Cluster distance geometry of polypeptide chains

Distance geometry has been a broadly useful tool for dealing with conformational calculations. Customarily each atom is represented as a point, constraints on the distances between some atoms are obtained from experimental or theoretical sources, and then a random sampling of conformations can be calculated that are consistent with the constraints. Although these methods can be applied to small proteins having on the order of 1000 atoms, for some purposes it is advantageous to view the problem at lower resolution. Here distance geometry is generalized to deal with distances between sets of points. In the end, much of the same techniques produce a sampling of different configurations of these sets of points subject to distance constraints, but now the radii of gyration of the different sets play an important role. A simple example is given of how the packing constraints for polypeptide chains combine with loose distance constraints to give good calculated protein conformers at a very low resolution.