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.

Looks can be deceiving: Getting misled by crystal structures – part 3

It’s been a while since we’ve touched on some of the hazards of interpreting crystal structures (see here, here, and here). In a recent issue of J. Comput. Aided Mol. Des., Alpeshkumar Malde and Alan Mark of the University of Queensland, Australia describe some mishaps taken from the literature, and how molecular modeling could have avoided them.

The authors start by noting that although protein structure determination using crystallography has been highly optimized, small molecule ligands are a different matter. Part of the problem is that small molecules may show more disorder than protein side chains, thus making it more challenging to fit the model into the observed electron density. Moreover, the parameters for refining protein structures do not always transfer to small molecules: electrostatic interactions are frequently ignored, as are alternative conformations.

As an example, the authors revisit the structure of noradrenochrome bound to an enzyme that synthesizes adrenaline. A racemic mixture of the ligand was used during crystallization, and when the crystal was solved at modest resolution it was possible to fit the ligand within the electron density in eight different orientations – four for each enantiomer. Despite this ambiguity, only a single structure was deposited in the protein data bank (pdb). Malde and Mark ran molecular dynamics (MD) simulations and free energy calculations and found that this structure is likely incorrect: it is higher energy than other structures and binds in a different orientation than the natural ligand, whose structure had previously been solved. In fact, the conformation suggested by MD is the opposite enantiomer from that deposited in the pdb and rotated 180 degrees.

In another example, the authors examine a high-resolution structure of a pyrazole-containing compound bound to the kinase CDK2. Pyrazoles can adopt two different tautomers in which the hydrogen is on either of two adjacent nitrogens, and in this particular case the original paper suggested that both tautomers were present in equal amounts, and both were deposited in the pdb. However, computations suggested that one tautomer is 7 kJ/mol higher energy than the other, and Malde and Mark suggest that in fact probably just a single tautomer is present in the structure.

Finally, the authors describe cases where a primary amide or primary sulfonamide group is in the wrong orientation. In most cases it is difficult to distinguish between a nitrogen and oxygen atom on the basis of electron density alone, and given that there are about 1000 ligands containing a -CONH2 group and about 200 containing a -SO2NH2 there are probably many mistakes.

The authors acknowledge that the examples they present are relatively simple, and one could argue that some of them would have been caught if they were critical structures in a lead optimization program. Nonetheless, the fact that they weren’t suggests that one must always be on guard, particularly in virtual screening where dozens or hundreds of structures are used in an automated fashion to develop or validate docking algorithms. Malde and Mark also note that, in the case of fragment screening with very small low-affinity ligands, one needs be especially cautious.

There is something extremely attractive about a crystal structure: it looks so real that it is easy to lose sight of the fact that it is just a model. Checking one’s assumptions with a bit of computation can prevent costly mistakes.