Why fragments?

Paramin panorama

Crystallographic fragment screens have been run recently against the main protease (at Diamond) and the Nsp3 macrodomain (at UCSF and Diamond) of SARS-Cov-2 and I thought that it might be of interest to take a closer look at why we screen fragments. Fragment-based lead discovery (FBLD) actually has origins in both crystallography [V1992 | A1996] and computational chemistry [M1991 | B1992 | E1994]. Measurement of affinity is important in fragment-to-lead work because it allows fragment-based structure-activity relationships to be established prior to structural elaboration. Affinity measurement is typically challenging when fragment binding has been detected using crystallography although affinity can be estimated by observation of the response of occupancy to concentration (the ∆G° value of −3.1 kcal/mol reported for binding of pyrazole to protein kinase B was derived in this manner).

Although fragment-based approaches to lead discovery are widely used, it is less clear why fragment-based lead discovery works as well as it appears to. While it has been stated that “fragment hits form high-quality interactions with the target”, the concept of interaction quality is not sufficiently well-defined to be useful in design. I ran a poll which asked about the strongest rationale for screening fragments.  The 65 votes were distributed as follows: ‘high ligand efficiency’ (23.1%), ‘enthalpy-driven binding’ (16.9%), ‘low molecular complexity’ (26.2%) and ‘God loves fragments’ (33.8%). I did not vote.

The belief is that fragments are especially ligand-efficient has many adherents in the drug discovery field and it has been asserted that “fragment hits typically possess high ‘ligand efficiency’ (binding affinity per heavy atom) and so are highly suitable for optimization into clinical candidates with good drug-like properties”. The fundamental problem with ligand efficiency (LE), as conventionally calculated, is that perception of efficiency varies with the arbitrary concentration unit in which affinity is expressed (have you ever wondered why Kd , Ki or IC50 has to be expressed in mole/litre for calculation of LE?). This would appear to be an rather undesirable characteristic for a design metric and LE evangelists might consider trying to explain why it’s not a problem rather than dismissing it as a “limitation” of the metric or trying to shift the burden of proof is onto the skeptics to show that the evangelists’ choice of concentration unit for calculation of LE is not useful.

The problems associated with the arbitrary nature of the concentration unit used to express affinity were first identified in 2009 and further discussed in 2014 and 2019. Specifically, it was noted that LE has a nontrivial dependency on the concentration,  C°, used to define the standard state. If you want to do solution thermodynamics with concentrations defined then you do need to specify a standard concentration. However, it is important to remember that the choice of standard concentration is necessarily arbitrary if the thermodynamic analysis is to be valid. If your conclusions change when you use a different definition of the standard state then you’ll no longer be doing thermodynamics and, as Pauli might have observed, you’ll not even be wrong. You probably don't know it, but when you use the LE metric, you’re making the sweeping assumption that all values of Kd, Ki and IC50 tend to a value of 1 M in the limit of zero molecular size. Recalling the conventional criticism of homeopathy, is there really a difference between a solute that is infinitely small and a solute that is infinitely dilute?

I think that’s enough flogging of inanimate equines for one blog post so let’s take a look at enthalpy-driven binding. My view of thermodynamic signature characterization in drug discovery is that it’s, in essence, a solution that’s desperately seeking a problem. In particular, there does not appear to be any physical basis for claims that the thermodynamic signature is a measure of interaction quality.  In case you’re thinking that I’m an unrepentant Luddite, I will concede that thermodynamic signatures could prove useful for validating physics-based models of molecular recognition and in, in specific cases, they may point to differences in binding mode within congeneric series. I should also stress that the modern isothermal calorimeter is an engineering marvel and I'd always want this option for label-free, affinity measurement in any project.

