Reconciling Cooperativity Definition in PROTACs and Molecular Glues: Thermodynamic Dissection into PPI and Ligand Entropic Contributions

Douglass' Cooperativity α and Ciulli's Cooperativity α in induced-proximity systems, remains controversial with paradoxes such as path-dependent metrics and apparent universal negative Cooperativity. We noticed that in "partial-embedded" model, a substantial portion of giant ligand remains exposed outside and does not engage with the host protein's force field. It incurs an entropic cost due to the restriction of translational/rotational degrees of freedom. This large, mass-dependent unfavorable ligand entropy penalty normally shifts binding affinity to 104~108-fold. ITC thermodynamic cycles analysis confirmed the dramatic entropy loss among reaction pair. This reconciles the conflicting Cooperativity definitions, yielding true path-independent positive PPI Cooperativity from observed entropy loss subtracting ligand entropy penalty. ITC data showed rigid linkers appear superior to flexible linkers with respect to both oral bioavailability and safety profile in PROTAC design. "ligand entropy barrier wall/Cooperativity ladder"pair is not only impact induced-proximity systems but also constitute the physical basis for all biosystems.