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.     

Reviewing the reviewers

I recently published The Nature of Ligand Efficiency (NoLE) as a ChemRxiv preprint and this was featured (for all the right reasons) in a post at In The Pipeline. The material had been previously submitted to J Med Chem but it proved a bit too spicy for two of the three reviewers. I'll review the J Med Chem reviewers in this blog post and I hope that the feedback will be useful in the event of the journal being presented with similarly flavored material in the future. NoLE was my second publication from Berwick-on-Sea in the village of Blanchisseuse on the north coast of my native Trinidad and I'll include some photos from there to break up the text a bit.

Gate at Berwick-on-Sea in Blanchisseuse. The house was built (quite literally) by my late father (who would have been 89 today) and was named for my mother's home town of Berwick-upon-Tweed which has changed hands between England and Scotland on a number of occasions and may even still be at war with Imperial Russia.

The selection of reviewers for manuscripts that criticize previous studies presents a dilemma for journal editors. While it is prudent to consult those with a stake in what is being criticized, these may not the best people to ask about whether or not the criticism should be made. In particular, a reviewer using his/her position as a reviewer to suppress criticism of something in which he/she has a stake raises ethical questions. A stake in ligand efficiency (LE) could take any of a number of forms. First, one could have introduced a metric for LE. Second, one could have written articles endorsing ligand efficiency metrics or asserting their validity. Third, one could have enthusiastically promoted the LE metric at one's institution (e.g. by mandating that LE values be quoted when presenting project updates at the dog and pony shows that are an essential part of modern drug discovery). Fourth, one might be a devout member of the Fragment Cult (for whom the Doctrinal Correctness of LE is an Article of Faith).

There were three reviewers for my manuscript and I'll call them A, B and C since their numbers got scrambled between different rounds of review (also using the term 'Reviewer 3' might give some readers anxiety attacks). Reviewer A had nothing constructive to say and simply spat feathers. Reviewer B was very positive about the manuscript and made a number of  helpful suggestions. Reviewer C demanded that the manuscript be watered down to homeopathic levels (and that was never going to happen).

Here's my office at Berwick-on-Sea. That's a printout of NoLE on my desk (under the hanging beach towel).

The central theme of my manuscript is the argument that ligand efficiency is physically meaningless because perception of efficiency changes with the concentration unit in which affinity is expressed. This is actually a very serious criticism since since a change in perception resulting from a change in a unit would normally be regarded in physical science as an error in the "not even wrong" category.  It's not something that one can simply sweep under the carpet as a "limitation" of ligand efficiency. Despite their howls of protest, neither Reviewer A nor Reviewer C offered coherent counter-argument.

The tactic adopted by Reviewer C was to simply dismiss the physical arguments presented in the manuscript as "opinion" without presenting counter-argument. J Med Chem really does need to make it clear to reviewers that they need to do much better than this since it reflects badly on the journal.

Reviewer C. "'Physically meaningless' is at best an inflammatory opinion whereas the fact that other choices could have been made is often under-appreciated."

PWK. This criticism appears to be doctrinal rather than scientific and I note that Reviewer C has not offered counter-argument to the argument that LE is physically meaningless.

Here's a view of the Caribbean Sea. The 20 m drop from the gap in the vegetation is just as precipitous as you would expect although we've not (yet) lost any personnel or household pets over the edge.

Reviewer A struggled woefully with rudimentary physical chemistry throughout the review process and, given that I'd suggested a number of potential reviewers with the necessary expertise in molecular recognition and chemical thermodynamics, I was at a loss to understand why a reviewer who was so ill-equipped for the task at hand had been invited to review the manuscript.

Reviewer A. Reactions are considered to be spontaneous under standard conditions when the free energy is negative, but by changing the definition of C° in an arbitrary manner, any reaction can be said to be spontaneous or not. This is true in a trivial sense, but generations of researchers have found the concept of negative or positive free energies useful.

PWK. The flaw in this argument is that if you change the value of C° then you also change whether or not the reaction is spontaneous under the standard conditions. This is the basis of the law of mass action and it is also important to remember that KD values are not measured at single concentration. A chemical process (at constant temperature and pressure) by which the system changes from state A to state B will be spontaneous if DG[A®B]  is negative. Regardless of experiences of generations of researchers, medicinal chemists rarely (if ever) appear to use the sign of  DG  (e.g. for binding under assay conditions) when analyzing SAR or for making any other decisions.

This is the start to the path down to the lower deck

In one round of review, Reviewer C stated “I believe that it is incumbent on the author to argue that the choice of standard state used by medicinal chemists is not useful” and Reviewer A repeated the criticism in a subsequent round, noting that this was "the central problem with the manuscript". I thought this was a bit rich given that Reviewer A and Reviewer C had each accused me of using straw man tactics at different points in the review process. The more serious problem, however, is that we have two LE advocates each attempting to to transfer the burden of proof that (in science) one accepts as soon as one advocates that people take an action (e.g. use LE metrics). Reviewers A and C appeared to do this in order to evade their responsibility as reviewers to present counter-argument to the arguments in the manuscript. This would be like a thought leader (yes, there really are people who call themselves 'thought leaders') responding to criticism of a claim that AI was going to transform drug discovery by saying that it was incumbent on the critics to argue that AI was not useful. Imagine if they ran clinical trials like this?

