Does configurational entropy explain why fragment linking is so hard?
Linking two weak fragments to get a potent binder is something many of us hope for. Unfortunately, as a polltaken a few years back indicates, it often doesn’t work. But why? This is the question tackled by Lingle Wang and collaborators at Schrödinger and D. E. Shaw in a recent J. Chem. Theory Comput. paper.
When a ligand binds to a protein it pays a thermodynamic cost in terms of lost translational and orientational entropy. By linking two fragments, this cost is paid only once instead of twice. In theory this should lead to an improvement of 3.5-4.8 kcal/mol in binding energy, resulting in a 400-3000-fold improvement in affinity over what would be expected from simple additivity. As we noted here, this is possible, though rare. Linker strain often takes the blame as a primary villain. But is there more to the story?
The researchers computationally examined published examples of fragment linking (most of which we’ve covered on Practical Fragments) using free energy perturbation (FEP) to try to understand why the linked molecules bound more or less tightly than expected. Impressively, they were able to computationally reproduce experimentally derived numbers, and by building a thermodynamic cycle they could extract the various components of the “connection Gibbs free energy.” These included changes in binding mode or tautomerization, linker strain or linker interactions with the protein, and the previously mentioned entropic benefits of fragment linking.
The analysis also identified two additional components. If two fragments favorably interact with each other, covalently linking them may not give as much of a boost. This concept had been considered decades ago, though the current work provides a more general understanding.
The more important factor appears to be what the researchers refer to as “configurational entropy.” The notion is that even when a fragment is bound to a protein, both the ligand and protein retain considerable flexibility, which is entropically favorable. Linking two fragments reduces the configurational entropy of each component fragment, and the linked molecule binds less tightly than would be expected. The researchers argue that this previously unrecognized “unfavorable change in the relative configurational entropy of two fragments in the protein pocket upon linkage is the primary reason most fragment linking strategies fail.” They advise that maintaining a bit of flexibility in the linker can help, as has been previously suggested.
This is an interesting analysis, and explicitly considering configurational entropy is likely to improve our understanding of molecular interactions. But is it really the main barrier to successful fragment linking? The researchers explore only nine different protein-ligand systems, though they did consider multiple linked molecules for three of these (pantothenate synthetase, RPA, and LDHA). Still, these represent just a fraction of the 45 examples collected in a recent review, and they only considered one somewhat contrived case (avidin) in which especially strong superadditivity was observed. It will be interesting to see whether the analysis holds true for more examples of fragment linking.