Figure depicts how the induced PPIs are modulated by four types of geometric perturbations from the unique bound state shown in Figure . A ligand that causes a unary perturbation can lead to induced PPIs stronger or weaker than the intrinsic PPIs, depending on the respective strength of the unary and binary perturbation in Eq. . A "binary-perturbative" ligand does not influence the intramolecular geometry of individual proteins but alters the intermolecular geometry between two proteins to another binding pose. This induces new PPIs that must be weaker than the intrinsic PPIs. With a non-perturbative ligand, which binds at any surface of the two proteins without perturbing the energetically favorite binary state, induced PPIs are equal to the intrinsic PPIs. Lastly, a non-cooperative ligand that separates the two proteins back to the unbound state essentially reverses the binding process and leads to zero induced PPIs. Thus, non-perturbative and non-cooperative modulation of cooperativity become optimal solutions for proteins with negative and positive intrinsic PPIs without unary perturbation, respectively.