Optimization of Potential-Energy Parameters for Folding of Several Proteins

We introduce a novel approach to the study of the folding of proteins whose native structures are already known. We use an off-lattice atomistic potential energy. The parameters of the potential energy are simultaneously optimized for several proteins. The low-lying local-energy minima for these proteins are found by conformational space annealing. The parameters are modified in such a way that the native-like conformations are energetically more favored than the others. After the parameter optimization, one set of the parameters is obtained for the proteins. We then investigate Monte Carlo dynamics of these proteins by using this optimized potential energy. Our work is distinguished from earlier work in the literature, where folding was achieved by using simplified models such as lattice models. We apply our method to four proteins: betanova, 1fsd, 1vii, and 1bdd, and observe that at appropriate temperatures they fold into their native structure, starting from various non-native states. In all cases, rapid collapse is followed by a subsequent folding process, that takes place on a longer timescale. We also observe that for all proteins at low temperatures, the probability distributions of various quantities such as RMSD depend on initial conformations, showing their glassy behavior. At higher temperatures, this non-ergodic glassy behavior disappears. The results provide new insights into the folding mechanism, which is controlled not only by thermodynamic factors but also by kinetic factors. The way a protein folds into its native structure is also determined by the convergence point of early folding trajectories, which cannot be obtained from the free-energy surface.