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Homepage of Christian Michel THEORETICAL
BIOINFORMATICS Responsable Prof. Christian MICHEL
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Bioinformatique Théorique CSTB, ICube Université de Strasbourg, CNRS 300 Boulevard Sébastien Brant 67400 Illkirch, France Site: https://dpt-info.di.unistra.fr/~c.michel/ Site équipe: http://icube-cstb.unistra.fr/fr/index.php/Accueil |
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THEORETICAL BIOINFORMATICS
RESEARCH CIRCULAR CODE AND GENETIC CODE |
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SURPRISING DISCOVERY OF
A NEW GALAXY ! OF STARS ?
OF GENOMES ? An answer in the article of Michel and Sereni (2023)
[PDF].
THEORETICAL
BIOINFORMATICS RESEARCH The
objectives of the Theoretical Bioinformatics group are placed on the level of
fundamental and theoretical knowledge with the identification of rules and
properties in genes (more than 200 theorems, lemmas, propositions). Review: Article A38 Identification of statistical signals in genes: Articles
[A1,3-8,11,14,16] Identification of circular codes in genes: Articles
[A19,21,22,30,33,61,67,74,83,85,89,95,97] Identification of circular code motifs: Articles
[A53,59,65,72,73,77,79,80,82,84,87,88] Properties of circular codes in genes: Articles
[A36,41,46,49,63,64,66] Combinatorics of circular codes: Articles
[A27,39,40,47,50,52,54,55,57,58,60,70,71,75,76,78,81,86, 90,91,93,94,96] Genome galaxy: Articles [A92,98] Computer models of gene evolution: Articles
[A8-10,12,20] Probabilistic models of gene evolution by substitution: Articles
[A13,15,17,23,24,31,32,34,35,37,42, 43,45,51] Probabilistic models of gene evolution by substitution, insertion and deletion: Articles [A48,56,62, 65,68] Phylogenetic distances and inference
methods: Articles [A35,37,44] Research software in bioinformatics: Articles
[A9,28,45,65,68] CIRCULAR
CODE AND GENETIC CODE
Figure 1. Main
research fields of the theory of circular code in genes. Developed
since 1996, the circular code theory provides a mathematical framework for gene coding. Such a mathematical approach is rare in biology compared to other
scientific disciplines such as cosmology, particle physics, etc. It offers a means to model and quantify the ability of genes to recover the reading frame (defined by the ATG start codon) while simultaneously
encoding amino acids. More
than 200 articles related to the subject, either as a main
focus or a partial topic, have been published in international
journals. The
theory has led to the formulation of over 300 theorems, lemmas, and
propositions. Over
50 authors have contributed to this field, with a core group of active
researchers developing the theoretical foundations over the past seven years.
This group has been primarily composed of Prof. Elena Fimmel, Prof.
Jean-Sébastien Sereni, and Prof. Lutz Strüngmann, working both
collaboratively and independently. Personal
theoretical remarks about the genetic code The mathematical structure of the genetic code G is notably limited: (i) The genetic code corresponds to a maximal code
consisting of 64 trinucleotides, or codons. It exhibits self-complementarity, but lacks any meaningful permutation map P beyond the identity transformation
(i.e., P(G) = G). (ii)
Its circularity property is highly degraded with respect to reading frame
identification: only a single start codon (ATG, coding for methionine) is used, along with three stop codons
(TAA, TAG, and TGA) that do
not code for any amino acid. Moreover, this circularity is only present at
the beginning and end of genes, with no such structure detectable in the
internal regions. (iii)
The genetic code is a highly specific instance: given a 4-letter nucleotide
alphabet and codons of length 3, the total number of possible codes is 264
≈ 1019 (including the empty set), highlighting the vast
space of alternative codes that remain unexplored. (iv)
Finally, it is worth noting that despite the existence of several thousand
articles on codon usage, none has yielded a genuine theoretical understanding
of the genetic code — largely because alternative codes have been entirely
neglected. The circular code theory: (i) It provides a mathematical framework to analyse the
vast space of 1019 possible genetic codes, focusing particularly
on their circularity properties, as exemplified by its generalization to the k-circular codes. (ii)
