A Universal Equation for Predicted Fold Improvement of Bivalent Inhibitor Binding Affinities

Monovalent small molecules traditionally inhibit proteins, but other proteins that have multiple shallow sites fail to do so. Several researchers have tethered two monovalents (called bivalents) targeting different shallow sites to increase the overall inhibitory potency. Bivalent molecules provide this potency gain through the tether which effectively concentrates the second ligand around the first. However, predicting the fold improvement in binding has proven challenging, specifically when the tethered monovalents feature differing dissociation constants (KDs). This work uses the reacted-site probability model to predict theoretical best fold improvements possible for heterodimeric bivalents. The model shows a correlation between the increase in tether lengths and the decrease in fold improvement from bivalents. Additionally, we found the fold improvement varies universally as the inverse root of both the KD and the cube of the full tether length. Maximum tether lengths to obtain at least a 10-fold improvement fall naturally out of this equation. Surprisingly long tethers are predicted to increase effective potencies significantly. Researchers can now determine the viability of their bivalent designs against shallow binding pockets.