Property Forecast Index Validated

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I arrived in Korea on Friday night and am greatly enjoying it here. Photos below show the Jungbu Dried Seafoods Market near where I'm staying and dinner on Sunday (spicy beef noodles).

I visited the War Memorial on Sunday and took selfies with the Shenyang J-6 (Chinese version of MiG-19) 'liberated' by Capt. Lee Woong-pyeong when he defected to South Korea on 25th February 1983, a 'liberated' T-34 (as Uncle Joe is said to have observed, quantity has a quality all of its own) and Great Leader's car (also 'liberated' although it was not clear exactly when). 

So enough of the travel photos for now and let's get back to the science. Regular readers (both of them) of this blog will be well aware of my visceral dislike for drug design metrics. One reason for this visceral dislike is that I consider these metrics to trivialise the problems faced by medicinal chemists and I remain sceptical that one can make meaningful predictions of developability or likelihood of clinical success for compounds based only on their chemical structures without knowing anything about their biological activities. One metric that I have criticised harshly in the past is property forecast index (PFI) which was originally introduced as solubility forecast index (SFI). Specifically, I denounced SFI as a ‘draw pictures and wave arms’ data analysis strategy and privately I even considered the possibility that it had been created by a toddler armed with a box of colored crayons.

Let’s take a look at the HY2010 article in which SFI was introduced. Proprietary aqueous solubility measurements (continuous variable) were first processed to assign compounds to one of three aqueous solubility categories. Histograms showing the proportions of measurements in each aqueous solubility category were created by binning values of SFI and of c log D_pH7.4 and the histograms were compared visually:    

This graded bar graph (Figure 9) can be compared with that shown in Figure 6b to show an increase in resolution when considering binned SFI versus binned c log D_pH7.4 alone.

Recently, I have been forced to revise my negative view of PFI and I have to admit that it pains me deeply to realise that I could have been so utterly wrong for so long in my assessment of what is actually an elegant and highly-predictive drug design metric. Indeed I have now come to the conclusion that the only reason that the Journal of Medicinal Chemistry did not include PFI in its nomination for the Nobel Prize in Physiology or Medicine was that the introduction of the Ro5, LipE and Fsp3 principles led directly to so many marketed drugs being approved.

What has caused such a fundamental shift in my views? First, PFI is highlighted in the European Federation of Medicinal Chemistry (EFMC) ‘Best Practices from Hits to Lead Generation’ webinar.  Now it goes without saying that EFMC includes some of the sharpest minds in medicinal chemistry and, given that they consider PFI to be sufficiently important for inclusion in a best practices webinar, it became abundantly clear that I needed to revise my hopelessly naïve thinking. Let’s join the webinar at 27:53 and you’ll see in the webinar slide that SFI (as PFI was originally introduced) has been strongly endorsed by Practical Cheminformatics, a blog that many, including me, accept without question as the source of a number of fundamental ground truths in the AI field.

However, what convinced me of the sublime elegance and extreme predictivity of PFI is a seminal study by the world-renowned expert on tetrodotoxin pharmacology, Prof. Angelique Bouchard-Duvalier of the Port-au-Prince Institute of Biogerontology, working in collaboration with the Budapest Enthalpomics Group (BEG). The manuscript has not yet been made publicly available although I was able to access it with the help of my associate ‘Anastasia Nikolaeva’ (not sure exactly what she’s doing these days although she did post a photo from Pyongyang showing her and a burly chap with a toothy grin and a bizarre haircut). There is no doubt that this genuinely disruptive study will comprehensively reshape the predictive ADME landscape, enabling drug discovery scientists, for the very first time, to make accurate predictions for developability and probability of critical trial success using only chemical structures as input.

Prof. Bouchard-Duvalier’s seminal study clearly demonstrates that graphical presentation of categorized continuous data outperforms regression analysis performed on the uncategorized continuous data. The math is truly formidable (my rudimentary understanding of Haitian patois didn’t help either) and involves first projecting the atomic isothermal compressibility matrix into the quadrupole-normalized polarizability tensor before applying the Barone-Samedi transformation, followed by hepatic eigenvalue extraction using an algorithm devised by E. V. Tooms (a reclusive Baltimore resident whose illustrious research career in analytic topology was abruptly halted almost 31 years ago by an unfortunate escalator accident). The incisive analysis of Prof. Bouchard-Duvalier shows without a shadow of doubt that the data visualization used to establish PFI as a fundamental drug design principle will reliably and robustly outperform all AI approaches to prediction of aqueous solubility. Furthermore, ‘Anastasia Nikolaeva’ was also able to ‘liberate’ a prepared press release in which the beaming BEG director Prof. Kígyó Olaj explains: 

Possibilities are limitless now that we can accurately and robustly predict the developability of a compound using only its chemical structure as input and we can now finally consign regression analysis to the dustbin of history. Surely the Editors of Journal of Medicinal Chemistry will recognize the impact of PFI on real world drug discovery when they make their Nobel Prize nominations later this year. 

Standard states and solution thermodynamics

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Readers of this blog know that, on more than one occasion, I have denounced the ligand efficiency metric as physically meaningless on the grounds that perception of efficiency varies with the concentration value that defines the standard state. As I argue in NoLE this is clearly thermodynamic nonsense (Pauli might even have suggested that it wasn’t even wrong) and the equivalent cheminformatic argument is that perception shouldn’t change when you use a different unit to express a quantity.

