Quantitative Structure-Activity Relationships Quantitative Structure-Property-Relationships

Alexandre VarnekFaculté de Chimie, ULP, Strasbourg, FRANCE

QSAR/QSPR modeling

• Development• Validation• Application

QSAR/QSPR models

Development QSAR models• Selection and curation of experimental data• Preparation of training and test sets (optionaly)• Selection of an initial set of descriptors and their

normalisation• Variables selection• Selection of a machine-learning method

Validation of models• Training/test set• Cross-validation

- internal,- external

Application of the Models• Models Applicability Domain

Development the QSAR models

• Experimental Data• Descriptors • Mathematical techniques• Statistical criteria

Preparation of training and test sets

Building of structure - property models

Selection of the best models according to statistical criteria

Splitting of an initial data set into training and test sets

Training set

Test

Initial data set

“Prediction” calculations using the best structure - property models

10 – 15 %

Recommendations to prepare a test set

• (i) experimental methods for determination of activities in the training and test sets should be similar;

• (ii) the activity values should span several orders of magnitude, but should not exceed activity values in the training set by more than 10%;

• (iii) the balance between active and inactive compounds should be respected for uniform sampling of the data.

References: Oprea, T. I.; Waller, C. L.; Marshall, G. R. J. Med. Chem. 1994, 37, 2206-2215

Selection of descriptors for QSAR model

QSAR models should be reduced to a set of descriptors which is QSAR models should be reduced to a set of descriptors which is as information rich but as small as possible.as information rich but as small as possible.

Rules of thumb:Rules of thumb:good good ““spreadspread”” ,,55--6 structure points per descriptor.6 structure points per descriptor.

Objective selection (independent variable only) Objective selection (independent variable only) Statistical criteria of correlations Statistical criteria of correlations Pairwise selection (Forward or Backward Stepwise selection) Pairwise selection (Forward or Backward Stepwise selection) Principal Component AnalysisPrincipal Component AnalysisPartial Least Square analysisPartial Least Square analysisGenetic AlgorithmGenetic Algorithm

………………………………..

Subjective selection Subjective selection Descriptors selection based on mechanistic studiesDescriptors selection based on mechanistic studies

1. identify a subset of columns (variables) with significantcorrelation to the response; 2. remove columns (variables) with small variance; 3. remove columns (variables) with no unique information; 4. identify a subset of variables on which to construct a model; 5. address the problem of chance correlation.

D. C. Whitley, M. G. Ford, D. J. LivingstoneJ. Chem. Inf. Comput. Sci. 2000, 40, 1160-1168

Preprocessing strategy for the derivation of modelsfor use in structure-activity relationships (QSARs)

Machine-Learning Methods

Fitting models’ parameters

The goal is to minimize Residual Sum of Squared (RSS)

∑=

−=N

iicalci yyRSS

1

2,exp, )(

Y = F(ai , Xi )

Xi - descriptors (independent variables)ai - fitted parameters

Multiple Linear Regression

Activity Descriptor

Y1 X1

Y2 Y2

… …

Yn Xn

Y

X

Yi = a0 + a1 Xi1

Multiple Linear Regression

y=ax+b

a

b

Residual Sum ofSquared (RSS)

∑=

−=N

iicalci yyRSS

1

2, )(

Multiple Linear Regression

Activity Descr 1 Descr 2 … Descr m

Y1 X11 X12 … X1m

Y2 X21 X22 … X2m

… … … … …

Yn Xn1 Xn2 … Xnm

Yi = a0 + a1 Xi1 + a2 Xi2 +…+ am Xim

kNN (k Nearest Neighbors)

Activity Y assessment calculating a weighted mean of the activities Yi of its k nearest neighbors in the chemical space

A.Tropsha, A.Golbraikh, 2003

Des

crip

tor 1

Descriptor 2

TRAINING SET

Biological and Artificial Neuron

Multilayer Neural Network

Neurons in the input layer correspond to descriptors, neurons in the output layer – to properties being predicted, neurons in the hidden layer – to nonlinear latent variables

• Development• Validation• Application

QSAR/QSPR models

Validating the QSAR Equation

actual

predicted

r2 is the fraction of the total variation in the dependent variables that is explained by the regression equation.

How well does the model predicts the activity of known compounds?For a perfect model:

• All data points would reside on the diagonal.• All variance existing in the original data is explained by the

model.

Calculating r2

Variance OriginalVarianceExplained2 =r

Original variance = Explained variance (i.e., variance explained by the equation) + Unexplained variance (i.e., residual variance around regression line)

Original variance Variance around regression line

Calculating r2

Compound Number Log EC50

Calculated Log EC50 Residual

1 1.07 0.79 0.282 0.09 0.21 -0.123 0.66 1.02 -0.364 1.42 1.26 0.165 -0.62 -0.81 0.196 0.64 0.65 -0.017 -0.46 -0.12 -0.348 ?? 1.6 ??

