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

 

Molecular Complexity (follow up)

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Dan Erlanson, who needs no introduction in this forum, commented on the previous post. I have to agree with him that the Hann complexity model is not easy to apply in practice. It predicts that there will be an optimum level of complexity for a given assay system (detection technology + target) but doesn’t really tell us where a specific combination of molecule and assay system sits relative to the optimum.

Screening library design, as Dan correctly points out, involves striking a balance. One needs to think a bit about screening technology and the likely number of compounds that you’ll be screening. Another consideration is whether the screening library is generic or directed at specific targets or target families. I’m very interested in screening library design and expect to post on this topic in the future.

Dan notes that low complexity molecules often don’t find favour with medicinal chemists and I‘ve experienced this as well. Having structural information available gives us confidence to do something other than what a former MedChem colleague called ‘pretty vanilla chemistry’. Put another way, to make the most of the output from fragment screening, the medicinal chemist needs to be seeing a phenyl group as a synthetic handle

Molecular Complexity

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Molecular complexity is perhaps the single most important theoretical concept in fragment-based drug discovery (FBDD). The concept was first articulated in a 2001 article by Mike Hann at GSK and has implications that extend beyond FBDD. You might ask why I think that molecular complexity is so much more important than ligand efficiency and variations on that theme. My response is that the concept of molecular complexity helps us understand why fragment screening might be a good idea. Ligand efficiency is just a means with which to compare ligands with different potencies.

A complex molecule can potentially bind tightly to a target because it can form lots of interactions. Put another way, the complex molecule can present a number of diverse molecular recognition elements to a target. Sulfate anions and water molecules don’t have the same options although you’ll have ‘seen’ both binding to proteins if you’ve looked at enough crystal structures. There is a catch, however. The catch is that the complex molecule has to position all of those molecular recognition elements exactly where they are needed if that binding potential is to be realised.

Let’s take a look at Figure 3 from the article (the success landscape) in which three probabilities are plotted as a function of ligand complexity. The red line represents the probability of measuring binding assuming that the ligand uses all of its molecular recognition elements. This probability increases with complexity but can’t exceed 1. This tells us that if we just want to observe binding, nanomolar is likely to work just as well as picomolar. The green line is the really interesting one and it represents the probability of the ligand matching one way. It is this requirement for a one way match that gives this curve its maximum. Multiply the probability of a one way match by the probability of measuring binding and you get the probability of a useful event (yellow line) which also has a maximum. This tells us that there is an optimum complexity when you’re selecting compounds for your screening library. This optimum is a function of your assay system (i.e. target + detection technology) and improving your assay will shift the red line to the left.

This molecular complexity model is a somewhat abstract and it’s not easy to place an arbitrary molecule in Figure 3 for an arbitrary assay system. I’m not convinced of the importance of a unique binding mode for fragments because one fragment binding at two locations counts as two fragment hits. This is not a big deal because relaxing the requirement for unique binding leads gives a curve that decreases with complexity and we still end up with a maximum in the probability of a useful event.

I’ve used a different view of molecular complexity when designing compound libraries for fragment screening. This view is conceptually closer to ‘needle screening’ which was described by a group at Roche (11 authors, all with surnames in first half of the alphabet) in 2000. The needles are low molecular weight compounds which can ‘penetrate into deep and narrow channels and subpockets of active sites like a fine sharp needle probing the surface of an active site’. The needles are selected to be ‘devoid of an unnecessary structural elements’. My view of molecular complexity is that it increases with the extent to which a molecule is substituted. Substituents in molecules can be specified (and counted) using SMARTS notation so low complexity molecules can be identified by restricting the extent of substitution in addition to size. I’ve prepared a cartoon graphic which shows why you might want to do this.



This is a probably a good point to stop although it’s likely that I’ll return to this theme in future posts. Before that I’ll need to take a look at Ligand Efficiency…

Literature reviewed
Hann et al, J. Chem. Inf. Comput. Sci., 2001, 41, 856–864. | DOI
Boehm et al, J. Med. Chem. 2000, 43, 2664-2674. | DOI