It introduces a rare mathematical structure into the field of biology,
offering a conceptual framework that is often lacking in this domain. (iii)
Moreover, it has led to a large number of statistically significant results
within this theoretical structure, suggesting a potential feedback between
theory and biological reality. However,
to date, circular codes and their associated motifs have not been
experimentally observed or validated in biological systems. Conclusion: While
the circular code theory offers a mathematical structure to analyse gene
coding, it currently lacks a biological foundation. A scientific mystery… Main
properties of the circular code theory The circular code theory proposes that a circular code has preceded
the genetic code. The circular code X identified in genes of bacteria, archaea,
eukaryotes, plasmids and viruses (Michel, 2017, Life 7, 20, 1-16, doi:10.3390/life7020020; Michel,
2015, J. Theor. Biol. 380, 156-177, doi:10.1016/j.jtbi.2015.04.009; Arquès and Michel, 1996, J. Theor. Biol. 182,
45-58, doi:10.1006/jtbi.1996.0142) is based on the 20 following
trinucleotides:
Precisely, X is a maximal
C3 self-complementary trinucleotide circular code and has 3
major properties: (i) to retrieve, maintain and synchronize the
reading (correct) frame at any position in a gene; (ii) to code 12 amino acids (according to the standard amino acid
code):
(iii) to generate X circular
code motifs in genes (Michel, Nguefack Ngoune, Poch, Ripp
and Thompson, 2017, Life 7, 52, 1-20,
doi:10.3390/life7040052) which can pair with the X circular
code motifs in tRNAs and rRNAs, in particular in the ribosome decoding center
(Michel, 2012, Comput. Biol. Chem. 37,
24-37, doi:10.1016/j.compbiolchem.2011.10.002; El Soufi and Michel, 2014, Comput. Biol. Chem. 52, 9-17,
doi:10.1016/j.compbiolchem.2014.08.001). The universally conserved
nucleotides A1492 and A1493 and the conserved nucleotide G530 are included in
X circular code motifs. Reviews
in english [PDF] and [PDF] Review
in french [PDF] Fimmel
et Strüngmann, review article in Biosystems (2018, vol. 164, 186-198):
MOTIFS OF THE CIRCULAR CODE X (X MOTIFS) IN THE RIBOSOME
DECODING CENTER
Motifs
of the circular code X in the ribosome decoding center: X
motifs of mRNA in green, X motif containing the universally conserved
A1492 and A1492 of rRNA in purple, X motif containing the universally converved G530 of rRNA in fuchsia and X motifs of
tRNAs in dark blue (anticodon in black) (Michel, 2012;
El Soufi and Michel, 2014). Graphical representation here with the 16s rRNA
of Thermus thermophilus (PDB 3I8G). Models
of gene evolution by substitution of genetic motifs (Benard, Michel) [PDF] Models
of gene evolution by substitution, insertion and deletion of nucleotides (Lèbre, Michel) [PDF] Models
of gene evolution by substitution, insertion and deletion of genetic motifs
(Benard, Lèbre, Michel) [PDF] GETEC (Genome
Evolution by Transformation, Expansion and Contraction) (Benard E., Lèbre S., Michel C.J., 2015; [PDF]) to determine
evolutionary analytical solutions of genetic motifs based on substitution,
insertion and deletion as a function of time or sequence length, as well as
in direct time direction (past-present) or in inverse time direction
(present-past) THEORETICAL
BIOINFORMATICS ARTICLES IN INTERNATIONAL JOURNALS 2025 [A98] Michel C.J., Sereni J.-S.
2025. Genome galaxy identified
by the circular code theory. Bulletin of Mathematical Biology
87:5, 1-35 [PDF] 2024 [A97] Michel C.J. 2024. Circular code identified by
the codon usage. Biosystems 244, 105308, 1-12. [PDF] [A96] Fimmel E., Michel C.J., Strüngmann L. 2024. Circular
cut codes in genetic information. Biosystems 243,
105263, 1-10. [PDF] [A95] Michel C.J. 2024. Circular code in introns. Biosystems 239,
105215, 1-9. [PDF] 2023 [A94] Fimmel E., Michel C.J., Strüngmann L. 2023. Circular
mixed sets. Biosystems 229, 104906, 1-11. [PDF] [A93] Fimmel E., Michel C.J.,
Pirot F., Sereni J.-S., Strüngmann L. 2023. Diletter and triletter
comma-free codes over finite alphabets. The
Australasian Journal of Combinatorics 86(2),
233-270. [PDF] [A92] Michel C.J., Sereni J.-S.
2023. Reading frame retrieval of genes:
a new parameter of codon usage based on the circular code theory. Bulletin
of Mathematical Biology 85:24, 1-21. [PDF] 2022 [A91] Michel C.J., Sereni J.-S.
