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Chaos game representation of functional protein sequences, and simulation and multifractal analysis of induced measures |
Yu Zu-Guo(喻祖国) a)b)†, Xiao Qian-Jun(肖前军)a), Shi Long(石龙)a), Yu Jun-Wu(余君武)c), and Vo Anhb) |
a School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China; b School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia; c Department of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China |
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Abstract Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation (CGR) of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the $D_q$ curves, one sees that these functional protein sequences are not completely random. The $D_q$ of all linked functional proteins studied are multifractal-like and sufficiently smooth for the $C_q$ (analogous to specific heat) curves to be meaningful. Furthermore, the $D_q$ curves of the measure $\mu$ based on their CGRs for different orders to link the functional protein sequences are almost identical if $q\geq 0$. Finally, the $C_q$ curves of all linked functional proteins resemble a classical phase transition at a critical point.
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Received: 30 September 2009
Accepted manuscript online:
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PACS:
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87.14.E-
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(Proteins)
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87.15.Cc
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(Folding: thermodynamics, statistical mechanics, models, and pathways)
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87.15.H-
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(Dynamics of biomolecules)
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87.15.B-
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(Structure of biomolecules)
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02.50.Le
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(Decision theory and game theory)
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Fund: Project partially supported by the
National Natural Science Foundation of China (Grant No.~30570426),
the Chinese Program for New Century Excellent Talents in University
(Grant No.~NCET-08-06867), Fok Ying Tung Education Foundation (Grant
No.~101004), and |
Cite this article:
Yu Zu-Guo(喻祖国), Xiao Qian-Jun(肖前军), Shi Long(石龙), Yu Jun-Wu(余君武), and Vo Anh Chaos game representation of functional protein sequences, and simulation and multifractal analysis of induced measures 2010 Chin. Phys. B 19 068701
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[1] |
Venter J C, Adams M D, Myers E W, et al . 2001 Science 291 1304
|
[2] |
Pandey A and Mann M 2000 Nature 405 837
|
[3] |
Jeffrey H J 1990 Nucleic Acids Research 18 2163
|
[4] |
Goldman N 1993 Nucleic Acids Research 21 2487
|
[5] |
Deschavanne P J, Giron A, Vilain J, Fagot G and Fertil B 1999 Mol. Biol. Evol. 16 1391
|
[6] |
Almeida J S, Carrico J A, Maretzek A, Noble P A and Fletcher M 2001 Bioinformatics 17 429
|
[7] |
Joseph J and Sasikumar R 2006 BMC Bioinformatics 7 243(1-10)
|
[8] |
Gao J and Xu Z Y 2009 Chin. Phys. B 18 370
|
[9] |
Gao J, Jiang L L and Xu Z Y 2009 Chin. Phys. B 18 4571
|
[10] |
Fiser A, Tusnady G E and Simon I 1994 J. Mol. Graphics 12 302
|
[11] |
Basu S, Pan A, Dutta C and Das J 1998 J. Mol. Graphics and Modelling 15 279
|
[12] |
Yu Z G, Anh V V and Lau K S 2004 J. Theor. Biol. 226 341
|
[13] |
Yu Z G, Anh V V and Lau K S 2004 Physica A 337 171
|
[14] |
Dill K A 1985 Biochemistry 24 1501
|
[15] |
Wang J and Wang W 2000 Phys. Rev. E 61 6981
|
[16] |
Brown T A 1998 Genetics 3rd ed. (London: Chapman &Hall)
|
[17] |
Huang Y Z and Xiao Y 2003 Chaos, Solitons and Fractals 17 895
|
[18] |
Huang Y Z, Li M F and Xiao Y 2007 Chaos, Solitons and Fractals 34 782
|
[19] |
Feng J, Liu J H and Zhang H G 2008 Acta Phys. Sin. 57 6868 (in Chinese)
|
[20] |
Chen Y P, Fu P P, Shi M H, Wu J F and Zhang C B 2009 Acta Phys. Sin. 58 7050 (in Chinese)
|
[21] |
Yu Z G and Anh V V 2001 Chaos, Solitons and Fractals 12(10) 1827
|
[22] |
Yu Z G and Wang B 2001 Chaos, Solitons and Fractals 12 519
|
[23] |
Yu Z G, Anh V V, Gong Z M and Long S C 2002 Chin. Phys. 11 1313
|
[24] |
Barnsley M F and Demko S 1985 Proc. R. Soc. London Ser. A 399 243
|
[25] |
Falconer K 1997 Techniques in Fractal Geometry (London: John Wiley &Sons)
|
[26] |
Vrscay E R 1991 Fractal Geometry and Analysis ed. Belair J and Dubuc S (Dordrecht: Kluwer) pp.~405--468
|
[27] |
Anh V V, Lau K S and Yu Z G 2002 Phys. Rev. E 66 031910
|
[28] |
Yu Z G, Anh V V and Lau K S 2001 Phys. Rev. E 64 031903
|
[29] |
Yu Z G, Anh V V and Lau K S 2003 Int. J. Mod. Phys. B 17 4367
|
[30] |
Yu Z G, Anh V V and Lau K S 2003 J. Xiangtan Univ. (Natural Science Edition) 25(3) 131
|
[31] |
Wanliss J A, Anh V V, Yu Z G and Watson S 2005 J. Geophys. Res. 110 A 08214
|
[32] |
Anh V V, Yu Z G, Wanliss J A and Watson S M 2005 Nonlin. Processes Geophys. 12 799
|
[33] |
Yu Z G, Anh V V, Wanliss J A and Watson S M 2007 Chaos, Solitons and Fractals 31 736
|
[34] |
Hentschel H G E and Procaccia I 1983 Physica D 8 435
|
[35] |
Gutierrez J M, Iglesias A and Rodriguez M A 1998 Chaos and Noise in Biology and Medicine ed. Barbi M and Chillemi S (Singapore: World Scientific) pp.~315--319
|
[36] |
Gutierrez J M, Rodriguez M A and Abramson G 2001 Physica A 300 271
|
[37] |
Yu Z G, Anh V V, Lau K S and Zhou L Q 2006 Phys. Rev. E 63 031920
|
[38] |
Yang J Y, Yu Z G and Anh V V 2009 Chaos, Solitons and Fractals 40 607
|
[39] |
Barnley M F, Elton J H and Hardin D P 1989 Constr. Approx. B 5 3
|
[40] |
Halsy T, Jensen M, Kadanoff L, Procaccia I and Schraiman B 1986 Phys. Rev. A 33 1141
|
[41] |
Tel T, Fulop A and Vicsek T 1989 Physica A 159 155
|
[42] |
Canessa E 2000 J. Phys. A : Math. Gen. 33 3637
|
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