Flexibility of bovine pancreatic trypsin inhibitor

The native conformation of a protein may be expressed in terms of the dihedral angles, phi's and psi's for the backbone, and kappa's for the side chains, for a given geometry (bond lengths and bond angles). We have developed a method to obtain the dihedral angles for a low-energy structure of a protein, starting with the X-ray structure; it is applied here to examine the degree of flexibility of bovine pancreatic trypsin inhibitor. Minimization of the total energy of the inhibitor (including nonbonded, electrostatic, torsional, hydrogen bonding, and disulfide loop energies) yields a conformation having a total energy of -221 kcal/mol and a root mean square deviation between all atoms of the computed and experimental structures of 0.63 A. The optimal conformation is not unique, however, there being at least two other conformations of low-energy (-222 and -220 kcal/mol), which resemble the experimental one (root mean square deviations of 0.66 and 0.64 A, respectively). These three conformations are located in different positions in phi, psi space, i.e., with a total deviation of 81 degrees, 100 degrees and 55 degrees from each other (with a root mean square deviation of several degrees per dihedral angle from each other). The nonbonded energies of the backbones, calculated along lines in phi, psi space connecting these three conformations, are all negative, without any intervening energy barriers (on an energy contour map in the phi, psi plane). Side chains were attached at several representative positions in this plane, and the total energy was minimized by varying the kappa's. The energies were of approximately the same magnitude as the previous ones, indicating that the conformation of low energy is flexible to some extent in a restricted region of phi, psi space. Interestingly, the difference delta phi i+1 in phi i+1 for the (i + 1)th residue from one conformation to another is approximately the same as -delta psi i for the ith residue; i.e., the plane of the peptide group between the ith and (i + 1)th residues re-orient without significant changes in the positions of the other atoms. The flexibility of the orientations of the planes of the peptide groups is probably coupled in a cooperative manner to the flexibility of the positions of the backbone and side-chain atoms.