Thinking About Aqueous Solvation

Given that it was International Women's Day yesterday, I'll open the the post (and blogging for 2025) with a photo of a gravestone at St James' Church in Bramley (Hampshire).

In the current post I’ll be taking a look at some aspects of aqueous solvation and Richard Wolfenden’s 1983 “Waterlogged Molecules” article (W1983) is still worth reading today (as an aside, Prof Wolfenden will turn ninety in May of this year and hopefully mentioning this won't put what is called "goat mouth" in my native Trinidad and Tobago on him as I did for Oscar Niemeyer with the words "ele vive ainda" while studying Portuguese in 2012). As noted in W1983 the formation of a target-ligand complex requires partial desolvation of both target and ligand:

When biological compounds combine, react with each other, or change shape in watery surroundings, solvent molecules tend to be reorganized in the neighborhood of the interacting groups.

Formation of a target-ligand can also be seen as an “exchange reaction” and this point is very well made in SGT2012:

Molecular binding in an aqueous solvent can be usefully viewed not as an association reaction, in which only new intermolecular interactions are introduced between receptor and ligand, but rather as an exchange reaction in which some receptor–solvent and ligand–solvent interactions present in the unbound state are lost to accommodate the gain of receptor–ligand interactions in the bound complex.

In HBD3 I briefly discuss ‘frustrated hydration’ as a phenomenon that could be exploited in drug design and I’ll quote from the Summary section of W1983:  

When two or more functional groups are present within the same solute molecule, their combined effects on its free energy of solvation are commonly additive. Striking departures from additivity, observed in certain cases, indicate the existence of special interactions between different parts of a solute molecule and the water that surrounds it.

I’ll try to explain how this could work for ligand design and let’s suppose that we have two polar atoms that are close together in the binding site. The proximity of the polar atoms in the binding site means that water molecules forming ideal interactions with the polar atoms in the binding sites are also likely to be close together. However, the mutual proximity of the water molecules can lead to unfavourable interactions between the water molecules which ‘frustrate’ the (simultaneous) hydration of the two polar atoms in the binding site. Now if we design a ligand with two polar atoms positioned to form good interactions with polar atoms in the binding site it is likely that these will also be in close proximity and that their hydration will be similarly frustrated. I would generally anticipate that frustration of hydration will not be handled well by implicit solvent models (RT1999 | FB2004 | CBK2008 |  KF2014)  or computational tools such as WaterMap that calculate energetics for individual water molecules (especially in cases where the two hydration sites cannot be simultaneously occupied).

To illustrate frustration of hydration I’ve taken a graphic from a talk from 2023. The unfavorable interactions between solvating water molecules that frustrate hydration are shown as red double-headed water molecules (in some cases these interactions will be repulsive to the extent that only one of the hydration sites can be occupied at a time). You’ll also notice two thick green lines in the right hand panel and these show secondary interactions that stabilize the bound complex. Secondary interactions of this nature were discussed in a molecular recognition context in the JP1990 study and the observation (see A1989) that pyridazine is a better hydrogen bond acceptor (HBA) than its pK_a would have you believe can be seen in a similar light.  Secondary interactions like these only enhance affinity when the proximal polar atoms are of the same ‘type’ (the proximal polar atoms in the 1,8-naphthyridine are both HBAs) and we should anticipate that the secondary interactions for the contact between pyrazole and the ‘hinge’ of a tyrosine kinase will be deleterious for affinity. In contrast to secondary interactions, frustration of hydration can be beneficial for affinity even when the proximal polar atoms are of opposite types, as would be the case for an HBA that is near to a hydrogen bond donor (HBD).     

While it is clearly important to account for aqueous solvation when using physics-based approaches for prediction of binding affinity, passive permeability and aqueous solubility, the measurement of gas-to-water transfer free energy is not exactly routine (I’m not aware that any companies offer measurement aqueous solvation energy as a service nor do I believe that this is an activity that would readily funded). Measurements for aqueous solvation energy reported in the literature tend to be for relatively volatile compounds and I’ll direct readers to the C1981, W1981 and A1990 studies.

A view is that I've held for many years is that a partition coefficient could be used as an alternative to gas-to-water transfer free energy for studying aqueous solvation. It's also worth noting that when we think about desolvation in drug design we're often considering the energetic cost of bringing polar atoms into contact with non-polar atoms (as opposed to transferring the polar atoms to gas phase). Partition coefficient measurement is a lot more routine than solvation free energy measurement and most drug discovery scientists are of aware that the octanol/water partition coefficient (usually quoted as its base 10 logarithm logP) is an important design parameter. However, the octanol/water partition coefficient is not useful for assessing aqueous solvation because the hydroxyl group of octanol can form hydrogen bonds with solutes and the water-saturated solvent is actually quite 'wet' (the DC1992 study reports that the room temperature solubility of water in octanol is 2.5 M). If we’re going to use partition coefficient measurements for studying aqueous solvation then I would argue that we should make these measurements with a saturated hydrocarbon such as cyclohexane or hexadecane that lacks hydrogen bonding capability.

