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Quantitative StructureActivity Relationships QSAR Comparative Molecular Field Analysis CoMFA

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Electrostatic Potential Contour Lines. CoMFA Model Derivation. Van der Waals field ... 3D Contour Map for Electronegativity. CoMFA Pros and Cons ... – PowerPoint PPT presentation

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Title: Quantitative StructureActivity Relationships QSAR Comparative Molecular Field Analysis CoMFA


1
Quantitative Structure-Activity Relationships
(QSAR) Comparative Molecular Field Analysis
(CoMFA)
Gijs Schaftenaar
2
Outline
  • Introduction
  • Structures and activities
  • Analysis techniques Free-Wilson, Hansch
  • Regression techniques PCA, PLS
  • Comparative Molecular Field Analysis

3
QSAR The Setting
Quantitative structure-activity relationships are
used when there is little or no receptor
information, but there are measured activities of
(many) compounds
4
From Structure to Property
EC50
5
From Structure to Property
LD50
6
From Structure to Property
7
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
8
Free Energy of Binding and Equilibrium Constants
The 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
K Rate constants kon (association) and koff
(dissociation)
9
Concentration as Activity Measure
  • A critical molar concentration C that produces
    the biological effect is related to the
    equilibrium constant K
  • Usually log (1/C) is used (c.f. pH)
  • For meaningful QSARs, activities need to be
    spread out over at least 3 log units

10
Free Energy of Binding
DGbinding DG0 DGhb DGionic DGlipo
DGrot DG0 entropy loss (translat.
rotat.) 5.4 DGhb ideal hydrogen bond
4.7 DGionic ideal ionic interaction
8.3 DGlipo lipophilic contact
0.17 DGrot entropy loss (rotat. bonds)
1.4 (Energies in kJ/mol per unit
feature)
11
Molecules Are Not Numbers!
Where are the numbers? Numerical
descriptors
12
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
13
An Example Capsaicin Analogs
14
An Example Capsaicin Analogs
MR molar refractivity (polarizability)
parameter p hydrophobicity parameter s
electronic sigma constant (para position) Es
Taft size parameter
15
An Example Capsaicin Analogs
log(1/EC50) -0.89
0.019 MR
0.23 p
-0.31 s -0.14 Es
16
An Example Capsaicin Analogs
17
First Approaches The Early Days
  • Free- Wilson Analysis
  • Hansch Analysis

18
Free-Wilson Analysis
log (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
19
Free-Wilson Analysis
  • Computationally straightforward
  • Predictions only for substituents already
    included
  • Requires large number of compounds

20
Hansch Analysis
Drug transport and binding affinity depend
nonlinearly on lipophilicity log (1/C) a
(log P)2 b log P c Ss k P
n-octanol/water partition coefficient s
Hammett electronic parameter a,b,c regression
coefficients k constant term
21
Hansch Analysis
  • Fewer regression coefficients needed for
    correlation
  • Interpretation in physicochemical terms
  • Predictions for other substituents possible

22
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

23
2D Fingerprints
24
Regression Techniques
  • Principal Component Analysis (PCA)
  • Partial Least Squares (PLS)

25
Principal Component Analysis (PCA)
  • Many (gt3) 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

26
PCA From 2D to 1D
27
PCA From 3D to 3D-
28
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
    X into 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

29
Partial Least Squares (PLS)
(compound 1) (compound 2) (compound
3) … (compound n)
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
X independent variables Y dependent variables
30
PLS Cross-validation
  • Squared correlation coefficient R2
  • Value between 0 and 1 (gt 0.9)
  • Indicating explanative power of regression
    equation

With cross-validation
  • Squared correlation coefficient Q2
  • Value between 0 and 1 (gt 0.5)
  • Indicating predictive power of regression
    equation

31
PCA vs PLS
  • PCA The Principle Components describe the
    variance in the independent variables
    (descriptors)
  • PLS The Principle Components describe the
    variance in both the independent variables
    (descriptors) and the dependent variable
    (activity)

32
Comparative Molecular Field Analysis (CoMFA)
  • Set of chemically related compounds
  • Common substructure required
  • 3D structures needed (e.g., Corina-generated)
  • Bioactive conformations of the active compounds
    are to be aligned

33
CoMFA Alignment
34
CoMFA Grid and Field Probe
(Only one molecule shown for clarity)
35
Electrostatic Potential Contour Lines
36
CoMFA Model Derivation
  • Molecules are positioned in a regular
    grid according to alignment
  • Probes are used to determine the molecular field

Van der Waals field (probe is neutral carbon)
Electrostatic field (probe is charged atom)
Evdw S (Airij-12 - Birij-6)
Ec S qiqj / Drij
37
3D Contour Map for Electronegativity
38
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
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