in silico prediction of solubility: solid progress but no solution? dr john mitchell university of...
TRANSCRIPT
In silico prediction of solubility:
Solid progress but no solution?
Dr John MitchellUniversity of St Andrews
Given accurately measured solubilities of 100 molecules, can you predict the solubilities of 32 similar ones?
For this study Toni Llinàs measured 132 solubilities using the CheqSol method.
He used a Sirius glpKa instrument
K0
Solid
Solution
AH
AHS
][
][K 00
Ka
0a
]][[
][
]][[K
S
AH
AH
AH
Solution
Intrinsic solubility- Of an ionisable compound is the thermodynamic solubility of the free acid or base form (Horter, D, Dressman, J. B., Adv. Drug Deliv. Rev., 1997, 25, 3-14)
A Na A- ……….Na+ AHAH
][1
][][][S 0
00t H
KS
H
SKSAAH aa
Solubility Versus pH Profile
logS
pH (Concentration scale)
-5
-4
-3
-2
-1
2 3 4 5 6 7 8 9 S0 is essentially the solubility of the neutral form only.
DiclofenacDiclofenac
NH
O
Cl Cl
ONa NH
OCl Cl
O
Na+
NH
OCl Cl
OH
NH
OCl Cl
OH
In SolutionPowder
● We continue “Chasing equilibrium” until a specified number of crossing points have been reached ● A crossing point represents the moment when the solution switches from a saturated solution to a subsaturated solution; no change in pH, gradient zero, no re-dissolving nor precipitating….
SOLUTION IS IN EQUILIBRIUM
Random error less than 0.05 log units !!!!
dpH/dt Versus Time
dpH
/dt
Time (minutes)
-0.008
-0.004
0.000
0.004
0.008
20 25 30 35 40 45
Supersaturated Solution
Subsaturated Solution8 Intrinsic solubility values8 Intrinsic solubility values
* A. Llinàs, J. C. Burley, K. J. Box, R. C. Glen and J. M. Goodman. Diclofenac solubility: independent determination of the intrinsic solubility of three crystal forms. J. Med. Chem. 2007, 50(5), 979-983
● First precipitation – Kinetic Solubility (Not in Equilibrium)● Thermodynamic Solubility through “Chasing Equilibrium”- Intrinsic Solubility (In Equilibrium)
Supersaturation Factor SSF = Skin – S0
“CheqSol”
Caveat: the official results are used in the following slides, but most of the interpretation is my own.
Solubility Challenge Results
0
2
4
6
8
10
12
14
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Number of Correct Predictions out of 32 Molecules per Entry
Nu
mb
er o
f E
ntr
ies
A “null prediction” based on predicting everything to have the mean training set solubility would have got 9/32 correct
Correlation Achieved by Entrants
0
5
10
15
20
25
30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
R squared
Nu
mb
er o
f E
ntr
ies
Using an R2 threshold of 0.500, only 18/99 entries were good
Number of Correct Predictions vs R squared
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
4 6 8 10 12 14 16 18 20 22
Number of Correct Predictions
R s
qu
ared
Number of Correct Predictions vs R squared
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
4 6 8 10 12 14 16 18 20 22
Number of Correct Predictions
R s
qu
ared
GOOD
BAD
Number of Correct Predictions vs R squared
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
4 6 8 10 12 14 16 18 20 22
Number of Correct Predictions
R s
qu
ared
3 “WINNERS”
3 Pareto optimal entries which I think of as “winners”. These combine best R2 with most correct predictions.
Some molecules proved much harder to predict than others – the most insoluble were amongst the most difficult.
• My opinion is that the overall standard was rather poor;
• It’s obvious that some entries were much better than others;
• But entries were anonymous;
• So we can’t judge between either specific researchers or between their methods;
• We can only rely on the “official” summary …
Conclusions from Solubility Challenge
• We can only rely on the “official” summary …
… “a variety of methods and combinations of methods all perform about equally well.”
