Three-residue loop closure in proteins: A new kinematic method reveals a locus of connected loop conformations

The closure of a three-residue loop was studied using a developed kinematic method. It was shown that there are infinite number of three-residue loops (a locus of conformations), which can connect two segments of a polypeptide. This adds to the current understanding of a finite number of conformations for three-residue loop-closure. In the developed method, some of the equations can be solved analytically to reduce the computation cost. Benefiting from the reduced computation time, we determined all the relative positions of two polypeptide segments that can be connected by a three-residue loop.