At this point, Reviewer A did rather lose it and I was half expecting to have to fend off a counterattack by Steiner's division. Needless to say, the latest version of the manuscript now opens with "Ligand efficiency (LE) is, in essence, a good concept that is poorly served by a bad metric." and this can be considered the equivalent of a two-fingered gesture that is mistakenly attributed to the English and Welsh longbowmen at Agincourt.

Reviewer A. Dr. Kenny dodges this challenge by stating that the burden of proof should not be on him, but by arguing that LE is a “bad metric” despite its wide usage, he does in fact have to explain why free energy is also a “bad” concept. Not doing so makes the manuscript deeply misleading and therefore inappropriate for publication.

PWK. I only used the term “bad metric” in the conclusions where I wrote “Ligand efficiency is, in essence, a good concept served by a bad metric.” so it is incorrect to state that I have argued that LE is a “bad metric”. In any case, in the revised manuscript, I now question whether LE can accurately be described as a metric since neither its creators nor its advocates appear able (or willing) to say what it measures. Wide usage does not validate rules, guidelines or metrics and I note that, at one time, the prevailing view was that the sun orbited the earth. Once again, Reviewer A is making the serious error of assuming that everything that applies to free energy also applies to any function of free energy. The simple counter to Reviewer A’s challenge is that free energy is a state function and an integral part of the framework of thermodynamics. Although defined in terms of free energy, the LE metric is not is part of thermodynamics simply because it appears to require a privileged standard state.

I have occasionally stated that "useful is the last refuge of the scoundrel" and this tends to be misinterpreted as an assertion that utility of a model is unimportant. Nothing could actually be further from the truth and the statement is more a comment on the way that models can be 'validated' by simply labeling them as "useful". In some ways "useful" is analogous to the "God created it that way" statements that you will encounter if you are careless enough to become ensnared in arguments with Creationists. I should also point out that the manuscript did discuss the difficulties of demonstrating the utility of LE while neither A nor C presented any evidence (fervent belief does not usually constitute evidence in science) to support their assertion that the 1 M standard state is more useful than any other standard state.

Reviewer A appeared particularly aggrieved that one of The Great Unwashed should have the temerity to even question the value of LE and the toys were duly ejected from the pram. As my response below indicates, Reviewer A's comment is more what one might have expected from an inquisitor at a fifteenth century heresy trial than from an expert reviewer of a manuscript submitted to the premier medicinal chemistry journal. It is also worth pointing out that LE was touted as "useful" even as it was introduced in a 2004 letter to Drug Discovery Today and all three coauthors of that seminal contribution to the medicinal chemistry literature appeared to be blissfully unaware of the nontrivial dependency of their creation on the standard concentration. As such, I would argue that it would actually be a dereliction of duty not to question the utility of LE.

Reviewer A. Sixth, Dr. Kenny repeatedly questions the utility of LE; for example “The LE metric is claimed by advocates to be useful although it is rarely, if ever, shown to be predictive of pharmaceutically-relevant behavior” (p. 15) and “the LE metric is rarely, if ever, shown to be predictive of phenomena that are relevant to drug discovery” (p. 39).

PWK. This appears to be a doctrinal rather than scientific criticism.

Lower deck. I only swim from here if snorkeling because it's rocky.

Reviewer B was very positive about the "Molecular Size and Design Risk" section and made useful suggestions for its expansion. It's also worth mentioning that Derek quoted from this section in his post. However, Reviewer C suggested that the whole section be purged from the manuscript although it is possible that Reviewer C's underlying objective was to ensure that certain articles were not discussed. Reviewer C complained that my criticism of ref 48 was unfair although it may be that the reviewer considered ref 48 to be a liability (this post will give readers an idea why some LE advocates might consider ref 48 to be a liability). Another possibility is that the objection to criticism of ref 48 was actually a smokescreen and the real reason for suggesting that the section be purged was actually to avoid discussion of ref 45 (which might be considered to be an even greater liability by LE advocates).

Ref 58 and ref 59 are rare examples of articles that respond to criticism of LE and and a study such as NoLE really does need to discuss them (especially since both articles completely miss the point). The fundamental flaw that is common to both articles is that neither addresses the problems associated with the change in perception that results from using a different unit to express affinity. Reviewer C protested that it was gratuitous to single out ref 58 and even cited this 2014 post from Molecular Design in support of the charge that I was unfairly picking on ref 58. Reviewer C did seem rather rattled and also complained that I had quoted "non-scientific sections" of ref 59. I must confess to being unfamiliar with the concept that a scientific article can have non-scientific sections that can be declared off-limits for challenge. This was, perhaps, not Reviewer C's finest moment.

