中国物理B ›› 2002, Vol. 11 ›› Issue (12): 1313-1318.doi: 10.1088/1009-1963/11/12/318

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Fractals in DNA sequence analysis

Vo Anh1, 喻祖国2, 龚志民3, 龙顺湖3   

  1. (1)Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia; (2)Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia; Department of Mathematics, Xiangtan University, Xiangtan 411105, China; (3)Department of Mathematics, Xiangtan University, Xiangtan 411105, China
  • 收稿日期:2002-05-26 修回日期:2002-07-28 出版日期:2002-12-12 发布日期:2005-06-12
  • 基金资助:
    Project supported partially by the Youth Foundation of National Natural Science Foundation of China (Grant No 10101022) and Postdoctoral Research Support Grant No 9900658 of Queensland University of Technology, Australia to Yu Zu-Guo and the Foundation of Province Educational Committee of Hunan (Grant No 99803) to Long Shun-Chao.

Fractals in DNA sequence analysis

Yu Zu-Guo (喻祖国)ab, Vo Anha,  Gong Zhi-Min (龚志民)b, Long Shun-Chao (龙顺湖)b   

  1. a Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia; b Department of Mathematics, Xiangtan University, Xiangtan 411105, China
  • Received:2002-05-26 Revised:2002-07-28 Online:2002-12-12 Published:2005-06-12
  • Supported by:
    Project supported partially by the Youth Foundation of National Natural Science Foundation of China (Grant No 10101022) and Postdoctoral Research Support Grant No 9900658 of Queensland University of Technology, Australia to Yu Zu-Guo and the Foundation of Province Educational Committee of Hunan (Grant No 99803) to Long Shun-Chao.

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摘要： Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance, and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view) to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.

Abstract: Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance, and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view) to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.

Key words: time series model, visual representation, multifractal analysis, DNA sequences

中图分类号:  (Nucleic acids)

  • 87.14.G-
36.20.Fz (Constitution (chains and sequences)) 87.15.Cc (Folding: thermodynamics, statistical mechanics, models, and pathways) 05.45.Df (Fractals) 02.30.Lt (Sequences, series, and summability)