CALCULATION OF PROTEIN BACKBONE GEOMETRY FROM BETA-CARBON COORDINATESBASED ON PEPTIDE-GROUP DIPOLE ALIGNMENT

An algorithm is proposed for the conversion of a virtual-bond polypept ide chain (connected C(alpha) atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the pept ide groups of the backbone, while maintaining all of the backbone atom s in energetically feasible conformations. Hydrogen bonding is represe nted by aligning the peptide-group dipoles. These peptide groups are n ot contiguous in the amino acid sequence. The first dipoles to be alig ned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to op timize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable am ino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipole s are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is u sed to keep the geometry of the alpha-carbon trace of the resulting ba ckbone close to that of the input virtual-bond chain. This procedure i s sufficient to convert the virtual-bond chain to a real chain; in app lications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry result ing from the solution of the alignment equations. When applied to mode l alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone ge ometry characteristic of these alpha-helical and beta-sheet structures . Application to the alpha-carbon trace of the backbone of the crystal lographic 5PTI structure of bovine pancreatic trypsin inhibitor, follo wed by ECEPP/2 energy minimization with C(alpha)-distance constraints, led to a structure with almost as low energy and root mean square dev iation as the ECEPP/2 geometry analog of 5PTI, the best agreement betw een the crystal and reconstructed backbone being observed for the resi dues involved in the dipole-path network.