Reviewer A and Reviewer C both seemed rather keen that ref 94 not be discussed and they said that I should not be "attacking" fit quality (FQ) because it is rarely, if ever, used. I suspect the real reason was that both reviewers consider the metric (and ref 94) to be a significant liability from the LE perspective. I responded by noting that FQ had got its own box in the NRDD LE review and that ref 94 was cited in ref 58 (which asserts the validity of LE), suggesting that FQ may be of greater interest than Reviewer A and Reviewer C would have us believe. Another reason that Reviewer C might have preferred that the spotlight not be focused on FQ is that the discussion further exposes the illusion that fragments bind more efficiently than ligands of greater molecular size.

This is where I go swimming. It's a 5 minute walk from the house

So that concludes my review of the reviewers. I believe that the J Med Chem editors do need to think carefully about how (or even whether) they wish to have controversial topics addressed in their journal. Dr Eric Williams, the first Prime Minister of Trinidad and Tobago, suggested that his hearing impairment was an advantage in dealing with dissent because he could simply switch off his hearing aid. However, dealing with controversial topics in drug discovery might not be quite so simple. In particular, a journal needs to consider the potential vested interests of those from whom it seeks advice. For example, the Editors of a number of ACS journals may find it quite instructive to take a very close look at exactly how their journals came to endorse a frequent hitter model (trained on results from a panel of only six assays that all use the same readout) as a predictor of pan-assay interference...

I'll leave you with a selfie taken on the roof. A few minutes earlier I'd seen off a determined counter-attack by some jack spaniards (or should that be jacks spaniard?). Normally, I'd leave them alone but they were too close to where I needed to work. The technique is simple but its execution takes some nerve. First, arm yourself with a can of Baygon (don't forget to test it beforehand) and a broom. Second, with Baygon aimed, prod nest with broom. Third, spray a protective curtain of Baygon as the jack spaniards attack you (they are aggressive and they always attack). 

PWK one, jack spaniards nil 

Hydrogen bonding asymmetries

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Have you ever wondered why the Rule of 5 (Ro5) specifies hydrogen bond (HB) thresholds of 10 acceptors but only 5 donors? This is, perhaps, the prototypical example of what I'll call a 'hydrogen bonding asymmetry' and it is sometimes invoked in support of the folklore that HB donors are somehow 'worse' than HB acceptors in drug design. I have, on occasion, tried to track down the source of this folklore but that trail has always gone cold on me. In any case, I don't think the HB asymmetry in Ro5 has any physical significance since HB acceptors (especially as defined for Ro5) tend to be more common in chemical structures of interest to medicinal chemists than HB donors. This was discussed in our correlation inflation article and the bigger Ro5 question for me is why the high polarity limit is defined by counts of HB donors and acceptors while the low polarity limit is defined in terms of lipophilicity. As may become a blogging habit, I'll include some random photos (these are from a visit to India late in 2013) to break up the text a bit. 

Drum fest at Buland Darwaza

It was this article in JCAMD about the 'polarized' nature of protein-ligand interfaces that got me thinking again about hydrogen bonding asymmetries. The study found that proteins donate twice as many HBs as they accepted. While the observation is certainly interesting, I do think that the authors might be over-interpreting it. For example, the authors suggest that it appears to be an underlying explanation for Ro5 and they may find that there are significant differences in their definitions of HB acceptors and those used to apply Ro5. The authors also state "Peptidyl ligands, on the other hand, showed no strong preference for donating versus accepting H-bonds". This observation would more be consistent with 'polarization' of protein-ligand interfaces being determined by nature of the ligand.

The authors assert that "lone pairs available to accept H-bonds are actually 1.6 times as prevalent as protons available to donate, both on the protein and ligand side of the interface." While it is appropriate to count lone pairs in situations where only one lone pair accepts an HB (e.g. when considering 1:1 hydrogen bonded complexes in low polarity solvents), I would argue that it is not appropriate to do so when considering biomolecular recognition in aqueous media because the acceptance of an HB by one oxygen lone pair makes the other lone pair less able to accept an HB. You can see this effect using molecular electrostatic potential as discussed in this article (see polarization effects section and Table 4). Put another way, how often is a carbonyl oxygen observed to accept two HBs from a binding partner? How many docking tools would explictly penalize a pose in which a carbonyl oxygen accepted two HBs?

