginning of microRNAs. This method based only on the internal structure of genes, i.e. the circular code, allows sensible and precise microRNA site identification in precursor microRNAs with a sliding window of only 14 nucleotides. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： circular code Plant microRNAs Site identification Computer method

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An evolutionary analytical model of a complementary circular code

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BIOSYSTEMS 1999年第2期49卷 83-103页

作者： Arquès, DG Fallot, JP Marsan, L Michel, CJ Univ Marne La Vallee Inst Gaspard Monge Equipe Biol Theor F-93160 Noisy Le Grand France Inst Polytech Sevenans Equipe Biol Theor F-90010 Belfort France

The subset X-0,={AAC,AAT,ACC,ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG,GAT,GCC,GGC,GGT,GTA, GTC,GTT,TAC,TTC} of 20 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. This subset X-0 is a complementary maximal circular code with two permutated maximal circular codes X-1 and X-2 in the frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5'-3' direction). X-0 is called a C-3 code (Arquis and Michel, 1997, J. Biosyst 44, 107-134). A quantitative study of these three subsets, X-0, X-1, and X-2 in the three frames 0, 1 and 2 of eukaryotic protein genes shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of X-0, X-1 and X-2 in the frame 0 of eukaryotic protein genes are 48.5%, 29% and 22.5% respectively. These properties are not observed in the 5' and 3' regions of eukaryotes where X-0, X-1 and X-2 occur with variable frequencies around the random value (1/3). Several frequency asymmetries unexpectedly observed, e.g. the frequency difference between X-1 and X-2 in the frame 0, are related to a new property of the C-3 code X-0 involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 20 codons (trinucleotides in the frame 0) of X-0 with equiprobability (1/20) followed by t approximate to 4 substitutions per codon according to the proportions p approximate to 0.1, q approximate to 0.1 and r = 1 - p - q approximate to 0.8 in the three codon sites respectively, retrieves the frequencies of X-0, X-1 and X-2 observed in the three frames of protein genes and explains these asymmetries. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine. Finally, the evolutionary analytical method developed could be applied to the phylogenetic tr

关键词： circular code protein coding gene frequency asymmetry evolutionary analytical model substitution trinucleotide probability

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An analytical model of gene evolution with 9 mutation parameters: An application to the amino acids coded by the common circular code

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BULLETIN OF MATHEMATICAL BIOLOGY 2007年第2期69卷 677-698页

作者： Michel, Christian J. Univ Louis Pasteur Strasbourg 1 CNRS UMR 7005ULP LSIITEquipe Bioinformat Theor F-67400 Illkirch Graffenstaden France

We develop here an analytical evolutionary model based on a trinucleotide mutation matrix 64 x 64 with nine substitution parameters associated with the three types of substitutions in the three trinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4 x 4 and the trinucleotide mutation matrix 64 x 64 with three and six parameters. It determines at some time t the exact occurrence probabilities of trinucleotides mutating randomly according to these nine substitution parameters. An application of this model allows an evolutionary study of the common circular code C of eukaryotes and prokaryotes and its 12 coded amino acids. The main property of this code C is the retrieval of the reading frames in genes, both locally, i.e. anywhere in genes and in particular without a start codon, and automatically with a window of a few nucleotides. However, since its identification in 1996, amino acid information coded by C has never been studied. Very unexpectedly, this evolutionary model demonstrates that random substitutions in this code C and with particular values for the nine substitution parameters retrieve after a certain time of evolution a frequency distribution of these 12 amino acids very close to the one coded by the actual genes.

关键词： analytical model parameter evolution mutation circular code gene amino acid

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Essential molecular functions associated with the circular code evolution

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JOURNAL OF THEORETICAL BIOLOGY 2010年第2期264卷 613-622页

作者： Ahmed, Ahmed Frey, Gabriel Michel, Christian J. Univ Strasbourg CNRS Equipe Bioinformat Theor FDBTLSIITPole APIULPUMR 7005 F-67400 Illkirch Graffenstaden France

