Critique of ligand efficiency metrics (presented at Cancer Research UK, Manchester, 01-June-2015)

1. Ligand efficiency: nice concept, shame about the metrics
Peter W Kenny
http://fbdd-lit.blotspot.com | http://www.slideshare.net/pwkenny

2. Some stuff to think about
• We need to be honest with ourselves and make a
clear distinction between what we know and what we
believe
• If we do bad data analysis then how will we be able
to convince people that drug discovery is really
difficult?

3. Things that make drug discovery difficult
• Having to exploit targets that are weakly-linked to
human disease
• Poor understanding and predictability of toxicity
• Inability to measure free (unbound) physiological
concentrations of drug for remote targets (e.g.
intracellular or on far side of blood brain barrier)
Dans la merde, FBDD & Molecular Design blog :

4. Molecular Design
• Control of behavior of compounds and materials by
manipulation of molecular properties
• Sampling of chemical space
– For example, does fragment-based screening allow better
control of sampling resolution?
• Hypothesis-driven or prediction-driven
– There’s more to molecular design than making predictions
(from Molecular Design blog): link
Montanari, Propopczyk, Sala, Sartori (2013) JCAMD 27:655-664 DOI
Kenny JCIM 2009 49:1234-1244 DOI
New year, new blog name, Molecular Design blog

5. TEP = log10([𝐷𝑟𝑢𝑔 𝑿,𝑡 ] 𝑓𝑟𝑒𝑒
𝐾 𝑑
)
Target engagement potential (TEP)
A basis for pharmaceutical molecular design?
Design objectives
• Low Kd for target(s)
• High (hopefully undetectable) Kd for antitargets
• Ability to control [Drug(X,t)]free
Kenny, Leitão & Montanari JCAMD 2014 28:699-710 DOI

6. Property-based design as search for ‘sweet spot’
Green and red lines represent probability of achieving ‘satisfactory’ affinity and
‘satisfactory’ ADMET characteristics respectively. The blue line shows the product of
these probabilities and characterizes the ‘sweet spot’. This way of thinking about the
‘sweet spot’ has similarities with molecular complexity model proposed by Hann et al.
Kenny & Montanari, JCAMD 2013 27:1-13 DOI

7. Rules, guidelines and metrics
• It’s not a rule, it’s a guideline… OK why did you call it
a rule?
• Strength of a trend tells us how rigidly we should
adhere to guidelines based on that trend
• Think carefully about physicochemical basis of
guidelines and metrics
– Using logD to define compound quality metrics suggests
that compounds can be made better by simply increasing
the extent of ionization

8. Know your data
• Assays are typically run in replicate making it possible
to estimate assay variance
• Every assay has a finite dynamic range and it may not
always be obvious what this is for a particular assay
• Dynamic range may have been sacrificed for
thoughput but this, by itself, does not make the
assay bad
• We are likely to need to be able analyse in-range and
out-of-range data within single unified framework
– See Lind (2010) QSAR analysis involving assay results which are only known to
be greater than, or less than some cut-off limit. Mol Inf 29:845-852 DOI

9. Introduction to ligand efficiency metrics (LEMs)
• We use LEMs to normalize activity with respect to risk factors
such as molecular size and lipophilicity
• What do we mean by normalization?
• How predictive are risk factors of bad outcomes?
• We make assumptions about underlying relationship between
activity and risk factor(s) when we define an LEM
• LEM as measure of extent to which activity beats a trend?
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI
Ligand efficiency metrics considered harmful, Molecular design blog

10. Scale activity/affinity by risk factor
LE = ΔG/HA
Offset activity/affinity by risk factor
LipE = pIC50  ClogP
Ligand efficiency metrics
There is no reason that normalization of activity with respect to risk factor
should be restricted to either of these functional forms.
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI

11. Use trend actually observed in data for normalization
rather than some arbitrarily assumed trend
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI
Can we accurately claim to have normalized a data set if we have
made no attempt to analyse it?
Green: line of fit
Purple: constant LE
Blue: constant LipE

12. There’s a reason why we say standard free energy
of binding
DG = DH TDS = RTln(Kd/C0)
• Adoption of 1 M as standard concentration is
arbitrary
• A view of a chemical system that changes with
the choice of standard concentration is
thermodynamically invalid (and, with apologies to
Pauli, is ‘not even wrong’)
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI
Efficient voodoo thermodynamics, FBDD & Molecular design blog

13. NHA Kd/M C/M (1/NHA) log10(Kd/C)
10 10-3 1 0.30
20 10-6 1 0.30
30 10-9 1 0.30
10 10-3 0.1 0.20
20 10-6 0.1 0.25
30 10-9 0.1 0.27
10 10-3 10 0.40
20 10-6 10 0.35
30 10-9 10 0.33
Effect on LE of changing standard concentration
Analysis from Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI
Note that our article overlooked similar observations 5 years earlier by
Zhou & Gilson (2009) Chem Rev 109:4092-4107 DOI

14. Scaling transformation of parallel lines by dividing Y by X
(This is how ligand efficiency is calculated)
Size dependency of LE in this example is consequence of non-zero intercept
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI

15. Affinity plotted against molecular weight for minimal binding
elements against various targets in inhibitor deconstruction
study showing variation in intercept term
Data from Hajduk (2006)
JMC 49:6972–6976 DOI
Each line corresponds to a different target and no attempt has been
made to indicate targets for individual data points. Is it valid to
combine results from different assays when using LE?
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI

16. Offsetting transformation of lines with different slope and
common intercept by subtracting X from Y
(This is how lipophilic efficiency is calculated)
Thankfully (hopefully?) lipophilicity-dependent lipophilic
efficiency has not yet been ‘discovered’
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI

17. Water
Octanol
pIC50
LipE
What we try to capture when we use lipophilic efficiency
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI
There are two problems with this approach. Firstly octanol, is not ideal non-polar reference state
because it can form hydrogen bonds with solutes (and is also wet). Secondly, logP does not
model cost of transfer from water to octanol for ligands that bind as ionized forms
logP

18. Linear fit of ΔG to HA for published PKB ligands
Data from Verdonk & Rees (2008) ChemMedChem 3:1179-1180 DOI
HA
ΔG/kcalmol-1 ΔG/kcalmol-1  0.87  (0.44  HA)
R2  0.98 ; RMSE  0.43 kcalmol-1
-ΔGrigid

19. Ligand efficiency, group efficiency and residuals
plotted for PKB binding data
Resid|GE
GE/kcalmol-1HA-1
Resid/kcalmol-1
LE/kcalmol-1HA-1
Residuals and group efficiency values show similar trends with pyrazole (HA = 5) appearing
as outlier (GE is calculated using ΔGrigid ). Using residuals to compare activity eliminates
need to use ΔGrigid estimate (see Murray & Verdonk 2002 JCAMD 16:741-753 DOI) which is
subject to uncertainty.

20. Use residuals to quantify extent to which activity
beats trend
• Normalize activity using trend(s) actually observed in
data (this means we have to model the data)
• All risk factors can be treated within the same data-
analytic framework
• Residuals are invariant with respect to choice of
concentration units
• Uncertainty in residuals is not explicitly dependent of
value of risk factor (not the case for scaled LEMs)
• Residuals can be used with other functional forms (e.g.
non-linear and multi-linear)
Kenny, Leitão & Montanari (2014) JCAMD 28:699-701 DOI

21. Some more stuff to think about
• The function of a metric is to measure and not
tell you what you want to hear
• Efficiency as response of activity to risk factor
• Efficiency as extent to which to which activity
beats a trend
• Need to model activity data if you’re claiming to
have normalized it
• Using LEMs distorts your perception of data
unnecessarily