Fractal Analysis of Proteins Based on Box Dimension

Proteins with rough surfaces and irregular structures are characteristic of fractal nature. Fractal dimensions of a set of 72 proteins including typical enzyme, globulin and membrane protein selected from PDB database were calculated based on the principle of intuitive box dimension. The results showed that fractal dimensions of proteins were between 1 and 3, and the more complicated structure a protein has, the larger value of fractal dimension the protein is, so the fractal theory could be used to quantitatively describe the complexity of proteins structure. The discordance between fractal dimensions and the number of residues demonstrated that proteins not only were composed of peptide chains, but also had the specifically spatial structure. The close D(f) values of the enzymes with similar function indicated that D(f), differed from a variety of macro-parameters, was a useful tool for the characterization of micro-structure and function of proteins.