A circular code is a set of trinucleotides allowing the reading frames in genes to be retrieved locally, i.e. anywhere in genes and in particular without start codons, and automatically with a window of few nucleotides. In 1996, a common circular code, called X, was identified in large populations of eukaryotic and prokaryotic genes. Hence, it is believed to be an ancestral structural property of genes. A new computational approach based on comparative genomics is developed to identify essential molecular functions associated with circular codes. It is based on a quantitative and sensitive statistical method (FPTF) to identify three permuted trinucleotide sets in the three frames of genes, a flower automaton algorithm to determine if a trinucleotide set is a circular code or not, and an integrated Gene Ontology and Taxonomy (iGOT) database. By carrying out automatic circular code analyses on a huge number of gene populations where each population is associated with a particular molecular function, it identifies 266 gene populations having circular codes close to X. Surprisingly, their molecular functions include 98% of those covered by the essential genes of the DEG database (Database of Essential Genes). Furthermore, three trinucleotides GIG, AAG and GCG, replacing three trinucleotides of the code X and called "evolutionary" trinucleotides, significantly occur in these 266 gene populations. Finally, a new method developed to analyse and quantify the stability of a set of trinucleotides demonstrates that these evolutionary trinucleotides are associated with a significant increase of the stability of the common circular code X. Indeed, its stability increases from the 1502th rank to the 16th rank after the replacement of the three evolutionary trinucleotides among 9920 possible trinucleotide replacement sets. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： circular code Evolution Evolutionary trinucleotides circular code stability Trinucleotide stability Comparative genomics Database Molecular functions Essential genes

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Identification of protein coding genes in genomes with statistical functions based on the circular code

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BIOSYSTEMS 2002年第1-2期66卷 73-92页

作者： Arquès, DG Lacan, M Michel, CJ Univ Louis Pasteur Strasbourg 1 ULP CNRS LSIITEquipe Bioinformat TheorUMR 7005 F-67400 Illkirch Graffenstaden France Univ Marne Vallee Inst Gaspard Monge Equipe Biol Theor F-93160 Noisy Le Grand France ENSICA Dept Math Appl & Informat F-31056 Toulouse France

A new statistical approach using functions based on the circular code classifies correctly more than 93% of bases in protein (coding) genes and non-coding genes of human sequences. Based on this statistical study, a research software called 'Analysis of Coding Genes' (ACG) has been developed for identifying protein genes in the genomes and for determining their frame. Furthermore, the software ACG also allows an evaluation of the length of protein genes, their position in the genome, their relative position between themselves, and the prediction of internal frames in protein genes. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

关键词： protein coding genes genomes circular code statistical functions research software

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Frameshift signals in genes associated with the circular code

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In Silico Biology 2007年第2期7卷 155-168页

作者： Ahmed, Ahmed Frey, Gabriel Michel, Christian J. Equipe de Bioinformatique Théorique LSIIT (UMR CNRS-ULP 7005) Université Louis Pasteur de Strasbourg 67400 Illkirch Boulevard Sébastien Brant France

Three sets of 20 trinucleotides are preferentially associated with the reading frames and their 2 shifted frames of both eukaryotic and prokaryotic genes. These 3 sets are circular codes. They allow retrieval of any frame in genes (containing these circular code words), locally anywhere in the 3 frames and in particular without start codons in the reading frame, and automatically with the reading of a few nucleotides. The circular code in the reading frame, noted X, which can deduce the 2 other circular codes in the shifted frames by permutation, is the information used for analysing frameshift genes, i.e. genes with a change of reading frame during translation. This work studies the circular code signal around their frameshift sites. Two scoring methods are developed, a function P based on this code X and a function Q based both on this code X and the 4 trinucleotides with identical nucleotides. They detect a significant correlation between the code X and the -1 frameshift signals in both eukaryotic and prokaryotic genes, and the +1 frameshift signals in eukaryotic genes. © 2007 IOS Press. All rights reserved.

关键词： circular code Frame Frameshift gene Frameshift signal Statistical method Trinucleotide

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Genes on the circular code alphabet

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BIOSYSTEMS 2021年 206卷 104431-104431页

作者： Michel, Christian J. Univ Strasbourg CNRS ICube Theoret Bioinformat 300 Blvd Sebastien Brant F-67400 Illkirch Graffenstaden France

The X motifs, motifs from the circular code X, are enriched in the (protein coding) genes of bacteria, archaea, eukaryotes, plasmids and viruses, moreover, in the minimal gene set belonging to the three domains of life, as well as in tRNA and rRNA sequences. They allow to retrieve, maintain and synchronize the reading frame in genes, and contribute to the regulation of gene expression. These results lead here to a theoretical study of genes based on the circular code alphabet. A new occurrence relation of the circular code X under the hypothesis of an equiprobable (balanced) strand pairing is given. Surprisingly, a statistical analysis of a large set of bacterial genes retrieves this relation on the circular code alphabet, but not on the DNA alphabet. Furthermore, the circular code X has the strongest balanced circular code pairing among 216 maximal C3 self-complementary trinucleotide circular codes, a new property of this circular code X. As an application of this theory, different tRNAs studied on the circular code alphabet reveal an unexpected stem structure. Thus, the circular code X would have constructed a coding stem in tRNAs as an outline of the future gene structure and the future DNA double helix.

