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Molecular Modeling: Conformational Molecular Field Analysis (CoMFA)
Dr. Kelsey Forsythe
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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
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CoMFA Assumptions Activity is directly related to structural properties of system Structural properties determined by non-bonding forces
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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 Add citation
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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 Add citation
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CoMFA Structural Focus
Poor alignment Quality based on directional h-bonding (arrows) Better alignment
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CoMFA Equilibrium Geometry
Find equilibrium geometry Ab Initio, Semi-Empirical or Molecular Mechanics Method depends Size Accuracy Add citation
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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
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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) Add citation
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CoMFA Field Data Generation
Compute interaction of probe with molecule at each point Ncalc=Ngrid * Ncmpds* Nprobes Add citation
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Outline of CoMFA Apply PLS
Problem overrepresented in field variables/descriptors Sieve most important field components (PCA) Use in regression Add citation
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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
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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)
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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
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CoMFA PLS Regression Sij field value for jth probe at ith grid point
cij regression weight for Sij
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3-D QSAR (CoMFA) Post-Qualifications
Confidence in Regression TSS-Total Sum of Squares ESS-Explained Sum of Squares RSS-Residual Sum of Squares
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3-D QSAR (CoMFA) Post-Qualifications
Cross-validation Bootstrapping Reassign ‘wrong’ activity
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3-D QSAR (CoMFA) Post-Qualifications
Standard Deviation in Error Prediction N - Number of observations No penalty for exclusions/inclusion of latent variables
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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)
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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
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3-D QSAR (CoMFA) Dependencies
Active compounds in data set Grid size Energy model Probe groups (# and type)
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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)
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Application 30 aligned set of benzamides and napthamides
Regions indicate principal components
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Application Field Generation
5 Modes Molecular (1) 30 molecules Field (3) X, Y and Z Probes (1) Steric ( C ) Hydrophobic (H2O) Electrostatic (H+)
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Application Pre-Qualifications
Scaling (Not Applied Here) Unit Variance (Auto Scaling) Ensures equal statistical weights (initially) Mean Centering
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Application Principal Components
First 4 PCs in space of original descriptors
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Application Regression
X - Principal Components B - Regression coefficients
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Application Steric Plot
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Steric Plot
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Application Steric Plot
Y=x1b1+…xibi Guide placement of substituents on novel compounds depending on the value of Y (log(Ki)) desired
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Application Validation
Cross Validation Leave-One-Out External Predictions Test Set 21 compounds
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Application Validation
Cross Validation Leave-One-Out (ypred from 29) External Predictions Test Set (ypred from regression)
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Application Theory vs. Experiment
Circles are for test set
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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)
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CoMFA Assumptions Activity is directly related to structural properties of system Dynamical corrections? Structural properties determined by non-bonding forces Covalent Hydrophobic
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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
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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)
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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)
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Additional Resources The QSAR and Modelling Society ( Quantitative Structure Activity Relationships (Journal)
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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
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