Quantitative Structure-Activity Relationship (QSAR) computational-drug-design.html

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1 Quantitative Structure-Activity Relationship (QSAR) computational-drug-design.html Ahmad Reza Mehdipour

2 Course Outline 1. 1.Ligand- based approaches 1.(Quantitative) structure- activity relationship (SAR & QSAR) 2.Pharmacophore modeling 2.Bioinformatics approaches (target recognition and structural modeling) 1.Sequence alignments and searches 2.Gene identibication and prediction 3.Homology modeling 3.Structure- based approaches 1.Molecular docking 1.Ligand docking: theory and scoring functions 2.Virtual screening 3.Protein- protein docking and interaction 2.Molecular dynamics simulation 1.Introduction into molecular dynamics 3.Estimation of ligand binding afbinity 1.Free energy perturbation 2.Enhance sampling methods

3 Ligand-based approach Structure-Activity Relationships (SAR) Quantitative Structure-Activity Relationships (QSAR) Biological activity = f ( ) Molecular descriptors

4 QSAR: Historical perspective Meyer-Overton Public Domain,

5 QSAR: Historical perspective Hansch analysis log 1 = + + log + Hansch & Fujita, JACS 1964

6 Quantitative Structure-Activity Relationships (QSAR) Definition QSAR is building a mathematical model correlating a set of structural descriptors of a set of chemical compounds to their biological activity. QYXR is building a mathematical model correlating a set of independent variables of a set of samples to a set of dependent variables.

7 Quantitative Structure-Activity Relationships (QSAR) 1. Set of compounds 4. Biological activities

8 Considerations All compounds should belong to congeneric series Same mechanism of action A similar binding mechanism Biological activity should be exactly the same Biological activity is correlated to binding affinity

9 Quantitative Structure-Activity Relationships (QSAR) 1. Set of compounds 2. Molecular descriptors 4. Biological activities

10 Quantitative Structure-Activity Relationships (QSAR) 1. Set of compounds Mul$ple Linear Regression (MLR) = Molecular descriptors Par$al Least Square (PLS) 3. Mathematical models Ar$ficial Neural Network (ANN) 4. Biological activities Gene$c Algorithm (GA)

11 Molecular descriptors Molecular descriptors

12 Molecular descriptors 1D descriptors 2D descriptors 3D descriptors Molecular weight, LogP, No. of functional groups Topological indices Geometrical parameters, Molecular surfaces, Quantum chemistry descriptors

13 2D descriptors Topological indices based on adjacency matrix TI = 29 = 1 2 "

14 3D descriptors Quantum chemical descriptors Descriptors calculated by Quantum Mechanic methods (semi empirical, Ab initio or DFT ) Partial atomic charges Lowest occupied molecular orbital energy (LUMO) Highest occupied molecular orbital energy (HOMO) Electrostatic potential Molecular polarizability

15 Molecular descriptors Softwares Dragon GAUSSIAN HyperChem CODESSA MOE

16 Quantitative Structure-Activity Relationships (QSAR) 1. Set of compounds Mul$ple Linear Regression (MLR) = Molecular descriptors Par$al Least Square (PLS) 3. Mathematical models Ar$ficial Neural Network (ANN) 4. Biological activities Gene$c Algorithm (GA)

17 Multiple Linear Regression (MLR) = Intercept Coefficients Objective Function,, = ( ) = = ( )

18 Multiple Linear Regression (MLR) = Expr ȓ = - Estimated 1 2 " = /( 1) Akaike Information Criterion "# = log + 2( + 1) = 1 = 1

19 Multiple Linear Regression (MLR) X1 X2 X3 X4 Yexp Ycalc Residual = =0.170 R 2 =0.899 F= Y=0.712

20 Variable selection 1. Systematic approaches 1. Forward selection 2. Backward elimination 2. Heuristic approaches 1. Genetic algorithm 2. Simulated annealing

21 Forward selection Y X1 X2 X3 X4 X5 X1 X2 X3 X4 X5 "# = log AIC Y=a+Xn X1 X2 X3 X4 X5 AIC Y=a+X3+Xn + 2( + 1) X1 X2 X3 X4 X5 AIC Y=a+X3+X2+Xn X1 X2 X3 X4 X5 AIC Y=a+X3+X2+X1+Xn X1 X2 X3 X4 X5 AIC 15.7 Y=a+X3+X2+X1+X4+Xn

