The hydrophobic moment detects periodicity in protein hydrophobicity

Periodicities in the polar/apolar character of the amino acid sequence of a protein can be examined by assigning to each residue a numerical hydrophobicity and searching for periodicity in the resulting one-dimensional function. The strength of each periodic component is the quantity that has been termed the hydrophobic moment. When proteins of known three-dimensional structure are examined, it is found that sequences that form alpha helices tend to have, on average, a strong periodicity in the hydrophobicity of 3.6 residues, the period of the alpha helix. Similarly, many sequences that form strands of beta sheets tend to have a periodicity in their hydrophobicity of about 2.3 residues, the period typical of beta structure. Also, the few sequences known to form 3(10) helices display a periodicity of about 2.5 residues, not far from the period of 3 for an ideal 3(10) helix. This means that many protein sequences tend to form the periodic structure that maximizes their amphiphilicity. This observation suggests that the periodicity of the hydrophobicity of the protein primary structure is a factor in the formation of secondary structures. Moreover, the observation that many protein sequences tend to form segments of maximum amphiphilicity suggests that segments of secondary structure fold at a hydrophobic surface, probably formed from other parts of the folding protein.