2022. Trinucleotide k-circular
codes II: Biology. Biosystems 217, 104668, 1-18. [PDF]. [A90] Michel C.J., Mouillon B., Sereni J.-S. 2022. Trinucleotide
k-circular codes I: Theory. Biosystems 217, 104667,
1-11. [PDF]. 2021 [A89] Michel C.J. 2021. Genes on the
circular code alphabet. Biosystems 206, 104431,
1-12. [PDF]. [A88] Thompson J.D., Ripp R., Mayer
C., Poch O., Michel C.J. 2021. Potential role of the X circular code in the regulation of
gene expression. Biosystems 203, 104368,
1-15. [PDF]. 2020 [A87] Michel C.J., Mayer
C., Poch O., Thompson J.D. 2020. Characterization of accessory
genes in coronavirus genomes. Virology Journal 17:131, 1-13.
[PDF]. [A86] Fimmel E., Michel C.J., Pirot F., Sereni J.-S., Starman M., Strüngmann L.
2020. The relation between k-circularity
and circularity of codes. Bulletin of Mathematical Biology 82:105,
1-34. [PDF] [A85] Michel C.J. 2020. The maximality of circular
codes in genes statistically verified. Biosystems
197, 104201, 1-7. [PDF] [A84] Dila G., Michel C.J., Thompson J.D. 2020.
Optimality of circular codes versus the genetic code after frameshift errors. Biosystems
195, 104134, 1-11. [PDF] [A83] Michel C.J., Thompson J.D. 2020.
Identification of a circular code periodicity in the bacterial ribosome:
origin of codon periodicity in genes? RNA
Biology 17, 571-583. [PDF] 2019 [A82] Dila G., Ripp R., Mayer
C., Poch O., Michel C.J., Thompson J.D. 2019. Circular code
motifs in the ribosome: a missing link in the evolution of translation? RNA
25, 1714-1730. [PDF] [PDF Suppl. Mat.] [A81] Fimmel E., Michel C.J., Pirot F., Sereni J.-S., Strüngmann L. 2019. Mixed circular codes. Mathematical
Biosciences 317, 108231, 1-14. [PDF] [A80] Michel C.J. 2019. Single-frame, multiple-frame
and framing motifs in genes. Life 9, 18, 1-22. [PDF] [A79] Dila G., Michel C.J., Poch O., Ripp R.,
Thompson J.D. 2019. Evolutionary conservation and functional implications of
circular code motifs in eukaryotic genomes. Biosystems 175,
57-74. [PDF] 2018 [A78] Fimmel E., Michel C.J., Starman M., Strüngmann L.
2018. Self-complementary
circular codes in coding theory. Theory
in Biosciences 137, 51-65. [PDF] 2017 [A77] Michel C.J., Nguefack Ngoune V., Poch O., Ripp
R., Thompson J.D. 2017. Enrichment of circular code motifs in the genes of
the yeast Saccharomyces cerevisiae.
Life 7, 52, 1-20. [PDF] [A76] Fimmel E., Michel C.J., Strüngmann
L. 2017. Diletter circular codes
over finite alphabets. Mathematical Biosciences
294, 120-129. [PDF] [A75] Fimmel E., Michel C.J., Strüngmann
L. 2017. Strong comma-free codes in
genetic information. Bulletin of Mathematical Biology 79,
1796-1819. [PDF] [A74] Michel C.J. 2017. The maximal C3
self-complementary trinucleotide circular code X in genes of bacteria,
archaea, eukaryotes, plasmids and viruses. Life 7, 20, 1-16. [PDF] [A73] El Soufi K., Michel C.J. 2017. Unitary
circular code motifs in genomes of eukaryotes. Biosystems 153, 45-62.