22 Backward elimination Y X1 X2 X3 X4 X5 "# = log + 2( + 1) X1 X2 X3 X4 X5 AIC 15.7 Y=a+X1+X2+X3+X4+X5 AIC X1 X2 X3 X4 X Y=a+X1+X2+X3+X4 AIC X1 X2 X3 X Y=a+X1+X2+X3+X4

23 Genetic algorithm X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 GENOME Mutation = Mutation AIC

24 Partial least square The X-variables are correlated The number of X-variables is relatively high compared with the number of samples Y =ß X + ℇ X = TP T Y =UQT U =ß T + ℇ

25 Other modeling methods Non-linear regression Artificial neural network Classification methods Multiple logistic regression Support vector machine X1 = Y X2 X3

26 Validation Valida&on is required to ensure model quality Over- fi6ng Chance correla&on 1. Cross-validation 1. Leave-one-out 2. Leave-N-out 2. Bootstrapping 3. External validation (prediction set) 4. Y randomization

27 Cross-validation Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y19 Y20 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y19 Y20 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y20 Y19 P Times Leave-one-out Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y19 Y20 Leave-N-out Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y20 Y19 Y18 Y17 Y1 Y2 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y20 Y3 Y4 Y5 Y6 P/N Times Rcv 2 LOO Rcv 2 LNO

28 Bootstrapping Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y19 Y20 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y15 Y17 Y19 Y20 Y16 Y18 Y14 Y2 Y3 Y4 Y5 Y8 Y9 Y11 Y12 Y13 Y14 Y15 Y16 Y17 Y18 Y20 Y7 Y10 Y1 Y6 N Times RBS 2

29 External validation Y1 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y14 Y15 Y3 Y4 Y5 Y6 Y7 Y8 Y10 Y11 Y12 Y13 Y15 Y16 Y17 Y19 Variable selection Cross-validation Predict Final model Y16 Y17 Y18 Y19 Y20 Y2 Y9 Y14 Y18 Y20 R 2 EV

30 Y-randomization Y1 X1 Y20 X1 Y2 X2 Y19 X2 Y3 X3 Y18 X3 Y4 X4 Y17 X4 Y5 X5 Y16 X5 Y6 X6 Y15 X6 Y7 X7 Y14 X7 Y8 X8 Y13 X8 Y9 Y10 Y11 Y12 X9 X10 X11 X12 Y =ß X + ℇ Y12 Y11 Y10 Y9 X9 X10 X11 X12 Y new =ß X + ℇ RYrand 2 Y13 Y14 Y15 Y16 Y17 Y18 Y19 Y20 X13 X14 X15 X16 X17 X18 X19 X20 Y8 Y7 Y6 Y5 Y4 Y3 Y2 Y1 X13 X14 X15 X16 X17 X18 X19 X20 N Times

31 Good model? = Model Robustness 2 R 2 F (R)MSE "#$ = "#$ 1 Model Quality Rcv 2 LOO Rcv 2 LNO RBS 2 RMSEcv Model Predictability REV 2 RMSEEv Model Reliability RYrand 2 RMSEYrand

32 Good model? = Model Robustness 2 R 2 >0.8 F (R)MSE Model Quality Rcv 2 LOO >0.6 Rcv 2 LNO >0.6 RBS 2 >0.6 RMSEcv R 2 - Rcv 2 < 0.3 Model Predictability Model Reliability REV 2 >0.6 RMSEEV R 2 - REV 2 < 0.3 RYrand 2 <0.3 RMSEYrand R 2 - RYrand 2 > 0.4

33 Applicability domain = + + X2 X1 Principal component analysis

34 Prediction Vs Description = " _" 2 =0.003 R 2 =0.951 REV 2 =0.891 F=260.2 VE_b(e): coefficient sum of the last eigenvector from Burden matrix weighted by Sanderson electronegativity ATS1v: Broto-Moreau autocorrelation of lag 1 (log function) weighted by van der Waals volume SM02_AEA: spectral moment of order 2 from augmented edge adjacency mat. weighted by resonance integral = "#$ "# 2 =0.113 R 2 =0.811 REV 2 =0.761 F=43.2 LogP: water-oil partition coefficient NAR: Number of aromatic rings

Coefficient Symbol Equation Limits

1 Coefficient Symbol Equation Limits Squared Correlation Coefficient R 2 or r 2 0 r 2 N 1 2 ( Yexp, i Ycalc, i ) 2 ( Yexp, i Y ) i= 1 2 Cross-Validated R 2 q 2 r 2 or Q 2 or q 2 N 2 ( Yexp, i Ypred, i