Structural Diversity of Protein Segments Follows a Power- law Distribution

¹ National Institute of Advanced Industrial Science and Technology (AIST)

^* To whom correspondence should be addressed. E-mail: s.honda{at}aist.go.jp.

Submitted on October 26, 2005
Revised on January 6, 2006
Accepted on 9 May 2006

	Abstract

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 converge to constant values. This suggests that the number of protein conformations resides within the range between 1.2^L and 1.5^L and that 10~20-residue segments are already protein-like in terms of their structural diversity.

Key Words: Zipf's law, clustering, fractal, local structure, protein universe