[PDF] 2016 [A72] El Soufi K., Michel C.J. 2016. Circular
code motifs in genomes of eukaryotes. Journal of Theoretical Biology
408, 198-212. [PDF] [A71] Fimmel E., Michel C.J., Strüngmann
L. 2016. n-Nucleotide circular codes in graph theory. Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374,
20150058, 1-19. [PDF] [A70] Michel C.J., Pellegrini M., Pirillo G. 2016. Maximal dinucleotide and trinucleotide circular codes. Journal of Theoretical Biology
389, 40-46. [PDF] 2015 [A69] El Soufi K., Michel
C.J. 2015. Circular code motifs near the ribosome decoding
center. Computational Biology and Chemistry 59, 158-176. [PDF] [A68] Benard E., Lèbre S.,
Michel C.J. 2015. Genome evolution by transformation, expansion and
contraction GETEC. Biosystems 135, 15-34. [PDF] [A67] Michel C.J. 2015. The maximal C3
self-complementary trinucleotide circular code X in genes of bacteria,
eukaryotes, plasmids and viruses. Journal of Theoretical Biology 380,
156-177. [PDF] [A66] Michel C.J. 2015. An extended genetic scale of
reading frame coding. Journal of Theoretical Biology 365, 164-174. [PDF] 2014 [A65] El Soufi K., Michel
C.J. 2014. Circular code motifs in the ribosome decoding
center. Computational Biology and Chemistry 52, 9-17. [PDF] [A64] Michel C.J. 2014. A genetic scale of reading
frame coding. Journal of Theoretical Biology 355, 83-94. [PDF] [A63] Michel C.J., Seligmann H. 2014. Bijective
transformation circular codes and nucleotide exchanging RNA transcription. Biosystems
118, 39-50. [PDF] 2013 [A62] Lèbre S., Michel
C.J. 2013. A new molecular evolution model for limited
insertion independent of substitution. Mathematical Biosciences 245,
137-147. [PDF] [A61] Herrmann M., Michel C.J., Zugmeyer
B. 2013. A necklace algorithm to determine the growth function of
trinucleotide circular codes. Journal of Applied Mathematics and
Bioinformatics 3, 1-40. [PDF] [A60] Benard E., Michel C.J. 2013. Transition and
transversion on the common trinucleotide circular code. Computational
Biology Journal 2013, Article ID 795418, 1-10. [PDF] [A59] Michel C.J. 2013. Circular code motifs in
transfer RNAs. Computational Biology and Chemistry 45, 17-29. [PDF] [A58] Michel C.J., Pirillo G. 2013. Dinucleotide
circular codes. ISRN
Biomathematics 2013, Article ID 538631, 1-8. [PDF] [A57] Michel C.J., Pirillo G. 2013. A permuted set
of a trinucleotide circular code coding the 20 amino acids in variant nuclear
codes. Journal of Theoretical Biology 319, 116-121. [PDF] 2012 [A56] Lèbre S., Michel
C.J. 2012. An evolution model for sequence length based on residue
insertion-deletion independent of substitution: an application to the GC
content in bacterial genomes. Bulletin of Mathematical Biology 74,
1764-1788. [PDF] [A55] Michel C.J., Pirillo G., Pirillo M.A. 2012. A
classification of 20-trinucleotide circular codes. Information and Computation 212, 55-63. [PDF] [A54] Bussoli L., Michel C.J., Pirillo G. 2012. On
conjugation partitions of sets of trinucleotides. Applied Mathematics
3, 107-112. [PDF] [A53] Michel C.J. 2012. Circular code motifs in
transfer and 16S ribosomal RNAs: a possible translation code in genes. Computational
Biology and Chemistry 37, 24-37. [PDF] 2011 [A52] Bussoli L., Michel
C.J., Pirillo G. 2011. On some forbidden configurations for
self-complementary trinucleotide circular codes. Journal for Algebra and
Number Theory Academia 2, 223-232. [PDF] [A51] Benard E., Michel C.J. 2011. A generalization
of substitution evolution models of nucleotides to genetic motifs. Journal
of Theoretical Biology 288, 73-83. [PDF] [A50] Michel C.J., Pirillo G. 2011. Strong
trinucleotide circular codes. International Journal of Combinatorics
2011, Article ID 659567, 1-14. [PDF] [A49] Ahmed A., Michel C.J. 2011. Circular code
signal in frameshift genes. Journal of
Computer Science and Systems Biology 4,
7-15. [PDF] 2010 [A48] Lèbre S., Michel
C.J. 2010. A stochastic evolution model for residue
insertion-deletion independent from substitution. Computational Biology
and Chemistry 34, 259-267. [PDF] [A47] Michel C.J., Pirillo G. 2010. Identification
of all trinucleotide circular codes. Computational Biology and Chemistry
34, 122-125. [PDF] [A46] Ahmed A., Frey G., Michel C.J. 2010. Essential
molecular functions associated with the circular code evolution. Journal
of Theoretical Biology 264, 613-622. [PDF] 2009 [A45] Benard E., Michel C.J. 2009.