关键词： circular code Alphabet Trinucleotide Pairing rule Protein coding gene Transfer RNA gene

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Potential role of the X circular code in the regulation of gene expression

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BIOSYSTEMS 2021年 203卷 104368-104368页

作者： Thompson, Julie D. Ripp, Raymond Mayer, Claudine Poch, Olivier Michel, Christian J. Univ Strasbourg CNRS ICube Dept Comp Sci Strasbourg France Inst Pasteur Unite Microbiol Struct CNRS F-75724 Paris 15 France Univ Paris Diderot Sorbonne Paris Cite F-75724 Paris 15 France

The X circular code is a set of 20 trinucleotides (codons) that has been identified in the protein-coding genes of most organisms (bacteria, archaea, eukaryotes, plasmids, viruses). It has been shown previously that the X circular code has the important mathematical property of being an error-correcting code. Thus, motifs of the X circular code, i.e. a series of codons belonging to X and called X motifs, allow identification and maintenance of the reading frame in genes. X motifs are significantly enriched in protein-coding genes, but have also been identified in many transfer RNA (tRNA) genes and in important functional regions of the ribosomal RNA (rRNA), notably in the peptidyl transferase center and the decoding center. Here, we investigate the potential role of X motifs as functional elements of protein-coding genes. First, we identify the codons of the X circular code which are frequent or rare in each domain of life (archaea, bacteria, eukaryota) and show that, for the amino acids with the highest codon bias, the preferred codon is often an X codon. We also observe a correlation between the 20 X codons and the optimal codons/dicodons that have been shown to influence translation efficiency. Then, we examined recently published experimental results concerning gene expression levels in diverse organisms. The approach used is the analysis of X motifs according to their density ds(X), i.e. the number of X motifs per kilobase in a gene sequence s. Surprisingly, this simple parameter identifies several unexpected relations between the X circular code and gene expression. For example, the X motifs are significantly enriched in the minimal gene set belonging to the three domains of life, and in codon-optimized genes. Furthermore, the density of X motifs generally correlates with experimental measures of translation efficiency and mRNA stability. Taken together, these results lead us to propose that the X motifs may represent a genetic signal contributing to the maint

关键词： Gene expression Codon optimization Codon usage Genetic code circular code

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Optimality of circular codes versus the genetic code after frameshift errors

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BIOSYSTEMS 2020年 195卷 104134-104134页

作者： Dila, Gopal Michel, Christian J. Thompson, Julie D. Univ Strasbourg Dept Comp Sci CNRS ICube Strasbourg France

The standard genetic code (SGC) describes how 64 trinucleotides (codons) encode 20 amino acids and the stop translation signal. Biochemical and statistical studies have shown that the standard genetic code is optimized to reduce the impact of errors caused by incorporation of wrong amino acids during translation. This is achieved by mapping codons that differ by only one nucleotide to the same amino acid or one with similar biochemical properties, so that if misincorporation occurs, the structure and function of the translated protein remain relatively unaltered. Some previous studies have extended the analysis of SGC optimality to the effect of frameshift errors on the conservation of amino acids. Here, we compare the optimality of the SGC with a set of circular codes, and in particular the X circular code identified in genes, on the basis of various biochemical properties over all possible frameshift errors. We show that the X circular code is more optimized to minimize the impact of frameshift errors than the SGC for the chosen amino acid properties. Furthermore, in the context of a problem that has been unresolved since 1996, we also demonstrate that the X circular code has a frameshift optimality in its combinatorial class of 216 maximal self-complementary C-3 circular codes. To our knowledge, this is the first demonstration of the role of the X circular code in mitigation of translation errors. These results lead us to discuss the potential role of the X circular code in the evolution of the standard genetic code.

关键词： circular code Standard genetic code Frameshift Optimization Evolution

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