Residue network in protein native structure belongs to the universality class of a three-dimensional critical percolation cluster

Hidetoshi Morita, Mitsunori Takano

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    18 Citations (Scopus)

    Abstract

    Single protein molecules are regarded as contact networks of amino-acid residues. Relationships between the shortest path lengths and the numbers of residues within single molecules in the native structures are examined for various sized proteins. A universal scaling among proteins is obtained, which shows that the residue networks are fractal networks. This universal fractal network is characterized with three kinds of dimensions: the network topological dimension Dc ≈1.9, the fractal dimension Df ≈2.5, and the spectral dimension Ds ≈1.3. These values are in surprisingly good coincidence with those of the three-dimensional critical percolation cluster. Hence the residue contact networks in the protein native structures belong to the universality class of the three-dimensional percolation cluster. The criticality is relevant to the ambivalence in the protein native structures, the coexistence of stability and instability, both of which are necessary for protein functions.

    Original languageEnglish
    Article number020901
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume79
    Issue number2
    DOIs
    Publication statusPublished - 2009 Feb 2

    Fingerprint

    Protein Structure
    Universality
    proteins
    Three-dimensional
    Protein
    fractals
    Fractal
    Contact
    Spectral Dimension
    Path Length
    Criticality
    Coincidence
    Fractal Dimension
    Coexistence
    Shortest path
    amino acids
    Amino Acids
    Class
    molecules
    Molecules

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Statistics and Probability

    Cite this

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    abstract = "Single protein molecules are regarded as contact networks of amino-acid residues. Relationships between the shortest path lengths and the numbers of residues within single molecules in the native structures are examined for various sized proteins. A universal scaling among proteins is obtained, which shows that the residue networks are fractal networks. This universal fractal network is characterized with three kinds of dimensions: the network topological dimension Dc ≈1.9, the fractal dimension Df ≈2.5, and the spectral dimension Ds ≈1.3. These values are in surprisingly good coincidence with those of the three-dimensional critical percolation cluster. Hence the residue contact networks in the protein native structures belong to the universality class of the three-dimensional percolation cluster. The criticality is relevant to the ambivalence in the protein native structures, the coexistence of stability and instability, both of which are necessary for protein functions.",
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