Ligand efficiency (LE) is one of the more controversial topics we cover at Practical Fragments. One critic asserted – incorrectly – that it is mathematically invalid. Another has stated that it is “not even wrong,” because the metric is predicated on standard state conditions and thus "arbitrary". (As he acknowledges, this also applies to the value and even the sign of the Gibbs free energy for a reaction.) A related metric that has received less attention is group efficiency (GE). In a paper just published in ChemMedChem, Chris Abell and colleagues at the University of Cambridge use this to help them optimize pantothenate synthetase (Pts) inhibitors.
Ligand efficiency is defined simply as the free energy of binding divided by the number of non-hydrogen, or “heavy” atoms (often abbreviated as HAC for heavy atom count) in the ligand. (Geek notes: although the binding energy is negative, LE is expressed as a positive number, so LE = - ΔG / HAC. Also, on Practical Fragments, units are assumed to be kcal mol-1 per heavy atom unless otherwise stated.)
Instead of focusing on a single ligand, group efficiency compares two ligands that differ by the presence or absence of a given group of atoms. To calculate GE, you simply subtract the ΔG values for the two ligands and divide by the number of heavy atoms in the group. For example, if you add a methyl group to your molecule and are lucky enough to get a 100-fold pop in potency, the methyl group has a group efficiency of 2.7 kcal mol-1 per heavy atom.
The current paper chronicles lead discovery for Pts, a potential target for tuberculosis. Previous screening efforts followed by fragment growing and fragment linking had generated low micromolar and high nanomolar inhibitors. The researchers turned to group efficiency to improve their molecules further.
As expected from ligand deconstruction studies (see for example here, here, and here), different portions of a molecule are likely to have vastly different group efficiencies. Indeed, this turned out to be the case here: the acetate moiety had high group efficiency, whereas the pyridyl moiety had lower group efficiency. Thus, the researchers set out to replace the pyridyl with ten diverse substituents. Happily, one of these improved the dissociation constant to 200 nM as assessed by isothermal titration calorimetry of the fully elaborated molecule. Compound 11 also showed reasonable enzyme inhibition in a functional assay.
One potential problem with group efficiency is that it assumes the molecules being compared bind in a similar fashion, which is not always a safe assumption. In this case, the researchers obtained a crystal structure of compound 11 bound to the enzyme, which not only revealed that it binds similarly to compound 5, but also suggested that inserting a methylene may improve binding. The resulting compound 20 showed better activity in the inhibition assay, as well as activity against M. tuberculosis in a cell assay (though unfortunately the dissociation constant was not reported).
This paper offers a clear illustration of how group efficiency can be useful for prioritizing which portions of a molecule to change. In some cases, such as the example here, it makes sense to try to replace groups with low group efficiency. On the other hand, the core fragment may bind in a hot spot, and so just a slight tweak can dramatically boost potency. As with lead optimization in general, there are many paths – both to enlightenment and to perdition.