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We propose an automated protocol for designing the energy landscape of a protein energy function by optimizing its parameters. The parameters are optimized so that not only the global minimum-energy conformation becomes nativelike but also the conformations distinct from the native structure have higher energies than those close to the native structure. We classify low-energy conformations into three groups: supernative, nativelike, and non-native. The supernative conformations have all backbone dihedral angles fixed to their native values, and only their side chains are minimized with respect to energy. However, the nativelike and non-native conformations all correspond to the local minima of the energy function. These conformations are ranked according to their root-mean-square deviation (rmsd) of backbone coordinates from the native structure, and a fixed number of conformations with the smallest rmsd values are selected as nativelike conformations, whereas the rest are considered to be non-native conformations. We define two energy gaps E gap(1) and E gap (2) . The energy gap E gap (1) (E gap (2) ) is the energy difference between the lowest energy of the non-native conformations and the highest energy of the nativelike (supernative) conformations. The parameters are modified to decrease both E gap (1) and E gap (2) . In addition, the non-native conformations with larger rmsd values are made to have higher energies relative to those with smaller rmsd values. We successfully apply our protocol to the parameter optimization of the UNRES potential energy using the training set of betanova, 1fsd, the 36-residue subdomain of chicken villin headpiece (PDB ID 1vii), and the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd). The new protocol of the parameter optimization shows better performance than earlier methods where only the difference between the lowest energies of nativelike and non-native conformations was adjusted without considering various nativelike degrees of the conformations. We also perform jackknife tests on other proteins not included in the training set and obtain promising results. The results suggest that the parameters we obtained using the training set of the four proteins are transferable to other proteins to some extent.

Using action-derived molecular dynamics (ADMD), we study the dynamic folding pathway models of the Trp-cage protein by providing its sequential conformational changes from its initial disordered structure to the final native structure at atomic details. We find that the numbers of native contacts and native hydrogen bonds are highly correlated, implying that the native structure of Trp-cage is achieved through the concurrent formations of native contacts and native hydrogen bonds. In early stage, an unfolded state appears with partially formed native contacts (~40%) and native hydrogen bonds (~30%). Afterward, the folding is initiated by the contact of the side chain of Tyr3 with that of Trp6, together with the formation of the N-terminal α-helix. Then, the C-terminal polyproline structure docks onto the Trp6 and Tyr3 rings, resulting in the formations of the hydrophobic core of Trp-cage and its near-native state. Finally, the slow adjustment processes of the near-native states into the native structure are dominant in later stage. The ADMD results are in agreement with those of the experimental folding studies on Trp-cage and consistent with most of other computational studies.