As I see it, a typical protein is more likely to have a surplus of HB donors under normal physiological conditions. Some parts (e.g. serine, threonine, tyrosine and histidine side chains and the backbone) of a protein can be regarded as having equal numbers of HB donor and acceptor atoms. While the anionic side chains of aspartate and glutamate cannot donate HBs, the cationic side chains of arginine and lysine have five and three donor hydrogen atoms respectively while lacking HB acceptors. The tryptophan side chain has only a single HB donor (although its p-system is likely to be able to accept HBs) while each side chain of aspargine and glutamine has two donor hydrogen atoms and one acceptor oxygen atom. The histidine side chain is sometimes observed to be protonated in X-ray crystal structures which means that it should be considered to be more HB donor than HB acceptor in the constext of protein-ligand recognition. The tyrosine hydroxyl would be expected to be a stronger HB donor (and weaker HB acceptor) than the hydroxyls of either serine or threonine.  

A magical place

The study considers the "possibility is that nature avoids the presence of chemical groups bearing both H-bond donor and acceptor capacity, such as hydroxyl groups, in the binding sites of proteins or ligands" although it is not clear what glycobiologists would have to say about this. Let's think a bit about what happens when a hydroxyl group donates its hydrogen atom. Let's suppose you've spotted a nice juicy hydrogen bond acceptor at the bottom of a deep binding pocket that is otherwise hydrophobic. The ligandability is eye-wateringly awesome (the ligandometer is beeping loudly and appears to have gone into dynamic range overload). Even the tiresome Mothers Against Molecular Obesity (MAMO) are impressed and have recommended that you deploy a hydroxyl group since this will be great for property forecast index (PFI). What could possibly go wrong?

The main problem is that the hydroxyl HB donor comes with baggage. In order to donate an HB to the acceptor at the bottom of that pocket, you're going to need to force an HB acceptor into contact with the non-polar part of that binding pocket. Although this contact is not inherently repulsive, it is destabilizing. Another factor is that donation of an HB by the hydroxyl group is likely to increase the HB basicity of the oxygen (which will exacerbate the problem). You can think of other neutral HB donors (e.g. amide NH) but the vast majority of them come with baggage the form of an accompanying HB acceptor. Exceptions such as NH in pyrrole (not renowned for stability) and indole (steric demands) come with baggage of their own. In contrast, the drug designer has access to a diverse set (e.g. heteroaromatic N, nitrile N, tertiary amide O, sulfoxide O, ether O) of HB acceptors that are not accompanied by HB donors. If you use one of these, you don't have the problem of having to also accommodate a ligand HB donor.

This is a good place to wrap up. In the next post, I'll talk about a completely different type of hydrogen bonding asymmetry, but for now, I'll leave you with some photos from an afternoon spent admiring asses in the Rann of Kutch. 

Até mais!

Hydrogen bonding and electronegativity

So once again it's #RealTimeChem Week and to 'celebrate' we'll be taking a look at the relationship between hydrogen bond basicity and electronegativity in this blog post. The typical hydrogen bond is an interaction between an electronegative atom and a hydrogen atom that is covalently bonded to an another electronegative atom. We tend to think about hydrogen bonding as electrostatic in nature and we often use electrostatic models to describe the phenomenon. Let's take a look at hydrogen fluoride dimer which is probably the simplest hydrogen bonded system.

Fluorine is more electronegative than hydrogen which means that it tends to draw the electrons it shares with hydrogen towards itself. This gives fluorine a partial negative charge and hydrogen a partial positive charge. This simple electrostatic model suggests that a hydrogen bond will get stronger in response to increases in the electronegativity of either the acceptor atom or the atom to which the donor hydrogen is covalently bonded. 

Hydrogen bond strength can be quantified as the equilibrium constant for the association of a hydrogen bond donor with a hydrogen bond acceptor in a non-polar solvent. For example, pK_BHX can be used as a measure of hydrogen bond basicity where K_BHX is the equilibrium constant for association of the hydrogen bond acceptor compound (e.g. pyridine) with 4-fluorophenol in carbon tetrachloride.  Let's take a look at some pK_BHX values for three structurally prototypical  compounds that present nitrogen, oxygen or fluorine to a hydrogen bond donor. 

The trend is the complete opposite of what you might have expected on the basis of the simple electrostatic model for hydrogen fluoride dimer. However, this is not as weird as you might think because electronegativity tells us about distribution of charge between atoms but at hydrogen bonding distances the donor can 'sense' the distribution of charge within the acceptor atom. Electronegativity quantifies the extent to which an atom can function as an 'electron sink' and this is also related to how effectively the atom can 'hide' the resulting excess charge from the environment around it. Put another way, fluorine will appear to be really weird if you think of it as a large, negative partial atomic charge

This is a good place to wrap up and, if you're interested in this sort of thing, why not take a look at this article on prediction of hydrogen bond basicity from molecular electrostatic potential. My most up to date hydrogen bond basicity data set can be found in the supplemental information (check the zip file) for this article and that's where I got the figures for the table.

