A united‐residue force field for off‐lattice protein‐structure simulations. II. Parameterization of short‐range interactions and determination of weights of energy terms by Z‐score optimization

Continuing our work on the determination of an off‐lattice united‐residue force field for protein‐structure simulations, we determined and parameterized appropriate functional forms for the local‐interaction terms, corresponding to the rotation about the virtual bonds (U tor ), the bending of virtual‐bond angles (U b ), and the energy of different rotameric states of side chains (U rot ). These terms were determined by applying the Boltzmann principle to the distributions of virtual‐bond torsional and virtual‐bond angles and side‐chain rotameric states, respectively, calculated from a data base of 195 high‐resolution nonhomologous proteins. The complete energy function was constructed by combining the individual energy terms with appropriate weights. The weights were determined by optimizing the so‐called Z‐score value (which is the normalized difference between the energy of the native structure and the mean energy of non‐native structures) of the histidine‐containing phosphocarrier protein from Streptococcus faecalis (1PTF; an 88‐residue α + β protein). To accomplish this, a database of C α patterns was created using high‐resolution nonhomologous protein structures from the Protein Data Bank, and the distributions of energy components of 1PTF were obtained by threading its sequence through ∼500 randomly chosen C α ‐patterns from the X‐ray structures in the PDB, followed by energy minimization, with the energy function incorporating initially guessed weights. The resulting minimized energies were used to optimize the Z‐score value of 1PTF as a function of the weights of the various energy terms, and the new weights were used to generate new energy‐component distributions. The process was iterated, until the weights used to generate the distributions and the optimized weights were self‐consistent. The potential function with the weights of the various energy terms obtained by optimizing the Z‐score value for 1PTF was found to locate the native structures of other test proteins (within an average RMS deviation of 3 Å): calcium‐binding protein (4ICB), ubiquitin (1UBQ), α‐spectrin (1SHG), major cold‐shock protein (1MJC), and cytochrome b 5 (3B5C) (which included α and β structures) as distinctively lowest in energy in similar threading experiments. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 874–887, 1997