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.

Is Structure-Based Drug Design Ready for Selectivity Optimization?

Alchemical free-energy calculations are now widely used to drive or maintain potency in small-molecule lead optimization with a roughly 1 kcal/mol accuracy. Despite this, the potential to use free-energy calculations to drive optimization of compound selectivity among two similar targets has been relatively unexplored in published studies. In the most optimistic scenario, the similarity of binding sites might lead to a fortuitous cancellation of errors and allow selectivity to be predicted more accurately than affinity. Here, we assess the accuracy with which selectivity can be predicted in the context of small-molecule kinase inhibitors, considering the very similar binding sites of human kinases CDK2 and CDK9 as well as another series of ligands attempting to achieve selectivity between the more distantly related kinases CDK2 and ERK2. Using a Bayesian analysis approach, we separate systematic from statistical errors and quantify the correlation in systematic errors between selectivity targets. We find that, in the CDK2/CDK9 case, a high correlation in systematic errors suggests that free-energy calculations can have significant impact in aiding chemists in achieving selectivity, while in more distantly related kinases (CDK2/ERK2), the correlation in systematic error suggests that fortuitous cancellation may even occur between systems that are not as closely related. In both cases, the correlation in systematic error suggests that longer simulations are beneficial to properly balance statistical error with systematic error to take full advantage of the increase in apparent free-energy calculation accuracy in selectivity prediction.