A change in perception resulting from using a different standard concentration can also be a problem when analysing thermodynamic signatures. One particular absurdity is that binding can be switched from enthalpy-driven to entropy-driven simply by using a different concentration to define the standard state. This statement in the W2014 article unintentionally highlights the issue:

Consequently, we define the dimensionless ratio (ΔH + TΔS)/ΔG as the Enthalpy–Entropy Index (I_E–E) and use it here to indicate the enthalpy content of binding. Its advantageous feature is that it is normalised by the free energy ΔG (= ΔH  – TΔS), and so it can be used to compare compounds with millimolar to nanomolar binding affinities during the course of a hit-to-lead optimisation.

I do indeed think that it makes a lot of sense to use (ΔH + TΔS) and ΔG as parameters for exploring thermodynamic signatures. However, the dimensionless ratio of the two quantities is physically meaningless because of its dependence on the concentration used to define the standard state (this dependence stems from the fact that ΔS depends on the standard concentration while ΔH is invariant to change in the standard concentration).

One article that I’ve been particularly critical of in the past is “The role of ligand efficiency metrics in drug discovery” NRDD 133:105-121 (2014) DOI. Specifically, I have expressed concerns about this sentence in Box 1 (Ligand efficiency metrics) of the article:

Assuming standard conditions of aqueous solution at 300K, neutral pH and remaining concentrations of 1M, –2.303RTlog(K_d/C°) approximates to –1.37 × log(K_d) kcal/mol.

I do need to mention a potential source of confusion when analysing K_d values. In biochemistry, biophysics and drug discovery K_d values are conventionally quoted as dimensioned quantities in units of concentration. However, K_d values may also be quoted as dimensionless ratios and, in these cases, the K_d value depends on the concentration used to define the standard state. There seems to be an error in that the approximation appears to eliminate the dimensions of the standard concentration C°.

I should say that I’ve always been a bit nervous about denouncing the approximation as an error because the authors are all renowned thought leaders in the drug discovery field. Furthermore, the journal impact factor of NRDD is a significant multiple of my underwhelming h-index and any error of such apparent grossness would surely have been detected during the rigorous peer review process applied by this elite journal. It turns out that my nervousness was indeed well placed and, when calculated at 300 K, the product RT actually serves as an annihilation operator that eliminates the dimensionality associated with K_d. This also explains why a temperature of 300 K must be used when calculating the ligand efficiency even though biochemical assays are usually run at human body temperature (310 K). 

I became convinced of the validity of the above approximation recently after examining a manuscript by the world-renowned expert on tetrodotoxin pharmacology, Prof. Angelique Bouchard-Duvalier of the Port-au-Prince Institute of Biogerontology, who is currently on secondment to the Budapest Enthalpomics Group (BEG). The manuscript has not yet been made publicly available although I was able to access it with the help of my associate ‘Anastasia Nikolaeva’ (she decamped last year from Tel Aviv to Uzbekistan and, to Derek’s likely disapproval, is currently running an open access journal out of a van in Samarkand). There is no doubt that this genuinely disruptive study will comprehensively reshape the generative AI landscape, enabling drug discovery scientists, for the very first time, to rationally design novel clinical candidates using only gene sequences as input.

Prof. Bouchard-Duvalier’s seminal study clearly demonstrates that it is indeed possible to eliminate the need to define standard states for the thermodynamic analysis of liquid solutions, provided that the appropriate temperature is used. The math is truly formidable (my rudimentary understanding of Haitian patois didn’t help either) and involves first projecting the atomic isothermal compressibility matrix into the quadrupole-normalized polarizability tensor before applying the Barone-Samedi transformation, followed by hepatic eigenvalue extraction using the algorithm introduced by E. V. Tooms (a reclusive Baltimore resident better known for his research in analytic topology). ‘Anastasia Nikolaeva’ was also able to ‘liberate’ a prepared press release in which a beaming BEG director Prof. Kígyó Olaj explains that, “possibilities are limitless now that we have eliminated the standard state from solution thermodynamics and thereby consigned the tedious and needlessly restrictive Second Law to the dustbin of history." 

Enthalpy-driven pharmacokinetics

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Drug design is a multi-objective endeavor. Some objectives such as maximization of affinity against target(s) and minimization of affinity against anti-targets are easily defined. Other objectives such as controllability of exposure are much less easily defined and this means that drug design is indirect. Controllability of exposure is the focus of pharmacokinetic optimization and I recently became aware of an exciting new development that will surely reshape the pharmacokinetic field and transform drug discovery beyond all recognition.

Target engagement potential and the multiple objectives of drug design 

The exciting results from another seminal study by the Budapest Enthalpomics Group (BEG) look set to revolutionize the way that we think about pharmacokinetics. The work, funded by Mothers Against Molecular Obesity (MAMO), was described in a book chapter that was prematurely posted online although the error does appear to have been recognized because the article is no longer publicly visible. In a study that will undoubtedly disrupt drug discovery, it is clearly shown that the thermodynamic signature for the binding of a ligand to a protein is predictive of the physicochemical behavior of the ligand even when that protein is absent from the system.

The theoretical treatment introduced in this groundbreaking study is formidable and the starting point is is an eigenvalue decomposition of the entropic field tensor in reciprocal heavy atom space. Machine learning using the Blofeld Optimized Ligand Lipophilicity Of Cryogenic Krypton Solvates algorithm demonstrates unequivocally that the Grayling annihilation operator can be used to eliminate the entropy (and its efficacy-limiting dependence on the definition of the standard state) from any in vivo system. This leads to highly-efficient, enthalpy-driven pharmacokinetics in which the clearance (shown to be strongly correlated with the trace of the entropic field tensor) can be significantly attenuated. "The key to successful pharmacokinetic optimization is to eliminate the elimination", explains institute director Prof Kígyó Olaj, "and we have shown, for the first time, that entropy can be exorcised from the equations of pharmacokinetics with even greater efficiency than if it had been done by Torquemada himself."