More hydrogen bonding asymmetries

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I examined an article on the polarized nature of protein-ligand binding interfaces previously and promised that I'd discuss a completely different type of hydrogen bond asymmetry which is based not on structure but on energetics. Readers may be familiar with hydrogen bond (HB) acidity and basicity which may be quantified by measurement of 1:1 association constants for hydrogen bonded complexes in non-hydrogen bonding solvents (e.g. carbon tetrachloride). Here are three references (1 | 2 | 3) and I'll also mention that molecular electrostatic potential (MEP) can be used for prediction of both HB acidity and HB basicity.

As discussed in this article, measurements of HB acidity and basicity have their limitations when trying to use them to understand and predict solvation behavior in aqueous media. First, measuring the association constant for a 1:1 complex does not tell us what will happen when two water molecules simultaneously donate hydrogen bonds to the oxygen atom of a carbonyl group. Second, the measured association constants cannot be used to compare HB acceptors with HB donors. This may seem a perverse sort of thing to want to do but one of the things that drug designers are interested in is the ease of dragging different HB donors and acceptors out of water.

Lake Liadskoye

Prediction of alkane/water partition coefficients (logPalk) has been a long standing interest (1 | 2 | 3) of mine for a number of years. It turns out that analysis of logPalk values measured for structurally prototypical model compounds can tell us quite a lot about what happens when you drag individual HB donors and acceptors out of water. The analysis is based on the observation of a very strong correlation between molecular surface area (MSA) and logPalk. The figure below shows the response of logPalk to MSA for saturated hydrocarbons, aliphatic alcohols (single hydroxyl group) and aliphatic diols. The lines of fit are essentially parallel and equally spaced which suggests that the effect on logPalk of adding a hydroxyl group to a saturated hydrocarbon or to an aliphatic alcohol is constant. This suggests treating polar groups as perturbations of saturated hydrocarbons for prediction of logPalk and analysis of data like what is shown in Figure 1 can be used to parameterize the perturbations for different polar groups. The approach, described in this article is to first calculate logPalk for a hypothetical saturated hydrocarbon with the same MSA as the compound of interest and then to sum the parameters for the polar groups in the molecular structure to account for the introduction of these polar groups. 

Figure 1. Relationship between alkane/water logP and molecular surface area (MSA) for saturated hydrocarbons, saturated alcohols and saturated diols. Neither of the aliphatic diols (1,4-butanediol and 1,6-hexanediol) would be expected to form intramolecular HBs in water.  

I think we'll need more data (especially for heterocycles and species with intramolecular HBs) to make this approach to prediction of logPalk generally useful.  However, the size of the effect on logPalk of introducing an HB acceptor or donor into a saturated hydrocarbon does tell us how strongly the HB donor or acceptor interacts with water. It was actually this article which was published after our article on logPalk prediction that got me thinking along these lines. In our article, we showed how polarity can be defined for HB acceptors and donors and calculated from measured alkane/water partition coefficients. Polarity defined in this manner brings HB donors and acceptors onto the same scale and allows us to explore another type of hydrogen bonding asymmetry.

Insects exploiting surface tension in Belovezhskaya Pushcha

For HB acceptors, the approach is simple. First you need to identify appropriate model compounds for which logPalk has been measured. These have only the HB acceptor functional group of interest, saturated carbon and hydrogen in their molecular structures. Next, calculate logPalk for a saturated hydrocarbon with the same MSA as that for the model compound (use line for saturated hydrocarbons in Figure 1 to do this) and subtract the measured logPalk value from the calculated value. Things are a bit more complicated for HB donors because you can't usually have these without an HB acceptor (this is the 'baggage' I discussed in the previous post) and you need to deal with these on a case-by-case basis. For example, you might estimate the polarity of an amide NH by subtracting the polarity of the tertiary amide group from that of the secondary amide group.  Here's a table of polarity estimates for some hydrogen bond acceptors and donors (our article explains how these were derived).  