Here’s another slide from that 2023 talk showing that pyridine is lipophilic for octanol/water but hydrophilic for hexadecane/water. The difference in the logP values for a solute is sometimes referred to as ΔlogP (it is equivalent to the hexadecane/water logP value with both solvents water-saturated) and can be considered to quantify the solute’s ability to form hydrogen bonds (see Y1988 | A1994 | T2008). I'll mention in passing that ΔlogP measurements with toluene as the less polar organic solvent have been used to study intramolecular hydrogen bonding (see S2013 | C2016 | C2018).     

It should be stressed  that people have been thinking about using different organic solvents for partition coefficient measurement for a lot longer than me. My view, expressed in K2013, is that the justification in H1963 for using octanol was partly based on a misinterpretation of Collander's C1951 study. I really like this quote from Alan Finkelstein's 1976 article (as an aside the partition coefficient literature is not exactly awash with alkane/water logP measurements for amides and the article reports measured values of the hexadecane/water partition coefficient for acetamide, formamide, urea, butyramide and isobutyramide): 

It has long been fashionable to worry about which organic solvent (and polarity) is the best model for the lipoidal region of a particular cell membrane (Collander, 1954). These solvents have ranged from isobutanol (the most polar) to olive oil (the least polar). I have never understood the point of this. If the lipoidal region of the plasma membrane is a lipid bilayer, then clearly the appropriate model solvent is hydrocarbon. For artificial bilayers this is obviously so. I chose n-hexadecane as the particular hydrocarbon, because its chain length is comparable to that of the fatty acid residues in most phospholipids, and it is conveniently available.

I also need to mention the B2016 study (Blind prediction of cyclohexane–water distribution coefficients from the SAMPL5 challenge) since the the cyclohexane/water distribution coefficient was used as a surrogate for gas-to-water transfer free energy in the challenge:

The inclusion of distribution coefficients replaces the previous focus on hydration free energies which was a fixture of the past five challenges (SAMPL0-4) [1 | 2 | 3 | 4 | 5 | 6 | 7]. Due to a lack of ongoing experimental work to generate new data, hydration free energies are no longer a practical property to include in blind challenges. It has become increasingly difficult to find unpublished or obscure hydration free energies and therefore impossible to design a challenge focusing on target compounds, functional groups or chemical classes.

I consider initiatives such as the SAMPL5 cyclohexane/water distribution challenge to be valuable for assessing model predictivity in an objective and transparent manner. Generally, I would avoid including logD measurements for compounds that are significantly ionized under experimental conditions because these require that account be taken of ionization when making predictions (better to measure logD at a pH at which ionizable functional groups are not significantly ionized). While challenges such as SAMPL5 are certainly valuable for assessment of predictivity of models, I consider them less useful in model development which requires measured data for structurally-related compounds. 

The isosteric pairs 1/2  and 3/4 shown in the graphic below will give you an idea of what I'm getting at. The predicted pK_BHX values taken from K2016 suggest that 1 is less polar than than its isostere 2 and I'd expect 3 to be more polar than 4.

While the three N-butylated purines shown in the graphic below are not strictly isosteric I would consider it valid to interpret the cyclohexane/water logP values taken from S1998 as reflecting differences in hydrogen bond acceptor strength.

This is a good point at which wrap up and, given the fundamental importance of aqueous solvation in biomolecular recognition and drug design, I see tangible advantages in having a large body of measured data in the public domain. My view is that to measure gas-to-water transfer free energy for significant numbers of compounds of interest to drug discovery scientists would be both technically demanding and unlikely to get funded although I would be delighted to be proven wrong on either point. This means that we need to learn to use other types of data in order to study aqueous solvation and my view is that an alkane/water partition coefficient would be the best option. Using alkane/water partition coefficients as an alternative to gas-to-water transfer free energies for studying aqueous solvation would also enable enthalpic (see RT1984) and volumetric aspects of aqueous solvation to be investigated more easily.     

A Nobel for property-based drug design?

[This post was updated on 10-Aug-2025 to mention my review of CNM2025 (Return to Flatland) which  critically examines (35) (Escape from Flatland: Increasing Saturation as an Approach to Improving Clinical Success)] 

 

This post was updated on 04-Aug-2024. I thank Tim Ritchie (see RM2009 | RM2014) for bringing YG2003 (Prediction of Aqueous Solubility of Organic Compounds by Topological Descriptors) to my attention.]

"The problems of ADME are precisely those that determine success or failure of a drug in vivo. In vitro data can give a clearer picture of the receptor characteristics, but knowledge and control of ADME are also vital. A common trap in binding studies is that binding generally increases with lipophilicity, so that one may obtain extremely potent binding that is totally unattainable in vivo."

SH Unger (1987) Computer-Aided Drug Design in the Year 2000. 

