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 

From schwefeläther to octanol

So in this blog post, written specially for #RealTimeChem week on an #OldTimeChem theme, I'll start ten years after the Kaiser's grandmother became Queen of the United Kingdom of Great Britain and Ireland.  I first came across Ernst Friherr von Bibra while doing some literature work for an article on predicting alkane/water partition coefficients and learned that he was from an illustrious family of Franconian Prince-Bishops. Von Bibra certainly seems to have been a colorful character who is said to have fought no less than 49 duels as a young man. Presumably these were not the duels to the death that did for poor Galois and Pushkin but more like the München frat house duels that leave participants with the dueling scars that München Fräuleins find so irresistible.

So that's how I learned about von Bibra and it was his 1847 study with Harless 'Die Ergebnisse der Versuche über die Wirkung des Schwefeläthers' (The results of the experiments on the effect of the sulfuric ether) that we cited. Schwefeläther is simply diethyl ether and so named because in 1847 you needed to make it from ethanol and sulfuric acid. Von Bibra was a pioneer in the anesthesia field and proposed that anesthetics like ether exerted their effects by dissolving the fatty fraction of brain cells. Now it's easy in 2015 to scoff at this thinking but remember that in 1847 nobody knew about cell membranes or molecules and you couldn't just pick up the phone and expect the ether to arrive the next day. Put another way, if it was 1847 and I was in the laboratory (or kitchen?) gazing at a bowl of brains and a bottle of ether, I would probably have come to a similar conclusion.

What we know now is that anesthetics (and other drugs) dissolve IN lipids as opposed to dissolving THE lipids. Nobody in 1847 knew about partition coefficients and Walther Nernst didn't articulate his famous distribution law (Verteilung eines Stoffes zwischen zwei Lösungsmitteln und zwischen Lösungsmittel und Dampfraum. Z Phys Chem 8:110–139) until 1891 by which time the Kaiser had already handed Bismarck his P45. Within ten years Ernest Overton and Hans Meyer had shown incredible foresight in using amphibians as animal models and the concept of the cell membrane would soon be introduced.

Before moving on, let's take a look at the 'introduction to partition coefficients' graphic below in which the aqueous phase is marked by a the presence of fish (they're actually piranhas and have have graced my partition coefficient powerpoints since my first visit to Brazil in 2009). We would describe the compound on the left as lipophilic because its neutral form prefers the organic phase to water and, for now, I'm not going to be too specific about exactly what that organic phase is. The compound on the right prefers to be in the water so we describe it as hydrophilic.  The red molecule on the left represents an ionized form of the compound on the left and typically these don't particularly like to go into the organic phase (especially not without counter ions for company).  A compound that prefers to to be in the organic phase can still be drawn into the aqueous phase by increasing the extent to which it is ionized (e.g. by decreasing pH if the compound is basic).

  

Now I'd like to introduce Runar Collander (whom many of you will have heard of) and Calvin Golumbic (whom few of you will have heard of).  Let's first take a look at Golumbic's 1949 study of the effects of ionization on the partitioning of phenols between water and cyclohexane.  Please observe the responses to pH in Fig 1 in that article but also take a look at equation 5 which accounts for self-association in the organic phase and the discussion about how methyl group ortho the phenolic hydroxyl compromises the hydrogen bonding of that hydroxyl group and has observable effects on the partition coefficient.

Collander's study (The Partition of Organic Compounds Between Higher Alcohols and Water) explores how differences in the organic solvent affect partitioning behaviour of solutes.  Collander presented evidence for strong linear relationships between partition coefficients measured using different alcohols (see Fig 1 in his article) although he notes that compounds with two or more hydrophilic groups in their molecular structure tend to deviate from the trend. Now take a look at Fig 2 in Collander's study which shows a plot of octanol/water partition coefficients against their ether/water equivalents. Now the correlation doesn't look so strong although relationships within chemical families appear to be a lot better. In particular, amines appear to be more soluble in octanol than they are in ether and Collander attributes this to the greater acidity of octanol. 

When reading these articles from over sixty years ago, I'm struck by the way the authors ratioanalize their observations in physical terms.  Don't be misled by what we would regard as the obscure use of language (e.g. Collander's "double molecules"  and Golumbic's description of partition coefficients as "true") because the conceptual and linguistic basis of chemistry in 2015 is richer than it was when these pioneering studies were carried out.  How these pioneers would have viewed some of the more mindless metrics by which chemists of 2015 have become enslaved can only be speculated about.

So I'm almost done but one last character in this all-star cast has yet to make his entrance and that, of course, is Corwin Hansch. Most drug discovery scientists 'know' that octanol 'defines' lipophilicity and only a small minority actually question the suitability of octanol for this purpose or even ask how this situation came to be. In order to address the second question, let's take a look at what Hansch et al have to say in this 1963 article,

"We have chosen octanol and water as a model system to approximate the effect of step I on the growth reaction in much the same fashion as the classical work of Meyer and Overton rationalized the relative activities of various anesthetics. This assumption is expressed in 2 where P is the partition coefficient (octanol-water) of the auxin.

          A = f(P)                              (2)

Collander has shown that the partition coefficients for a given compound in two different solvent systems (e.g., ether-water, octanol-water) are related as in 3.

          log P1 = a log P2 + b        (3)

This would also indicate, as does the Meyer-Overton work, that it is not unreasonable to use the results from one set of solvents to predict results in a second set". 

Now if you take another look at Collander's article, you'll see that he only claims that a linear relationship exists between partition coefficients when the organic phase is an alcohol. Collander's Fig 2 seems to suggest that Hansch et al's equation 3 cannot be used to relate octanol/water and ether/water partition coefficients. Can Collander's study be used to justify what appears to be a rather arbitrary choice of octanol as a solvent for partition coefficient measurements? That question, I will leave to you, the reader but, if you're interested, let me point you towards a short talk that I did recently at Ripon College. 

See you next year at #RealTimeChem week and don't forget to take a look at Laura's nails which get my vote for highlight of the week.