1. Molecular Modeling: Conformational Molecular Field Analysis (CoMFA)
Dr. Kelsey Forsythe

2. CoMFA Cramer and Milne (1979) Wold (1986)
Comparison of molecules by alignment and field generation
Wold (1986)
Proposes using PLS instead of PCA for overrepresented (1000’s of field non-orthogonal “variables”) problem (correlate field values with activities)
Cramer, Patterson and Bunce (1988)
Introduced CoMFA

3. CoMFA Assumptions
Activity is directly related to structural properties of system
Structural properties determined by non-bonding forces

4. Outline of CoMFA Hypothesize mechanism for binding
Structure of binding site
Most important/difficult
Find equilibrium geometry
Construct lattice or grid of points
Compute interaction of probe with molecule at each point
Apply PLS
Predict
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5. CoMFA Structural Focus
Hypothesize mechanism for binding
Structure of active site and/or common pharmacophore between all compounds
Most important/difficult
Structural errors propagate to later stages
Superpose structures
SEAL
Similarity index
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6. CoMFA Structural Focus
Poor alignment
Quality based on directional h-bonding (arrows)
Better alignment

7. CoMFA Equilibrium Geometry
Find equilibrium geometry
Ab Initio, Semi-Empirical or Molecular Mechanics
Method depends
Size
Accuracy
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8. CoMFA Lattice Construction
Construct lattice or grid of points for field analysis
Figure?
Steroid (1 representative conformer shown)
14 x 11 x 7 = 1078 points

9. CoMFA Field Data Generation
Compute interaction of probe with molecule at each point
Interaction is typically non-covalent (e.g. non-bonding forces)
Steric, electrostatic and hydrophobic
Probe depends on interaction
Kim et. al.
H+ (electrostatic)
CH3 (steric)
H2O (hydrophobic)
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10. CoMFA Field Data Generation
Compute interaction of probe with molecule at each point
Ncalc=Ngrid * Ncmpds* Nprobes
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11. Outline of CoMFA Apply PLS
Problem overrepresented in field variables/descriptors
Sieve most important field components (PCA)
Use in regression
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12. QSAR/QSPR-Regression Types
Partial Least Squares
Cross-validation determines number of descriptors/components to use
Derive equation
Use bootstrapping and t-test to test coefficients in QSAR regression

13. QSAR/QSPR-Regression Types
Partial Least Squares (a.k.a. Projection to Latent Structures)
Regression of a Regression
Provides insight into variation in x’s(bi,j’s as in PCA) AND y’s (ai’s)
The ti’s are orthogonal
M= (# of field points OR molecules whichever smaller)

14. QSAR/QSPR-Regression Types
PLS is NOT MR or PCR in practice
PLS is MR w/cross-validation
PLS Faster
couples the target representation (QSAR generation) and component generation while PCA and PCR are separate
PLS well applied to multi-variate problems

15. CoMFA PLS Regression Sij field value for jth probe at ith grid point
cij regression weight for Sij

16. 3-D QSAR (CoMFA) Post-Qualifications
Confidence in Regression
TSS-Total Sum of Squares
ESS-Explained Sum of Squares
RSS-Residual Sum of Squares

17. 3-D QSAR (CoMFA) Post-Qualifications
Cross-validation
Bootstrapping
Reassign ‘wrong’ activity

18. 3-D QSAR (CoMFA) Post-Qualifications
Standard Deviation in Error Prediction
N - Number of observations
No penalty for exclusions/inclusion of latent variables

19. 3-D QSAR (CoMFA) Post-Qualifications
Standard Deviation in Predictions
PRESS (Predictive Error Sum of Squares)
N - Number of observations
c - Number of latent variables used in regression
Want ‘c’ s.t. (c + 1 results in 5% decrease in sPRESS)

20. 3-D QSAR (CoMFA) Post-Qualification
Randomly re-assign activities to compounds
Compare predictability of ‘wrong’ regressions with true regression
Determine random correlation
Determine efficacy of ‘true’ regression

21. 3-D QSAR (CoMFA) Dependencies
Active compounds in data set
Grid size
Energy model
Probe groups (# and type)

22. Application Nilsson, J. , De Jong, S. Smilde, A. K
Application Nilsson, J. , De Jong, S. Smilde, A. K. Multiway Calibration in 3D QSAR. J of Chemometrics 1997, 11,
Multilinear PLS applied to group of benzamides interacting with dopamine D3 receptor subtype (anti-schizophrenia drugs)

23. Application 30 aligned set of benzamides and napthamides
Regions indicate principal components

24. Application Field Generation
5 Modes
Molecular (1)
30 molecules
Field (3)
X, Y and Z
Probes (1)
Steric ( C )
Hydrophobic (H2O)
Electrostatic (H+)

25. Application Pre-Qualifications
Scaling (Not Applied Here)
Unit Variance (Auto Scaling)
Ensures equal statistical weights (initially)
Mean Centering

26. Application Principal Components
First 4 PCs in space of original descriptors

27. Application Regression
X - Principal Components
B - Regression coefficients

28. Application Steric Plot

29. Steric Plot

30. Application Steric Plot
Y=x1b1+…xibi
Guide placement of substituents on novel compounds depending on the value of Y (log(Ki)) desired

31. Application Validation
Cross Validation
Leave-One-Out
External Predictions
Test Set
21 compounds

32. Application Validation
Cross Validation
Leave-One-Out (ypred from 29)
External Predictions
Test Set (ypred from regression)

33. Application Theory vs. Experiment
Circles are for test set

34. 3-D QSAR (CoMFA) Potent Pitfalls
Sensitivity to binding structure
Hydrophobicity not well-quantified
Sensitivity to Nlatent
Relation between latent variables NOT intuitive
Test compounds should not differ significantly in properties from training set
Low S/N (too many useless field variables)

35. CoMFA Assumptions
Activity is directly related to structural properties of system
Dynamical corrections?
Structural properties determined by non-bonding forces
Covalent
Hydrophobic

36. Advanced CoMFA SRD (Smart Region Definition) Reduced PLS
LOCAL Set of variables/grid values will display similar behavior due to structural changes
Reduce M-grid points to one focal point or seed
Use “distance” cutoff (nearest, next nearest etc.) to define reduced set of field points
Reduced PLS
Use only high weight PCs in regression

37. Other QSAR-based Methods
HQSAR
Convert 3D --> 2D string
Generate random collections of string elements
CoMSIA (Conformational Molecular Similarity Indices Analysis
Wprobe,k=+1(charge),+1(hydrophobicity),1A,+1(h-bond acceptor),+1(h-bond donor)

38. References
Cramer III, R. D., Patterson, D. E., Bunce, J. D. Comparative Molecular Field Analysis (CoMFA). 1. Effect of Shape on Binding of Steroids to Carrier Proteins. J. Am. Chem. Soc. 1988, 110,
Hansch, C. and Leo, A. Exploring QSAR: Fundamentals and Applications in Chemistry and Biology American Chemical Society (1995)
Leach, Andrew R. Molecular Modelling: Principles and Applications Prentice Hall, New York (2001)

39. Additional Resources
The QSAR and Modelling Society (
Quantitative Structure Activity Relationships (Journal)

40. Additional Resources
SYBYL-Molecular Modeling Software, 6.9, Tripos Incorporated, 1699 S. Hanley Rd. St. Louis, Mo , USA
GRID, Goodford, P. J. Molecular Discovery Ltd, University of Oxford, England