TSSRSS

TSSRSSTSS

TSSESSr −≡

−≡= 12

89.049.309.3

49.340.049.32 ==

−=r

Original variance: ∑=

><−=N

ii yyTSS

1

2)(

Explained variance:Improvement in predicting y from just using the mean of y

∑=

><−=N

icalci yyESS

1

2, )(

∑=

−=N

iicalci yyRSS

1

2, )(Variance around regression line:

F-test

Tests the assumption that a significant portion of the original variance has been explained by the model.

In statistical terms tests that the ratio between the explained variance (ESS/k; k = number of parameters) and the original variance (RSS/N-k-1; N = number of data points) significantly differs from 0. This implies that ESS = 0, i.e., the model didn’t explain any of the variance.

F-distributionAs N and k decrease, the probability of getting large r2 values purely by chance increases.Thus, as N and k decrease, a larger F-value is required for the test to be significant.

Nk

Calculating F Values

Calculate F according to the above equation.Select a significance level (e.g., 0.05).Look up the F-value from an F-distribution derived for the correct number of N and k at the selected significance level.If the calculated F-value is larger than the listed F-value, then the regression equation is significant at this significance level.

Example:r2 = 0.89 N = 7 k = 1 F = 40.46For an F-distribution with N=7, k=1, a value of 40.46 corresponds to a significance level of 0.9997 . Thus, the equation is significant at this level. The probability that the correlation is fortuitous is < 0.03%

)1()1(1

2

2

rkkNr

RSSkN

kESSF

−−−

=−−

=

5‐fold external cross‐validation procedure

Validation of Models

Cross Validation

( )∑∑ =

=

−=><−

−=N

iiipredN

i i

yyPRESSyy

PRESSQ1

2,

12

2 ;)(

1

( )∑∑ =

=

−=><−

−=N

iiicalcN

i i

yyRSSyy

RSSr1

2,

12

2 ;)(

1

A measure of the predictive ability of the model (as opposed to the measure of fit produced by r2).

r2 always increases as more descriptors are added.Q2 initially increases as more parameters are added but then starts to decrease indicating data over fitting. Thus Q2 is a better indicator of the model quality.

Other Model Validation Parameters

1. s is the standard deviation about the regression line. This is a measure of how well the function derived by the QSAR analysis predicts the observed biological activity. The smaller the value of s the better is the QSAR.

N is the number of observations and k is the number of variables.

2. Scrambling of y.

( )1

2

−−−

= ∑kN

yys calcobs

Scrambling:to mix randomly:• Y values (Y-scrambling), or • X values (X-scrambling), or • simulteneously Y and X values (X,Y-scrambling)

Statistical tests for « chance correlations »

Randomization:to generat random number s: • from Ymin to Ymax (Y – randomization),• from Xmin to Xmax (X – randomization),• or do this simulteneously for Y and X (X, Y – randomization)

Calculate statistical parameters of correlations and compare them with those obtained for the model

ScramblingStruc.1Struc.2

Struc.n

..

..

Pro.1

Struc.3....

Pro.2

Pro.3

Pro.n

Struc.1Struc.2

Struc.n

..

..

Pro.1

Struc.3....

Pro.2

Pro.3

Pro.n

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70

Number of Variablesq2

The lowest q2 = 0.51 in the top 10 models

The highest q2 =0.14 for randomized datasets

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70

Number of Variablesq2

The lowest q2 = 0.51 in the top 10 models

The highest q2 =0.14 for randomized datasets

• Development• Validation• Application

QSAR/QSPR models

Is a test compound similar to the training set compounds?

- Descriptors type;- Descriptors selection;- Machine-learning methods;- Validation of models.

Prediction Performance

QSPR Models Test compound

Robustness of QSPR models Applicability domain of models

Applicability domain of QSAR models

= TEST COMPOUNDDescriptor 1

Descriptor 2

TRAINING SET

OUTSIDE THE DOMAIN

Will not be predicted

Di ≤ <Dk > + Z ×

skwith Z, an empirical parameter (0.5 by default)

The new compound will be predicted bythe model, only if :

INSIDE THE DOMAIN

Will be predicted

Range –based methods

Bounding Box (BB)

Applicability domain of QSAR models

ensemble modeling

Should one use only one individual model or many models ?

