Quantitative Structure-Activity Relationships (QSAR)

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Quantitative Structure-Activity Relationships
(QSAR)
Objectives The physical properties of drugs, in
part, dictate their biological activity.  In
addition, use of descriptors of physical
properties allow for the application of
mathematical models to analyze and predict drug
activity.  Upon completion of the QSAR lectures,
the student will be aware of the different
physical properties that influence biological
activity, use of those properties in the
development of mathematical models that relate
the physical properties to biological activity,
and how those mathematical models may be used to
understand drug action.
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QSAR Systematic approach to lead compound
optimization
Assume drug action is related to the physical
properties of the ligand. Historical
Galileo Galilei (1564-1642) Richet (1893)
Overton and Meyer (1890s) Ferguson
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Applications of QSAR(Hansch Analysis)

• 1) Classification
• 2) Diagnosis of Mechanism of Drug Action B.A.
  0.94 logP 0.87, r 0.97, n 51
• 3) Prediction of Activity (congeneric series)
• 4) Lead Compound Optimization

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Sulmazole
Systematic approach to relate physical properties
to activity that is applicable for a large number
of chemical and biological systems
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Hammett electronic parameter or substituent
constant, s
Equilibrium between the unionized and ionized
forms of benzoic acid and the definition of Ka
Note pKa - log Ka
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Positive versus negative s values for chemical
substituents, x.
Positive s electron withdrawing, log (Kx/KH) gt
1 Negative s electron donating, log (Kx/KH) lt
1 Substituent effects contributing to s Meta
inductive (through space and through bond)
Para resonance Ortho minimal
transferability Multiple substituents on a
compound additive treatment of s
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Example of resonance forms that stabilize the
negatively charged carboxylate in p-nitrobenzoic
acid
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General utility of ? valuesSaponification of
substituted ethyl benzoates

• Measure k for training set of compounds
• Plot s versus k, determine slope
• Relate electronic effects to k positive slope
  indicates electron withdrawing groups favor k
  negative slope indicates electron donating groups
  favor k
• Predict k for unknown compounds
• Generality is that the same ? values may be
  applied to all reactions and equilibria, such
  that they do not have to be re-determined for
  every study.

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The Hammett constants, s,, can be related to the
free energy of ionization via the vant Hoff
relationship (In this case s would correspond to
the equilibrium constant, K, allowing for Hammett
relationships to also be referred to as a linear
free energy relationship (LFER)).
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Ester hydrolysis reaction and equation used to
define the Taft steric parameter, Es
Es is always 0 or negative
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Equation for the molar refractivity
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Consideration of asymmetric shape of functional
groups and molecules in QSAR
Verloop steric parameter
Solvent Accessible Surface
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Application of QSAR to biological systems
(Biological Hammett Relationship)Hansch, 1962
Consideration of need to cross membranes Blood
brain barrier Lipophilicity (hydrophobicity)
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Equations for the determination of the partition
coefficient, P, and the hydrophobicity parameter,
px
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Determination of partition coefficient, P
Experimentally Shaker flask Reversed
phase HPLC Computationally Fragmental
constants, fi Interaction factors, Fi
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Example of calculation of log P
log P of benzene 2.5 (parent compound) fi of
methyl 0.6 fi or aromatic fluorine -0.4 Fi
for fluorine atom ortho to a methyl group is
-0.3 log P 2.5 0.6 (-0.4) (-0.3) 2.4
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Example of a linear equation where multiple
variables are used to obtain a correlation with
biological activity (1/C).
Why use log(1/C)?
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Multiple Regression AnalysisHypothetical
training set of biological activities,
hydrophobicities and sigma values
compound log(1/C) p ?
cmpd 1 0.2 1.2 -0.5
cmpd 2 0.1 1.8 0.2
cmpd 3 0.9 1.1 2.0
cmpd 4 0.4 0.9 1.0
cmpd 5 1.3 -0.1 1.1
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Individual plots of log(1/C) versus p or s,
including least-squares analysis
BA -0.63 p 1.20, r2 0.73
BA 0.37 s 0.30, r2 0.49
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Example of multiple regression least squares
fitting
Influence of variables (coefficients) on the
agreement between the experimental and calculated
activities
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Application of multiple regression to the
training set

• BA -0.51 p 0.23 s 0.90, r2 0.90
• Versus (from linear regression)
• BA -0.63 p 1.20, r2 0.73
• and
• BA 0.37 s 0.30, r2 0.49

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Multiple regression alonestill didnt work!
Need to consider transport from aqueous
environment through a cell membrane and back into
an aqueous environment
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Log P versus biological activity(y -x2)
parabolic plot
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Hansch equation
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Example of an extended Hansch Equation where the
Taft steric parameter, Es, has been included.
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Advantages of Hansch analysis

• A) Use of descriptors (p, s, Es etc.) from small
  organic molecules may be applied to biological
  systems.
• B) Predictions are quantitative and may be
  evaluated statistically.
• C) Quick and easy.
• D) Potential extrapolation conclusions reached
  may be extended to chemical substituents not
  included in the original analysis.

