In silico prediction of solubility: Solid progress but no solution?

1. In silico prediction of solubility: Solid progress but no solution? Dr John Mitchell University of St Andrews

3. Given accurately measured solubilities of 100 molecules, can you predict the solubilities of 32 similar ones?

4. For this study Toni Llinàs measured 132 solubilities using the CheqSol method. He used a Sirius glpKa instrument

5. Ka K0 ANa A- ……….Na+ AH AH 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) S0 is essentially the solubility of the neutral form only.

6. Diclofenac Supersaturated Solution 8 Intrinsic solubility values Subsaturated Solution ● First precipitation – Kinetic Solubility (Not in Equilibrium) ● Thermodynamic Solubility through “Chasing Equilibrium”- Intrinsic Solubility (In Equilibrium) Supersaturation Factor SSF = Skin – S0 In Solution Powder Random error less than 0.05 log units !!!! ●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 “CheqSol” * 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

7. Caveat: the official results are used in the following slides, but most of the interpretation is my own.

8. A prediction was considered correct if it was within 0.5 log units

9. Not a very generous margin of error!

10. A “null prediction” based on predicting everything to have the mean training set solubility would have got 9/32 correct

11. Using an R2 threshold of 0.500, only 18/99 entries were good

13. GOOD BAD

14. 3 “WINNERS” 3 Pareto optimal entries which I think of as “winners”. These combine best R2 with most correct predictions.

15. Some molecules proved much harder to predict than others – the most insoluble were amongst the most difficult.

16. Conclusions from Solubility Challenge • 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 …

17. 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.”

18. How should we approach the prediction/estimation/calculation of the aqueous solubility of druglike molecules? Two (apparently) fundamentally different approaches: theoretical chemistry & informatics.

19. 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.

20. 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?

21. Theoretical Approaches

22. 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”

23. 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.

24. Drug Disc.Today, 10 (4), 289 (2005)

25. Thermodynamic Cycle

26. Thermodynamic Cycle Gas Solution Crystal

27. Sublimation Free Energy Gas Crystal

28. Sublimation Free Energy Gas Crystal

29. Sublimation Free Energy Gas Crystal

30. Sublimation Free Energy Gas Crystal Calculating Gsub is a standard procedure in crystal structure prediction

31. Crystal Structure Prediction • Given the structural diagram of an organic molecule, predict the 3D crystal structure. Slide after SL Price, Int. Sch. Crystallography, Erice, 2004

32. 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.

33. 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.

34. These methods can get relative lattice energies of different structures correct, probably to within a few kJ/mol. Absolute energies harder. 34

35. Additional possible benefit for solubility: if we don’t know the crystal structure, we could reasonably use best structure from CSP. 35

36. 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.

37. 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).

38. Thermodynamic Cycle Gas Solution Crystal

39. Hydration Free Energy

40. 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.

42. Parameterised continuum models Simulation: MD/FEP

43. … and of course the parameterised RISM work of our hosts. Quoted RMS error ~5kJ/mol or 0.9 log units.

44. … and this one both calculates solubility directly and is simulation based: FEP or Monte Carlo.

45. 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 ….

46. … their uncorrected results are less impressive.

47. Hydration Energy Our currrent methodology here is just to try the various different PCM continuum models available in Gaussian.

48. We observe than our TD cycle method based on lattice energy minimisation for sublimation and a PCM continuum model of hydrationcorrelates reasonably with experiment, but is not quantitatively predictive (at least without arbitrary correction). Caveat: currently only a small sample of molecules.

50. An alternative route is via octanol, then using logP.