Drug Information Journal 21:267-275 DOI

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In this post I’ll be reviewing an Editorial (Property-Based Drug Design Merits a Nobel Prize) that was recently published in J Med Chem. For me, the Editorial raises questions about the critical thinking skills of its authors and of the judgement of the J Med Chem Editors (I’m guessing that some of the courteous and cultured members of the Nobel Prize committee might regard it to be somewhat pushy, and possibly even uncouth, for journals to be publishing nominations for Nobel Prizes as editorials). My advice to anybody nominating individuals for a Nobel Prize is to be aware of an observation, usually attributed to Jocelyn Bell Burnett, that it’s better that people ask why you didn’t win a Nobel Prize than why you did. Where applicable, I've used the the same reference numbers that were used in the Editorial and I’ll start by reproducing the Nobel Prize proposal (as is usual in posts at Molecular Design, I’ve inserted some comments, italicized in red and enclosed in square brackets, into the quoted text):

We propose that a Nobel Prize in Physiology or Medicine should be awarded for property-based drug design, with Christopher A. Lipinski, Paul D. Leeson, and Frank Lovering as the proposed recipients for their development of “important principles for drug design” [I would describe what the proposed Nobel laureates have introduced as a rule, a metric and a molecular descriptor rather than principles.], principles that have contributed to the development of numerous approved drugs. [The authors do need to provide convincing evidence to support what appear to be some wildly extravagant claims. Specifically, the authors need to demonstrate that the rule, metric and molecular descriptor (which they describe as “principles”) were actually critical to the decision-making in projects that led to the development of numerous drugs.] While drug design previously focused primarily on optimizing potency, they introduced a more holistic approach based on the consideration of how fundamental molecular and physicochemical properties affect pharmaceutical, pharmacodynamic, pharmacokinetic, and safety properties. [My view is that none of proposed Nobel laureates even demonstrated a single convincing link between molecular and physicochemical properties, and pharmaceutical, pharmacodynamic, pharmacokinetic, and safety properties.] The development of the Rof5 by Christopher A. Lipinski in 1997 introduced a new principle for how molecular and physicochemical properties affect oral bioavailability. The development of LipE by Paul D. Leeson in 2007 introduced a new principle for how physicochemical properties impact potency, selectivity, and safety. Finally, the development of Fsp3 by Frank Lovering in 2009 introduced a new principle for how molecular shape affects pharmaceutical properties and developability.

Before examining the contributions of the three nominated individuals it's worth saying something about the objectives of drug design. First, a drug needs to be highly active against its target(s). Second, activity against anti-targets should be very low (ideally too low to even be measured). Third, as I note in 34, the exposure (concentration at the site of action) of the drug needs to be controllable (one challenge in drug design is that intracellular drug concentration can’t generally be measured in vivo and I recommend that all drug discovery scientists read SR2019). I see controlling exposure as the primary focus of property-based design and one fundamental challenge is that structural modifications that lead to increased engagement potential for the therapeutic target(s) frequently result in reduced controllability of exposure as well as increased engagement potential for anti-targets. I’ve tried to capture these points in the graphic shown below.

It's generally accepted that excessive lipophilicity and molecular size are risk factors in drug design and the “compound quality” (CQ) literature abounds with fire-and-brimstone sermons on the evils of "molecular obesity" (see H2011). Nevertheless, the relationships between these descriptors and properties such as binding affinity for anti-targets, permeability, aqueous solubility and metabolic lability are generally not quite as strong as is commonly believed (or claimed). When using trends in data to inform design it’s really important to know how strong the trends are because this tells you how much weight to give to the trends when making decisions. It’s not unknown in CQ studies for trends in data to be made to appear to be stronger than they actually are which endows the CQ field with what I’ll politely call a “whiff of the pasture” (the term “correlation inflation” has been used; see KM2013). Transformation of continuous data (IC₅₀ values) to categorical data (high | medium | low) prior to analysis should trigger a deafening cacophony of alarm bells as should any averaging of groups of continuous data values without showing the spread in the data values. Some examples of studies in which I consider the strengths of trends to have been exaggerated include 29, 35, HMO2016 and HY2010.

I think that one thing that everybody who actually works (or has worked) on drug discovery projects agrees on is that drug discovery is really difficult. My view is that, by focusing on Rof5, LipE and Fsp3, the Editorial actually trivializes the challenges faced by drug discovery scientists. Most drug design (as opposed to ligand design) takes place during lead optimization and lead optimization teams are typically addressing specific problems (for example, structural changes that result in increased potency also result in reduced aqueous solubility).  Lead optimization teams typically work with a lot of measured data (a significant component of drug design is efficient generation of data to enable decision-making) and a weak correlation between logP and aqueous solubility reported in the literature would be of no practical relevance when the lead optimization team is using aqueous solubility measurements for compounds in the structural series that they’re optimizing. It is common (see M2001 | G2008) for the simplicity of rules, guidelines and metrics to be touted and we noted in KM2013 that:   

Given that drug discovery would appear to be anything but simple, the simplicity of a drug-likeness model could actually be taken as evidence for its irrelevance to drug discovery.

