Thermodynamics for medicinal chemistry design

Thermodynamics for medicinal chemistry design
Peter W Kenny
http://fbdd-lit.blotspot.com | http://www.slideshare.net/pwkenny

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 :

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

TEP = log10([𝐷𝑟𝑢𝑔 𝒓,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(r,t)]free
Kenny, Leitão & Montanari JCAMD 2014 28:699-710 DOI

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

In tissues
Free in
plasma
Bound to
plasma
protein
Dose of drug
Eliminated drug
Simplifed view of what happens to drugs after dosing
ΔH-TΔS

Molecular interactions and drug action

Molecular design frequently focuses on structural
relationships between compounds
Tanimoto coefficient (foyfi) for structures is 0.90
Ester is methylated acid Amides are ‘reversed’

Relationships between structures as framework for analysing
activity and properties (G)
?
Date of Analysis N logFu SE SD %increase
2003 7 -0.64 0.09 0.23 0
2008 12 -0.60 0.06 0.20 0
Mining PPB database for carboxylate/tetrazole pairs suggested that bioisosteric replacement would
lead to decrease in Fu . Tetrazoles were not synthesised even though their logP values are expected to
be 0.3 to 0.4 units lower than for corresponding carboxylic acids.
Birch et al (2009) BMCL19:850-853 DOI

Amide N logS SE SD %Increase
Acyclic (aliphatic amine) 109 0.59 0.07 0.71 76
Cyclic 9 0.18 0.15 0.47 44
Benzanilides 9 1.49 0.25 0.76 100
Effect of amide N-methylation on aqueous solubility is
dependent on substructural context
Birch et al (2009) BMCL 19:850-853 DOI

Thermodynamics and molecular interactions
The contribution of an intermolecular contact (or group of
contacts) to affinity (or the changes in enthalpy, entropy,
volume or heat capacity associated with binding) is not an
experimental observable

Where does ITC fit into medicinal chemistry design?
• Direct, label-free method for measuring binding affinity
– Primary project assay
– Validation of higher-throughput project assays
– Input for computational affinity models
• Thermodynamic signature (H, TS) may be more
sensitive than G for detection of discontinuities in SAR
– e.g. change in binding mode within structural series

On enthalpic optimization
• How do isothermal systems like live humans sense the
benefits of an enthalpically-optimized drugs?
• Why would we expect measurement of H and S for
binding of compound to a protein to be predictive of the
behaviour of the compound in the absence of the
protein?

There’s a reason why we say standard free energy
of binding
G = H - TS = 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

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

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?
Ligand efficiency metrics considered harmful, Molecular design blog

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.

Use trend actually observed in data for normalization
rather than some arbitrarily assumed trend
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

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

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

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?

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’

Water
Octanol
pIC50
LipE
Thermodynamics and lipophilic efficiency
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

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

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.

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)

Some stuff to think about
• We need to 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?

Thermodynamics for medicinal chemistry design

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