Comparing short protein substructures by a method based on backbone torsion angles

An efficient algorithm was characterized that determines the similarity in main chain conformation between short protein substructures. The algorithm computes delta t, the root mean square difference in phi and psi torsion angles over a small number of amino acids (typically 3-5). Using this algorithm, large numbers of protein substructure comparisons were feasible. The parameter delta t was sensitive to variations in local protein conformation, and it correlates with delta r, the root mean square deviation in atomic coordinates. Values for delta t were obtained that define similarity thresholds, which determine whether two substructures are considered structurally similar. To set a lower bound on the similarity threshold, we estimated the component of delta t due to measurement noise from comparisons of independently refined coordinates of the same protein. A sample distribution of delta t from nonhomologous protein comparisons identified an upper bound on the similarity threshold, one that refrains from incorporating large numbers of nonmatching comparisons. Unlike methods based on C alpha atoms alone, delta t was sensitive to rotations in the peptide plane, shown to occur in several proteins. Comparisons of homologous proteins by delta t showed that the active site torsion angles are highly conserved. The delta t method was applied to the alpha-chain of human hemoglobin, where it readily demonstrated the local differences in the structures of different ligation states.