Computation of direct and inverse mutations with the SEGM web server
Stochastic Evolution of Genetic Motifs: an application to splice sites of
human genome introns. Computational Biology and Chemistry 33,
245-252. [PDF] [A44] Criscuolo A., Michel C.J. 2009. Phylogenetic
inference with weighted codon evolutionary distances. Journal
of Molecular Evolution 68, 377-392. [PDF] [A43] Bahi J.M., Michel C.J. 2009. A stochastic
model of gene evolution with time dependent pseudochaotic mutations. Bulletin
of Mathematical Biology 71, 681-700. [PDF] 2008 [A42] Bahi J.M., Michel C.J. 2008. A stochastic
model of gene evolution with chaotic mutations. Journal of Theoretical
Biology 255, 53-63. [PDF] [A41] Ahmed A., Michel C.J. 2008. Plant microRNA
detection using the circular code information. Computational Biology and
Chemistry 32, 400-405. [PDF] [A40] Michel C.J., Pirillo G., Pirillo M.A. 2008. A
relation between trinucleotide comma-free codes and trinucleotide circular
codes. Theoretical Computer Science 401, 17-26. [PDF] [A39] Michel C.J., Pirillo G., Pirillo M.A. 2008. Varieties
of comma free codes. Computer and Mathematics with Applications 55,
989-996. [PDF] [A38] Michel C.J. 2008. A 2006 review of circular
codes in genes. Computer and Mathematics with Applications 55,
984-988. [PDF] 2007 [A37] Michel C.J. 2007. Evolution probabilities and
phylogenetic distance of dinucleotides. Journal of Theoretical Biology
249, 271-277. [PDF] [A36] Ahmed A., Frey G., Michel C.J. 2007.
Frameshift signals in genes associated with the circular code. In
Silico Biology 7, 155-168. [PDF] [A35] Michel C.J. 2007. Codon phylogenetic distance.
Computational Biology and Chemistry 31, 36-43. [PDF] [A34] Michel C.J. 2007. An analytical model of gene
evolution with 9 mutation parameters: an application to the amino acids coded
by the common circular code. Bulletin of Mathematical Biology 69,
677-698. [PDF] 2006 [A33] Frey G., Michel C.J. 2006. Identification of
circular codes in bacterial genomes and their use in a factorization method
for retrieving the reading frames of genes. Computational Biology and
Chemistry 30, 87-101. [PDF] [A32] Frey G., Michel C.J. 2006. An analytical model
of gene evolution with 6 mutation parameters: an application to archaeal
circular codes. Computational Biology and Chemistry 30, 1-11. [PDF] 2004 [A31] Bahi J.M., Michel C.J. 2004. A
stochastic gene evolution model with time dependent mutations. Bulletin of
Mathematical Biology 66, 763-778. [PDF] 2003 [A30] Frey G., Michel C.J. 2003. Circular codes in
archaeal genomes. Journal of Theoretical Biology 223, 413-431. [PDF] [A29] Michel C.J. 2003. A computer method for
identifying patterns in the electroencephalogram signals. Journal
of Medical Engineering and Technology 27,
267-275. [PDF] 2002 [A28] Arquès D.G., Lacan
J., Michel C.J. 2002. Identification of protein coding genes in genomes
with statistical functions based on the circular code. Biosystems 66,
73-92. [PDF] 2001 [A27] Lacan J., Michel C.J. 2001. Analysis
of a circular code model. Journal of Theoretical Biology 213, 159-170.
