Optimizing Physical Energy Functions for Protein Folding

We optimize a physical energy function for proteins with the use of the available structural database and perform three benchmark tests of the performance: (1) recognition of native structures in the background of predefined decoy sets of Levitt, (2) de novo structure prediction using fragment assembly sampling, and (3) molecular dynamics simulations. The energy parameter optimization is based on the energy landscape theory and uses a Monte Carlo search to find a set of parameters that seeks the largest ratio δE/ΔE for all proteins in a training set simultaneously. Here, δE_s is the stability gap between the native and the average in the denatured states and ΔE is the energy fluctuation among these states. Some of the energy parameters optimized are found to show significant correlation with experimentally observed quantities: (1) In the recognition test, the optimized function assigns the lowest energy to either the native or a near-native structure among many decoy structures for all the proteins studied. (2) Structure prediction with the fragment assembly sampling gives structure models with root mean square deviation less than 6 Å in one of the top five cluster centers for five of six proteins studied. (3) Structure prediction using molecular dynamics simulation gives poorer performance, implying the importance of having a more precise description of local structures. The physical energy function solely inferred from a structural database neither utilizes sequence information from the family of the target nor the outcome of the secondary structure prediction but can produce the correct native fold for many small proteins.