Guidelines for successful drug discovery are often presented in terms of something good (or bad) being more likely to happen when the value of a calculated property such as Fsp3 exceeds a threshold. When using guidelines like these be aware that it’s actually very difficult to set these threshold values objectively and that the guidelines would have been stated in an identical manner had different threshold values been chosen to specify them. One difficulty with using guidelines like these is that the creators of the guidelines don’t usually say what they mean by “more likely” (millions of people book flights knowing that one is “more likely” to die in a plane crash if one takes a flight than if one doesn’t take a flight). A number of published guidelines (some of which have been referenced in the Editorial) claim that compounds that comply with the guidelines are more likely to be developable. However, giving weight to these claims would require that developability be defined in an objective manner that enables compounds with arbitrary molecular structures and differing biological activity to be meaningfully compared.   

I’ll examine the contributions of the three proposed laureates for the Nobel Prize in Physiology or Medicine following the order in the Editorial. Let's start with the first:

  

The development of the Rof5 by Christopher A. Lipinski in 1997 introduced a new principle for how molecular and physicochemical properties affect oral bioavailability. [As a reviewer of the manuscript I would have pressed the authors to explicitly state the new principle that their first nominee for the Nobel Prize for Physiology or Medicine had introduced 1997.]

My view is that the publication of the Rof5 (22) has certainly proven to be highly influential in that it made many drug discovery scientists aware of the need to take account of physicochemical properties, in particular lipophilicity, in drug design. What is less well-known, but possibly more important in my view, is that publication of the Rof5 sent a clear message to Pharma/Biotech management that high-throughput screening wasn’t going to be the panacea that many believed that it would be. However, I don't see the Rof5 as quite the epiphany that the authors of the Editorial would have us believe it to be. The quote with which I started this post was taken from an article that had been published ten years before 22 and the inverse nature of the relationship between aqueous solubility and lipophilicity was being discussed in the scientific literature (see YV1980) more than forty years ago. The NC1996 study is also worthy of mention because it was published more than a year before 22 and it makes the important point that optimal logP values are likely to vary with chemotype ("each congeneric series for a drug backbone usually demonstrates its own optimal log P").       

Questions can be raised about the data analysis presented in support of the Rof5 and readers may find it helpful to take a look at the S2019 study as well as my comments on the Rof5 in HBD3 and in this post. I would argue that the Rof5 does not have any practical value as a drug design tool and I would challenge the assertion made in the Editorial that the publication of 22 demonstrated how “molecular and physicochemical properties affect oral bioavailability”. One aspect of the analysis presented (22) in support of the Rof5 that isn't always fully appreciated is that the compounds for which the descriptors are calculated were all treated as having equivalent oral bioavailability (compounds were selected for the analysis on the basis of having been taken into phase 2 clinical trials at some point before the Rof5 had been published in 1997). This is one reason that it’s not credible to assert that the analysis demonstrates that these molecular and physicochemical properties are linked to bioavailability (it must be stressed that, like many, I do actually believe that excessive lipophilicity and molecular size are risk factors in drug design). I make the following point in a blog post (I’ve modified the original text very slightly for consistency with the Editorial):

The Rof5 is stated in terms of likelihood of poor absorption or permeation although no measured oral absorption or permeability data are given in 22 and the Rof5 should therefore be regarded as a statement of belief. I realise that to make such an assertion runs the risk of an appointment with the auto-da-fé and I stress that had the Rof5 been stated in terms of physicochemical and molecular property distributions I would not have made the assertion.

To see what I was getting at let’s take a look at how the Rof5 was stated in 22 (“The ‘rule of 5’ states that: poor absorption or permeation are more likely when…”). However, the analysis presented in support of the Rof5 was of the distribution of compounds in chemical space defined by molecular weight, logP and numbers of hydrogen bond donors and acceptors with no account being taken of variation in either absorption or permeation for the compounds. Analysis like this can be informative but you need to demonstrate that the chemical space is actually relevant to the phenomena of interest. One way that you can demonstrate that a chemical space is relevant is to build predictive models for the phenomena of interest using only the dimensions of the chemical space as descriptors. Alternatively you might observe meaningful differences between the distributions in the chemical space for compounds that have respectively passed and failed at at a particular stage in clinical development.  

So that’s all that I’ll be saying about Rof5 and it’s time to take a look at the contributions of the second proposed Nobel Laureate:

The development of LipE by Paul D. Leeson in 2007 introduced a new principle for how physicochemical properties impact potency, selectivity, and safety. [As a reviewer of the manuscript I would have pressed the authors to explicitly state the new principle that their second nominee for the Nobel Prize for Physiology or Medicine had introduced 2007.]

