title: Residue network in protein native structure belongs to the universality class of a three-dimensional critical percolation cluster.
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 D{c} approximately 1.9 , the fractal dimension D{f} approximately 2.5 , and the spectral dimension D{s} approximately 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.
authors.affiliation: Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan. Hidetoshi.Morita@inln.cnrs.fr
authors.forename: Hidetoshi
authors.initials: H
authors.lastname: Morita
authors.forename: Mitsunori
authors.initials: M
authors.lastname: Takano
mesh_terms: D000595:Amino Acid Sequence; D000596:Amino Acids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D008969:Molecular Sequence Data; D011487:Protein Conformation; D011506:Proteins / Q000737:chemistry*
chemical_list: D000596:Amino Acids; D011506:Proteins