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. For this reason, 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.Author summary: We present an algorithm that fits into existing protein design software that allows researchers to penalize unsatisfied polar atoms in protein structures during design. These polar atoms usually make hydrogen-bonds to other polar atoms or water molecules and the absence of such interactions leaves them unsatisfied energetically. Penalizing this condition is tricky because protein design software only looks at pairs of amino acids when considering which amino acids to choose. Current approaches to solve this problem use additive approaches where satisfaction or unsatisfaction is approximated on a continuous scale; however, in reality, satisfaction or unsatisfaction is an all-or-none condition. The simplest all-or-none method is to penalize polar atoms for simply existing and then to give a bonus any time they are satisfied. This fails when two different amino acids satisfy the same atom; the pairwise nature of the protein design software will double count the satisfaction bonus. Here we show that by anticipating the situation where two amino acids satisfy the same polar atom, we can apply a penalty to the two amino acids in advance and assume the polar atom will be there. This scheme correctly penalizes unsatisfied polar atoms and does not fall victim to overcounting.