It is common to see statements in the thermodynamic signature literature to the effect that binding is ‘enthalpy-driven’ or ‘entropy-driven’ although it was noted in 2009 (coincidentally, in the same article that highlighted the nontrivial dependence of LE on C°) that these terms are not particularly meaningful. The problems start when you make comparisons between the numerical values of ∆H (which is independent of C°) and T∆S° (which depends on C°). If I’d presented such a comparison in physics class at high school (I was taught by the Holy Ghost Fathers in Port of Spain), I would have been caned with a ferocity reserved for those who’d dozed off in catechism class.  I’ll point you toward an article which asserts that, “when compared with many traditional druglike compounds, fragments bind more enthalpically to their protein targets”. I have a number of issues with this article although this is not the place for a comprehensive review (although I’ll probably pick it up in ‘The Nature of Lipophilic Efficiency’ when that gets written).

While I don’t believe that the authors have actually demonstrated that fragments bind more enthalpically than ligands of greater molecular size, I wouldn’t be surprised to discover that gains in affinity over the course of a fragment-to-lead (F2L) campaign had come more from entropy than enthalpy. First, the lost translation entropy (the component of ∆S° that endows it with its dependence on C°) is shared over greater number of intermolecular contacts for structurally-elaborated compounds and this article is relevant to the discussion. Second, I’d expect the entropy of any water molecule to increase when it is moved to bulk solvent from contact with molecular surface of ligand or target (regardless of polarity of the molecular surface at the point of contact). Nevertheless, this is something that you can test easily by examining the response of (∆H + T∆S°) to ∆G° (best to not to aggregate data for different targets and/or temperatures when analyzing isothermal titration calorimetry data in this manner). But even if F2L affinity gains were shown generally to come more from entropy than enthalpy, would that be a strong rationale for screening fragments?

This gets us onto molecular complexity and this article by Mike Hann and GSK colleagues should be considered essential reading for anybody thinking about selecting of compounds for screening. The Hann model is a conceptual framework for molecular complexity but it doesn’t provide much practical guidance as to how to measure complexity (this is not a criticism since the thought process should be more about frameworks and less about metrics). I don’t believe that it will prove possible to quantify molecular complexity in an objective manner that is useful for designing compound libraries (I will be delighted to be proven wrong on this point). The approach to handling molecular complexity that I’ve used in screening library design is to restrict extent of substitution (and other substructural features that can be considered to be associated with molecular complexity) and this is closer to ‘needle screening’ as described by Roche scientists in 2000 than to the Hann model.

Had I voted in the poll, ‘low molecular complexity’ would have got my vote.  Here’s what I said in NoLE (it’s got an entire section on fragment-based design and a practical suggestion for redefining ligand efficiency so that perception does not change with C°):

"I would argue that the rationale for screening fragments against targets of interest is actually based on two conjectures. First, chemical space can be covered most effectively by fragments because compounds of low molecular complexity [18, 21, 22] allow TIP [target interaction potential] to be explored [70,71,72,73,74] more efficiently and accurately. Second, a fragment that has been observed to bind to a target may be a better starting point for design than a higher affinity ligand whose greater molecular complexity prevents it from presenting molecular recognition elements to the target in an optimal manner."

To be fair, those who advocate the use of LE and thermodynamic signatures in fragment-based design do not deny the importance of molecular complexity. Let’s assume for the sake of argument that interaction quality can actually be defined and is quantified by the LE value and/or the thermodynamic signature for binding of compound to target. While these are massive assumptions, LE values and thermodynamic signatures are still effects rather than causes.

The last option for poll was ‘God loves fragments’ and more respondents (33.8%) voted for this than any of the first three options. I would interpret a vote for ‘God loves fragments’ in three ways. First, the respondent doesn’t consider any one of the first three options to be a stronger rationale for screening fragments than the other two. Second, the respondent doesn’t consider any of the first three options to be a valid rationale for screening fragments. Third, the respondent considers fragment-based approaches to have been over-sold.

