Structural diversity of protein segments follows a power-law distribution

The local structures of protein segments were classified and their distribution was analyzed to explore the structural diversity of proteins. Representative proteins were divided into short segments using a sliding L-residue window. Each set of local structures consisting of consecutive 1-31 amino acids was classified using a single-pass clustering method. The results demonstrate that the local structures of proteins are very unevenly distributed in the protein universe. The distribution of local structures of relatively long segments shows a power-law behavior that is formulated well by Zipf's law, implying that a protein structure possesses recursive and fractal characteristics. The degree of effective conformational freedom per residue as well as the structure entropy per residue decreases gradually with an increasing value of L and then converges to constant values. This suggests that the number of protein conformations resides within the range between 1.2L and 1.5L and that 10- to 20-residue segments are already proteinlike in terms of their structural diversity.