Wavelet based fractal analysis of DNA sequences

被引:126
作者
Arneodo, A
dAubentonCarafa, Y
Bacry, E
Graves, PV
Muzy, JF
Thermes, C
机构
[1] CNRS, CTR GENET MOL, F-91198 GIF SUR YVETTE, FRANCE
[2] UNIV PARIS 07, UFR MATH, F-75251 PARIS 05, FRANCE
[3] INST BIOL & GENET CELLULAIRE, F-33077 BORDEAUX, FRANCE
关键词
wavelet transform; fractal scaling; multifractal formalism; fractional Brownian motions; DNA sequences;
D O I
10.1016/0167-2789(96)00029-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The fractal scaling properties of DNA sequences are analyzed using the wavelet transform. Mapping nucleotide sequences onto a ''DNA walk'' produces fractal landscapes that can be studied quantitatively by applying the so-called wavelet transform modulus maxima method. This method provides a natural generalization of the classical box-counting techniques to fractal signals, the wavelets playing the role of ''generalized oscillating boxes''. From the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima, this method allows us to determine the singularity spectrum of the considered signal and thereby to achieve a complete multifractal analysis, Moreover, by considering analyzing wavelets that make the ''wavelet transform microscope'' blind to ''patches'' of different nucleotide composition that are observed in mic sequences, we demonstrate and quantify the existence of long-range correlations in the noncoding regions. Although the fluctuations in the patchy landscape of the DNA walks reconstructed from both noncoding and (protein) coding regions are found homogeneous with Gaussian statistics, our wavelet-based analysis allows us to discriminate unambiguously between the fluctuations of the former which behave like fractional Brownian motions, from those of the latter which cannot be distinguished from uncorrelated random Brownian walks. We discuss the robustness of these results with respect to various legitimate codings of the DNA sequences, Finally, we comment about the possible understanding of the origin of the observed long-range correlations in noncoding DNA sequences in terms of the nonequilibrium dynamical processes that produce the ''isochore structure of the genome''.
引用
收藏
页码:291 / 320
页数:30
相关论文
共 147 条
  • [1] AHARONY A, 1989, PHYS D, V38
  • [2] ALLEGRINI P, IN PRESS
  • [3] [Anonymous], RANDOM FLUCTUATIONS
  • [4] HIGH-ORDER VELOCITY STRUCTURE FUNCTIONS IN TURBULENT SHEAR FLOWS
    ANSELMET, F
    GAGNE, Y
    HOPFINGER, EJ
    ANTONIA, RA
    [J]. JOURNAL OF FLUID MECHANICS, 1984, 140 (MAR) : 63 - 89
  • [5] WAVELET ANALYSIS OF TURBULENCE REVEALS THE MULTIFRACTAL NATURE OF THE RICHARDSON CASCADE
    ARGOUL, F
    ARNEODO, A
    GRASSEAU, G
    GAGNE, Y
    HOPFINGER, EJ
    FRISCH, U
    [J]. NATURE, 1989, 338 (6210) : 51 - 53
  • [6] WAVELET TRANSFORM OF FRACTAL AGGREGATES
    ARGOUL, F
    ARNEODO, A
    ELEZGARAY, J
    GRASSEAU, G
    MURENZI, R
    [J]. PHYSICS LETTERS A, 1989, 135 (6-7) : 327 - 336
  • [7] WAVELET ANALYSIS OF THE SELF-SIMILARITY OF DIFFUSION-LIMITED AGGREGATES AND ELECTRODEPOSITION CLUSTERS
    ARGOUL, F
    ARNEODO, A
    ELEZGARAY, J
    GRASSEAU, G
    [J]. PHYSICAL REVIEW A, 1990, 41 (10): : 5537 - 5560
  • [8] OSCILLATING SINGULARITIES IN LOCALLY SELF-SIMILAR FUNCTIONS
    ARNEODO, A
    BACRY, E
    MUZY, JF
    [J]. PHYSICAL REVIEW LETTERS, 1995, 74 (24) : 4823 - 4826
  • [9] BEYOND CLASSICAL MULTIFRACTAL ANALYSIS USING WAVELETS: UNCOVERING A MULTIPLICATIVE PROCESS HIDDEN IN THE GEOMETRICAL COMPLEXITY OF DIFFUSION LIMITED AGGREGATES
    Arneodo, A.
    Argoul, F.
    Muzy, J. F.
    Tabard, M.
    Bacry, E.
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 1993, 1 (03) : 629 - 649
  • [10] THE THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS
    ARNEODO, A
    BACRY, E
    MUZY, JF
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1995, 213 (1-2) : 232 - 275