I'll start by saying that LipE is a simple mathematical formula and I suggest that one shouldn't be confusing simple mathematical formulae with principles when nominating people for Nobel Prizes. There are, however, other errors and these are not the kind of errors that you can afford to make when nominating people for Nobel Prizes. First, the term used in 29 is actually “ligand-lipophilicity efficiency” (LLE) although this appears to have mutated to “lipophilic ligand efficiency” (also LLE) by 2014 (see H2014). The term “LipE” was actually introduced by Pfizer scientists (see R2009) and it is significant that the more recent J2018 article defines LipE in terms of logD rather than logP (doing so means that you can make compounds more efficient simply by increasing extent of ionization and, as a drug design tactic, this is likely to end about as well as things did for the Sixth Army at Stalingrad).

The second (and more serious from the perspective of a Nobel nomination) error is that the metric had already been discussed, although not named, in the literature when 29 was published (I’m guessing that a suggestion that naming a metric merits a Nobel Prize for Physiology or Medicine might cause some members of the Nobel Prize committee to choke on their surströmming).  The L2006 book chapter, published fifteen months before 29, states:

Thus, to achieve compounds with a not too high log P while still retaining potency, the difference between the log potency and the log D can be utilised.

From the A2007 perspective which was published three months before 29: 

Lipophilicity is thought to be a driving force for binding to anti-targets such as the hERG ion channel and cytochrome p450 enzymes and potency can be scaled by lipophilicity by subtracting measured or calculated 1-octanol water partition coefficients from pIC₅₀.

It might be helpful to say something about efficiency metrics since LiPE (or LLE if you prefer) is an example of an efficiency metric. The idea behind efficiency metrics is to “normalize” a compound’s activity (typically quantified by potency or affinity) by the value of a risk factor such as lipophilicity or molecular size (for the masochists among you there’s an entire section in 34 on normalization of binding affinity). Ligand efficiency (LE) was introduced in 2004 (see H2004) and is generally regarded as the original efficiency metric although its creators do acknowledge the influence of the K1999 study. I’ve argued at length in 34 (Table 1 and Figure 1 in the article capture the essence of the argument) that LE is physically meaningless because perception of efficiency changes if you use a different concentration to define the standard state (by convention ΔG_binding values correspond to an arbitrary 1 M standard concentration) and there is no way to objectively select any particular value of the standard concentration for calculation of LE.  The problem doesn’t go away if you try to define ligand efficiency in terms of logarithmically expressed values of IC₅₀, K_i or K_d instead of ΔG_binding because these quantities still have to be divided by an arbitrary concentration value in order to be expressed as logarithms (see M2011).  My view is that LE shouldn't even be described as a metric and I sometimes appropriate a quote ("it's not even wrong") that is usually attributed to Pauli because those who advocate the use of LE in drug design are unable (or unwilling) to say what it measures.

The meaninglessness of LE stems from it being defined by scaling ΔG_binding by the design risk factor (molecular size). In contrast, LipE is defined by offsetting pIC₅₀ by the risk factor (logP) and can be interpreted (see 34) as the energetic cost of moving the ligand from octanol to its target binding site (this interpretation is only valid when the ligand binds in its neutral form and is predominantly neutral in the aqueous phase).  When considering lipophilicity in property-based design it is important to be aware that octanol is an arbitrary choice of solvent for measurement of partition coefficients and that the logP (or logD) calculated for a compound may differ significantly depending on the algorithm used for the calculations. That said, the hydrogen bond donors/acceptors and ionizable groups tend to be relatively conserved within structural series which means that the details of exactly how lipophilicity is quantified are likely to be less critical in lead optimization than for structurally-diverse sets of compounds.

When we use LipE we’re actually assuming that logP (or logD) is predictive of properties such as aqueous solubility, affinity for anti-targets and metabolic lability. That is why it’s not accurate to state that the introduction of LipE showed how “physicochemical properties impact potency, selectivity, and safety”.  In some published studies the focus is less on the LipE metric and more on what might be called the "lipophilic efficiency concept" (aim for top left corner of a plot of potency against lipophilicity). It is common to show reference lines of constant LipE to plots of potency against lipophilicity in this type of analysis and if you're doing this you really should be citing R2009 rather than 29. 

I'll finish the commentary on LipE (or LLE if you prefer) with this statement made in the Editorial:

Emerging from an analysis of approved drugs, this rubric predicts a compound is more likely to be clinically developable when LipE > 5. [I don’t know what the authors of the Editorial mean by “rubric” (I'm not even sure that they do) but as a reviewer of the manuscript I would have pressed them to justify their claim. Specifically I would have been looking for a literature reference (for me, the choice of the word “emerging” does rather conjure up an image of hot gases and stoned priestesses at Delphi) and a coherent explanation for why a value of 5 yields a better rubric than values of 4 or 6.]