A real world perspective on molecular design

I'll be taking a look at a Real-World Perspective on Molecular Design which has already been reviewed by Ash. I don't agree that this study can accurately be described as 'prospective' although, in fairness, it is actually very difficult to publish molecular design work in a genuinely prospective manner. Another point to keep in mind is that molecular modelers (like everybody else in drug discovery) are under pressure to demonstrate that they are making vital contributions. Let's take a look at what the authors have to say:

"The term “molecular design” is intimately linked to the widely accepted concept of the design cycle, which implies that drug discovery is a process of directed evolution (Figure 1). The cycle may be subdivided into the two experimental sections of synthesis and testing, and one conceptual phase. This conceptual phase begins with data analysis and ends with decisions on the next round of compounds to be synthesized. What happens between analysis and decision making is rather ill-defined. We will call this the design phase. In any actual project, the design phase is a multifaceted process, combining information on status and goals of the project, prior knowledge, personal experience, elements of creativity and critical filtering, and practical planning. The task of molecular design, as we understand it, is to turn this complex process into an explicit, rational and traceable one, to the extent possible. The two key criteria of utility for any molecular design approach are that they should lead to experimentally testable predictions and that whether or not these predictions turn out to be correct in the end, the experimental result adds to the understanding of the optimization space available, thus improving chances of correct prediction in an iterative manner. The primary deliverable of molecular design is an idea [4] and success is a meaningful contribution to improved compounds that interrogate a biological system."

This is a certainly a useful study although I will make some criticisms in the hope that doing so stimulates discussion. I found the quoted section to lack coherence and would argue that  the design cycle is actually more of a logistic construct than a conceptual one. That said, I have to admit that it's not easy to clearly articulate what is meant by the term 'molecular design'. One definition of molecular design is control of behavior of compounds and materials by manipulation of molecular properties. Using the term 'behavior' captures the idea that we design compounds to 'do' rather than merely to 'be'. I also find it useful to draw a distinction between hypothesis-driven molecular design (ask good questions) and prediction-driven molecular design (synthesize what the models, metrics or tea leaves tell you to). Asking good questions is not as easy as it sounds because it it is not generally possibly to perform controlled experiments in the context of molecular design as discussed in another post from Ash. Hypothesis-driven molecular design can also be thought of as a framework in which to efficiently obtain the information required to make decisions and, in this sense, there are analogies with statistical molecular design. I believe that the molecular design that the authors describe in the quoted section is of the hypothesis-driven variety but hand-wringing about how "ill-defined" it is doesn't really help move things forward. The principal challenges for hypothesis-driven molecular design are to make it more objective, systematic and efficient. I'll refer you to a trio of blog posts ( 1 | 2 | 3) in which some of this is discussed in more detail.

I'll not say anything specific about the case studies presented in this study except to note that sharing specific examples of application of  molecular design as case studies does help to move the field forward even when the studies are incomplete. The examples do illustrate how the computational tools and structural databases can be used to provide a richer understanding of molecular properties such as conformational preferences and interaction potential. The CSD (Cambridge Structural Database) is a particularly powerful tool and, even in my Zeneca days, I used to push hard to get medicinal chemists using it. Something that we in the medicinal chemistry community might think about is how incomplete studies can be published so that specific learning points can be shared widely in a timely manner.  

But now I'd like to move on to the conclusions, starting with 1 (value of quantitative statements), The authors note:

"Frequently, a single new idea or a pointer in a new direction is sufficient guidance for a project team. Most project impact comes from qualitative work, from sharing an insight or a hypothesis rather than a calculated number or a priority order. The importance of this observation cannot be overrated in a field that has invested enormously in quantitative prediction methods. We believe that quantitative prediction alone is a misleading mission statement for molecular design. Computational tools, by their very nature, do of course produce numerical results, but these should never be used as such. Instead, any ranked list should be seen as raw input for further assessment within the context of the project. This principle can be applied very broadly and beyond the question of binding affinity prediction, for example, when choosing classification rather than regression models in property prediction."

  
This may be uncomfortable reading for QSAR advocates, metric touts and those who would have you believe that they are going to disrupt drug discovery by putting cheminformatics apps on your phone. It also is close to my view of the role of computational chemistry in molecular design (the observant reader will have noticed that I didn't equate the two activities) although, in the interests of balance, I'll refer you to a review article on predictive modelling. We also need to acknowledge that predictive capability will continue to improve (although pure prediction-driven pharmaceutical design is likely to be at least a couple of decades away) and readers might find this blog post to be relevant. 

Let's take a look at conclusion 5 (Staying close to experiment) and the authors note:

"One way of keeping things as simple as possible is to preferentially utilize experimental data that may support a project, wherever this is meaningful. This may be done in many different ways: by referring to measured parameters instead of calculated ones or by utilizing existing chemical building blocks instead of designing new ones or by making full use of known ligands and SAR or related protein structures. Rational drug design has a lot to do with clever recycling."

