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• Comparative Molecular Field Analysis

QSAR: The Setting

Quantitative structure-activity relationships are usedwhen there is little or no receptor information, butthere are measured activities of (many) compounds

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

From Structure to Property

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

0

1

2

3

4

5

6

7

8

9

1 3 5 7 9 11 13 15

EC5

0

From Structure to Property

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

LD50

From Structure to Property

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

O

H

H H

OH

QSAR: Which Relationship?

Quantitative structure-activity relationships correlate chemical/biological activitieswith structural features or atomic, group ormolecular properties

within a range of structurally similar compounds

Free Energy of Binding andEquilibrium Constants

The free energy of binding is related to the reaction constants of ligand-receptor complex formation:Gbinding = –2.303 RT log K

= –2.303 RT log (kon / koff)

Equilibrium constant KRate constants kon (association) and koff (dissociation)

Concentration as Activity Measure

• A critical molar concentration Cthat produces the biological effectis related to the equilibrium constant K

• Usually log (1/C) is used (c.f. pH)

• For meaningful QSARs, activities needto be spread out over at least 3 log units

Molecules Are Not Numbers!

O

NCH3

OH

H

HOH-1.09.109*10-31

2.99792*108

-½

0 -0.3183

-180.156

196.967

149,597,870,691

e

43

7

Where are the numbers? Numerical descriptors

An Example: Capsaicin Analogs

X EC50(M) log(1/EC50)

H 11.80 4.93Cl 1.24 5.91

NO2 4.58 5.34CN 26.50 4.58

C6H5 0.24 6.62NMe2 4.39 5.36

I 0.35 6.46NHCHO ? ?

X

NH

O

OH

MeO

An Example: Capsaicin Analogs

X log(1/EC50) MR Es

H 4.93 1.03 0.00 0.00 0.00Cl 5.91 6.03 0.71 0.23 -0.97

NO2 5.34 7.36 -0.28 0.78 -2.52CN 4.58 6.33 -0.57 0.66 -0.51

C6H5 6.62 25.36 1.96 -0.01 -3.82NMe2 5.36 15.55 0.18 -0.83 -2.90

I 6.46 13.94 1.12 0.18 -1.40NHCHO ? 10.31 -0.98 0.00 -0.98

MR = molar refractivity (polarizability) parameter; = hydrophobicity parameter;

= electronic sigma constant (para position); Es = Taft size parameter

An Example: Capsaicin Analogs

X

NH

O

OH

MeO

log(1/EC50) = -0.89 + 0.019 *

MR + 0.23 * + -0.31 * +

-0.14 * Es

Basic Assumption in QSAR

The structural properties of a compound contributein 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 weight

• Physicochemical properties, e.g. polarisability, hydrophobicity (logP), water-solubility

• Group properties, e.g. Hammett and Taft constants, volume

• 2D Fingerprints based on fragments• 3D Screens based on fragments

2D Fingerprints

Br

NH

O

OH

MeO

C N O P S X F Cl Br I Ph CO NH OH Me Et Py CHO SO C=C CΞC C=N Am Im

1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0

Principal Component Analysis (PCA)

• Many (>3) variables to describe objects= high dimensionality of descriptor data

• PCA is used to reduce dimensionality• PCA extracts the most important factors

(principal components or PCs) from the data• Useful when correlations exist between

descriptors• The 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 PCA

• Statistically, PCA is a multivariate analysis technique closely related to eigenvector analysis

• In matrix terms, PCA is a decomposition of matrix Xinto two smaller matrices plus a set of residuals: X = TPT + R

• Geometrically, 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 Analysis

log (1/C) = aixi + xi: presence of group i (0 or 1) ai: activity group contribution of group i : activity value of unsubstituted compound

Free-Wilson Analysis

+ Computationally straightforward

– Predictions only for substituents already included

– Requires large number of compounds

Hansch Analysis

Drug transport and binding affinitydepend nonlinearly on lipophilicity:

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

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

Hansch Analysis

+ Fewer regression coefficients needed for correlation

+ Interpretation in physicochemical terms

+ Predictions for other substituents possible

Pharmacophore

• Set of structural features in a drug molecule recognized by a receptor

• Sample features: H-bond donor charge hydrophobic center

• Distances, 3D relationship

Pharmacophore Selection

L = lipophilic site; A = H-bond acceptor;D = H-bond donor; PD = protonated H-bond donor

DopaminePharmacophore

LPD

D

d1

d2 d3

LPD

D

d1

d2 d3L

PD

D

d1

d2 d3

NH+

CO2H

CH3H

NH

NH+H

CH3

OH

OH

OH

OH

NH3+

OH

NH3+

OH

NH+H

CH3

OH

OH

Pharmacophore Selection

L = lipophilic site; A = H-bond acceptor;D = H-bond donor; PD = protonated H-bond donor

DopaminePharmacophore

LPD

D

d1

d2 d3

LPD

D

d1

d2 d3L

PD

D

d1

d2 d3

NH+

CO2H

CH3H

NH

LPD

D

d1

d2 d3

Comparative Molecular Field Analysis (CoMFA)

• Set of chemically related compounds• Common pharmacophore or

substructure required• 3D structures needed (e.g., Corina-

generated)• Flexible molecules are “folded” into

pharmacophore constraints and aligned

CoMFA Alignment

C7OH

OH

A

D

B

C1

MeO OMe

ClClCl

BA

O

OC7OH

OHOH

A

B

C1

O

NMe2

OH

A B

CL

LL d1

d2d3L

LL

d1

d2

d3

L

LL

d1

d2

d3

L

L

L

d1 d2

d3

L

LL

d1

d2

d3

"Pharmacophore"

CoMFA Grid and Field Probe

(Only one molecule shown for clarity)

Electrostatic Potential Contour Lines

CoMFA Model Derivation

Van der Waals field(probe is neutral carbon)

Evdw = (Airij-12 - Birij

-6)

Electrostatic field(probe is charged atom)

Ec = qiqj / Drij

• Molecules are positioned in a regular gridaccording to alignment

• Probes are used to determine the molecular field:

3D Contour Map for Electronegativity

CoMFA Pros and Cons

+ Suitable to describe receptor-ligand interactions

+ 3D visualization of important features+ Good correlation within related set+ Predictive power within scanned space– Alignment is often difficult– Training required