Optimization of van der Waals energy for protein side-chain placement and design

Computational determination of optimal side-chain conformations in protein structures has been a long-standing and challenging problem. Solving this problem is important for many applications including homology modeling, protein docking, and for placing small molecule ligands on protein-binding sites. Programs available as of this writing are very fast and reasonably accurate, as measured by deviations of side-chain dihedral angles; however, often due to multiple atomic clashes, they produce structures with high positive energies. This is problematic in applications where the energy values are important, for example when placing small molecules in docking applications; the relatively small binding energy of the small molecule is drowned by the large energy due to atomic clashes that hampers finding the lowest energy state of the docked ligand. To address this we have developed an algorithm for generating a set of side-chain conformations that is dense enough that at least one of its members would have a root mean-square deviation of no more than R Å from any possible side-chain conformation of the amino acid. We call such a set a side-chain cover set of order R for the amino acid. The size of the set is constrained by the energy of the interaction of the side chain to the backbone atoms. Then, side-chain cover sets are used to optimize the conformation of the side chains given the coordinates of the backbone of a protein. The method we use is based on a variety of dead-end elimination methods and the recently discovered dynamic programming algorithm for this problem. This was implemented in a computer program called Octopus where we use side-chain cover sets with very small values for R, such as 0.1 Å, which ensures that for each amino-acid side chain the set contains a conformation with a root mean-square deviation of, at most, R from the optimal conformation. The side-chain dihedral-angle accuracy of the program is comparable to other implementations; however, it has the important advantage that the structures produced by the program have negative energies that are very close to the energies of the crystal structure for all tested proteins.