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Visualization and Fractal Analysis of Biological Sequences

  • Zu-Guo Yu
  • Vo Anhl
  • Yi-Ping Phoebe Chen

Keywords

Complete Genome Fractal Analysis Measure Representation Iterate Function System Biological Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Anfinsen, C. (1973) Principles that govern the folding of protein chains. Science 181: 223–230.Google Scholar
  2. Anh, V.V., Lau, K.S. and Yu, Z.G. (2001) Multifractal characterization of complete genomes. J. Phys. A: Math. Gene. 34: 7127–7139.MathSciNetGoogle Scholar
  3. Anh, V.V., Lau, K.S. and Yu, Z.G., (2002) Recognition of an organism from fragments of its complete genome, Phys. Rev. E 66: 031910.Google Scholar
  4. Balafas, J.S. and Dewey, T.G. (1995) Multifractal analysis of solvent accessibilities in proteins. Phys. Rev. E. 52: 880–887.Google Scholar
  5. Barnsley, M.F. and Demko, S. (1985) Iterated function systems and the global construction of Fractals. Proc. R. Soc. Lond. A 399: 243–275.MathSciNetGoogle Scholar
  6. Basu, S., Pan, A., Dutta, C. and Das, J. (1998) Chaos game representation of proteins. J. Mol. Graphics and Modeling 15: 279–289.Google Scholar
  7. Berthelsen, C.L., Glazier, J.A. and Skolnick, M.H. (1992) Global fractal dimension of human DNA sequences treated as pseudorandom walks. Phys. Rev. A 45: 8902–8913.Google Scholar
  8. Brown, T.A. (1998) Genetics (3rd Edition). CHAPMAN & HALL, LondonGoogle Scholar
  9. Buldyrev, S.V., Dokholyan, N.V., Goldberger, A.L., Havlin, S., Peng, C.K., Stanley, H.E. and Visvanathan, G.M. (1998) Analysis of DNA sequences using method of statistical physics. Physica A 249: 430–438.Google Scholar
  10. Buldyrev, S.V., Goldgerger, A.I., Havlin, S., Peng, C.K. and Stanley, H.E. (1994) in: Fractals in Science, Edited by A. Bunde and S. Havlin, Springer-verlag Berlin Heidelberg, Page 49–87.Google Scholar
  11. Canessa, E. (2000) Multifractality in time series. J. Phys. A: Math. Gene. 33: 3637–3651.MATHMathSciNetGoogle Scholar
  12. Chothia, C. (1992) One thousand families for the molecular biologists. Nature (London) 357: 543–544.CrossRefGoogle Scholar
  13. Dewey, T.G. (1993) Protein structure and polymer collapse. J. Chem. Phys. 98: 2250–2257.CrossRefGoogle Scholar
  14. Dill, K.A. (1985) Theory for the folding and stability of globular proteins, Biochemistry 24: 1501–1509.CrossRefGoogle Scholar
  15. Falconer, K.J. (1990) Fractal geometry: Mathematical foundations and applications. John wiley & sons LTD.Google Scholar
  16. Feder, J. (1988) Fractals. Plenum Press, New York, London..Google Scholar
  17. Fedorov, B.A., Fedorov, B.B. and Schmidt, P.W. (1993) An analysis of the fractal properties of the surfaces of globular proteins, J. Chem. Phys. 99: 4076–4083.CrossRefGoogle Scholar
  18. Fiser, A., Tusnady, G.E., Simon, I. (1994) Chaos game representation of protein structures. J. Mol. Graphics 12: 302–304.Google Scholar
  19. Fraser, C.M. et al. (1995) The minimal gene complement of Mycoplasma genitalium. Science 270: 397–404.Google Scholar
  20. Grassberger, P. and Procaccia, I. (1983) Characterization of strange attractors. Phys. Rev. Lett. 50: 346–349.CrossRefMathSciNetGoogle Scholar
  21. Halsy, T., Jensen, M., Kadanoff, L., Procaccia, I. and Schraiman, B. (1986) Fractal measures and their singularities: the characterization of strange sets. Phys. Rev. A 33: 1141–1151.Google Scholar
  22. Hao, B.L., Lee, H.C. and Zhang, S.Y. (2000) Fractals related to long DNA sequences and complete genomes. Chaos, Solitons and Fractals 11(6): 825–836.CrossRefGoogle Scholar
  23. Hao, B.L., Xie, H.M., Yu, Z.G. and Chen, G.Y. (2001) Factorizable language: from dynamics to bacterial complete genomes. Physica A 288: 10–20.MathSciNetGoogle Scholar
  24. Jeffrey, H.J. (1990) Chaos game representation of gene structure. Nucleic Acids Research 18(8): 2163–2170.Google Scholar
  25. Larhammar, D. and Chatzidimitriou-Dreismann, C.A. (1993) Biological origins of long-range correlations and compositional variations in DNA. Nucl. Acids Res. 21: 5167–5170.Google Scholar
  26. Lewis, M., Rees, D.C. (1985) Fractal Surface of Proteins. Science 230: 1163–1165.Google Scholar
  27. Li, H., Helling, R., Tang, C. and Wingreen, N.S. (1996) Emergence of Preferred Structures in a Simple Model of Protein Folding, Science 273: 666–669.Google Scholar
  28. Li, W.H. and Graur, D. (1991) Fundamental of Molecular Evolution. Sinauer Associates, Inc. Sunderland, Massachusetts.Google Scholar