This makes a lot of sense although I don't recommend use of the tautological term 'rational drug design' (has anybody ever done irrational drug design?). What they're effectively saying here is that it is easier to predict the effect of structural changes on properties of compounds than it is to predict those properties directly from molecular structure. The implications of this for cheminformaticians (and others seeking to predict behaviour of compounds) is that they need to look at activity and chemical properties in terms of relationships between the molecular structures of compounds. I've explored this theme, both in an article and a blog post, although I should point out that there is a very long history of associating changes in the values of properties of compounds with modifications to molecular structures.

However, there is another side to "staying close to experiment" and that is recognizing what is and what isn't an experimental observable. The authors are clearly aware of this point when they state: 

"MD trajectories cannot be validated experimentally, so extra effort is required to link such simulation results back to truly testable hypotheses, for example, in the qualitative prediction of mechanisms or protein movements that may be exploited for the design of binders."

When interpreting structures of protein-ligand complexes, it is important to remember that the contribution of an intermolecular contact to affinity is not, in general, an experimental observable. As such, it would have been helpful if the authors had been a bit more explicit about exactly which experimental observable(s) form the basis of the "Scorpion network analysis of favorable interactions". The authors make a couple of references to ligand efficiency and I do need to point out that scaling free energy of binding has no thermodynamic basis because, in general, our perception of efficiency changes with the concentration used to define the standard state. On a lighter note there is a connection between ligand efficiency and homeopathy that anybody writing about molecular design might care to ponder and that's where I'll leave things.

Halogen bonding and the curious case of the poisoned dogs

In this blog post, written specially for #RealTimeChem week on an #OldTimeChem theme, I'm going to start in the current century and work back to just a couple of years after the Kaiser's grandmother became Queen of the United Kingdom of Great Britain and Ireland. Readers might want to consider how history might have turned out differently had her eldest child succeeded her to the throne.

One can be forgiven for thinking that halogen bonding is a new phenomenon.  The term halogen bonding refers to attractive interactions between halogens and hydrogen bond acceptors which should be repulsive because hydrogen bond acceptors and halogens are electronegative and would therefore be expected to carry negative partial charges. Nevertheless halogens (other than fluorine) do seem to rather enjoy the company of hydrogen bond acceptors and molecular interaction 'catalogs' such as A Medicinal Chemist's Guide to Molecular Interactions and Molecular Recognition in Chemical and Biological Systems ensure that the medicinal chemist of 2015 is made aware of the importance of halogen bonding and of potential opportunities for exploiting them.

I was first made aware of halogen bonding in the mid 1990s through interactions with Zeneca colleagues at Jealotts Hill and, some time after that, The Nature and Geometry of Intermolecular Interactions between Halogens and Oxygen or Nitrogen was published with one of those colleagues (who had by then moved to CCDC) as a co-author.  A few years ago, I reproduced some of the analysis from that paper for a talk and here is one of the slides which shows how the closest contacts between the carbonyl oxygen and halogen are observed when the two atoms approach along along the axis defined by the halogen and the carbon atom to which it is bound.

If the halogen is bound to something that is sufficiently electron-withdrawing, the molecular electrostatic potential (MEP) on a circular patch on the van der Waals surface of the halogen becomes positive and sometimes this is described as a s-hole.  This article shows that of the s-hole is most pronounced for iodine and non-existent for fluorine, which is consistent with what X-ray crystal structures tell us about halogen bonding. I created a slightly different picture of the s-hole for my talk which shows MEP as a function of distance along two orthogonal directions of approach to the chlorine.  The significance of the  s-hole is that you doesn't actually have to invoke polarization to 'explain' halogen bonding even though it will always happen when atoms get up close and personal. 

When I first encountered halogen bonding, I remembered learning about the reaction of iodine with iodide anion as a schoolboy in Port-of-Spain in the 1970s. Iodine is not particularly water-soluble and this is a way to coax it into solution. That iodine forms complexes with Lewis bases has been known for many years and the Nantes group, better known for their extensive studies of hydrogen bond basicity, have used this to develop a halogen bond basicity scale based on this chemistry.

So in the spring of 2008 I found myself charged with doing a talk on halogens at EuroCUP (OpenEye European user group meeting) and halogen bonding was clearly going to be an important topic. To understand why I was doing this, we need to go back to the 2007 Computer-Aided Drug Design Gordon Conference and specifically the election of the vice chair for the 2009 conference. My good friend Anthony Nicholls was one of the nominees and in his candidacy speech said that he was going to have a session on halogens.  Although Ant didn't win that election, this is by far the most lucid and sensible suggestion that I've heard in a GRC candidacy speech. Needless to say the session on halogens happened in Strasbourg at EuroCUP (the morning after the conference dinner in a winery) and it was on the bus ride to that dinner that I had this conversation with my favorite Austro-Hungarian:

 "Onkel Hugo, where are you from in Germany?   
I am from AUSTRIA!   
Is that in Bavaria?"