That’s all that I’ll be saying about LipE (or LLE if you prefer) and it’s time to take a look at the contributions of the third nominee for the Nobel Prize in Physiology or Medicine:

Finally, the development of Fsp3 by Frank Lovering in 2009 introduced a new principle for how molecular shape affects pharmaceutical properties and developability. [As a reviewer of the manuscript I would have pressed the authors to explicitly state the new principle that their third nominee for the Nobel Prize for Physiology or Medicine had introduced in 2009. My view is that Fsp3 is a thoroughly unconvincing descriptor of molecular shape and I suggest readers consider the suggestion that cyclohexane (Fsp3 = 1) would have a better shape match with benzene (Fsp3 = 0) than with either methane (Fsp3 = 1) or adamantane (Fsp3 = 1).]

[10-Aug-2025 update: The authors of the CNM2025 study claim "we repeated an analysis similar to that of Lovering et al. to assess Fsp3 in drugs approved post-2009 and those in active clinical development as of mid-2024" and conclude "there appeared to be no clear relationship between highest phase reached and Fsp3, suggesting the key conclusion noted by Lovering et al. has not persisted". My view expressed in this 05-Aug-2025 post is that the analysis is not sufficiently similar to support this conclusion.] 

 

[04-Aug-2024 update: The Fsp3 descriptor had actually been used as i_ali in the YG2003 study (Prediction of Aqueous Solubility of Organic Compounds by Topological Descriptors) six years before the publication of 35:

The aliphatic indicator of a molecule (i_ali) is equal to the number of sp3 carbons divided by the total number of carbon atoms in the molecule.

The YG2003 study discussed prediction of aqueous solubility using i_ali (renamed as Fsp3 in 35) in conjunction with other topological descriptors. In contrast with the claims made in 35 for Fsp3 the YG2003 study made no suggestion that i_ali was a highly effective predictor of aqueous solvation when used by itself.]   

Before discussing the contributions of the third nominee for the Nobel Prize for Physiology or Medicine I should stress that I certainly consider gratuitous use of aromatic rings to be a very bad thing in drug design (it was the data analysis in 35 that was criticized in KM2013 but not the eminently sensible suggestion that drug designers should look beyond what the authors referred to as ‘Flatland’). Having sp3 carbon atoms in a scaffold provides drug designers with a wider range of options for placement of substituents than would be the case for a fully aromatic scaffold and we stated in KM2013 that:   

One limitation of aromatic rings as components of drug molecules is that some regions above and below the plane defined by the atomic nuclear positions are not directly accessible to substituents. Molecular recognition considerations suggest a focus on achieving axial substitution in saturated rings with minimal steric footprint, for example by exploiting the anomeric effect or by substituting N-acylated cyclic amines at C2. 

My view is that deleterious effects of aromatic rings on aqueous solubility would be more plausibly explained by molecular interactions stabilizing the solid state than in terms of molecular shape (this point is discussed in more detail in HBD3). I also see saturated ring systems such as bicyclo[1.1.1]pentane and cubane as potentially more resistant to metabolism than benzene. 

There’s one point that I need to make before discussing 35 from the data analysis perspective which is that molecular structures with basic nitrogen atoms tend to have higher Fsp3 values than molecular structures that lack basic nitrogen atoms (see L2013). This means that you can’t tell whether the benefits of higher Fsp3 values are actually caused by the higher Fsp3 values or by the presence of basic nitrogen atoms.

The Editorial states:

Stemming from an analysis of discovery compounds, investigational drugs, and approved drugs, Fsp3 predicts a discovery compound is more likely to become a drug when Fsp3 > 0.40. [Figure 3 in 35 does not actually depict a significant difference between mean Fsp3 values for for discovery compounds and marketed drugs (the significant difference between mean Fsp3 values is for discovery and Phase 2 compounds).]  

It’s not clear (at least to me) where the figure of 0.40 comes from and I would argue that that compound X (IC₅₀ against therapeutic target = 50 μM; Fsp3 = 0.80) would actually be less likely to become a drug than compound Y (IC₅₀ against therapeutic target = 10 nM; Fsp3 = 0.20). I’m assuming that what the Editorial refers to as “analysis of discovery compounds, investigational drugs, and approved drugs” is what is shown by Figure 3 in 35. Presenting data in this manner hides the variation in Fsp3 for the compounds at each stage of development and makes the trends look much stronger than they actually are (this is verboten according to current J Med Chem author guidelines which state "If average values are reported from computational analysis, their variance must be documented.") I would challenge the suggestion that what is shown in Figure 3 in 35 can be used to calculate the probability that an arbitrary compound will become a drug (my view is that it’s not feasible to even define the probability that a compound will become a drug in a meaningful manner). Analyses of success in clinical development are generally more convincing when comparisons are made between compounds that pass or fail in individual phases of clinical development than between compounds in different phases of clinical development. 

The Editorial continues:        

This observation was ascribed to increased Fsp3 leading to increased aqueous solubility, a critical physiochemical property for successful drug discovery.

