A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: application to the UNRES force field.

A method for optimizing potential-energy functions of proteins is proposed. The method assumes a hierarchical structure of the energy landscape, which means that the energy decreases as the number of native-like elements in a structure increases, being lowest for structures from the native family and highest for structures with no native-like element. A level of the hierarchy is defined as a family of structures with the same number of native-like elements (or degree of native likeness). Optimization of a potential-energy function is aimed at achieving such a hierarchical structure of the energy landscape by forcing appropriate free-energy gaps between hierarchy levels to place their energies in ascending order. This procedure is different from methods developed thus far, in which the energy gap and/or the Z score between the native structure and all non-native structures are maximized, regardless of the degree of native likeness of the non-native structures. The advantage of this approach lies in reducing the number of structures with decreasing energy, which should ensure the searchability of the potential. The method was tested on two proteins, PDB ID codes and, with an off-lattice united-residue force field. For, the search of the conformational space with the use of the conformational space annealing method and the newly optimized potential-energy function found the native structure very quickly, as opposed to the potential-energy functions obtained by former optimization methods. After even incomplete optimization, the force field obtained by using located the native-like structures of two peptides, and betanova (a designed three-stranded beta-sheet peptide), as the lowest-energy conformations, whereas for the 46-residue N-terminal fragment of staphylococcal protein A, the native-like conformation was the second-lowest-energy conformation and had an energy 2 kcal/mol above that of the lowest-energy structure.