  29. Lidar, D.A., Thirumalai, D., Elber, R. and Gerber, R.B. (1999) Fractal analysis of protein potential energy landscapes. Phys. Rev. E 59: 2231–2243.Google Scholar
  30. Luo, L., Lee, W., Jia, L., Ji, F. and Lu, T. (1998) Statistical correlation of nucleotides in a DNA sequence. Phy. Rev. E 58(1): 861–871.Google Scholar
  31. Luo, L. and Tsai, L. (1988) Fractal analysis of DNA walk. Chin. Phys. Lett. 5: 421–424.Google Scholar
  32. Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. W.H. Freeman, New York.Google Scholar
  33. Micheletti, C., Banavar, J.R., Maritan, A. and Seno, F. (1998) Steric Constraints in Model Proteins, Phys. Rev. Lett. 80: 5683–5686.Google Scholar
  34. Noonan, J. and Zeilberger, D. (1999) The Goulden-Jackson cluster method: extensions, applications and implementations, J. Difference Eq. Appl. 5, 355–377, http://www.math.rutgers.edu/~zeilberg/papers1.html.MathSciNetGoogle Scholar
  35. Pande, V.S., Grosberg, A.Y. and Tanaka, T. (1994) Nonrandomness in Protein Sequences: Evidence for a Physically Driven Stage of Evolution? Proc. Natl. Acad. Sci. USA 91: 12972–12975Google Scholar
  36. Peng, C.K., Buldyrev, S., Goldberg, A.L., Havlin, S., Sciortino, F., Simons, M. and Stanley, H.E. (1992) Long-range correlations in nucleotide sequences. Nature 356: 168–170.CrossRefGoogle Scholar
  37. Pfiefer, P., Welz, U. and Wipperman, H. (1985) Fractal surface dimension of proteins: Lysozyme. Chem. Phys. Lett. 2113: 535–540Google Scholar
  38. Prabhu, V.V. and Claverie, J.M. (1992) Correlations in intronless DNA. Nature 359: 782–782.CrossRefGoogle Scholar
  39. Qi, J., Wang, B. and Hao, B.L. (2004) Prokaryote phylogeny based on complete genomes—tree construction without sequence alignment. J. Mol. Evol. 58: 1–11.CrossRefGoogle Scholar
  40. Russell, R.B. (2000) Classification of Protein Folds, in Protein structure prediction: Methods and Protocls, Eds, D. Webster, Humana Press Inc., Totowa, NJ.Google Scholar
  41. Shih, C.T., Su, Z.Y., Gwan, J.F., Hao, B.L., Hsieh, C.H. and Lee, H.C. (2000) Mean-Field HP Model, Designability and Alpha-Helices in Protein Structures, Phys. Rev. Lett. 84(2): 386–389.CrossRefGoogle Scholar
  42. Shih, C.T., Su, Z.Y., Gwan, J.F., Hao, B.L., Hsieh, C.H., Lee, H.C. (2002) Geometric and statistical properties of the mean-field HP model, the LS model and real protein sequences. Phys. Rev. E 65: 041923.Google Scholar
  43. Strait, B.J. and Dewey, T.G. (1995) Multifractals and decoded walks: Applications to protein sequence correlations, Phys. Rev. E. 52: 6588–6592.Google Scholar
  44. Tino, P. (2001) Multifractal properties of Hao’s geometric representation of DNA sequences, Physica A 304: 480–494.MathSciNetGoogle Scholar
  45. Vrscay, E.R. (1991) Iterated function systems: theory, applications and the inverse problem, in Fractal Geometry and analysis, Eds, J. Belair, NATO ASI series, Kluwer Academic Publishers.Google Scholar
  46. Wang, B. and Yu, Z.G. (2000) One way to characterize the compact structures of lattice protein model. J. Chem. Phys. 112(13): 6084–6088CrossRefGoogle Scholar
  47. Wang, J. and Wang, W. (2000) Modeling study on the validity of a possibly simplified representation of proteins. Phys. Rev. E 61: 6981–6986.Google Scholar
  48. Xie, H.M. (1996) Grammatical Complexity and One-Dimensional Dynamical Systems. World Scientific, Singapore.Google Scholar
  49. Yu, Z.G., Anh, V.V. and Lau, K.S. (2001) Measure representation and multifractal analysis of complete genome. Phys. Rev. E 64: 031903.Google Scholar
  50. Yu, Z.G., Anh, V.V. and Lau, K.S. (2003) Multifractal and correlation analysis of protein sequences from complete genome. Phys. Rev. E 68: 021913.Google Scholar
  51. Yu, Z.G., Anh, V.V. and Lau, K.S. (2004) Fractal analysis of large proteins based on the Detailed HP model. Physica A (in press).Google Scholar
  52. Yu, Z.G., Hao, B.L., Xie, H.M. and Chen, G.Y. (2000) Dimension of fractals related to language defined by tagged strings in complete genome. Chaos, Solitons and Fractals 11(14): 2215–2222.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Hiedelberg 2005

Authors and Affiliations

  • Zu-Guo Yu
    • 1
    • 2
  • Vo Anhl
    • 3
    • 4
  • Yi-Ping Phoebe Chen
    • 3
    • 4
  1. 1.Program in Statistics and Operations ResearchQueensland University of TechnologyBrisbaneAustralia
  2. 2.School of Mathematics and Computing ScienceXiangtan UniversityHunanChina
  3. 3.School of Information Technology, Faculty of Science and TechnologyDeakin UniversityBurwoodAustralia
  4. 4.ARC Centre in BioinformaticsAustralia

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