Cooperative Free Energy: Induced Protein-Protein Interactions and Cooperative Solvation in Ternary Complexes.

Protein-protein interactions (PPIs) play an essential role in biological processes. Molecules that stabilize or induce PPIs in ternary complexes have received growing attention for their therapeutic potential in engaging "undruggable" targets and their high selectivity. Here, we investigate the thermodynamics of the cooperative phenomenon in ternary complexes. The thermodynamics of cooperativity are characterized by the cooperative free energy, which comprises induced PPIs, cooperative solvation free energy, ligand-associated geometric free-energy costs, and gas-phase correlation. Importantly, the induced PPIs only account for the binding affinity between stabilized conformations of the protein partners, i.e., the free-energy change associated with the conformational transition during protein-ligand binding is not accounted for. By introducing an approximated expression for the cooperative free energy, we developed a rapid computational method, which allowed us to crudely predict cooperativity in eight ternary complexes (Kendall τ = 0.79). We highlight that the term cooperativity used in protein-protein stabilization does not represent the cooperativity phenomenon in three-body systems. We also critically discuss the counterintuitive interpretation of cooperative free energy due to its asymmetric nature. Our study shows how cooperativity stabilizes ternary complexes and provides a thermodynamic basis of cooperativity in protein-ligand-protein complexes.