Proteins with ID domains are optimized for allosteric coupling. (A) 3D plot showing all parameter combinations that generate a CR ≥ 0.10. A wide range of parameter combinations is sufficient to elicit a high response. The absence of points in the region marked minimal coupling indicates that although a wide range of parameter values can combine to produce a high CR, significant interaction energy (i.e., for this case, |Δgint| > ≈1.0 kcal/mol) is a prerequisite to coupling. All energies are in kcal/mol. The star and dashed red lines indicate those parameter values used to generate Fig. 1B, and solid red axes denote the origin. (B) Plot of the folding probability of the ligand A site (i.e., PN + P1) vs. the folding probability of the ligand B site (i.e., PN + P2) showing only those parameter combinations where the CR exceeds a specified response threshold. Three different response thresholds are shown: 0.07 (yellow), 0.10 (orange), and 0.15 (red). The maximum responses (dashed boxes) are observed in two regions. In region 1, domain I is unfolded and domain II is folded. Binding of ligand A folds domain I, but because of unfavorable domain coupling, domain II unfolds. In region II, both domains are unfolded. Binding of ligand A folds domain I, and as a result of favorable domain coupling, domain II folds.