Calculation of protein conformations by proton-proton distance constraints. A new efficient algorithm.

We have developed a method to determine the three-dimensional structure of a protein molecule from such a set of distance constraints as can be determined by nuclear magnetic resonance studies. The currently popular methods for distance geometry based on the use of the metric matrix are applicable only to small systems. The method developed here is applicable to large molecules, such as proteins, with all atoms treated explicitly. This method works in the space of variable dihedral angles and determines a three-dimensional structure by minimization of a target function. We avoid difficulties hitherto inherent in this type of approach by two new devices: the use of variable target functions; and a method of rapid calculation of the gradient of the target functions. The method is applied to the determination of the structures of a small globular protein, bovine pancreatic trypsin inhibitor, from several artificial sets of distance constraints extracted from the X-ray crystal structure of this molecule. When a good set of constraints was available for both short- and long-range distances, the crystal structure was regenerated nearly exactly. When some ambiguities, such as those expected in experimental information, are allowed, the protein conformation can be determined up to a few local deformations. These ambiguities are mainly associated with the low resolving power of the short-range information.