Fig. 2. Two possible ways for large bound errors to occur during the design search.

A) When i_r is pairwise minimized with two different rotamers, j_s and k_t, the optimal position of i_r is different for the two pairwise interactions. When all three rotamers are minimized simultaneously, i_r cannot be in two places at once, so the globally optimal positioning of the rotamers is suboptimal with respect to the pairwise interactions. Therefore, the global minimum for all three rotamers is higher than the optimal pairwise minima. The shaded box represents the continuous voxel for continuous rotamer i_r. The colored dots show schematically the movement of the i_r rotamer within its voxel from its pairwise optimal positioning (with j_s, blue; with k_t, red) to its globally optimal positioning (green). B) Two rotamers, i_r and j_s, may minimize to the same real space position, but when minimized simultaneously protein sterics does not allow the rotamers to occupy the same Cartesian coordinates. As in A), the global minimum for all three rotamers is suboptimal relative to the pairwise bounds, resulting in a global minimum that is higher than the pairwise minima. The shaded boxes represent the continuous voxels for rotamers i_r and j_s. The colored dots show schematically the movement of the i_r and j_s rotamers within their voxel from their pairwise optimal positioning (blue and red) to their globally optimal positioning (green).