Reducing Data: Ligand Efficiency and Other Fallacies

Ben 21-10-2015 Picture 1This article refers to an interesting yet controversial work of Michael Schultz1 and the debate on the topic of Ligand Efficiency and other psuedometrics.2

This article represents the view of the author and not the SDDC as a whole, but hopes to open the discussion on this important topic.

As a computational chemist part of my time is spent in the realms of data theory (often debating the healthcare of cats in boxes, and how much it cares if we observe it), however today, I intend to take the cat from Schrodinger’s Thunderdome (two states enter, one state leaves) and set it firmly amongst the pigeons in an attempt to discuss the controversial topic of Ligand Efficiency.

Data reduction is, as its name suggests, the process of reducing the amount of data for any dataset, whilst trying to retain the information – that is, effectively reducing the noise and keeping the signal. Some may argue that the essence of this thing we call Science is in fact the way in which we conduct this data reduction.

All members of a drug discovery team use data reduction in slightly different ways according to their ilk, but realistically it normally boils down to analysing which components of a data set cause the greatest variance in the output metric (e.g. which chemical properties affect the largest change in activity). Lipinski’s seminal works on the Rule of Five (despite technically being a Texas sharpshooter fallacy) selected items such as Mass, LogP and number of acceptor and donors as key components in whether a material would be an orally available drug-like material. His work effectively forced data reduction of countless criteria down to a handful (despite them being selected ex post facto rather than letting the model decide – in recent pipelines the average MW is increasing, but failure rate due to PK/bioavailability is decreasing, so this clearly needs redressing, as there is little correlation between them.3 Modified subsets of these rules emerged (e.g. Rule of three), based, unfortunately also on the same fallacy – mistaking plausibility for probability. There is no doubt however, that Lipinski’s work made a significant change in the paradigm of compound development which was decidedly for the better. The problem comes in the application: calling it a Rule or a Law when realistically they are guidelines which are easily and successfully sidestepped.

Ligand Efficiency – data reduction for small molecules

Ligand efficiency is a term used a lot by those involved in fragment based drug discovery – though it has as much application in larger molecules as it does in FBDD. Ligand Efficiency (LE) attempts to provide a useful measure of the effective contribution of each atom in the material’s activity – it is not a normalisation as the authors suggested, but is in fact a simple average of atomic contribution. It works somewhat oversimply by taking the number of heavy (non-hydrogen) atoms as the size metric. The Ligand Efficiency equation is shown in Eqn 1.

Ben 21-10-2015 Picture 2

This gives a simple number where higher is better which determines how “efficient” a ligand is at binding. There are issues in this application which are discussed below:

All non-hydrogen atoms are the same: This equation treats all heavy atoms the same. Apart from the obvious reductio ad absurdum case that for any ligand, if you swap a carbon for a Uranium atom, the LE does not change, it has a more serious implication: atoms that are capable of being donors or acceptors (e.g. which contribute large parts of a binding energy) are treated the same as a carbon or any other atom). This over simplification tends towards “smaller is better”, not “functional is better”.

Group Contributions disallowed: π-stacking interactions are penalised in the sense that all atoms are counted as singular, and thusly effects on binding are considered as singular too. e.g. in order to keep LE high, we can reduce atom count. However slicing an aromatic ring in half will destroy its π-stacking capability and will thusly reduce the activity too.

Non-Linearity: LE exhibits non-linearity across heavy atom count: in very small materials (such as fragments) a single atom addition can have the same effect as a large number of additional atoms in a larger complex, as shown in the graph below.

Fig 1. For a given pIC50, Ligand Efficiency does not exhibit linearity – This applies a very heavy penalty in small compound size (and in a more mathematically real sense, tends to infinity as heavy atom count tends to zero).

Fig 1. For a given pIC50, Ligand Efficiency does not exhibit linearity – This applies a very heavy penalty in small compound size (and in a more mathematically real sense, tends to infinity as heavy atom count tends to zero).

Built for Failure: The premise of this metric is to demonstrate that a higher number is a more efficient ligand, however it is recognised that LE will typically degrade as a material goes through development. Final materials rarely have the better LE than the original hit due to the heavy small change penalty taken on from a fragment hit – so LE will go down in the case of any development. As a result, LE should only be used at immediate hit stages and loses relevance rapidly as the material is developed.

What IC50?: Ligand efficiency attempts to include an activity metric as a way of taking it out of a theoretical domain and linking it to real data. This is problematic however as the IC50 will of course vary in vivo, in vitro, by assay type and even by handling. This makes LE a very singularly applicable metric: They are ONLY comparable when the assay type is the same across the data range. Take any material from your development pipeline, it will have variable IC50s as it goes along your cascade. Which do you use for this metric – and, more importantly, is it the same IC50 that the rest of your team are using? Data from external sources are thusly equally non-comparable (as there is often variability from lab to lab). So given this information, when can you really use it in a meaningful way?

So far the analysis looks pretty poor in using LE as a metric for making decisions on development, however there is a real debate to be had over the importance of Useful vs. Accurate. Much like the aforementioned Rule of Five, whilst LE may be flawed in conception and in the very way it is banded about in project meetings, it does serve a purpose as a common language that allows medicinal chemists to engage in discussions comparing materials for development – as long as care is taken in understanding exactly what they are referring to when they cite a ligand efficiency.

As a computational chemist, data reduction is a normal part of many processes, from QSAR to MPOs, and in my opinion LE fails to capture a fair share of the information due it’s over simplified nature. A question that is rarely asked in a world of easily coined metrics is “what is this measure really showing us”. In the case of LE, I think the answer is “not a lot”.

1 (a) Improving the Plausibility of Success with Inefficient Metrics; Shultz, Med. Chem. Lett. 2014 5, 2-5

(b) Improving the Plausibility of Success in Drug Discovery with the Use of Inefficient Metrics; Shultz Proceedings of Guiding Optimal Compound Design Symposium, Cambridge, MA, March 19th 2015

2 (a) Myriad Metrics, but which are useful:

(b)Too Many Metrics:

(c)More Thoughts on Compound Metrics:

3 Relating Molecular Properties and in vitro assay results to in vivo drug disposition and toxicity outcomes; Sutherland et al. J.Med.Chem. 2012, 55, 6455-6466

Blog written by Ben Wahab

1 thought on “Reducing Data: Ligand Efficiency and Other Fallacies

  1. Pingback: Multiple Multiparameter Optimisations, and the Success of Confirmation Bias | Sussex Drug Discovery Centre

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