[PDF] 2000 [A26] Bahi J.M., Michel C.J. 2000. Convergence
of discrete asynchronous iterations. International Journal of Computer
Mathematics 74, 113-125. [PDF] 1999 [A25] Bahi J.M., Michel C.J. 1999. Simulations
of asynchronous evolution of discrete systems. Simulation Practice and
Theory 7, 309-324. [PDF] [A24] Arquès D.G., Fallot
J.-P., Marsan L., Michel C.J. 1999. An evolutionary analytical model of a
complementary circular code. Biosystems 49, 83-103. [PDF] 1998 [A23] Arquès D.G., Fallot
J.-P., Michel C.J. 1998. An evolutionary analytical model of a complementary
circular code simulating the protein coding genes, the 5' and 3' regions. Bulletin
of Mathematical Biology 60, 163-194. [PDF] 1997 [A22] Arquès D.G., Michel
C.J. 1997. A circular code in the protein coding genes of
mitochondria. Journal of Theoretical Biology 189, 273-290. [PDF] [A21] Arquès D.G., Michel
C.J. 1997. A code in the protein coding genes. Biosystems
44, 107-134. [PDF] [A20] Arquès D.G., Fallot
J.-P., Michel C.J. 1997. An evolutionary model of a complementary circular
code. Journal of Theoretical Biology 185, 241-253. [PDF] 1996 [A19] Arquès D.G., Michel
C.J. 1996. A complementary circular code in the protein coding
genes. Journal of Theoretical Biology 182, 45-58. [PDF] [A18] Arquès D.G., Fallot
J.-P., Michel C.J. 1996. Identification of several types of periodicities in
the collagens and their simulation. International Journal of Biological
Macromolecules 19, 131-138. [PDF] 1995 [A17] Arquès D.G., Michel
C.J. 1995. Analytical solutions of the dinucleotide probability
after and before random mutations. Journal of Theoretical Biology 175,
533-544. [PDF] [A16] Arquès D.G., Lapayre J.-C., Michel C.J. 1995. Identification
and simulation of shifted periodicities common to protein coding genes of
eukaryotes, prokaryotes and viruses. Journal of Theoretical Biology
172, 279-291. [PDF] 1994 [A15] Arquès D.G., Michel
C.J. 1994. Analytical expression of the purine/pyrimidine
autocorrelation function after and before random mutations. Mathematical
Biosciences 123, 103-125. [PDF] 1993 [A14] Arquès D.G., Michel
C.J. 1993. Identification and simulation of new non-random
statistical properties common to different eukaryotic gene subpopulations. Biochimie
75, 399-407. [PDF] [A13] Arquès D.G., Michel
C.J. 1993. Analytical expression of the purine/pyrimidine codon
probability after and before random mutations. Bulletin of Mathematical
Biology 55, 1025-1038. [PDF] [A12] Arquès D.G., Michel
C.J. 1993. A model of gene evolution based on recognizable
languages and on insertion and deletion operations. International Journal of Modelling and
Simulation 13, 110-113. [PDF] [A11] Arquès D.G., Michel
C.J., Orieux K. 1993. Identification
and simulation of new non-random statistical properties common to different
populations of eukaryotic non-coding genes. Journal of Theoretical Biology
161, 329-342. [PDF] 1992 [A10] Arquès D.G., Michel
C.J. 1992. A simulation of the genetic periodicities modulo 2
and 3 with processes of nucleotide insertions and deletions. Journal of
Theoretical Biology 156, 113-127. [PDF] [A9] Arquès D.G., Michel
C.J., Orieux K. 1992. Analysis of
Gene Evolution: the software AGE. Bioinformatics 8, 5-14. [PDF] 1990 [A8] Arquès D.G., Michel
C.J. 1990. A model of DNA sequence evolution. Part 1:
Statistical features and classification of gene populations, 743-753. Part 2:
Simulation model, 753-766. Part 3: Return of the model to the reality,
766-770. Bulletin of Mathematical Biology 52, 741-772. [PDF] [A7] Arquès D.G., Michel
C.J. 1990. Periodicities in coding and noncoding regions of the
genes. Journal of Theoretical Biology 143, 307-318. [PDF] 1989 [A6] Michel C.J. 1989. A study of the
purine/pyrimidine codon occurrence with a reduced centered
variable and an evaluation compared to the frequency statistic. Mathematical
Biosciences 97, 161-177. [PDF] 1987 [A5] Arquès D.G., Michel
C.J. 1987. Periodicities in introns. Nucleic Acids Research
15, 7581-7592. [PDF] [A4] Arquès D.G., Michel
C.J. 1987. A purine-pyrimidine motif verifying an identical
presence in almost all gene taxonomic groups. Journal of Theoretical
Biology 128, 457-461. [PDF] [A3] Arquès D.G., Michel
C.J. 1987. Study of a perturbation in the coding periodicity. Mathematical
Biosciences 86, 1-14. [PDF] 1986 [A2] Michel C.J., Jacq B., Arquès
D.G., Bickle T.A. 1986. A remarkable amino acid sequence homology between a
phage T4 tail fibre protein and ORF314 of phage lambda located in the tail
operon. Gene 44, 147-150. [PDF] [A1] Michel C.J. 1986. New statistical approach to discriminate between protein coding and non-coding regions in DNA sequences and its evaluation. Journal of Theoretical Biology 120, 223-236. [PDF] |
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