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It is well-known that many proteins fold into unique 3D structure (Anfinsen & Scheraga, 1975; Pain, 2000). The mechanisms by which an amino acid chain forms a complicated tertiary structure have been studied extensively (Sato et al,, 2006; Sato & Fersht, 2007; Sosnick & Barrick, 2011; Schaeffer & Daggett, 2011) but are still not understood in a comprehensive way (Bowman et al., 2011). It is well-recognized that all information on the 3D structure of a protein is coded in its amino acid sequence (Anfinsen & Scheraga, 1975; Pain, 2000). Hence we should be able to extract the information from the sequence. However, this is a significant, long-standing and unsolved problem in structural bioinformatics. Gross features of protein 3D structures or protein folds are characterized by some combination of secondary structural elements, and the ways of combination of secondary units are full of variety (Lesk, 2010). This situation does not allow us to construct a simple picture of the protein folding mechanisms. Among such a variety of protein folds, frequently appearing common folds, so-called superfolds (Orengo et al., 1994), are attractive targets for studying their folding mechanisms. The crucial point is that in general the fold of proteins tends to be more conservative than their sequences, i.e., sometimes proteins sharing the same fold show low sequence homology (Orengo et al., 1994; Jennings & Wright, 1993, Cavagnero et al., 1999; Nishimura et al., 2000). This fact implies the difficulty in approaching this problem using standard bioinformatics techniques such as multiple alignment techniques and so on.

Analyses of Sequences of (β/α) Barrel Proteins Based on the Inter-Residue Average Distance Statistics to Elucidate Folding Processes