Optimization of the UNRES Force Field by Hierarchical Design of the Potential-Energy Landscape. 2. Off-Lattice Tests of the Method with Single Proteins

We describe the application of our recently proposed method of hierarchical optimization of the protein energy landscape to optimize our off-lattice united-residue (UNRES) force field using single training proteins. First, the IgG-binding domain from streptococcal protein G (PDB code 1IGD) was treated; earlier attempts to use this protein to optimize the force field by optimizing the energy gap and Z score between the nativelike and non-native structures failed. The structure of this protein consists of an N-terminal antiparallel β-hairpin, a middle α-helix, and a C-terminal antiparallel β-hairpin, these elements being referred to as β 1 , α 2 , and β 3 , respectively, with the two hairpins forming a parallel β-sheet packed against the α-helix. In our earlier study, one of these elements was assumed to form at level 1, two at level 2, and three at level 3, and higher levels corresponded to the proper packing of two or more elements. This approach resulted in a structure with the wrong packing of the β-sheet, and attempts at further optimization failed. We therefore tried a hierarchy scheme that corresponds to the sequence of folding events deduced from NMR experiments. In this scheme, level I corresponds to structures with either β 3 or α 2 , level 2 to structures with both β 3 and α 2 , level 3 to structures with β 3 , α 2 , and the N-terminal strand packed against α 2 (with β 1 still not fully formed), and level 4 to structures with β 1 , α 2 , and β 3 , with β 3 being packed to β 1 , which also implies the packing of β 1 and β 3 against α 2 . This optimization was successful and resulted in a reasonably transferable force field that led to well-foldable proteins. This corroborates the conclusion from our model on-lattice studies (Liwo, A.; Arlukowicz, P.; Oldziej, S.; Czaplewski, C.; Makowski, M.; Scheraga, H. A. J. Phys. Chem. B 2004, 108, 16918) that a proper design of the structural hierarchy is of crucial importance to the foldability with the resulting potential-energy function. Moreover, in the off-lattice approach, the design of the hierarchy also appears to be important to the success of the optimization procedure itself. The next series of calculations was carried out with the LysM domain from the E. coli 1E0G (a + β) protein, which is smaller than 1IGD. In this case, no experimental information about the folding pathway is available; nevertheless, we were able to deduce the appropriate hierarchy by a trial-and-error method. The resulting force field performed worse in tests on a + β- and β-proteins than that derived on the basis of 1IGD with a correct hierarchy, which suggests that the structure of the I IGD protein encodes more structure-determining interactions common to all proteins than the 1E0G protein does. For 1E0G, we also attempted to carry out a single energy gap and Z-score optimization; this effort resulted in an unsearchable force field. (The nativelike structures could not be found by a global search, although they were the lowest in energy). Technical details of the method, including the maintenance of proper secondary structure and a method to classify structure, are also described.