xLE: solving problems or missing the point?

Ligand efficiency (LE) has been discussed repeatedly and extensively on Practical Fragments, most recently in September. Two criticisms are its dependence on standard state and the observation that larger molecules frequently have lower ligand efficiencies than smaller molecules. In a just-published open-access ACS Med. Chem. Lett. paper, Hongtao Zhao proposes a new metric, xLE, to address these concerns.

 

LE is defined as the negative Gibbs free energy of binding (ΔG) divided by the number of non-hydrogen (or heavy) atoms, and of course ΔG is state-dependent. Standard state assumptions are 298K and 1M concentrations, choices that some people see as arbitrary since few biologically relevant molecules ever achieve concentrations near 1M. To remove the dependence on standard state, Zhao proposes to remove the translational entropy term of the unbound ligand from the free energy calculation.

 

Zhao also addresses the second criticism, that larger molecules often have lower ligand efficiencies. This phenomenon was observed in an (open-access) 1999 paper titled “the maximal affinity of ligands,” which found that, beyond a certain threshold, larger ligands do not have stronger affinities; there are very few femtomolar binders even among the largest small molecules. Thus, Zhao proposes attenuating the size dependence.

 

The new metric, xLE, is defined as follows:

 

xLE = (5.8 + 0.9*ln(M_w) – ΔG)/(a*N^α) - b

Where N is the number of non-hydrogen atoms, α is chosen to reduce size dependence, and a and b are “scaling variables.” He chooses α=0.2, a=10, and b=0.5, with little explanation.

 

To assess performance, Zhao examined nearly 14,000 measured affinities from PDBbind. When plotted by number of atoms, median affinity increased up to about 35 heavy atoms but then leveled off. Median LE values decreased sharply from 6 to 12 heavy atoms and then leveled off somewhere in the 20s. But median xLE values were consistent regardless of ligand size.

 

Zhao also examined LE and xLE changes for 175 successful fragment-to-lead studies from our annual series of J. Med. Chem. perspectives. LE decreased from fragment to lead for 48% of these, but xLE increased for all but a single pair.

 

And this, in my opinion, is a problem.

 

In the seminal 2004 paper, LE was proposed as "a simple ‘ready reckoner’, which could be used to assess the potential of a weak lead to be optimized into a potent, orally bio-available clinical candidate." The metric was particularly important before FBLD was widely accepted, when chemists were even less inclined to work on weak binders.

 

Here is the situation for which LE was devised. Imagine two molecules, compounds 1 and 2. The first has just 12 non-hydrogen atoms, a molecular weight of 160, and a modest 1 mM affinity for a target - similar to some fragments that have yielded clinical compounds. The second is much larger: 38 non-hydrogen atoms, a molecular weight of 500, and 10 µM affinity for the same target. Considering potency alone, compound 2 is the winner.

 

However, the LE for compound 1 is a respectable 0.34 kcal/mol/atom, while the LE for compound 2 is 0.18 kcal/mol/atom. So while a 10 µM HTS hit may initially look appealing, the LE suggests that this is an inefficient binder, and further optimization may require adding too much molecular weight to get to a desired low nanomolar affinity.

 

In contrast, the xLE values for both compounds are nearly identical, 0.38, and so this metric would not help a chemist prioritize which hit to pursue. In other words, xLE does not provide the insight for which LE was created. It might even lead to suboptimal choices. 

 

Moreover, unlike LE, xLE is non-intuitive. And finally, with three scaling or normalization factors, xLE is arguably even more arbitrary than a metric dependent on the widely-accepted definition of standard state.

 

Personally I find the practical applications of xLE limited, but I welcome your thoughts.