This is a good place to wrap up. While I remain an enthusiast for fragment-based approaches to lead discovery, I do also believe that they have been somewhat oversold. The sensitivity of LE evangelists to criticism of their metric may stem from the use of LE to sell fragment-based methods to venture capitalists and, internally, to skeptical management. A shared (and serious) deficiency in the conventional ways in which LE and thermodynamic signature are quantified is that perception changes when the arbitrary concentration,  C°, that defines the standard state is changed. While there are ways in which this deficiency can be addressed for analysis, it is important that the deficiency be acknowledged if we are to move forward. Drug design is difficult and if we, as drug designers, embrace shaky science and flawed data analysis then those who fund our activities may conclude that the difficulties that we face are of our own making.     

Sailor Malan's guide to fragment screening library design

Today I'll take a look at a JMC Perspective on design principles for fragment libraries that is intended to provide advice for academics. When selecting compounds to be assayed the general process typically consists of two steps. First, you identify regions of chemical space that you hope will be relevant and then you sample these regions. This applies whether you're designing a fragment library, performing a virtual screen or selecting analogs of active compounds with which to develop structure-activity relationships (SAR). Design of compound libraries for fragment screening has actually been discussed extensively in the literature and the following selection of articles, some of which are devoted to the topic, may be useful: Fejzo (1999), Baurin (2004), Mercier (2005), Schuffenhauer (2005), Albert (2007) Blomberg (2009), Chen (2009), Law (2009), Lau (2011), Schulz (2011); Morley (2013). This series of blog posts ( 1 | 2 | 3 | 4) on fragment screening library design that may also be helpful.

The Perspective opens with the following quote:

"Rules are for the obedience of fools and the guidance of wise men"

Harry Day, Royal Air Force (1898-1977)

It wasn't exactly clear what the authors are getting at here since there appears to be no provision for wise women. Also it is not clear how the authors would view rules that required darker complexioned individuals to sit at the backs of buses (or that swarthy economists should not solve differential equations on planes). That said, the quote hands me a legitimate excuse to link Malan's Ten Rules for Air Fighting and I will demonstrate that the authors of this Perspective can learn much from the wise teachings of 'Sailor' Malan.

My first criticism of this Perspective is that the authors devote an inordinate amount of space to topics that are irrelevant from the viewpoint of selecting compounds for fragment screening. Whatever your views on the value of ligand efficiency metrics and thermodynamic signatures, these are things that you think about once you've got the screening results. The authors assert, "As a result, fragment hits form high-quality interactions with the target, usually a protein, despite being weak in potency" and some readers might consider the 'concept' of high-quality interactions to be pseudoscientific psychobabble on par with homeopathy, chemical-free food and the wrong type of snow. That said, discussion of some of these peripheral topics would have been more acceptable if the authors had articulated the library design problem clearly and discussed the most relevant literature early on. By straying from their stated objective, the authors have broken the second of Malan's rules ("Whilst shooting think of nothing else, brace the whole of your body: have both hands on the stick: concentrate on your ring sight").

The section on design principles for fragment libraries opens with a slightly gushing account of the Rule of 3 (Ro3). This is unfortunate because this would have been the best place for the authors to define the fragment library design problem and review the extensive literature on the subject. Ro3 was originally stated in a short communication and the analysis that forms its basis is not shared. As an aside, you need to be wary of rules like these because the cutoffs and thresholds may have been imposed arbitrarily by those analyzing the data. For example, the GSK 4/400 rule actually reflects the scheme used to categorize continuous data and it could just have easily been the GSK 3.75/412 rule if the data had been pre-processed differently. I have written a couple ( 1 | 2 ) of blog posts on Ro3 but I'll comment here so as to keep this post as self-contained as possible. In my view, Ro3 is a crude attempt to appeal to the herding instinct of drug discovery scientists by milking a sacred cow (Ro5). The uncertainties in hydrogen bond acceptor definitions and logP prediction algorithms mean that nobody knows exactly how others have applied Ro3. It also is somewhat ironic that the first article referenced by this Perspective actually states Ro3 incorrectly. If we assume that Ro5 hydrogen bond acceptor definitions are being used then Ro3 would appear to be an excellent way to ensure that potentially interesting acidic species such as tetrazoles and acylsulfonamides are excluded from fragment screening libraries. While this might not be too much of an issue if identification of adenine mimics is your principal raison d'etre, some researchers may wish to take a broader view of the scope of FBDD. It is even possible that rigid adherence to Ro3 may have led to the fragment starting points for this project being discovered in Gothenburg rather than Cambridge. Although it is difficult to make an objective assessment of the impact of Ro3 on industrial FBDD, its publication did prove to be manna from heaven for vendors of compounds who could now flog milligram quantities of samples that had previously been gathering dust in stock rooms.



