General Theory of Fragment Linking in Molecular Design: Why Fragment Linking Rarely Succeeds and How to Improve Outcomes.

Linking two fragments binding in nearby subpockets together has become an important technique in fragment-based drug discovery to optimize the binding potency of fragment hits. Despite the expected favorable translational and orientational entropic contribution to the binding free energy of the linked molecule, brute force enumeration of chemical linker for linking fragments is rarely successful, and the vast majority of linked molecules do not exhibit the expected gains of binding potency. In this paper, we examine the physical factors that contribute to the change of binding free energy from fragment linking and develop a method to rigorously calculate these different physical contributions. We find from these analyses that multiple confounding factors make successful fragment linking strategies rare, including (1) possible change of the binding mode of the fragments in the linked state compared to separate binding of the fragments, (2) unfavorable intramolecular strain energy of the bioactive conformation of the linked molecule, (3) unfavorable interaction between the linker and the protein, (4) favorable interaction energies between two fragments in solution when not chemically linked that offset the expected entropy loss for the formation of fragment pair, (5) complex compensating configurational entropic effects beyond the simplistic rotational and translational analysis. We here have applied a statistically mechanically rigorous approach to compute the fragment linking coefficients of 10 pharmaceutically interesting systems and quantify the contribution of each physical component to the binding free energy of the linked molecule. Based on these studies, we have found that the change in the relative configurational entropy of the two fragments in the protein binding pocket (a term neglected to our knowledge in all previous analyses) substantially offsets the favorable expected rotational and translational entropic contributions to the binding free energy of the linked molecule. This configurational restriction of the fragments in the binding pocket of the proteins is found to be, in our analysis, the dominant reason why most fragment linking strategies do not exhibit the expected gains of binding potency. These findings have further provided rich physical insights, which we expect should facilitate more successful fragment linking strategies to be formulated in the future.