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Bioinformatics IV Quantitative Structure-Activity Relationships (QSAR) and Comparative Molecular Field Analysis (CoMFA). Martin Ott. Outline. Introduction Structures and activities Regression techniques: PCA, PLS Analysis techniques: Free-Wilson, Hansch - PowerPoint PPT PresentationTRANSCRIPT

Bioinformatics IV

Quantitative Structure-Activity Relationships (QSAR)

and

Comparative Molecular Field Analysis (CoMFA)Martin Ott

OutlineIntroductionStructures and activities Regression techniques: PCA, PLSAnalysis techniques: Free-Wilson, HanschComparative Molecular Field Analysis

QSAR: The Setting Quantitative structure-activity relationships are usedwhen there is little or no receptor information, but there are measured activities of (many) compounds

They are also useful to supplement docking studies which take much more CPU time

From Structure to Property EC50

From Structure to Property LD50

From Structure to Property

QSAR: Which Relationship? Quantitative structure-activity relationships correlate chemical/biological activities with structural features or atomic, group or molecular properties

within a range of structurally similar compounds

Free Energy of BindingDGbinding = DG0 + DGhb + DGionic + DGlipo + DGrot

DG0 entropy loss (translat. + rotat.) +5.4DGhb ideal hydrogen bond 4.7DGionic ideal ionic interaction 8.3DGlipo lipophilic contact 0.17DGrot entropy loss (rotat. bonds) +1.4 (Energies in kJ/mol per unit feature)

Free Energy of Binding andEquilibrium ConstantsThe 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 KRate constants kon (association) and koff (dissociation)

Concentration as Activity MeasureA critical molar concentration C that produces the biological effect is related to the equilibrium constant KUsually log (1/C) is used (c.f. pH)For meaningful QSARs, activities need to be spread out over at least 3 log units

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

An Example: Capsaicin Analogs

XEC50(mM) log(1/EC50)H11.804.93Cl 1.245.91NO2 4.585.34CN26.504.58C6H5 0.246.62NMe2 4.395.36I 0.356.46NHCHO??

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

Xlog(1/EC50)MRpsEsH4.93 1.03 0.00 0.00 0.00Cl5.91 6.03 0.71 0.23-0.97NO25.34 7.36-0.28 0.78-2.52CN4.58 6.33-0.57 0.66-0.51C6H56.6225.36 1.96-0.01-3.82NMe25.3615.55 0.18-0.83-2.90I6.4613.94 1.12 0.18-1.40NHCHO?10.31-0.98 0.00-0.98

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

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

Molecular Descriptors Simple counts of features, e.g. of atoms, rings, H-bond donors, molecular weightPhysicochemical properties, e.g. polarisability, hydrophobicity (logP), water-solubilityGroup properties, e.g. Hammett and Taft constants, volume2D Fingerprints based on fragments3D Screens based on fragments

2D Fingerprints

CNOPSXFCl BrIPhCONHOHMeEtPyCHOSOC=CCCC=NAmIm111001001011111000010010

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

PCA From 2D to 1D

PCA From 3D to 3D-

Different Views on PCAStatistically, PCA is a multivariate analysis technique closely related to eigenvector analysisIn matrix terms, PCA is a decomposition of matrix X into two smaller matrices plus a set of residuals: X = TPT + RGeometrically, PCA is a projection technique in which X is projected onto a subspace of reduced dimensions

Partial Least Squares (PLS)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(compound 1)(compound 2)(compound 3)(compound n)

X = independent variablesY = dependent variables

PLS Cross-validation Squared correlation coefficient R2 Value between 0 and 1 (> 0.9) Indicating explanative power of regression equation

Squared correlation coefficient Q2 Value between 0 and 1 (> 0.5) Indicating predictive power of regression equation

With cross-validation:

Free-Wilson Analysislog (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

Free-Wilson AnalysisComputationally straightforwardPredictions only for substituents already includedRequires large number of compounds

Hansch AnalysisDrug transport and binding affinitydepend nonlinearly on lipophilicity:

log (1/C) = a (log P)2 + b log P + c Ss + k

P: n-octanol/water partition coefficients: Hammett electronic parametera,b,c:regression coefficientsk:constant term

Hansch AnalysisFewer regression coefficients needed for correlationInterpretation in physicochemical termsPredictions for other substituents possible

PharmacophoreSet of structural features in a drug molecule recognized by a receptorSample features: H-bond donor charge hydrophobic centerDistances, 3D relationship

Pharmacophore SelectionL = lipophilic site; A = H-bond acceptor;D = H-bond donor; PD = protonated H-bond donorDopaminePharmacophore

Pharmacophore SelectionL = lipophilic site; A = H-bond acceptor;D = H-bond donor; PD = protonated H-bond donorDopaminePharmacophore

Comparative Molecular Field Analysis (CoMFA)Set of chemically related compoundsCommon pharmacophore or substructure required3D structures needed (e.g., Corina-generated)Flexible molecules are folded into pharmacophore constraints and aligned

CoMFA Alignment

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

Electrostatic Potential Contour Lines

CoMFA Model DerivationVan der Waals field(probe is neutral carbon)Evdw = S (Airij-12 - Birij-6)Electrostatic field(probe is charged atom)Ec = S qiqj / Drij Molecules are positioned in a regular grid according to alignmentProbes are used to determine the molecular field:

3D Contour Map for Electronegativity

CoMFA Pros and ConsSuitable to describe receptor-ligand interactions3D visualization of important featuresGood correlation within related setPredictive power within scanned spaceAlignment is often difficultTraining required

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