Simulation for chaos game representation of genomes by recurrent iterated function systems

Affiliation(s)

School of Mathematics and Computational Science, Xiangtan University,Hunan 411105, China..

School of Mathematical Sciences, Queensland University of Technology,GPO Box 2434, Brisbane, Q 4001, Australia..

School of Mathematics and Computational Science, Xiangtan University,Hunan 411105, China..

School of Mathematical Sciences, Queensland University of Technology,GPO Box 2434, Brisbane, Q 4001, Australia..

ABSTRACT

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.

Cite this paper

nullYu, Z. , Shi, L. , Xiao, Q. and Anh, V. (2008) Simulation for chaos game representation of genomes by recurrent iterated function systems.*Journal of Biomedical Science and Engineering*, **1**, 44-51. doi: 10.4236/jbise.2008.11007.

nullYu, Z. , Shi, L. , Xiao, Q. and Anh, V. (2008) Simulation for chaos game representation of genomes by recurrent iterated function systems.

References

[1] J.S. Almeida, J.A. Carrico, A. Maretzek, P.A. Noble, M. Fletcher, “Analysis of genomic sequences by Chaos Game Representation”. Bioinformatics,17( 2001), pp 429-437.

[2] V.V. Anh, K.S. Lau, and Z.G. Yu, “Recognition of an organism from fragments of its complete genome”, Phys. Rev. E, 66 (2002), art. no..031910 , pp. 1-9.

[3] V.V. Anh, Z.G. Yu, J.A. Wanliss, and S.M. Watson, “Prediction of magnetic storm events using the Dst index”, Nonlin. Processes Geophys., 12 (2005), pp. 799-806.

[4] M.F. Barnley, J.H. Elton, and D.P. Hardin, “Recurrent iterated function systems”, Constr. Approx. B, 5 (1989), pp. 3-31.

[5] M.F. Barnsley, and S. Demko, “Iterated function systems and the global construction of fractals”, Proc. R. Soc. London, Ser. A, 399 (1985), pp. 243-275.

[6] S. Basu, A. Pan, C. Dutta and J. Das, “Chaos game representation of proteins”. J. Mol. Graphics and Modelling, 15 (1998), pp. 279-289.

[7] T.A. Brown, Genetics (3rd Edition). CHAPMAN & HALL,London, 1998.

[8] P.J. Deschavanne, A Giron, J. Vilain, G. Fagot and B. Fertil, “Genomics signature: Characterization and classification of species assessed by chaos game representation of sequences”. Mol. Biol. Evol. 16(1999), pp 1391-1399.

[9] K.A.Dill, “Theory for the folding and stability of globular Proteins”, Biochemistry, 24 (1985), pp. 1501-1509.

[10] K. Falconer, Techniques in Fractal Geometry, Wiley, 1997.

[11] A. Fiser, GE Tusnady and I. Simon, “Chaos game representation of protein structures”. J. Mol. Graphics, 12 (1994), pp. 302-304.

[12] N. Goldman, “Nucleotide, dinucleotide and trinucleotide frequencies explain patterns observed in chaos game representations of DNA sequences.

[13] H.J. Jeffrey, “Chaos game representation of gene structure”. Nucleic Acids Research, 18(8): (1990), pp. 2163-2170.

[14] J.Joseph, R. Sasikumar, “Chaos game representation for comparision of whole genomes”. BMC Bioinformatics, 7(2006), pp 243: 1-10.

[15] E.R. Vrscay, “Iterated function systems: theory, applications and inverse problem”, in: Fractal Geometry and Analysis, edited by: Belair, J. and Dubuc, S., Kluwer, Dordrecht, pp. 405-468, 1991.

[16] J. Wang and W. Wang, “Modeling study on the validity of a possibly simplified representation of proteins”, Phys. Rev. E, 61 (2000), pp. 6981-6986.

[17] J.A. Wanliss, V.V. Anh, Z.G. Yu, and S. Watson, “Multifractal modelling of magnetic storms via symbolic dynamics analysis”, J. Geophys. Res., 110 (2005), art. no. A08214, pp. 1-11,.

[18] Z.G. Yu, V.V. Anh, and K.S. Lau, “Measure representation and multifractal analysis of complete genomes”, Phys. Rev. E, 64 (2001), art. no. 031903, pp. 1-9,.

[19] Z.G. Yu, V.V. Anh, and K.S. Lau, “Iterated functionsystem and multifractal analysis of biological sequences”, International J. Modern Physics B, 17: (2003), pp. 4367-4375.

[20] Z.G. Yu, V.V. Anh, and K.S. Lau, “Fractal analysis of large proteins based on the Detailed HP model”, Physica A, 337 (2004a), pp. 171-184.

