quantum chemical and machine learning calculations of the intrinsic aqueous solubility of druglike...
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Quantum Chemical and Machine Learning Calculations of the Intrinsic Aqueous
Solubility of Druglike Molecules
Dr John MitchellUniversity of St Andrews
How should we approach the
prediction/estimation/calculation
of the aqueous solubility of
druglike molecules?
Two (apparently) fundamentally different approaches: theoretical chemistry & informatics.
The Two Faces of Computational Chemistry
TheoreticalChemistryInformatics
Theoretical Chemistry
“The problem is difficult, but by making suitable approximations we can solve it at reasonable cost based on our understanding of physics and chemistry”
Theoretical Chemistry
• Calculations and simulations based on real physics.
• Calculations are either quantum mechanical or use parameters derived from quantum mechanics.
• Attempt to model or simulate reality. • Usually Low Throughput.
Drug Disc.Today, 10 (4), 289 (2005)
Existing Theoretical Approaches
• Thus far, although theoretical methods have shown promise, they have not matched the accuracy of QSPR.
• There is no theoretical method that deals directly with solubility, so the problem has to be broken down into parts.
• There are several different ways of doing this.
Our First Principles Method
• We present one such approach and believe this to be the world’s most cost-effective first principles solubility method.
Thermodynamic Cycle
Gsub from lattice energy minimisation
Ghydr from Reference Interaction Site Model (RISM)
Different kinds of theoretical method are used for each part
Gsub from lattice energy & a phonon entropy term;DMACRYS using B3LYP/6-31G(d,p) multipoles and FIT repulsion-dispersion potential.
Ghydr from Reference Interaction Site Model with Universal Correction (RISM/UC).
Different kinds of theoretical method are used for each part
OUR DATASET (25 molecules)
We have experimental logS for all 25 molecules, but can only subdivide into ΔGsub and ΔGhydr for 10 of them.
Thermodynamic Cycle
Crystal
Gas
Solution
Sublimation Free Energy
Crystal
Gas
Sublimation Free Energy
Crystal
Gas
Sublimation Free Energy
Crystal
Gas
Calculating ΔGsub is a standard procedure in crystal structure prediction
Crystal Structure Prediction
• Given the structural diagram of an organic molecule, predict the 3D crystal structure.
S NBr
OO
Slide after SL Price, Int. Sch. Crystallography, Erice, 2004
CSP Methodology
• Based around minimising lattice energy of trial structures.
• Enthalpy comes from lattice energy and intramolecular energy (DFT), which need to be well calibrated against each other: trade-off of lattice vs conformational energy.
• Entropy comes from phonon modes (crystal vibrations); can get Free Energy.
-74
-73
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-69
149 150 151 152 153 154 155
Volume/molecule (Å3)
Lat
tice
Ene
rgy
(kJ/
mol
)
P1 P_1P21 P21/cCc C2C2/c PmP2/c P21/mP21212 PcP212121 Pca21Pna21 PbcnPbca Pmn21Pma21 ALPHABETA GAMMA
These methods can get relative lattice energies of different structures correct, probably to within a few kJ/mol. Absolute energies are harder.
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149 150 151 152 153 154 155
Volume/molecule (Å3)
Lat
tice
Ene
rgy
(kJ/
mol
)
P1 P_1P21 P21/cCc C2C2/c PmP2/c P21/mP21212 PcP212121 Pca21Pna21 PbcnPbca Pmn21Pma21 ALPHABETA GAMMA
Additional possible benefit for solubility: if we don’t know the crystal structure, we could reasonably use best structure from crystal structure prediction.
Lattice energies from DMACRYS with FIT atom-atom model potential and B3LYP/6-31G(d,p) distributed multipoles.
Results for ΔGsub
Reasonable prediction of ΔGsub, but small number of molecules.
Results for ΔGsub
80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 160.0080.00
100.00
120.00
140.00
160.00
180.00
200.00
f(x) = 1.07431033938862 x + 3.60559227465819R² = 0.531284409642467
ΔH sub experimental v ΔH sub predicted
dH Vs exp dH
Linear (dH Vs exp dH)
Experimental ΔH sub kJ mol-1
Pre
dic
ted
ΔH
su
b k
J m
ol-
1
To see the trends in errors, we need to look at more molecules.
RMSE = 20.4 kJ/mol(46 molecules)
80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 160.0080.00
100.00
120.00
140.00
160.00
180.00
200.00
f(x) = 1.07431033938862 x + 3.60559227465819R² = 0.531284409642467
ΔH sub experimental v ΔH sub predicted
dH Vs exp dH
Linear (dH Vs exp dH)
Experimental ΔH sub kJ mol-1
Pre
dic
ted
ΔH
su
b k
J m
ol-
1
The 46 compound set shown here has a larger error, mostly due to some large outliers. Error statistics vary with dataset.