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Disadvantages of Hansch analysis

• A) Descriptors required for substituents being
  studied.
• B) Large number of compounds required (training
  set for which physicochemical parameters and
  biological activity is available).
• C) Limitations associated with using small
  molecule descriptors, such as steric factors, on
  biological systems (i.e. descriptors from
  physical chemistry).
• D) Partial protontation of drugs at physiological
  conditions (can be included in mathematical
  model).
• E) Predictions limited to structural class
  (congeneric series).
• F) Extrapolations beyond the values of
  descriptors used in the study are limited.
• G) Correlation between physical descriptors. For
  example, the hydrophobicity will have some
  correlation with the size and, thus, the Taft
  steric term.

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QSAR interpolations versus extrapolations

• Spanned Substituent Space (SSS) range of
  physical properties covered by the compounds in
  the training set.
• Interpolative predictions within SSS
• Extrapolative predictions beyond SSS

SSS
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Statistical Significance in QSAR
Minimum of 5 compounds per term in the Hansch
equation.
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Free and Wilson Model
BA S Iij Fij k
Substituents Substituents Enhancement factors, F Enhancement factors, F Enhancement factors, F Enhancement factors, F  
j1 j2 j3 j4 j4
i1 methyl 0.4 0.6 0.8 0.3 0.3
i2 amine -1.2 -0.8 -0.5 0.1 0.1
i3 -CN 1.8 2.2 1.2 0.8 0.8
log(1/C) Ii,1Fi,1 Ii,2Fi,2 Ii,3Fi,3
Ii,4Fi,4 k
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Example of Free and Wilson Approach
A) methyl at position 1, amine at position 3 and
methyl at position 4 log(1/C) 0.4 0.0
(-0.5) 0.3 0.0 0.2 B) -CN at position 1,
methyl at position 2 and amine at position 4
log(1/C) 1.8 0.6 0.0 0.1 0.0 2.5
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Combine QSAR and Free and Wilson
Km for hydrolysis of esters by papain by amides
and sulfonamides log(1/Km) 0.57 MR 0.56 ? -
1.92 I 3.74
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Topliss Decision Tree for a Sulfa Drug

1. Measure activity of unsubstituted compound
2. Add substitutent with significant ? or ? value
   while keeping the other physical property close
   to zero
3. Measure activity of new compound
4. Select new substituent based on change in
   activity
5. Synthesize new compound and iterate over steps C,
   D and E.

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Craig plot of hydrophobicity versus smeta
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Craig plot of hydrophobicity versus the Taft
Steric Term, Es 
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Batchwise Approach
H 3,4-Cl 4-Cl 4-CH3 4-OCH3 A) Synthesize all
of the above 5 analogs for the compound being
studied. B) Experimentally determine biological
activity of 5 analogs and obtain the order of the
activity from highest 1 to lowest 5. C)
Based on order from step B, find which column in
the following table corresponds to that order. 
This identifies which descriptor (i.e. p or s)
and its sign are important for improving the
biological activity.D) Go to the second table,
identify the row that corresponds to the  p or s
relationship determined in step C and identify
substitutents to add to the compound to further
increase activity.

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Potency order for various Parameter Dependencies
for the Batchwise Approach
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New substituent selections based on parameter
dependencies from the Batchwise approach
Observed dependency Suggested substituents 
p, ps, s 3-CF3, 4-Cl 3-CF3 4-NO2 4-CF3 2,4-Cl2
p, 2p-s, p-s 4-CH(CH3)2 4-O(CH2)3CH3 4-N(C2H5)2
p-2s, p-3s, -s 4-N(CH3)2 4-NH2 4-OH 3-CH3
2p - p2 4-Br 3-CF3 3,4-(CH3)2 3-CH3
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Example of Batchwise approach
Measured order of biological activity4 gt 5 gt 2
3 gt 1or 4CH3 gt 4-OCH3 gt 3,4-Cl2 4-Cl gt H
Observed dependency Suggested substituents 
p, ps, s 3-CF3, 4-Cl 3-CF3 4-NO2 4-CF3 2,4-Cl2
p, 2p-s, p-s 4-CH(CH3)2 4-O(CH2)3CH3 4-N(C2H5)2
p-2s, p-3s, -s 4-N(CH3)2 4-NH2 4-OH 3-CH3
2p - p2 4-Br 3-CF3 3,4-(CH3)2 3-CH3
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Physiochemical parameters used in QSAR
Investigations.
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Additional descriptors for Hansch Analysis
pKa  (limited to ionizable compounds) chemical
shifts from NMR redox potentials dipole moments
quantum mechanical derived properties atomic
charges HOMO and LUMO orbital energies
electrostatic potential around a molecule (like a
magnetic field)
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3D QSAR or Compartive Molecular Field Analysis
(CoMFA)

• QSAR approach to deal with interactions of
  molecules with their environment taking into
  account 3D shape.
• Electrostatic and Steric interactions at selected
  points around molecules replace physical
  parameters in normal QSAR