Conclusions from Solubility Challenge
How should we approach the
prediction/estimation/calculation
of the aqueous solubility of
druglike molecules?
Two (apparently) fundamentally different approaches: theoretical chemistry & informatics.
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?
Theoretical Approaches
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.
Sublimation Free Energy
Crystal
Gas
Calculating Gsub 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.
CSP Methodology
• DFT calculation on monomer to obtain DMA electrostatics.
• Generate many plausible crystal structures using different space groups.
• Minimise lattice energy using DMA + repulsion-dispersion potential.
• Many structures may have similar energies.
-74
-73
-72
-71
-70
-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
34
These methods can get relative lattice energies of different structures correct, probably to within a few kJ/mol. Absolute energies harder.
-74
-73
-72
-71
-70
-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
35
Additional possible benefit for solubility: if we don’t know the crystal structure, we could reasonably use best structure from CSP.
Other approaches to Lattice Energy
• Periodic DFT calculations on a lattice are an alternative to the model potential approach.
• Advantageous to optimise intra- and intermolecular energies simultaneously using the same method.
• Disadvantage: it’s hard to get accurate dispersion.
Empirical routes to Gsub
• Alternatively one could estimate sublimation energy from QSPR (no crystal structure needed, but no obvious benefit over direct informatics approach to solubility).
Hydration Free Energy
We expect that hydration will be harder to model than sublimation, because the solution has an inexactly known and dynamic structure, both solute and solvent are important etc.
… and of course the parameterised RISM work of our hosts.
Quoted RMS error ~5kJ/mol or 0.9 log units.
Luder et al.’s results correspond to an RMS error of about 6kJ/mol, or 1 logS unit, but only when an empirical “correction” is applied ….
Hydration Energy
Our currrent methodology here is just to try the various different PCM continuum models available in Gaussian.
We observe than our TD cycle method based on lattice energy minimisation for sublimation and a PCM continuum model of hydration correlates reasonably with experiment, but is not quantitatively predictive (at least without arbitrary correction).
Caveat: currently only a small sample of molecules.
Theoretical Approachesish
So really these are
Using a training-test set split to optimise parameters & validate:
RMSE(te)=0.71r2(te)=0.77
Ntrain = 34; Ntest = 26
Informatics
“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.
Random Forest: Solubility Results
RMSE(te)=0.69r2(te)=0.89Bias(te)=-0.04
RMSE(tr)=0.27r2(tr)=0.98Bias(tr)=0.005
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
Random Forest: Replicating Solubility Challenge (post hoc)
RMSE(te)=1.09r2(te)=0.3910/32 correct within 0.5 logS units Ntrain 100; Ntest 32
CDK descriptors
What Descriptors Correlate with logS?
…amongst the solubility challenge training set, once intercorrelated descriptors with R2 > 0.64 are removed?
The first 21 are all negatively correlated with logS …
… things that reduce solubility.
Some of this is meaningful: aromatic groups reduce solubility.
Some is accidental: logP happens to be defined as octanol:water, rather than water:octanol.
Future Work
• Explore different models of hydration: PCM, simulation (MD/FEP), RISM …
• Route: Direct to water or via octanol?
• Machine Learning (Random Forest, SVM etc.) for hybrid experimental/parameterised models.
• Consistent training and validation sets and methodologies to compare methods: e.g., solubility challenge {100+32}.
Solubility has proved a difficult property to calculate.
It involves different phases (solid & solution) and different substances (solute and solvent), and both enthalpy & entropy are important.
The theoretical approaches are generally based around thermodynamic cycles and involve some empirical element.
Thanks• Pfizer & PIPMS• Gates Cambridge Trust• SULSA
• Dr Dave Palmer, Laura Hughes, Dr Toni Llinas• James McDonagh, Dr Tanja van Mourik• James Taylor, Simon Hogan, Gregor McInnes, Callum Kirk,
William Walton (U/G project)