The effect of end constraints on protein loop kinematics

Despite the prevalent involvement of loops in function little is known about how the constraining of end groups influences their kinematics. Using a linear inverse-kinematics approach and assuming fixed bond lengths, bond angles, and peptide bond torsions, as well as ignoring molecular interactions to assess the effect of the end-constraint only, it is shown that the constraint creates a closed surface in torsion angle space. For pentapeptides, the constraint gives rise to inaccessible regions in a Ramachandran plot. This complex and tightly curved surface produces interesting effects that may play a functional role. For example, a small change in one torsion angle can radically change the behavior of the whole loop. The constraint also produces long-range correlations, and structures exist where the correlation coefficient is 1.0 or -1.0 between rotations about bonds separated by >30 A. Another application allows some torsion angles to be targeted to specified values while others are constrained. When this application was used on key torsions in lactate dehydrogenase, it was found that the functional loop first folds forward and then moves sideways. For horse liver alcohol dehydrogenase, it was confirmed that the functional loop's Pro-Pro motif creates a rigid arm in an NAD-activated switch for domain closure.