Ligand Efficiency (or why size doesn't always matter)

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Ligand efficiency (LE), a term that has received a lot of attention recently in the drug discovery world, is defined generally as the binding energy of a ligand normalized by its size.   Being the avid bargain shopper that I am, the concept of LE excites me, similar to the thrill I get shopping at the sales after Christmas. And as a staunch advocate of FBDD, the idea of getting the most affinity bang for your chemical buck in general appeals to me. However, the definition of LE raises several questions, the obvious being what appropriate measures of binding energy and size are (more on this later).   But perhaps a larger nagging question, though, is why this metric is useful at all or, put more bluntly, aren't bigger molecules always better?  The first large scale study to address this question was published in 1999 by Kuntz et al, where they analyzed binding data for a set of metal ions, inhibitors, and ligands containing up to 68 heavy (i.e. non-hydrogen) atoms (HAs) [1].  The bulk of the results of this study are contained in Figure 1 from the paper, with free energy of binding, derived from both Ki and IC50 data, plotted against number of HAs.  From this plot a linear increase in binding free energy of -1.5 kcal/mol/HA is observed between molecules consisting of up to 15HAs, whereupon, strikingly, the gain in binding free energy with increased size becomes negligible.  Using a larger data set, this topic was revisited in a 2007 study published by Reynolds et al.  In their study [2] binding data for 8000 ligands and 28 protein targets were utilized to probe the relationship between molecular complexity and ligand efficiency. Using both pKi and pIC50 data, a linear relationship between affinity and size could not be established (Figures 1 and 2).  However, a trend was observed between the maximal affinity ligands and their size (Figure 3).  Starting with ligands containing roughly 10 HAs, an exponential increase in affinity was observed for ligands up to 25 HA in size but, similarly to the Kuntz study, affinity values plateaued after 25 HA.  The authors then plotted LE values, calculated as either pKi/HA or pIC50/HA, against HA to show that LE values decline drastically between 10 and 25 HA (Figures 4 and 5). Since LE values are demonstrably higher on average for smaller molecules, the authors warn against using LE values to compare compounds of disparate sizes.  For such purposes they propose a 'fit quality' (FQ) metric, where LE values are normalized by a scaled value that takes size into account.  

 The logical question that arises from these studies is why do we see a precipitous decline in affinity gains after a certain molecular size?  Since ligand binding affinity is attributed largely to van der Waal interactions, larger molecules should exhibit higher affinities.  In the Kuntz study they conjecture that their findings may be attributable to non-thermodynamic effects.  In particular, the use of tight-binding high molecular weight compounds may be selected against in the pharmaceutical community for pharmacokinetic and/or pharmacodynamic considerations, resulting in a lack of these molecules in their sample set.  Entropic penalties and molecular complexity arguments also come into play here.  The authors of the 2007 study note in their discussion that the surface area of a ligand available for interaction and its heavy atom count are not correlated, suggesting that the definition of size itself may be overly simplistic.  

So, what are the implications of LE in fragment-based drug design? Expounding on the 2007 study discussed above, where fragment-sized molecules exhibited significantly increased LE values as compared to larger molecules, a new study published by the same authors [3] looked closer at the purported advantages of using fragments as starting points for lead generation.  In this study LE and fit quality values of starting fragments and optimized leads for a variety of targets were analyzed (Table 1).  Interestingly, while LE values fall off as expected with an increase in size, fit quality values remain steady or improve, suggesting that optimization from fragment leads may be more efficient.  That said, the data presented in this study is limited and should be compared to leads generated via HTS campaigns or other strategies for more validity.  Let's hope the new year brings us such studies.

Literature cited:

1.Kuntz ID, Chen K, Sharp KA, Kollman PA. The maximal affinity of ligands. PNAS 1999 96:9997-10002. Link to free article.

2.Reynolds CH, Bembenek SD, Touge BA. The role of molecular size in ligand efficiency. Bioorg Med Chem Lett. 2007 17(15):4258-61. DOI

3. Bembenek SD, Touge BA, Reynolds CH. Ligand efficiency and fragment-based drug discovery. Drug Discov Today. In press.  DOI