Cutoff variation induces different topological properties: a new discovery of amino acid network within protein.

An increasing attention has been dedicated to the characterization of complex networks within the protein world. Before now most investigations about protein structures were only considered where the interactive cutoff distance R(c)=5 or 7A. It is noteworthy that the length of peptide bond is about 1.5A, the length of hydrogen bond is about 3A, the range of London-van der Waals force is about 5A and the range of hydrophobic effect can reach to 12A in protein molecule. Present work reports a study on the topological properties of the amino acid network constructed by different interactions above. The results indicate that the small-world property of amino acid network constructed by the peptide and hydrogen bond, London-van der Waals force and the hydrophobic effect is strong, very strong and relatively weak, respectively. Besides, there exists a precise exponential relation C is proportional to k(-0.5) at R(c)=12A. It means that the amino acid network constructed by the hydrophobic effect tend to be hierarchical. Functional modules could be the cause for hierarchical modularity architecture in protein structures. This study on amino acid interactive network for different interactions facilitates the identification of binding sites which is strongly linked with protein function, and furthermore provides reasonable understanding of the underlying laws of evolution in genomics and proteomics.