Table 1. Polarity of HB acceptors and donors estimated from measured alkane/water partition coefficient and molecular surface area

The results in Table 1 show that HB donors are typically more easily pulled out of water than HB acceptors and this can be seen as another hydrogen bonding asymmetry. This appears to go against the folklore that HB donors are somehow worse than HB acceptors from the perspective of drug-likeness. The polarity values for the NH (0.8) and carbonyl O (6.8) of the amide group may have some relevance to protein folding. This a good place to wrap up and I'll conclude by noting that, in the supplemental information for our article, you'll find an archive that contains files (in plain text format) of measured values for logPalk, hydrogen bond basicity and pKa that we extracted from the literature (DOI links are included). Here are some more photos from Belarus.  

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Flora and fauna of Belovezhskaya Pushcha

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. 

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On the Nature of QSAR

With EuroQSAR2018 fast approaching, I'll share some thoughts from Brazil since I won't be there in person. I've not got any QSAR related graphics handy so I'll include a few random photos to break the text up a bit.

East of Marianne River on north coast of Trinidad

Although Corwin Hansch is generally regarded as the "Father of QSAR", it is helpful to look further back to the work of Louis Hammett in order to see the prehistory of the field. Hammett introduced the concept of the linear free energy relationship (LFER) which forms the basis of the formulation of QSAR by Hansch and Toshio Fujita. However, the LFER framework encodes two other concepts that are also relevant to drug design. First, the definition of a substituent constant relates a change in a property to a change in molecular structure and this underpins matched molecular pair analysis (MMPA). Second, establishing an LFER allows the sensitivity of physicochemical behavior to structural change to be quantified and this can be seen as a basis for the activity cliff concept.

Kasbah cats in Ouarzazate 

As David Winkler and the late Prof. Fujita noted in this 2016 article, QSAR has evolved into "two QSARs":

Two main branches of QSAR have evolved. The first of these remains true to the origins of QSAR, where the model is often relatively simple and linear and interpretable in terms of molecular interactions or biological mechanisms, and may be considered “pure” or classical QSAR. The second type focuses much more on modeling structure–activity relationships in large data sets with high chemical diversity using a variety of regression or classification methods, and its primary purpose is to make reliable predictions of properties of new molecules—often the interpretation of the model is obscure or impossible.

I'll label the two branches of QSAR as "classical" (C) and "machine learning" (ML). As QSAR evolved from its origins into ML-QSAR, the descriptors became less physical and more numerous. While I would not attempt to interpret ML-QSAR models, I'd still be wary of interpreting a C-QSAR model if there was a high degree of correlation between the descriptors. One significant difficulty for those who advocate ML-QSAR is that machine learning is frequently associated with (or even equated to) artificial intelligence (AI) which, in turn, oozes hype. Here are a couple of recent In The Pipeline posts (don't forget to look at the comments) on machine learning and AI.

One difference between C-QSAR models and ML-QSAR models is that the former are typically local (training set compounds are closely related structurally) while the the latter are typically non-local (although not as global as their creators might have you believe). My view is that most 'global' QSAR models are actually ensembles of local models although many QSAR modelers would have me dispatched to the auto-da-fé for this heresy. A C-QSAR model is usually defined for a particular structural series (or scaffold) and the parameters are often specific (e.g. p value for C3-substituent) to the structural series. Provided that relevant data are available for training, one might anticipate that, within its applicability domain, local model will outperform a global model since the local model is better able to capture the structural context of the scaffold.

I would guess that most chemists would predict the effect on logP of chloro-substituting a compound more confidently than they would predict logP for the compound itself. Put another way, it is typically easier to predict the effect of a relatively small structural change (a perturbation) on chemical behavior than it is to predict chemical behavior directly from molecular structure. This is the basis for using free energy calculations to predict relative affinity and it also provides a motivation for MMPA (which can be seen as the data-analytic equivalent of free energy perturbation). This suggests viewing activity and properties in terms of structural relationships between compounds. I would argue that C-QSAR models are better able than ML-QSAR models to exploit structural relationships between compounds.

Down the islands with Venezuela in the distance 

ML-QSAR models typically use many parameters to fit the data and this means that more data is needed to build them. One of the issues that I have with machine learning approaches to modeling is that it is not usually clear how many parameters have been used to build the models (and it's not always clear that the creators of the models know). You can think of number of parameters as the currency in which you pay for the quality of fit to the training data and you need to account for number of parameters when comparing performance of different models. This is an issue that I think ML-QSAR advocates need to address.

