A UNITED-RESIDUE FORCE-FIELD FOR OFF-LATTICE PROTEIN-STRUCTURE SIMULATIONS .2. 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-resi due force field for protein-structure simulations, we determined and p arameterized appropriate functional forms for the local-interaction te rms, corresponding to the rotation about the virtual bonds (U-tor), th e bending of virtual-bond angles (U-b), and the energy of different ro tameric 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, res pectively, calculated from a data base of 195 high-resolution nonhomol ogous proteins. The complete energy function was constructed by combin ing the individual energy terms with appropriate weights. The weights were determined by optimizing the so-called Z-score value (which is th e 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-resid ue alpha + beta protein). To accomplish this, a database of C-alpha pa tterns was created using high-resolution nonhomologous protein structu res from the Protein Data Bank, and the distributions of energy compon ents of 1PTF were obtained by threading its sequence through similar t o 500 randomly chosen C-alpha-patterns from the X-ray structures in th e PDB, followed by energy minimization, with the energy function incor porating initially guessed weights. The resulting minimized energies w ere used to optimize the Z-score value of 1PTF as a function of the we ights of the various energy terms, and the new weights were used to ge nerate new energy-component distributions. The process was iterated, u ntil 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 f or 1PTF was found to locate the native structures of other test protei ns (within an average RMS deviation of 3 Angstrom): calcium-binding pr otein (4ICB), ubiquitin (1UBQ), alpha-spectrin (1SHG), major cold-shoc k protein (1MJC), and cytochrome b(5) (3B5C) (which included alpha and beta structures) as distinctively lowest in energy in similar threadi ng experiments. (C) 1997 by John Wiley & Sons, Inc.