Protein sequence optimization with a pairwise decomposable penalty for buried unsatisfied hydrogen bonds

In aqueous solution, polar groups make hydrogen bonds with water, and hence burial of such groups in the interior of a protein is unfavorable unless the loss of hydrogen bonds with water is compensated by formation of new ones with other protein groups. Hence, buried "unsatisfied" polar groups making no hydrogen bonds are very rare in proteins. Efficiently representing the energetic cost of unsatisfied hydrogen bonds with a pairwise-decomposable energy term during protein design is challenging since whether or not a group is satisfied depends on all of its neighbors. Here we describe a method for assigning a pairwise-decomposable energy to sidechain rotamers such that following combinatorial sidechain packing, buried unsaturated polar atoms are penalized. The penalty can be any quadratic function of the number of unsatisfied polar groups, and can be computed very rapidly. We show that inclusion of this term in Rosetta sidechain packing calculations substantially reduces the number of buried unsatisfied polar groups.