Hunting season …

Single hunter

Hunting season …

Many hunters

Ensemble modelling

Model 1

Model 2 Model 3

Model 4

Property (Y) predictions using best fit models

Compound model 1 model 2 … mean ± s

Compound 1 Y11 Y12 … <Y1 > ± ΔY1

Compound 2 Y21 Y22 … <Y2 > ± ΔY2

… …

Compound m Ym1 Ym2 … <Ym > ± ΔYm

Grubbs statistics is used to exclude les outliers

N

O

N

O

N

O

Etc.

DataSet

C-C-C

-C-C

-CC-C

-C-N

-C-C

C=OC-C

-C-N

C-N-C

-C*C

ISIDA FRAGMENTOR

0 10 1 5 0

0 8 1 4 0

0 4 1 2 4

the Pattern matrix

Calculation of Descriptors

+

PATTERN MATRIX PROPERTY VALUES

-0.222

0.973

-0.066

LEARNING STAGEBuilding of models

QSAR models

VALIDATION STAGEQSAR models filtering ->

selection of the most predictive ones

Example : linear QSPR model Daa i

k

ii.Propriété

10 ∑

=+=Property

PROPERTYcalc = -0.36 * NC-C-C-N-C-C + 0.27 * NC=O + 0.12 * NC-N-C*C + …

Virtual screening with QSAR/QSPR models

VirtualSreening

Database

ExperimentalTests

Hits

NOH

NOH

NOH

O

COOH

Br

Screening and hits selection

QSPR model

Uselesscompounds

O

ClCOOH

Br

Combinatorial Library Design

Generation of Virtual Combinatorial Libraries

if R1, R2, R3 = and then

Markush structure PO

R1 R3R2

PO

PO

PO

PO

PO

PO

PO

PO

1. Substituent variation (R1 )2. Position variation (R2 )3. Frequency variation 4. Homology variation (R3 )

(only for patent search)OH

R1

R3(CH2)n

Cl

R2

n = 1 – 3

R2 =NH2

R3 = alkyl orheterocycle

R1 = Me, Et, Pr

The types of variation in Markush structures:

IN SILICO design of new compounds

- Acquisition of Data;

- Acquisition of Knowledge;

- Exploitation of Knowledge

« In silico » design of new compounds

Markush structure The combinatorial module generates virtual libraries based on the Markush structures.

R1 NR2

O

R3

ISIDA combinatorial module

DatabaseFiltering2

Hits selection

6

Synthesis and experimental tests

7

QSAR models

1

Similarity Search

QSAR models 5Assessment of

properties

Applicabilitydomains

4

3

ISIDA

1000 molecules/second

COMPUTER-AIDED DESIGN OF NEW METAL BINDERS: Binding of UO2

2+ by monoamides

R1 NR2

O

R3

R = H, alkyl

A. Varnek, D. Fourches, V. Solov’ev, O. Klimchuk, A. Ouadi, I. BillardJ. Solv. Extr. Ion Exch., 2007, 25, N°4

D =[ U ] organic phase

[ U ] aqueous phase

SOLVENT EXTRACTION OF METALS

M1+

M2+

An-

L

COMPUTER-AIDED DESIGN OF NEW METAL BINDERS: Extraction of UO2

2+ by monoamides

Usine de La HAGUE, France

Reprocessing of the spent nuclear fuel

PUREX process

TBP : tributyl phosphate

1. T. H. Siddall III, J. Phys. Chem., 64, 1863 (1960)2. C. Rabbe, C. Sella, C. Madic, A. Godard, Solv. Extr. Ion Exch, 17, 87 (1999)

Goal: theoretical design of new uranyl binders more efficient than previously studied molecules

Selected Hits: 21 cmpds

EXPERT EXPERT SYSTEMSYSTEM

DATABASEDATABASE

DATA TREATMENTDATA TREATMENT

PREDICTORPREDICTOR

VIRTUAL VIRTUAL SCREENINGSCREENING

Hits selection

ISIDAISIDAVirtual library:

11.000 cmpds

“In silico” design of uranyl binders with ISIDA

New amides (ID)

logD

Experimental vs Predicted logD

logD

Nu

mbe

r of

com

pou

nds

Previously studied amidesNewly synthesized amides

4 compounds (previously studied)9 compounds (newly synthesized)

Enrichment of the initial data set by new efficient extractants:

logD > 0.9 :

Classification Models

Confusion Matrix• For N instances, K classes

and a classifier• Nij , the number of instances

of class i classified as j

Class1 Class2 … ClassK

Class1 N11 N12 … N1K

Class2 N21 N22 … N2K

… … … … …

ClassK NK1 NK2 … NKK

Classification Evaluation

Global measures of successMeasures are estimated on all classes

Local measures of successMeasures are estimated for each class

The most fundamental and lasting objective of synthesis is not

production of new compounds but production of properties

George S. HammondNorris Award Lecture, 1968