While preparing the harangue, I decided to follow the iodine/iodide trail to see how far back it led and I was thrilled to encounter The Periodides by Albert B Prescott, writing in 1895, in which it was noted that, 

"In I839 Bouchardat, a medical writer in Paris, recounts that, when dogs were being surreptitiously poisoned with strychnine in Paris, and an antidote was asked for, first Guibourt recommended powdered galls, and then Donne advised iodine tincture, whereupon Bouchardat himself, approving the use of iodine, said they should use it in potassium iodide solution."

Thirty one years after the nefarious activities of the notorious Parisian dog poisoners  a sudden influx of Prussian visitors demonstrated the inadequacy of Strasbourg's supply of sunbeds and and I probably should now let you take a look at that infamous EuroCUP2008 harangue.

Free energy perturbation in lead optimization

Free energy simulation methods such as free energy perturbation (FEP) have been around for a while and, back in the late eighties when my Pharma career started, they were being touted for affinity prediction in drug discovery.  The methods never really caught on in the pharma/biotech industry and there are a number of reasons why this may have been the case including the compute-intensive nature of the calculations and the level of expertise required to run them.  This is not to say that nobody in pharma/biotech was using the methods. It’s just that the capability was not widely-perceived to give those who had it a clear advantage over their competitors.   Also there are other ways to use protein structural information in lead optimization and I’ve already written about the importance of forming molecular interactions with optimal binding geometry but without incurring conformational/steric energy penalties. Nevertheless, being able to predict affinity accurately would be high on every drug discovery scientist’s wish list.

A recently published study appears to represent a significant step forward and I decided to take a closer after seeing it Pipelined and reviewed.  The focus of the study is FEP and a number of innovations are described including an improved force field, enhanced sampling and automated work flow.  The quantity calculated in FEP is ΔΔG° which is a measure of relative binding affinity and this is typically what you want to predict in lead optimization.  We say ΔΔG° because it’s the difference between two ΔG° values which might, for example, be a compound with an unsubstituted phenyl ring and the corresponding compound with a chloro substituent at C3 of that aromatic ring. When we focus on ΔΔG we are effectively assuming that it is easier to predict differences in affinity than it is to predict affinity itself from molecular structure and this is a theme that I've touched on in a previous post.  Readers familiar with matched molecular pair analysis (MMPA 1 | 2 | 3 | 4 | 5 ) will see a parallel with FEP which I failed draw when first writing about MMPA although the point has been articulated in subsequent publications (1 | 2).  Of course FEP has been around a lot longer than MMPA so it’s actually much more appropriate to describe the latter as the data-analytic analog of the former.

As with MMPA, the rationale is that it is easier to predict differences in the values of a quantity than it is to predict values of the quantity directly from molecular structure.  The authors state:

 “In drug discovery lead optimization applications, the calculation of relative binding affinities (i.e., the relative difference in binding energy between two compounds) is generally the quantity of interest and is thought to afford significant reduction in computational effort as compared to absolute binding free energy calculations”

This study does appear to represent the state of the art although I would like to have seen the equivalent of Figure 3 (plot of FEP-predicted ΔG° versus experimental ΔG°) for the free energy differences which are the quantities that are actually calculated.  I would argue that Figure 3 is somewhat misleading because some of the variation in FEP-predicted ΔG° is explained by variation in the reference ΔG° values.   That said, the relevant information is summarized in Table S2 of the supporting information and the error distribution for the relative binding free energies (ΔΔG°) is shown in Figure S1.

One perception of FEP is that it becomes more difficult to get good results if the perturbation is large and the authors note:

“We find that our methodology is robust up to perturbations of approximately 10 heavy atoms”

  

Counting atoms is not the only way to gauge the magnitude of a perturbations.  It’d also be interested to see how robustly the methodology handles perturbations that involve changes in ionization state and whether ΔΔG°values of greater magnitude are more difficult to predict than those of smaller magnitude.  Prediction of affinity for compounds that bind covalently, but reversibly, to targets like cysteine proteases would probably also be feasible using these methods.   Something I've wondered about for a few years is what would happen if the aromatic nitrogen that frequently accepts a hydrogen bond from the tyrosine kinase hinge was mutated into an aromatic carbon.  If the resulting loss of affinity for this structural transformation was as small as some seem to believe it ought to be then it would certainly open up some 'patent space' in what is currently a bit of a log jam. You can also see how FEP might be integrated with MMPA in a lead optimization setting by using the former to predict the effects of structural modifications on affinity and the latter to assess the likely impact of of these modifications on ADME characteristics like solubility, permeability and metabolic stability.

So lots of possibilities and this is probably a good place to leave it for now.      

Thermodynamics and molecular interactions

So it’s #RealTimeChem week on twitter and I thought I’d get into the spirit with a blog post.  The article that I’ve selected for review focuses on non-additivity of functional group contributions to affinity.  The protein in question is Thrombin and ligand binding was characterised using protein crystallography and isothermal titration calorimetry.  

