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Introduction to QSAR (Quantitative Structure
Activity Relationships)
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Introduction to QSAR

• Example of a Qualitative Structure Activity
  Relationship (SAR)

Affinity to Serotonin Receptor 1. decreases by
N-alkylation (R1/R2) 2. decreases by
bis-methylation (R3/R4) 3. increases by
methoxylation in R5 and/or R7 4. increases
by adding lipophilic substituents in R6
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Introduction to QSAR

• In contrast to Qualitative SAR, Quantitative SAR
  (QSAR) seeks to find a mathematical relationship
  between biological activity and molecular
  properties
• General form of a QSAR equation
• biol. activity f(P) with P molecular
  property/ies
• or more specifically
• biol. activity const. (c1.P1) (c2.P2)
  (c3.P3) ...
• Molecular properties (descriptors) P are
  calculated for each molecule in the data set
• Coefficients c and constant term are calculated
  by statistical methods (e.g. multiple linear
  regression)

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Molecular QSAR-Descriptors

• 1D Whole-molecule properties (e.g. molecular
  weight, melting point, logP etc.)
• 2D Substituent constants (e.g. ?, ?, molar
  refractivity), fragment fingerprints,
  topological indices
• 3D Surface or field properties (e.g.
  electrostatic potential, , steric fields,
  hydrophobicity, solvent accessible surface
  area etc.),

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Introduction to QSAR

• Why QSAR?
• QSAR models are derived from a series of
  (similar) molecules with known activity (training
  set)
• If a statistically relevant QSAR model has been
  found, it can be applied to new molecules in this
  series (test set) in order to predict their
  activity before biological testing (or even
  before synthesis!)

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Introduction to QSAR
Example Analgesic activity of Capsaicin analogs
(taken from Walpole et al., Sandoz)
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Introduction to QSAR
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Introduction to QSAR

• The Gibbs-Helmholtz equation (?GRTlnK) tells us
  that there is a logarithmic relationship between
  equilibrium constants (e.g. EC50) and free energy
  of binding
• Thus, we have to transform the EC50 values to a
  logarithmic scale

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Introduction to QSAR

• Now, we require some molecular properties
  (descriptors)...
• The Sandoz group decided to use two substituent
  constants the hydrophobic constant ? and the
  molar refractivity (MR) (correlated with the size
  and polarizability of the substituents)

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Introduction to QSAR

• We can plot the descriptor values vs. Log EC50 ...

• ...and we can calculate linear equations for both
  parameters
• Log EC50 0.76 - (0.82)?
• Log EC50 1.14 - (0.07)MR

Our first QSAR equations!!!
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Introduction to QSAR

• How larger are the errors that we make?

?-Equation Log EC50 0.76 - (0.82)?
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Introduction to QSAR

• How larger are the errors that we make?

MR-Equation Log EC50 1.14 - (0.07)MR
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Introduction to QSAR

• How larger are the errors that we make?

Actual (measured) Log EC50 vs Predicted Log EC50
Correlation coefficients (R2) 0.88 0.53
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Introduction to QSAR

• Can we do any better by using both parameters in
  the equation (multiple linear regression (MLR)
  instead of simple linear regression)?

Best MLR Equation Log EC50 0.76 - (0.82)?
(0.0003)MR (Corr. Coeff. R2 0.89)
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Introduction to QSAR

• How can we validate these QSAR models?
• Prediction within the training set (e.g. by
  leave-one-out cross validation)
• leave out each compound once
• calculate QSAR model with remaining compounds
  only
• predict activity of left-out compound
• compare prediction with "true" affinity
• calculate "cross validated" R2 (often reported as
  Q2)
• Prediction of the test set

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Introduction to QSAR

• How can we validate these QSAR models?
• Prediction of the training set (cross
  validation)
• Log EC50 0.76 - (0.82)? R20.88 Q20.72
• Log EC50 1.14 - (0.07)MR R20.53 Q20.28
• Log EC50 0.76 - (0.82)? (0.0003)MR R20.89
  Q20.58

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Introduction to QSAR

• How can we validate these QSAR models?
• Prediction of the test set (compound 6i in this
  example)

• Log EC50 0.76 - (0.82)? Predicted EC50
  for 6i 1.56
• Log EC50 1.14 - (0.07)MR Predicted
  EC50 for 6i 0.42
• Log EC50 0.76 - (0.82)? (0.0003)MR
  Predicted EC50 for 6i 1.57

• Now we have a problem....