I’m assuming that what the Editorial refers to as “increased Fsp3 leading to increased aqueous solubility” is the trend shown by Figure 5 of 35 (this featured prominently in the KM2013 correlation inflation article) which claims to show the relationship between Fsp3 and log S (aqueous solubility expressed as a logarithm).  This claim is not accurate because the log S values have been binned and the relationship is actually between centre point of bin and mean log S value for bin. The authors of 35 used public domain aqueous solubility data for their analysis and we showed (KM2013; see Figure 5) that the Pearson correlation coefficient for the relationship between log S and Fsp3 is only 0.25 (the corresponding value for the binned data is 0.97).  I consider the suggestion that such a weak correlation could have any relevance whatsoever to the the likelihood of success in clinical trials to be wild and uninformed conjecture.      

I'll finish my commentary on Fsp3 by reproducing this claim made in the Editorial:

Much like the Rof5 and LipE, Fsp3 has proven to be enduringly useful for the design of compounds with improved chances of clinical success. (37) [My view is there is insufficient evidence to justify this claim and I'm perplexed by the citation of 37. In any case, members of the Nobel committee are likely to focus more on whether or not Fsp3 is usefully predictive than on the endurance of this molecular descriptor.]  

It’s now time to summarise what has been a long and at times pedantic blog post, and I thank all readers who’ve stayed with me. I don’t consider any of the three studies (22 | 29 | 35) that form the basis of the Nobel Prize nomination to have reported significant scientific discoveries and I would also challenge the claim made in the Editorial that these studies introduced new principles. I’m aware that 22 is heavily cited and I certainly agree that it is common to see values of LipE and Fsp3 quoted in the drug discovery literature. Nevertheless, I would argue that that the Editorial failed to provide even a single convincing example of the Rof5, LipE or Fsp3 making a critical contribution to the discovery of a marketed drug (this should be quite sufficient to rule out the award of a share in the Nobel Prize for Physiology or Medicine to any of these nominees). Furthermore, the Editorial doesn’t provide any convincing evidence that the Rof5, LipE or Fsp3 are usefully predictive in drug discovery projects.

Aside from the failure of the Editorial to demonstrate significant impact for the Rof5, LipE and Fsp3, I do have some scientific concerns about this Nobel Prize nomination. First, the Rof5 is not actually supported by data in the form that it is stated. Second, LipE had already been discussed, although not named, in the drug discovery literature when 29 was published. Third, Fsp3 had been already been introduced (as i_ali) for aqueous solubility prediction and the data analysis in 35 would fail to comply with current J Med Chem author guidelines.

Efficient trajectories

I'll examine an article entitled ‘Mapping the Efficiency and Physicochemical Trajectories of Successful Optimizations’ (YL2018) in this post and I should note that the article title reminded me that abseiling has been described as the second fastest way down the mountain. The orchids in Blanchisseuse have been particularly good this year and I’ll include some photos of them to break the text up a bit.

It’s been almost 22 years since the rule of 5 (Ro5) was published. While the Ro5 article highlighted molecular size and lipophilicity as pharmaceutical risk factors, the rule itself is actually of limited utility as a drug design tool. Some of the problems associated with excessive lipophilicity had actually been recognized (see Yalkowsky | Hansch) over a decade before the publication of Ro5 in 1997 and there’s also this article that had been published in the previous year. However, it was the emergence of high-throughput screening that can be regarded as the trigger for Ro5 which, in turn, dramatically raised awareness of the importance of physicochemical properties in drug design. The heavy citation and wide acceptance of Ro5 provided incentives for researchers to publish their own respective analyses of large (usually proprietary) data sets and this has been expressed more succinctly as “Ro5 envy”.

So let's take a look at YL2018 and the trajectories. I have to concede that ‘trajectory’ makes it all seem so physical and scientifically rigorous even though ‘path’ would be more appropriate (and easier to say after a few beers). As noted in ‘The nature of ligand efficiency’ (NoLE), I certainly believe that it is a good idea for medicinal chemistry teams to both plot potency (e.g. pIC50) against risk factors such as molecular size or lipophilicity for their project compounds and to analyze the relationships between potency and these quantities. However, it is far from clear that a medicinal chemistry team optimizing a specific structural series against a particular target would necessarily find the plots corresponding to optimization of other structural series against other targets to be especially relevant to their own project.

YL2018 claims that “the wider employment of efficiency metrics and lipophilicity control is evident in contemporary practice and the impact on quality demonstrable”. While I would agree that efficiency metrics are integral to the philatelic aspects of modern drug discovery, I don’t believe that YL2018 actually presents a single convincing example of efficiency metrics being used for decision making in a specific drug design project. I should also point out that each of the authors of YL2018 provided cannon fodder (LS2007 | HY2010 ) for the correlation inflation article and you might want to keep that in mind when you read the words “evident” and “demonstrable”. They also published 'Molecular Property Design: Does Everyone Get It?' back in 2015 and you may find this review of that seminal contribution to the drug design literature to be informative.