Overfitting of training data is an issue even for C-QSAR models that use small numbers of parameters. Generally, it is assumed that if a model satisfies validation criteria it has not been over-fitted. However, cross-validation can lead to an optimistic assessment of model quality if the distribution of compounds in the training space is very uneven. An analogous problem can arise even when using external test sets. Hawkins advocated creating test sets by removing all representatives of particular chemotypes from training sets and I was sufficiently uncouth to mention this to one of the plenaries at EuroQSAR 2016. Training set design and model validation do not appear to be solved problems in the context of ML-QSAR.

The Corniche in Beirut 

I get the impression that machine learning algorithms may be better suited for classification than QSAR and it is common to see potency (or affinity) values classified as 'active' or 'inactive' for modeling. This creates a number of difficulties and I'll also point you towards the correlation inflation article that explains why gratuitous categorization of continuous data is very, very naughty. First, transformation of continuous data to categorical data throws away huge amounts of information which would seem to be the data science equivalent of shooting yourself in the foot. Second, categorization distorts your perception of the data (e.g. a pIC50 value of 6.5 might be regarded as more similar to one of 9.0 than one of 5.5). Third, a constant uncertainty in potency translates to a variable uncertainty in the classification. Fourth, if you categorize continuous data then you need to demonstrate that conclusions of analysis do not depend on the categorization scheme.

In the machine learning area not all QSAR is actually QSAR. This article reports that "the performance of Naïve Bayes, Random Forests, Support Vector Machines, Logistic Regression, and Deep Neural Networks was assessed using QSAR and proteochemometric (PCM) methods". However, the QSAR methods used appear to be based on categorical rather than quantitative definitions of activity. Even when more than two activity categories (e.g. high, medium, low) are defined, analysis might not be accounting for the ordering of the categories and this issue was also discussed in the correlation inflation article. Some clarification from the machine learning community may be in order as to which of their offerings can be used for modelling quantitative activity data.

I'll conclude the post by taking a look at where QSAR fits into the framework of drug design. Applying QSAR methods requires data and one difficulty for the modeler is that the project may have delivered its endpoint (or been put out of its misery) by the time that there is sufficient data for developing useful models. Simple models can be useful even if they are not particularly predictive. For example, modelling the response of pIC50 to logP makes it easy to see the extent to which the activity of each compound beats (or is beaten by) the trend in the data. Provided that there is sufficient range in the data, a weak correlation between pIC50 and logP is actually very desirable and I'll leave it to the reader to ponder why this might be the case. My view is that ML-QSAR models are unlikely to have significant impact for predicting potency against therapeutic targets in drug discovery projects.  

So that's just about all I've got to say. Have an enjoyable conference and make sure keep the speakers honest with your questions. It'd be rude not to.

Early evening in Barra 

Hammett

I first became aware of Louis Hammett during the third term of my first year as an undergraduate at the University of Reading. Hammett was a pioneer in physical-organic chemistry and is widely regarded as one of the founders of that field. He would have been 124 today and was less than a year younger than Christopher Ingold, another pioneer in the field. Hammett passed away in 1987 at the age of 92 (here is an excellent obituary).

Today Hammett is remembered primarily for the parameters that describe electronic interactions between aromatic rings and their substituents. He also introduced linear free energy relationships which form the basis of classical QSAR. These days, QSAR has evolved away from its origins in physical-organic chemistry into what many call machine learning and parameters have become less physical (and considerably more numerous). Hammett's work provided an early lesson to wannabe molecular designers in how to think about molecules.

Jens Sadowski and I introduced matched molecular pair analysis (MMPA) in a chapter of a cheminformatics book that was conceived and edited by my dear friend (and favorite Transylvanian) Tudor Oprea. Here's a photo of Tudor and me at an OpenEye meeting (I think CUP II in 2001) during which our props (Tudor is wearing a PoD cape) were provided by the session chair (the formidable Janet Newman who intimidates proteins to the extent that they 'voluntarily' crystallize).

Now you might be wondering what MMPA has to do with Hammett. The short answer is that our book chapter included a table of what are effectively substituent constants for aqueous solubility and these have Hammett's fingerprints all over them. The longer answer is that Hammett introduced the idea of associating parameters with structural relationships (e.g. X is chloro analog of Y) between compounds. This is an important idea because much pharmaceutical design is focused on understanding and predicting the effects of structural modifications on the activity and properties of compounds. One rationale for this focus is the belief that it is easier to predict differences (e.g. relative affinity) in chemical behavior between structurally-related compounds than it is to predict chemical behavior directly from molecular structure.