This is a good point to see what 'Sailor' Malan might have made of this article. While dropping Ro3 propaganda leaflets, you broke rule 7 (Never fly straight and level for more than 30 seconds in the combat area) and provided an easy opportunity for an opponent to validate rule 10 (Go in quickly - Punch hard - Get out). Faster than you can say "thought leader" you've been bounced by an Me 109 flying out of the sun. A short, accurate (and ligand-efficient) burst leaves you pondering the lipophilicity of the mixture of glycol and oil that now obscures your windscreen. The good news is that you have been bettered by a top ace whose h index is quite a bit higher than yours. The bad news is that your cockpit canopy is stuck. "Spring chicken to shitehawk in one easy lesson."

Of course, there's a lot more to fragment screening library design than counting hydrogen bonding groups and setting cutoffs for molecular weight and predicted logP. Molecular complexity is one of the most important considerations when selecting compounds (fragments or otherwise) and anybody even contemplating compound library design needs to understand the model introduced by Hann and colleagues. This molecular complexity model is conceptually very important but it is not really a practical tool for selecting compounds. However, there are other ways to define molecular complexity in ways that allow the general concept to be distilled into usable compound selection criteria. For example, I've used restriction of extent of substitution (as detailed in this article) to control complexity and this can be achieved using SMARTS notation to impose substructural requirements. The thinking here is actually very close to the philosophy behind 'needle screening' which was first described in 2000 by researchers at Roche although they didn't actually use the term 'molecular complexity'.


As one would expect, the purging of unwholesome compounds such as PAINS is discussed. The PAINS field suffers from ambiguity, extrapolation and convolution of fact with opinion. This series ( 1 | 2 | 3 | 4) of blog posts will give you a better idea of my concerns. I say "ambiguity" because it's really difficult to know whether the basis for labeling a compound as a PAIN (or should that be a PAINS) is experimental observation, model-based prediction or opinion. I say "extrapolation" because the original PAINS study equates PAIN with frequent-hitter behavior in a panel of six AlphaScreen assays and this is extrapolated to pan-assay (which many would take to mean different types of assays) interference. There also seems to be a tendency to extrapolate the frequent-hitter behavior in the AlphaScreen panel to reactivity with protein although I am not aware that any of the compounds identified as PAINS in the original study were shown to react with any of the proteins in the AlphaScreen panel used in that study. This is a good point to include a graphic to break the text up a bit and, given an underlying theme of this post, I'll use this picture of a diving Stuka.

One view of the fragment screening mission is that we are trying to present diverse molecular recognition elements to targets of interest. In the context of screening library design, we tend to think of molecular recognition in terms of pharmacophores, shapes and scaffolds. Although you do need to keep lipophilicity and molecular size under tight control, the case can be made for including compounds that would usually be considered to be beyond norms of molecular good taste. In a fragment screening situation I would typically want to be in a position to present molecular recognition elements like naphthalene, biphenyl, adamantane and (especially after my time at CSIRO) cubane to target proteins. Keeping an eye on both molecular complexity and aqueous solubility, I'd select compounds with a single (probably cationic) substituent and I'd not let rules get in the way of molecular recognition criteria. In some ways compound selections like those above can be seen as compliance with Rule 8 (When diving to attack always leave a proportion of your formation above to act as top guard). However, I need to say something about sampling chemical space in order to make that connection a bit clearer.

