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 (IE–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(Kd/C°) approximates to –1.37 × log(Kd) kcal/mol.
I do need to mention a potential source of confusion when analysing Kd values. In biochemistry, biophysics and drug discovery Kd values are conventionally quoted as dimensioned quantities in units of concentration. However, Kd values may also be quoted as dimensionless ratios and, in these cases, the Kd 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 Kd. 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."
