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Updated: Jun 23, 2026

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
Published on: July 14, 2015
Residue network in protein native structure belongs to the universality class of a three-dimensional critical
Hidetoshi Morita1, Mitsunori Takano
1Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan. Hidetoshi.Morita@inln.cnrs.fr
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.
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