Geometrical Description of Protein Structural Motifs

We present a geometrical method that can identify secondary structural motifs in proteins via angular correlations. The method uses crystal structure coordinates to calculate angular and radial signatures of each residue relative to an external reference point as the number of nearest-neighbor residues increases. We apply our approach to the blue copper protein amicyanin using the copper cofactor as the external reference point. We define a signature termed Δβ which describes the change in angular correlation as the span of nearest neighbor residues increases. We find that three turn regions of amicyanin harbor residues with Δβ near zero, while residues in other secondary structures have Δβ greater than zero: for β-strands, Δβ changes gradually residue by residue along the strand. Extension of our analysis to other blue copper proteins demonstrated that the noted structural trends are general. Importantly, our geometrical description of the folded protein accounts for all forces holding the structure together. Through this analysis, we identified some of the turns in amicyanin as symmetrical anchor points.