Martin Ott

1. Bioinformatics IVQuantitative Structure-Activity Relationships (QSAR)andComparative Molecular Field Analysis (CoMFA) Martin Ott

2. Outline • Introduction • Structures and activities • Regression techniques: PCA, PLS • Analysis techniques: Free-Wilson, Hansch • Comparative Molecular Field Analysis

3. QSAR: The Setting Quantitative structure-activity relationships are used when there is little or no receptor information, butthere are measured activities of (many) compounds They are also useful to supplement docking studies which take much more CPU time

4. From Structure to Property EC50

5. From Structure to Property LD50

6. From Structure to Property

7. QSAR: Which Relationship? Quantitative structure-activity relationships correlate chemical/biological activitieswith structural features or atomic, group ormolecular properties within a range of structurally similar compounds

8. Free Energy of Binding andEquilibrium Constants The free energy of binding is related to the reaction constants of ligand-receptor complex formation: DGbinding = –2.303 RT log K = –2.303 RT log (kon / koff) Equilibrium constant K Rate constants kon (association) and koff (dissociation)

9. Concentration as Activity Measure • A critical molar concentration Cthat produces the biological effectis related to the equilibrium constant K • Usually log (1/C) is used (c.f. pH) • For meaningful QSARs, activities needto be spread out over at least 3 log units

10. Molecules Are Not Numbers! Where are the numbers? Numerical descriptors

11. An Example: Capsaicin Analogs

12. An Example: Capsaicin Analogs MR = molar refractivity (polarizability) parameter; p = hydrophobicity parameter; s= electronic sigma constant (para position); Es = Taft size parameter

13. An Example: Capsaicin Analogs log(1/EC50) = -0.89 + 0.019 * MR + 0.23 * p + -0.31 * s + -0.14 * Es

14. Basic Assumption in QSAR The structural properties of a compound contributein a linearly additive way to its biological activity provided there are no non-linear dependencies of transport or binding on some properties

15. Molecular Descriptors • Simple counts of features, e.g. of atoms, rings,H-bond donors, molecular weight • Physicochemical properties, e.g. polarisability,hydrophobicity (logP), water-solubility • Group properties, e.g. Hammett and Taft constants, volume • 2D Fingerprints based on fragments • 3D Screens based on fragments

16. 2D Fingerprints

17. Principal Component Analysis (PCA) • Many (>3) variables to describe objects= high dimensionality of descriptor data • PCA is used to reduce dimensionality • PCA extracts the most important factors (principal components or PCs) from the data • Useful when correlations exist between descriptors • The result is a new, small set of variables (PCs) which explain most of the data variation

18. PCA – From 2D to 1D

19. PCA – From 3D to 3D-

20. Different Views on PCA • Statistically, PCA is a multivariate analysis technique closely related to eigenvector analysis • In matrix terms, PCA is a decomposition of matrix Xinto two smaller matrices plus a set of residuals: X = TPT + R • Geometrically, PCA is a projection technique in which X is projected onto a subspace of reduced dimensions

21. Partial Least Squares (PLS) (compound 1) (compound 2) (compound 3) … (compound n) y1 = a0 + a1x11 + a2x12 + a3x13 + … + e1 y2 = a0 + a1x21 + a2x22 + a3x23 + … + e2 y3 = a0 + a1x31 + a2x32 + a3x33 + … + e3 … yn = a0 + a1xn1 + a2xn2 + a3xn3 + … + en Y = XA + E X = independent variables Y = dependent variables

22. PLS – Cross-validation • Squared correlation coefficient R2 • Value between 0 and 1 (> 0.9) • Indicating explanative power of regression equation With cross-validation: • Squared correlation coefficient Q2 • Value between 0 and 1 (> 0.5) • Indicating predictive power of regression equation

23. Free-Wilson Analysis log (1/C) = S aixi + m xi: presence of group i (0 or 1) ai: activity group contribution of group i m: activity value of unsubstituted compound

24. Free-Wilson Analysis • Computationally straightforward • Predictions only for substituents already included • Requires large number of compounds

25. Hansch Analysis Drug transport and binding affinity depend nonlinearly on lipophilicity: log (1/C) = a (log P)2 + b log P + c Ss + k P: n-octanol/water partition coefficient s: Hammett electronic parameter a,b,c: regression coefficients k: constant term

26. Hansch Analysis • Fewer regression coefficients needed for correlation • Interpretation in physicochemical terms • Predictions for other substituents possible

27. Pharmacophore • Set of structural features in a drug molecule recognized by a receptor • Sample features: •  H-bond donor •  charge •  hydrophobic center • Distances, 3D relationship

28. Pharmacophore Selection Pharmacophore Dopamine L = lipophilic site; A = H-bond acceptor; D = H-bond donor; PD = protonated H-bond donor

29. Pharmacophore Selection Pharmacophore Dopamine L = lipophilic site; A = H-bond acceptor; D = H-bond donor; PD = protonated H-bond donor

30. Comparative Molecular Field Analysis (CoMFA) • Set of chemically related compounds • Common pharmacophore or substructure required • 3D structures needed (e.g., Corina-generated) • Flexible molecules are “folded” intopharmacophore constraints and aligned

31. CoMFA Alignment

32. CoMFA Grid and Field Probe (Only one molecule shown for clarity)

33. Electrostatic Potential Contour Lines

34. CoMFA Model Derivation • Molecules are positioned in a regular gridaccording to alignment • Probes are used to determine the molecular field: Electrostatic field (probe is charged atom) Van der Waals field (probe is neutral carbon) Ec = S qiqj / Drij Evdw = S (Airij-12 - Birij-6)

35. 3D Contour Map for Electronegativity

36. CoMFA Pros and Cons • Suitable to describe receptor-ligand interactions • 3D visualization of important features • Good correlation within related set • Predictive power within scanned space • Alignment is often difficult • Training required