RMSE = 20.4 kJ/mol(46 molecules)
30 35 40 45 50 55 60 65 70 75 8050.00
52.00
54.00
56.00
58.00
60.00
62.00
64.00
66.00
68.00
f(x) = 0.0857428957234206 x + 56.0784056418822R² = 0.0940590648113177
TΔS sub experimental v TΔS sub predicted
TdS Vs exp TdS
Linear (TdS Vs exp TdS)
TΔS experimental kJ mol-1
TΔ
S p
red
icte
d k
J m
ol-
1
RMSE = 9.3 kJ/mol(46 molecules)
30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.000.00
20.00
40.00
60.00
80.00
100.00
120.00
f(x) = 0.742207217400145 x + 28.1100057140445R² = 0.312904269021572
ΔG sub experimental v ΔG sub predicted
G Experimental Vs Predicted
Linear (G Experimental Vs Predicted)
ΔG sub Experimental
ΔG
su
b P
red
icte
d
RMSE = 22.4 kJ/mol(46 molecules)
• The predicted ΔHsub is much better correlated with experiment than is TΔSsub.
• However, ΔHsub has a much larger range of values and contributes more to the RMS error.
Thermodynamic Cycle
Crystal
Gas
Solution
Hydration Free Energy
We expected that hydration would be harder to model than sublimation, because the solution has an inexactly known and dynamic structure, both solute and solvent are important etc.
Reference Interaction Site Model (RISM)• Combines features of explicit and
implicit solvent models.• Solvent density is modelled, but no
explicit molecular coordinates or dynamics.
~45 CPU minsper compound
RISM
Reference Interaction Site Model (RISM)
•
Palmer, D.S., et al., Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model. The Journal of Chemical Physics, 2010. 133(4): p. 044104-11.
Perhaps surprisingly, error in Ghyd is smaller than in Gsub.
Results for ΔGhyd
Other Hydration Energy Approaches
An alternative methodology here is just to try the various different continuum solvent models available in Gaussian.
logS from Thermodynamic Cycle
Crystal
Gas
Solution
Add the two terms to get ΔGsol and hence logS.
Results for ΔGsol
Conclusions: Theory
• Must calculate Gsub & Ghyd separately;
• Expt data sparse and errors may be large;• RISM is efficient & fairly accurate for Ghyd;
• Dataset size and composition make comparisons of methods hard;
• Not yet matched accuracy of informatics.
Informatics Approaches
“The problem is too difficult to solve using physics and chemistry, so we will design a black box to link structureand solubility”
Informatics and Empirical Models
• In general, informatics methods represent phenomena mathematically, but not in a physics-based way.
• Inputs and output model are based on an empirically parameterised equation or more elaborate mathematical model.
• Do not attempt to simulate reality. • Usually High Throughput.
What Error is Acceptable?
• For typically diverse sets of druglike molecules, a “good” QSPR will have an RMSE ≈ 0.7 logS units.
• A RMSE > 1.0 logS unit is probably unacceptable.
• This corresponds to an error range of 4.0 to 5.7 kJ/mol in Gsol.
What Error is Acceptable?
• A useless model would have an RMSE close to the SD of the test set logS values: ~ 1.4 logS units;
• The best possible model would have an RMSE close to the SD resulting from the experimental error in the underlying data: ~ 0.5 logS units?
Machine Learning Method
Random Forest
Random Forest: Solubility Results
RMSE(te)=0.69r2(te)=0.89Bias(te)=-0.04
RMSE(oob)=0.68r2(oob)=0.90Bias(oob)=0.01
DS Palmer et al., J. Chem. Inf. Model., 47, 150-158 (2007) Ntrain = 658; Ntest = 300
Support Vector Machine
SVM: Solubility Results
et al.,
Ntrain = 150 + 50; Ntest = 87RMSE(te)=0.94r2(te)=0.79
100 Compound Cross-Validation
Theoretical energies don’t seem to improve descriptor models.
100 Compound Cross-Validation
McDonagh et al., J Chem Inf Model, 54, 844 (2014)
Replicating Solubility Challenge (post hoc)
McDonagh et al., J Chem Inf Model, 54, 844 (2014)
Replicating Solubility Challenge (post hoc)
RMSE(te)=1.00; 0.89; 1.08r2(te)= 0.49; 0.58; 0.41
12; 12; 13/28 correct within 0.5 logS units
Ntrain = 94; Ntest = 28
CDK descriptors: RF, PLS, SVM
Replicating Solubility Challenge (post hoc)
Ntrain = 94; Ntest = 28
CDK descriptors: RF, PLS, SVM
Although the test dataset is small, it is a standard set.
Conclusions: Informatics
• Expt data: errors unknown, but limit possible accuracy of models;
• CheqSol - step in right direction; • Dataset size and composition hinder
comparisons of methods; • Solubility Challenge – step in right direction.
Thanks• SULSA• James McDonagh, Dr Tanja van Mourik, Neetika Nath
(St Andrews)• Prof. Maxim Fedorov, Dr Dave Palmer (Strathclyde) • Laura Hughes, Dr Toni Llinas• James Taylor, Simon Hogan, Gregor McInnes, Callum Kirk,
William Walton (U/G project)