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 IPTF 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 b₅ (3B5C) (which included α and β structures) as distinctively lowest in energy in similar threading experiments.