[21] Z.G. Yu, V.V. Anh, and K.S. Lau, “Chaos game representation, and multifractal and correlation analysis of protein sequences from complete genome based on detailed HP model”, J. Theor. Biol., 226(3) (2004b), pp..341-348.

[22] Z.G. Yu, V.V. Anh, , J.A. Wanliss and S.M. Watson, “Chaos game representation of the Dst index and prediction of geomagnetic storm events”, Chaos, Solitons & Fractals, 31 (2007), pp. 736-746,

[1] J.S. Almeida, J.A. Carrico, A. Maretzek, P.A. Noble, M. Fletcher, “Analysis of genomic sequences by Chaos Game Representation”. Bioinformatics,17( 2001), pp 429-437.

[2] V.V. Anh, K.S. Lau, and Z.G. Yu, “Recognition of an organism from fragments of its complete genome”, Phys. Rev. E, 66 (2002), art. no..031910 , pp. 1-9.

[3] V.V. Anh, Z.G. Yu, J.A. Wanliss, and S.M. Watson, “Prediction of magnetic storm events using the Dst index”, Nonlin. Processes Geophys., 12 (2005), pp. 799-806.

[4] M.F. Barnley, J.H. Elton, and D.P. Hardin, “Recurrent iterated function systems”, Constr. Approx. B, 5 (1989), pp. 3-31.

[5] M.F. Barnsley, and S. Demko, “Iterated function systems and the global construction of fractals”, Proc. R. Soc. London, Ser. A, 399 (1985), pp. 243-275.

[6] S. Basu, A. Pan, C. Dutta and J. Das, “Chaos game representation of proteins”. J. Mol. Graphics and Modelling, 15 (1998), pp. 279-289.

[7] T.A. Brown, Genetics (3rd Edition). CHAPMAN & HALL,London, 1998.

[8] P.J. Deschavanne, A Giron, J. Vilain, G. Fagot and B. Fertil, “Genomics signature: Characterization and classification of species assessed by chaos game representation of sequences”. Mol. Biol. Evol. 16(1999), pp 1391-1399.

[9] K.A.Dill, “Theory for the folding and stability of globular Proteins”, Biochemistry, 24 (1985), pp. 1501-1509.

[10] K. Falconer, Techniques in Fractal Geometry, Wiley, 1997.

[11] A. Fiser, GE Tusnady and I. Simon, “Chaos game representation of protein structures”. J. Mol. Graphics, 12 (1994), pp. 302-304.

[12] N. Goldman, “Nucleotide, dinucleotide and trinucleotide frequencies explain patterns observed in chaos game representations of DNA sequences.

[13] H.J. Jeffrey, “Chaos game representation of gene structure”. Nucleic Acids Research, 18(8): (1990), pp. 2163-2170.

[14] J.Joseph, R. Sasikumar, “Chaos game representation for comparision of whole genomes”. BMC Bioinformatics, 7(2006), pp 243: 1-10.

[15] E.R. Vrscay, “Iterated function systems: theory, applications and inverse problem”, in: Fractal Geometry and Analysis, edited by: Belair, J. and Dubuc, S., Kluwer, Dordrecht, pp. 405-468, 1991.

[16] J. Wang and W. Wang, “Modeling study on the validity of a possibly simplified representation of proteins”, Phys. Rev. E, 61 (2000), pp. 6981-6986.

[17] J.A. Wanliss, V.V. Anh, Z.G. Yu, and S. Watson, “Multifractal modelling of magnetic storms via symbolic dynamics analysis”, J. Geophys. Res., 110 (2005), art. no. A08214, pp. 1-11,.

[18] Z.G. Yu, V.V. Anh, and K.S. Lau, “Measure representation and multifractal analysis of complete genomes”, Phys. Rev. E, 64 (2001), art. no. 031903, pp. 1-9,.

[19] Z.G. Yu, V.V. Anh, and K.S. Lau, “Iterated functionsystem and multifractal analysis of biological sequences”, International J. Modern Physics B, 17: (2003), pp. 4367-4375.

[20] Z.G. Yu, V.V. Anh, and K.S. Lau, “Fractal analysis of large proteins based on the Detailed HP model”, Physica A, 337 (2004a), pp. 171-184.

[21] Z.G. Yu, V.V. Anh, and K.S. Lau, “Chaos game representation, and multifractal and correlation analysis of protein sequences from complete genome based on detailed HP model”, J. Theor. Biol., 226(3) (2004b), pp..341-348.

[22] Z.G. Yu, V.V. Anh, , J.A. Wanliss and S.M. Watson, “Chaos game representation of the Dst index and prediction of geomagnetic storm events”, Chaos, Solitons & Fractals, 31 (2007), pp. 736-746,