This is a good point for another graphic and it's fair to say that the Stuka and the B-52 differed somewhat in their approaches to target engagement. The B-52 below is not in the best state of repair and, given that I took the photo in Hanoi, this is perhaps not totally surprising. The key to library design is coverage and former bombardier Joseph Heller makes an insightful comment on this topic. One wonders what First Lieutenant Minderbinder would have made of the licensing deals and mergers that make the pharma/biotech industry such an exciting place to work.  

The following graphic, pulled from an old post, illustrates coverage (and diversity) from the perspective of somebody designing a screening library.  Although I've shown the compounds in a 2 dimensional space, sampling is often done using molecular similarity which we can think of inversely related to distance. A high degree of molecular similarity between two compounds indicates that their molecular structures are nearby in chemical space.  This is a distance-geometric view of chemical space in which we know the relative positions of molecular structures but not where they are.  When we describe a selection of molecular structures as diverse, we're saying that the two most similar ones are relatively distant from each other. The primary objective of screening library design is to cover relevant chemical space as effectively as possible and devil is in the details like 'relevant' and 'effectively'. The stars in the graphic below show molecular structures that have been selected to cover the chemical space shown. When representing a number of molecular structures by a single molecular structure it is important, as it is in politics, that what is representative not be too distant from what is being represented. You might ask, "how far is acceptable?" and my response would be, as it often is in Brazil, "boa pergunta". One problem is scaffolds differ in their 'contributions' to molecular similarity and activity cliffs usually provide a welcome antidote to the hubris of the library designer.         

I would argue that property distributions are more important than cutoff values for properties and it is during the sampling phase of library design that these distributions are shaped. One way of controlling distributions is to first define regions of chemical space using progressively less restrictive selection criteria and then sample these in order, starting with the most restrictively defined region. However, this is not the only way to sample and might also try to weight fragment selection using desirability functions. Obviously, I'm not going to provide a comprehensive review of chemical space sampling in a couple of paragraphs of a blog post but I hope to have shown that the sampling of chemical space is an important aspect of fragment screening library design. I also hope to have shown that failing to address the issue of sampling relevant chemical space represents a serious deficiency of the featured Perspective. 

The Perspective concludes with a number of recommendations and I'll conclude the post with comments on some of these. I wouldn't have too much of a problem with the proposed 9 - 16 heavy atom range as a guideline although I would consider a requirement that predicted octanol/water logP be in the range 0.0 - 2.0 to be overly restrictive. It would have been useful for the authors to say how they arrived at these figures and I invite all of them to think very carefully about exactly what they mean by "cLogP" and "freely rotatable bonds" so we don't have a repeat of the Ro3 farce. There are many devils in the details of the statement:"avoid compounds/functional groups known to be associated with high reactivity, aggregation in solution, or false positives". My response to "known" is that it is not always easy to distinguish knowledge from opinion and "associated" (like correlated) is not a simple yes/no thing. It is not cleat how "synthetically accessible vectors for fragment growth" should be defined since there is also a conformational stability issue if bonds to hydrogen are regarded as growth vectors.   

This is a good point at which to wrap things up and I'd like to share some more of Sailor Malan's wisdom before I go. The first rule (Wait until you see the whites of his eyes. Fire short bursts of 1 to 2 seconds and only when your sights are definitely 'ON') is my personal favorite and it provides excellent, practical advice for anybody reviewing the scientific literature. I'll leave you with a short video in which a pre-Jackal Edward Fox displays marksmanship and escaping skills that would have served him well in the later movie. At the start of the video, the chemists and biologists have been bickering (of course, this never really happens in real life) and the VP for biophysics is trying to get them to toe the line. Then one of the biologists asks the VP for biophysics if they can do some phenotypic screening and you'll need to watch the video to see what happens next...

Molecular complexity in KL (Jan 2014)

I was in Kuala Lumpur about this time last year and visited International Medical University where I delivered a harangue.  It was a very enjoyable day and the lunch was excellent (as is inevitable in Malaysia where it seems impossible to find even mediocre food).  We discussed molecular complexity at lunch and, since a picture says a thousand words, I put the place mat to good use.

