Perverse trade-offs: the maximal enthalpy of ligands

Most readers of this blog are familiar with the concept of ligand efficiency:

LE = (free energy of ligand binding) / (number of heavy atoms)

The metric is easy to calculate, intuitive, and useful for evaluating fragments. Weirdly, as ligands get larger, the ligand efficiencies tend to decrease. This is a consequence of the fact that the maximal affinities of ligands also start to plateau as their sizes increase, a fact noted more than a decade ago by Kuntz and colleagues. The reason for this has never been satisfactorily explained, but the effect is so pronounced that some researchers have proposed alternatives to LE that take it into account, for example %LE and fit quality. In a paper published online in ACS Med. Chem. Lett., Charles Reynolds and M. Katherine Holloway have delved into the origins of declining LE with increasing size in more detail.

The researchers analyzed 102 ligand-protein complexes representing 14 target classes for which thermodynamic data had been collected using isothermal titration calorimetry (ITC). They calculated ligand efficiency as well as “enthalpy efficiency” and “entropy efficiency”, where enthalpy or entropy takes the place of free energy in the numerator. In the case of enthalpy efficiency, the trend was the same as for ligand efficiency: as molecules got larger, the enthalpy efficiencies tended to decrease. For entropy efficiencies, however, there was essentially no trend. In other words, the leveling out of binding energy is due to enthalpic effects more than to entropic effects. The authors suggest that:

The size effect on enthalpy is a result of increasing ligand complexity and the need to satisfy multiple geometric constraints simultaneously.

The findings thus provide further support for trying to identify fragments whose binding is largely enthalpically driven, but, as usual in the real world, things are not quite so easy. One of the frustrating things about medicinal chemistry is the phenomenon of enthalpy-entropy compensation: if you try to improve the enthalpy of binding, say by adding a hydrogen-bond acceptor, you may end up paying an entropic penalty such that overall binding increases only modestly, if at all. Indeed, the data in the paper show a very strong correlation between enthalpy and entropy: enthalpic binders tend to have negative (unfavorable) entropy, and the most entropic binders actually have positive (highly unfavorable) enthalpies of binding.

Worse, despite the striking correlation between enthalpy and entropy, there is almost no correlation between free energy of binding and enthalpy or entropy. The researchers suggest that these perverse trends (or lack thereof) explain why computational approaches to drug discovery are not more successful: most modeling relies on one or a few low-energy conformations, in effect ignoring entropy. However, there is a correlation between overall binding energy and enthalpy for certain targets, such as HIV protease and aldose reductase; perhaps such targets are more amenable to modeling.

In summary, the message seems to be that you should try to find enthalpic binders if you can, though the binding energetics may change unpredictably during optimization. For modelers, the research suggests that ignoring entropy is unwise. For medicinal chemists, I’m not sure how much of this is actionable, but sometimes it’s nice to know the origins behind the perversity of the universe.