I reckon that it would actually be a lot more difficult to demonstrate that efficiency metrics were used meaningfully (i.e. for decision making rather than presentation at dog and pony shows) in projects than it would be to demonstrate that they were predictive of pharmaceutically relevant behavior of compounds. In NoLE, I stated:

"However, a depiction [6] of an optimization path for a project that has achieved a satisfactory endpoint is not direct evidence that consideration of molecular size or lipophilicity made a significant contribution toward achieving that endpoint. Furthermore, explicit consideration of lipophilicity and molecular size in design does not mean that efficiency metrics were actually used for this purpose. Design decisions in lead optimization are typically supported by assays for a range of properties such as solubility, permeability, metabolic stability and off-target activity as well as pharmacokinetic studies. This makes it difficult to assess the extent to which efficiency metrics have actually been used to make decisions in specific projects, especially given the proprietary nature of much project-related data."

YL2018 states, “Trajectory mapping, based on principles rather than rules, is useful in assessing quality and progress in optimizations while benchmarking against competitors and assessing property-dependent risks.” and, as a general point, you need to show you're on top of the physical chemistry if you're going write articles like this.

Ligand efficiency represents something of a liability for anybody claiming expertise in physical chemistry. The reason for this is that perception of efficiency depends on the unit that you use to express affinity and this is a serious issue (in the "not even wrong" category) that was highlighted in 2009 and 2014 before NoLE was published. While YL2018 acknowledges that criticisms of ligand efficiency have been made, you really need to say exactly why this dependence of perception is not a problem if you're going lecture about principles to readers of Journal of Medicinal Chemistry.

Ligand lipophilic efficiency (LLE) which is also known as ligand lipophilicity efficiency (LLE) and lipophilic efficiency (LipE) can be described as offset efficiency metric (lipophilicity is subtracted from potency). As such, perception of efficiency does not change when you use a different unit to express potency and, provided that ionization of ligand is insignificant, efficiency can be seen as a measure of the ease of transfer of ligand from octanol to its binding site. Here's a graphic that illustrates this:

LLE (LipE) measures ease of transfer of ligand from octanol to binding site

I'm not entirely convinced that the authors of YL2018 properly understood the difference between logP and logD. Even if they did, they needed to articulate the implications for drug design a lot more clearly than they have done. Here's an equation that expresses logD as a function of logP and the fraction of ligand in the neutral form at the experimental pH (assuming that only neutral forms of ligands partition into the octanol).

The equation highlights the problems that result from using logD (rather than logP) to define "compound quality". In essence the difficulty stems from the composite nature of logD which means that logD can be also be reduced by increasing the extent of ionization. While this is likely to result in increased aqueous solubility, it is much less likely that problems associated with binding to anti-targets will be addressed. Increasing the extent of ionization may also compromise permeability.    

YL2018 is clearly a long article and I'm going to focus on two of the ways in which the authors present values of efficiency metrics. The first of these is the "% better" statistic which is used to reference specific compounds (e.g. optimization endpoints) to sets of compounds (e.g. everything synthesized by project chemists). The statistic is calculated as the fraction of compounds in the set for which both LE and LLE values are greater than the corresponding values for the compound of interest. The smallest values of the "% better" statistic are considered to correspond to the most optimal compounds. The use of the "% better" statistic could be taken as indicating that absolute thresholds for LE and LLE are not useful for analyzing optimization trajectories..

The fundamental problem with analyzing data in this manner is that LE has a nontrivial dependence on the concentration unit in which affinity is expressed (this is shown in Table 1 and Fig. 1 in NoLE). One consequence of this nontrivial dependence is that both perception of efficiency and the "% better" statistic vary with the concentration unit used to express efficiency.

The second way that the authors of YL2018 present values of efficiency metrics is to plot LE against LLE and, as has already been noted, this is a particularly bone-headed way to analyze data. One problem is that the plot changes in a nontrivial manner if you express affinity in a different unit. This makes it difficult to explain to medicinal chemists why they need to convert the micromolar potencies from their project database to molar units in order for The Truth to be revealed. Another problem is that LE and LLE are both linear functions of pIC50 (or pKi) and that means that the appearance of the plot is heavily influenced by the (trivial) correlation of potency with itself.

A much better way to present the data is to plot LLE against number of non-hydrogen atoms (or any other measure of molecular size that you might prefer). In such a plot, expressing potency (or affinity) in a different unit simply shifts all points 'up' or 'down' to the same extent which means that you no longer have the problem that the appearance of plot changes when you change units. The other advantage of plotting the data in this manner is that there is no explicit correlation between the quantities being plotted. I have used a variant of this plot in NoLE (see Fig. 2b) to compare some fragment to lead optimizations that had been analyzed previously.

I think this is a good point to wrap things up. Even if you have found the post to be tedious, I hope that you have at least enjoyed the orchids. As we would say in Brazil, até mais!

    

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.  

Até mais!

Flora and fauna of Belovezhskaya Pushcha

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