The upper limits of binding: Part 2

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Mel reviewed an important article on maximal affinity of ligands to kick off our sequence of posts on ligand efficiency. There are a number of reasons that this upper limit for potency might be observed and it's worth having a bit of think about them.

One interpretation of the upper limit is that it represents a validation of the molecular complexity concept. If a ligand makes many interactions with the protein they are less likely to be of ideal geometry. Hydrogen bonds between the binding partners and water are more likely to be of near-ideal geometry. Another factor that can impose limits on affinity is the finite size of a binding site. Once the site has been filled, increasing the size of the ligand does not lead to further increases in affinity because all the binding potential of the protein has already been exploited.

However, there is another reason that an upper limit for affinity might be observed and it has nothing to do with molecular complexity or fully exploited binding sites. Measuring very strong binding is not as easy as you might think it would be. In a conventional enzyme assay, you normally assume that the concentration of the ligand is much greater than that of the enzyme. This works well if you’ve got 10nM enzyme in the asaay and a micromolar ligand. However, things will get trickier if you’re trying to characterise a 10pM inhibitor since you’ll observe 50% inhibition of the enzyme for a 5nM concentration of the inhibitor. And you’ll see something very similar for a 1pM inhibitor…

This behaviour is well known and is called tight-binding inhibition. If you want to characterise very potent inhibitors you need reduce the concentration of the enzyme and be a bit more careful with the math. However, not everybody does this and I suspect that this may be one reason there appears to be an upper limit for affinity.

Literature cited

Kuntz et al, The maximal affinity of ligands. PNAS 1999, 96, 9997-10002. Link to free article.

Williams & Morrison, The kinetics of reversible tight-binding inhibition. Methods Enyzmol. 1979, 63, 437-467 DOI

Substituents and complexity

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In the previous post, I noted that two Astex kinase inhibitors were derived from fragments that lacked acyclic substituents. Dan points out that this is actually uncommon and wonders if this reflects a reluctance of medicinal chemists to work on fragments that were seen to be too simple.

The presence of certain molecular recognition elements, for example hydroxyl or carboxylate, implies that at least one acyclic substituent be present. I think this it probably the main reason that fragments are normally encountered with acyclic substituents. However, I do agree with Dan that some fragments can be seen as too simple and re-iterate my point that in the Brave New World of FBDD we really need to start seeing phenyl rings as synthetic handles.

A lack of acyclic substituents typically implies the presence of one or more polar atoms in a ring or spacer. When assembling screening libraries, I do try to select compounds that present heterocyclic molecular recognition elements without acyclic substituents (e.g. 4-phenypyrazole, 2-anilinopyrimidine). Interestingly compounds like these are not as easy to source as you might think.

Molecular complexity and extent of substitution

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Having introduced extent of substitution as a measure of molecular complexity in an earlier post, I was particularly interested by Dan's posts on AT7519 and AT9283. In each case, the screening hit used as a starting point for further elaboration lacked acyclic substituents.

You might wonder how you could impose this substructural requirement when selecting compounds for screening. This is actually very easy using SMARTS notation (Daylight SMARTS tutorial | OpenEye SMARTS pattern matching | SMARTS in wikipedia). The requirement that terminal non-hydrogen atoms be absent can be specified as:

[A;D1] 0

D1 indicates a non-hydrogen atom (A) that is connected to only one other non-hydrogen atom and 0 requires that these cannot be present in acceptable molecules. A requirement like this can be combined with a requirement for 10 to 20 non-hydrogen atoms:

* 10-20

I will discuss the use of SMARTS for compound selection in more detail in connection with design of screening libraries so think of this as a taster. I've also tried to keep things simple by assuming that hydrogen atoms are implicit which means that they are treated as a property of the atoms to which they are bonded rather than as atoms in their own right.

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