Statistical tools for discovering pseudo-periodicities in biological sequences
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 171-181.

Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics intending to increase the power of the method. Theoretical behaviour of these statistics are derived, and the corresponding tests are then described. In this paper we also present an application of these tests to a protein known to have sequence periodicity.

Classification : 62G10, 62P10
Mots-clés : biological sequences, proteins, periodicity, autocovariance funtion 
@article{PS_2001__5__171_0,
     author = {Prum, Bernard and Turckheim, \'Elisabeth de and Vingron, Martin},
     title = {Statistical tools for discovering pseudo-periodicities in biological sequences},
     journal = {ESAIM: Probability and Statistics},
     pages = {171--181},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1875669},
     zbl = {0992.62099},
     language = {en},
     url = {http://www.numdam.org/item/PS_2001__5__171_0/}
}
TY  - JOUR
AU  - Prum, Bernard
AU  - Turckheim, Élisabeth de
AU  - Vingron, Martin
TI  - Statistical tools for discovering pseudo-periodicities in biological sequences
JO  - ESAIM: Probability and Statistics
PY  - 2001
SP  - 171
EP  - 181
VL  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_2001__5__171_0/
LA  - en
ID  - PS_2001__5__171_0
ER  - 
%0 Journal Article
%A Prum, Bernard
%A Turckheim, Élisabeth de
%A Vingron, Martin
%T Statistical tools for discovering pseudo-periodicities in biological sequences
%J ESAIM: Probability and Statistics
%D 2001
%P 171-181
%V 5
%I EDP-Sciences
%U http://www.numdam.org/item/PS_2001__5__171_0/
%G en
%F PS_2001__5__171_0
Prum, Bernard; Turckheim, Élisabeth de; Vingron, Martin. Statistical tools for discovering pseudo-periodicities in biological sequences. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 171-181. http://www.numdam.org/item/PS_2001__5__171_0/

[1] P. Argos, Evidence for a repeating domain in type I restriction enzyme. European Molecular Biology Organization J. 4 (1985) 1351-1355.

[2] G. Benson and M.S. Waterman, A method for fast data search for all k-nucleotide repeats. Nucleic Acids Res. 20 (1994) 2019-2022.

[3] M.S.M. Boguski, R.C. Hardison, S. Schwart and W. Miller, Analysis of conserved domains and sequence motifs in cellular regulatory proteins and locus control using new software tools for multiple alignments and visualization. The New Biologist 4 (1992) 247-260.

[4] G.M. Bressan, P. Argos and K.K. Stanley, Repeating structure of chick tropoelastin revealed by complementary DNA cloning. Biochemistry 26 (1987) 1497-1503.

[5] P.J. Brockwell and R.A. Davis, Time Series: Theory and Methods. Springer-Verlag (1987). | MR | Zbl

[6] R.S. Brown, C. Sander and P. Argos, The primary structure of transcription factor TF III A has 12 consecutive repeats. Federation of European Biochemical Society Letter 186 (1985) 271-274.

[7] J.L. Cornette, K.B. Cease, H. Margalit, J.L. Sponge, J.A. Berzofsky and Ch. Delisi, Hydrophobicity scales and computational techniques for detecting amphipathic structures in proteins. J. Molecular Biology 195 (1987) 659-685.

[8] E. Coward, Detecting periodicity pattern in biological sequences. Bioinformatics 14-6 (1998) 498-507.

[9] M.O. Dayhoff, R. Schwartz and B.C. Orcutt, A model of evolutionary change in protein, edited by M.O. Dayhoff. National Biomedical Research Foundation, Washington D.C., Atlas of Protein Sequences and Structure 5-3 (1978) 345-352.

[10] P. Doukhan, Mixing, properties and examples. Springer Verlag, Lecture Notes in Statist. 85 (1985). | MR | Zbl

[11] V.A. Fischetti, G.M. Landau and P.H. Seller, Identifying period occurences of a template with application to protein structure. Inform. Process. Lett. 45-1 (1993) 11-18. | MR | Zbl

[12] W. Fitch, Phylogenies constrained by cross-over process as illustrated by human hemoglobins an a thirteen-cycle, eleven amino-acid repeat in human apolipoprotein AI. Genetics 86 (1977) 623-644.

[13] S. Hennikoff and J.G. Henikoff, Amino acid substitution matrices from protein blocks for database research. Nucleid Acid Res. 19 (1992) 6565-6572.

[14] J. Heringa and P. Argos, A method to recognize distant repeats in protein sequences. Proteins 17-4 (1993) 391-441.

[15] I.A. Ibragimov, On a central limit theorem for dependent random variables. Theory Probab. Appl.15 (1975).

[16] S. Labeit, M. Gautel, A. Lakey and J. Trinick, Towards a molecular understanding of titin. European Molecular Biology Organization J. 11 (1992) 1711-1716.

[17] A. Lupas, M. Van Dyke and J. Stock, Predicting coiled coils from protein sequences. Science 252 (1991) 1162-1164.

[18] A.D. Mclachlan, Analysis of periodic patterns in amino-acid sequences: Collagen. Biopolymers 16 (1977) 1271-1297.

[19] A.D. Mclachlan, Repeated helical patterns in apolipoprotein AI. Nature 267 (1977) 465-466.

[20] A.D. Mclachlan and J. Karn, Periodic features in the amino-acid sequence of nematod myosin rod. J. Molecular Biology 220 (1983) 79-88.

[21] A.D. Mclachlan and M. Stewart, The 14-fold periodicity in alpha-tropomyosin and the interaction with actin. J. Molecular Biology 103 (1976) 271-298.

[22] A.D. Mclachlan, M. Stewart, R.O. Hynes and D.J. Rees, Analysis of repeated motifs in talin rod. J. Molecular Biology 235-4 (1994) 1278-1290.

[23] J. Miller, A.D. Mclachlan and A. Klug, Repetitive zinc-binding domains in the transcription factor IIIA from Xenopus oocytes. European Molecular Biology Organization J. 4 (1985) 1609-1614.

[24] R.J. Serfling, Approximation Theorems of mathematical statistics. Wiley (1980). | MR | Zbl