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Introduction to QSAR

• Some problems associated with "classical" QSAR
• Only applicable within a chemical series
• A good training set must be available
• Activity data should be evenly spread
• Activity data should span 3-4 orders of magnitude
  (log units)
• Choice of meaningful descriptors
• Problem of extrapolation (e.g. descriptors of
  test compounds lie out of descriptor range of
  training set)
• Non-linear relationships are hard to detect

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Artificial Neural Nets (ANN) An alternative way
of deriving QSAR models
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J. Zupan, J. Gasteiger
Neural Networksin Chemistryand Drug Design
Second Edition
WILEY-VCH, Weinheim, 1999
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Artificial Neural Nets
number of chemistry-related publications
927
855
743
441
498
290
105
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5
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Artificial Neural Nets
The "100 Steps Paradoxon"
human brain computer reaction time of firing
of neuron clock ratebasic unit 10-3 sec 10-9
sec (500 MHz) recognition of the faceof a
friend 10-1 sec 10-1 sec no. of processing
steps 100 100,000,000

• The human brain works highly parallel

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Artificial Neural Nets
Visual Cortexof the Human Brain
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Artificial Neural Nets
Biological and Artificial Neurons
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Artificial Neural Nets
Input e.g. molecular descriptors Output e.g.
biological activity
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Artificial Neural Nets - Supervised learning
predict new compounds
change weights
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Artificial Neural Nets
Net architecture ("topology") in Capsaicin
example
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Artificial Neural Nets
Capsaicin dataset Predicted vs Actual Log EC50
using a trained Neural Net(Corr. Coeff. R2
0.92)
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Artificial Neural Nets

• Prediction of the test set (compound 6i)

• (Multiple) linear regression predictions
• Log EC50 0.76 - (0.82)? Pred. Log EC50 for 6i
  1.56
• Log EC50 1.14 - (0.07)MR Pred. Log EC50 for
  6i 0.42
• Log EC50 0.76 - (0.82)? (0.0003)MR Pred. Log
  EC50 for 6i 1.57

• Neural Net prediction Pred. Log EC50 for 6i
  1.05
• And the experimental affinity is......

• Log EC50 gt3!!!(totally inactive)

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Artificial Neural Nets - Unsupervised learning
?projection with preservation of the topology of
the input space
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Artificial Neural Nets - Unsupervised learning

• Molecules exhibit their activity via complex
  surface properties
• In a Kohonen Neural Net, compounds with similar
  surfaces are placed in similar areas in 2D
  space

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Artificial Neural Nets - Unsupervised learning
112 Dopamine and 60 Benzodiazepine Agonists in
the bulk of 8,323 structures of unknown activity
Kohonen map (40x30)
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Artificial Neural Nets - Unsupervised learning
benzodiazepine 50
benzodiazepine 39
benzodiazepine 43
benzodiazepine 22
benzodiazepine 49
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Artificial Neural Nets
Kohonen map unsupervised learning
multilayer network supervised learning
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3D QSAR Linking QSAR with Molecular Modeling
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3D QSAR

• Two standard methods
• CoMFA (Comparative Molecular Field Analysis,
  Cramer et al.)
• QuaSAR (Vedani et al.)

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3D QSAR - The CoMFA Approach
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3D QSAR - The CoMFA Approach
For the capsaicin example, CoMFA predicted Log
EC50-0.21!
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3D QSAR - The CoMFA Approach