At first, I didn't see the deeper connection between Hammett's work and pharmaceutical design. The main focus of our book chapter was preparing chemical structures in databases for virtual screening so the full extent of Hammett's influence on MMPA was not immediately recognized. As is often the case, we think we've discovered something really new only to find out later that somebody had been thinking along similar lines many years before. 

Happy 124th birthday, Louis Hammett.  

The maximal quality of molecular interactions

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There is a lot more to drug design than maximization of affinity and the key to successful design is actually that drugs form high quality interactions with their targets. Before the epiphany of ligand efficiency, measurement of interaction quality was a very inexact science. Ground-breaking research from the Budapest Enthalpomics Group (BEG) now puts the concept on a firm theoretical footing by unequivocally demonstrating that individual interactions can be localized on the affinity-quality axis in a unique manner that is completely independent of the standard state definition.

The essence of this novel approach is that, in addition to to its contributions to enthalpy and entropy of binding, each molecular interaction will now be awarded points for the artistic elements of the contact between ligand and target. This industry-leading application of Big Data uses the Blofeld-Auric Normalized Zeta Artificial Intelligence (BANZAI) algorithm to score aesthetic aspects of molecular interactions. This revolutionary machine learning application uses variable-depth, convolutional networks to model the covariance structure of the reduced efficiency tensor. Commenting on these seminal and disruptive findings the institute director, Prof. Kígyó Olaj, noted that "the algorithm is particularly accurate for scoring synchronization of vibrational modes and is even able to determine whether or not a hydrogen bond has made deliberate use of the bottom of the pool to assist another hydrogen bond during the binding routine".

Eu matei o Oscar Niemeyer

I never meant to kill Oscar Niemeyer. 

Vasily Grigoryevich Zaytsev was a pretty good shot. During the pivotal battle of Stalingrad he dispatched 225 enemy soldiers, including 11 snipers. Zaytsev died in Kyiv on Oscar Niemeyer's 84th birthday and was reburied 14 years later on Mamayev Hill in Volgograd with full military honors. 

Oscar Ribeiro de Almeida Niemeyer Soares Filho was born in Rio de Janeiro on 15th December, 1907 and he is best known for design of some of the buildings in Brasilia. Here are examples of his work:

I first learned of Curitiba in the 1980s from a Scientific American article on urban planning and it had been on my list of places to visit for almost 30 years when I arrived in Brazil in 2012. I also learned about Curitiba in Portuguese class and, while planning the trip, I was particularly excited to discover that Museu Oscar Niemeyer is in Curitiba.

I flew to Curitiba on Thursday November 30, 2012 and the museum visit was scheduled for the Saturday. I found a nice vegetarian restaurant near the museum and lunched there. Although not a vegetarian, I certainly enjoy vegetarian food and, in any case, there is only so much picanha that one can eat. As an aside, I can claim a degree of skill in finding vegetarian restaurants in unlikely places such as El Calafate (Peron and Kirchner must be turning in their respective graves) and Montevideo (didn't think that vegetables were allowed in Uruguay). The museum is sometimes called Museo do Olho (museum of the eye) on account of its most distinctive feature. Here are some photos:

I thoroughly enjoyed the afternoon in the museum and, as well as viewing the exhibits, I watched a video on the life of Niemeyer and also read some biographical material. However, neither source mentioned when he had died. On returning to São Carlos the next day, I googled him and was amazed to discover that he was still alive (and due to turn 105 in a couple of weeks). With all this talk about Zaytsev, you're probably thinking that I borrowed a sniper rifle and picked off Brazil's National Treasure as he shuffled around the garden on his zimmer frame. However, reality is even more bizarre.

At that time, I was taking Portuguese classes and the weekend in Curitiba was certainly going to give me something to talk about (typically the conversation would be about how deadly Friday's group meeting had been and why ponto de fusão is so important). On being asked about my weekend, I responded, "Eu viajei para Curitiba e visitei o museu Oscar Niemeyer. Ele vive ainda!" (I travelled to Curitiba and visited the Oscar Niemeyer museum. He is still alive!)

Oscar Niemeyer died a few hours later.

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.