Before reviewing the article, it’s probably a good idea to articulate my position on the thermodynamics of ligand-protein binding.  Firstly, G, H and S are three state functions, each of which can be written in terms of the other two, but only one of which is directly relevant to the binding of ligands to proteins.  K_d is no less thermodynamic than ΔH° or ΔS° and the contribution of a particular intermolecular contact to ΔG° (or ΔH° for that matter) is not in general an experimental observable.  Thermodynamics with state functions is like accountancy in that if you over-pay one interaction, the other interactions will lose out.

Now back to the featured article.  One observation presented as evidence for non-additivity is that the slopes of plots of ΔG° against hydrophobic contact area differ according to whether X (see figure below) is H or NH2.  Inhibitors with the amino group bind with greater affinity than the corresponding inhibitors lacking the amino group which interacts (in its cationic form) with the protein.   However, the difference is not constant and actually increases with hydrophobic contact area.   I would certainly agree that something interesting is going on and if we’re ever going to understand ligand-protein then combining affinity measurements for structurally-related ligands with structural information will be very useful.   

About enthalpy measurements, I am a lot less sure.  Isothermal titration calorimetry (ITC) is a direct, label-free method for measuring affinity but the fact that you get ΔH° from the experiment at no extra cost doesn’t by itself make ΔH° useful.     If measured values of ΔH° lead to improved predictions of ΔG° or provide clear insight into the nature of the interactions between ligand and protein then I certainly agree that we should make use of ΔH°.  However, there is still the problem that there is no unique way to distribute ΔG°  (or, for that matter, ΔH°) over intermolecular contacts and biomolecular recognition also takes place in aqueous media.    The cohesiveness of liquid water that drives hydrophobic association in aqueous media is a consequence of strong, cooperative hydrogen bonds between water molecules and I like to think of the hydrophobic force as a non-local, indirect, electrostatic interaction.  This non-local nature of hydrophobic interactions complicates interpretation of affinity measurements in structural terms.

Let's see what the authors have to say:

"Analysis of the individual crystal structures and factorizing the free energy into enthalpy and entropy demonstrates that the binding affinity of the ligands results from a mixture of enthalpic contributions from hydrogen bonding and hydrophobic contacts, and entropic considerations involving an increasing loss of residual mobility of the bound ligands."

I'm going to put my cards on the table and say that I believe this statement represents an exercise in arm waving.    See what you think and ask yourself the question as to whether this statement would help you design a higher affinity Thrombin inhibitor?  It's also worth thinking carefully about the relationship between mobility and entropy.   One way of looking at entropy is as the degree to which systems are constrained and a more highly constrained system will be less mobile.    The authors state:

"The present study shows, by use of crystal structure analysis and isothermal titration calorimetry for a congeneric series of thrombin inhibitors, that extensive cooperative effects between hydrophobic contacts and hydrogen bond formation are intimately coupled via dynamic properties of the formed complexes."

I think that one needs to be very careful when talking about 'dynamic properties' in the context of equilibrium thermodynamics.  Ultimately entropy is determined by the characteristics of potential energy surfaces and Statistical Mechanics tells us that entropy (and other thermodynamic properties) can be calculated from the partition function.  It may be instructive to think how one would use the partition function to put these 'dynamic properties' on a quantitative basis.

I'm now going to change direction because there is one factor that the authors appear not to have considered  and I think that it could be quite important.  The ligand amino group (see figure above; it's protonated under assay conditions) interacts with the protein but it can also affect affinity in another way.  Have a look a this figure (showing the stricture of complex with 3e) from the article which shows how one of the inhibitors lacking the amino group binds.  Now I'd like you to look at one of the dihedral angles in the ligand structure and you can see how it is defined by looking at the substructures inset in the histograms below.  

 

The histograms show the distributions of (the absolute value of) this dihedral angle observed for the instances of substructure in the CSD. The histogram on the left suggests that the dihedral angle will tend to be 180° when the carbon next to the carbonyl carbon has two attached hydrogens. The histogram on the right shows how a substituent (X ¹ H) on that carbon shifts the distribution of dihedral angles.  Now let's go back to the structure of complex 3e, which can be downloaded from the PDB as refcode 2ZIQ, and we can see that the relevant dihedral angle is 117°.  Comparing the two histograms tells us is that a substituent (such as an amino group) on the carbon next to the carbonyl group will tend to stabilise the bound conformations of these inhibitors in addition to making direct interactions with the protein.  Do the ITC results tell us this?       

Literature cited

Baum, Muley, Smolinski, Heine, Hangauer and Klebe (2010) Non-additivity of functional group contributions by protein-ligand binding: A comprehensive study by crystallography and isothermal titration calorimetry. J Mol Biol 397:1042-1054  doi