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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2009 Feb 2|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics