Quantitative Structure Activity Relationships QSAR

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Quantitative Structure- Activity Relationships
(QSAR)
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Rationale for QSAR Studies

• In drug design, in vitro potency addresses only
  part of the need a successful drug must also be
  able to reach its target in the body while still
  in its active form.
• The in vivo activity of a substance is a
  composite of many factors, including the
  intrinsic reactivity of the drug, its solubility
  in water, its ability to pass the blood-brain
  barrier, its non- reactivity with non-target
  molecules that it encounters on its way to the
  target, and others.

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Rationale for QSAR Studies...

• A quantitative structure-activity relationship
  (QSAR) correlates measurable or calculable
  physical or molecular properties to some specific
  biological activity in terms of an equation.
• Once a valid QSAR has been determined, it should
  be possible to predict the biological activity of
  related drug candidates before they are put
  through expensive and time-consuming biological
  testing. In some cases, only computed values
  need to be known to make an assessment.

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History of QSAR

• The first application of QSAR is attributed to
  Hansch (1969), who developed an equation that
  related biological activity to certain electronic
  characteristics and the hydrophobicity of a set
  of structures.
• log (1/C) k1log P - k2(log P)2 k3s
  k4
• for C minimum effective dose
• P octanol - water partition coefficient
• s Hammett substituent constant
• kx constants derived from regression analysis

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Hanschs Approach

• Log P is a measure of the drugs hydrophobicity,
  which was selected as a measure of its ability to
  pass through cell membranes.
• The log P (or log Po/w) value reflects the
  relative solubility of the drug in octanol
  (representing the lipid bilayer of a cell
  membrane) and water (the fluid within the cell
  and in blood).
• Log P values may be measured experimentally or,
  more commonly, calculated.

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Calculating Log P

• Log P Log K (o/w) Log
  (Xoctanol/Xwater)
• most programs use a group additivity approach
• 1 Aromatic ring 0.780
• 7 Hs on Carbon 1.589
• 1 C-Br bond -0.120
• 1 alkyl C 0.195 Sum 2.924 calc. log P
• some use more complicated algorithms, including
  factors such as the dipole moment, molecular size
  and shape.

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Hanschs Approach...

• The Hammett substituent constant (s) reflects the
  drug molecules intrinsic reactivity, related to
  electronic factors caused by aryl substituents.
• In chemical reactions, aromatic ring substituents
  can alter the rate of reaction by up to 6 orders
  of magnitude!
• For example, the rate of the reaction below is
  105 times slower when X NO2 than when X CH3

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Hammett Equation

• Hammett observed a linear free energy
  relationship between the log of the relative rate
  constants for ester hydrolysis and the log of the
  relative acid ionization (equilibrium) constants
  for a series of substituted benzoic esters
  acids.
• log (kx/kH) log (Kx/KH) rs
• He arbitrarily assigned r, the reaction constant,
  of the acid ionization of benzoic acid a value of
  1.

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Definition of Hammett r
These sp values are obtained from the best fit
line having a slope 1
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Hammett Plot

• Aryl substituent constants (s) were determined by
  measuring the effect of a substituent on a
  reaction rate (or Keq). These are listed in
  tables, and are constant in widely different
  reactions.
• Reaction constants (r) for other reactions may
  also be determined by comparison of the relative
  rates (or Keq) of two differently substituted
  reactants, using the substituent constants
  described above.
• Some of these values (s and r) are listed on the
  following slide.

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Hammett Rho Sigma Values
Reaction (Rho) Values r

• Substituent (Sigma) Values s (the electronic
  effect of the substituent
• negative values are electron donating)
• p-NH2 -0.66 p-Cl 0.23
• p-OCH3 -0.27 p-COCH3 0.50
• p-CH3 -0.17 p-CN 0.66
• m-CH3 -0.07 p-NO2 0.78

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Molecular Properties in QSAR

• Many other molecular properties have been
  incorporated into QSAR studies some of these are
  measurable physical properties, such as
• density ? pKa
• ionization energy ? boiling point
• Hvaporization ? refractive index
• molecular weight ? dipole moment (m)
• Hhydration ? reduction potential
• lipophilicity parameter
  p
  log PX - log PH

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Molecular Properties in QSAR

• Other molecular properties (descriptors) that
  have been incorporated into QSAR studies
  include calculated properties, such as
• ovality ? surface area, molec. volume
• HOMO energy ? LUMO energy
• polarizability ? charges on individual atoms
• molecular volume ? solvent accessible surface
  area
• vdW surface area ? maximum and - charge
• molar refractivity ? hardness
• hydration energy ? Tafts steric
  parameter

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QSAR Methodology

• Often it is found that several descriptors are
  correlated that is, they describe observables
  that are closely related, such as MW and boiling
  point in a homologous series.
• Statistical analysis is used to determine which
  of the variables best describe (correlate with)
  the observed biological activity, and which are
  cross-correlated. The final QSAR involves only
  the most important 3 to 5 descriptors,
  eliminating those with high cross-correlation.

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Limit to the of Descriptors

• The data set should contain at least 5 times as
  many compounds as descriptors in the QSAR.
• The reason for this is that too few compounds
  relative to the number of descriptors will give
  a falsely high correlation
• 2 points exactly determine a line (2 compds, 2
  prop)
• 3 points exactly determine a plane (etc., etc.)
• A data set of drug candidates that is similar in
  size to the number of descriptors will give
  a high (and meaningless) correlation.

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Statistical Analysis of Data

• Multiple linear regression analysis can be
  accomplished using standard statistical software,
  typically incorporated into sophisticated (and
  expensive) drug design software packages, such as
  MSIs Cerius2 (academic price, over 20K)
• An inexpensive statistical analysis software
  StatMost (academic price, 39) works just fine.
• To discover correlated variables and determine
  which descriptors correlate best, a partial least
  squares or principal component analysis is done.

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Example of a QSAR
Anti-adrenergic Activity and Physicochemical
Properties of 3,4- disubstituted
N,N-dimethyl-a-bromophenethylamines
p Lipophilicity parameter s
Hammett Sigma (for benzylic cations)
Es(meta) Tafts steric parameter
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Example of a QSAR...
Calc.
Calc.

• m-X p-Y p s Es(meta)
  log (1/C)obs log (1/C)a log (1/C)b
• H H 0.00 0.00 1.24 7.46 7.82 7.88
• F H 0.13 0.35 0.78 7.52 7.45 7.43
• H F 0.15 -0.07 1.24 8.16 8.09 8.17
• Cl H 0.76 0.40 0.27 8.16 8.11 8.05
• Cl F 0.91 0.33 0.27 8.19 8.38 8.34
• Br H 0.94 0.41 0.08 8.30 8.30 8.22
• I H 1.15 0.36 -0.16 8.40 8.61 8.51
• Me H 0.51 -0.07 0.00 8.46 8.51 8.36
• Br F 1.09 0.34 0.08 8.57 8.57 8.51
• H Cl 0.70 0.11 1.24 8.68 8.46 8.60
• Me F 0.66 -0.14 0.00 8.82 8.78 8.65
• H Br 1.02 0.15 1.24 8.89 8.77 8.94
• Cl Cl 1.46 0.51 0.27 8.89 8.75 8.77
• Br Cl 1.64 0.52 0.08 8.92 8.94 8.94
• Me Cl 1.21 0.04 0.00 8.96 9.15 9.08
• Cl Br 1.78 0.55 0.27 9.00 9.06 9.11
• Me Br 1.53 0.08 0.00 9.22 9.46 9.43
• H I 1.26 0.14 1.24 9.25 9.06 9.26

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Example of a QSAR...

• QSAR Equation a (using 2 variables)
• log (1/C) 1.151 p - 1.464 s 7.817
• (n 22 r 0.945)
• QSAR Equation b (using 3 variables)
• log (1/C) 1.259 p - 1.460 s 0.208 Es(meta)
  7.619 (n 22 r 0.959)

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Example of a QSAR...
Calc.
Calc.

• m-X p-Y p s Es(meta)
  log (1/C)obs log (1/C)a log (1/C)b
• H H 0.00 0.00 1.24 7.46 7.82 7.88
• F H 0.13 0.35 0.78 7.52 7.45 7.43
• H F 0.15 -0.07 1.24 8.16 8.09 8.17
• Cl H 0.76 0.40 0.27 8.16 8.11 8.05
• Cl F 0.91 0.33 0.27 8.19 8.38 8.34
• Br H 0.94 0.41 0.08 8.30 8.30 8.22
• I H 1.15 0.36 -0.16 8.40 8.61 8.51
• Me H 0.51 -0.07 0.00 8.46 8.51 8.36
• Br F 1.09 0.34 0.08 8.57 8.57 8.51
• H Cl 0.70 0.11 1.24 8.68 8.46 8.60
• Me F 0.66 -0.14 0.00 8.82 8.78 8.65
• H Br 1.02 0.15 1.24 8.89 8.77 8.94
• Cl Cl 1.46 0.51 0.27 8.89 8.75 8.77
• Br Cl 1.64 0.52 0.08 8.92 8.94 8.94
• Me Cl 1.21 0.04 0.00 8.96 9.15 9.08
• Cl Br 1.78 0.55 0.27 9.00 9.06 9.11
• Me Br 1.53 0.08 0.00 9.22 9.46 9.43
• H I 1.26 0.14 1.24 9.25 9.06 9.26

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QSAR of Antifungal Neolignans

• The PM3 semi-empirical method was employed to
  calculate a set of molecular properties
  (descriptors) of 18 neolignan compounds with
  activities against Epidermophyton floccosum, a
  most susceptible species of dermophytes. The
  correlation between biological activity and
  structural properties was obtained by using the
  multiple linear regression method. The QSAR
  showed not only statistical significance but also
  predictive ability. The significant molecular
  descriptors related to the compounds with
  antifungal activity were hydration energy (HE)
  and the charge on C1' carbon atom (Q1'). The
  model obtained was applied to a set of 10 new
  compounds derived from neolignans five of them
  presented promising biological activities against
  E. floccosum.

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Neolignans
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Descriptors Used

• Log P the values of this property were obtained
  from the hydrophobic parameters of the
  substituents
• superficial area (A) and molecular volume (V),
  log of the partition coefficient (Log P),
  hydration energy (HE) properties evaluated with
  the molecular modeling package HyperChem 5.0
• partial atomic charges (Qn) and bond orders (Ln)
  derived from the electrostatic potential
• energy of the HOMO (H) and LUMO (L) frontier
  orbitals
• hardness (h) obtained from the equation h
  (ELUMO-EHOMO)/2
• Mulliken electronegativity (c) calculated from
  the equation c -(EHOMOELUMO)/2
• other electronic properties were calculated
  total energy (ET), heat of formation (DHf)
  ionization potential (IP), dipole moment (m)
  and polarizability (POL), whose values were
  obtained from the molecular orbital pprogram
  Ampac 5.0.

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Two Most Important Descriptors

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Antifungal QSAR

• Log 1/C -2.85 - 0.38 HE - 1.45 Q1'
• F29.63, R20.86, Q20.80, SEP0.
• where
• F is the Fisher test for significance of the
  eqn. R2 is the general correlation coefficient,
  Q2 is the predictive capability, and
  SEP is the
  standard error of prediction.

A.A.C. Pinheiro, R.S. Borges, L.S. Santos, C.N.
Alves, Journal of Molecular Structure THEOCHEM,
Vol 672, pp 215-219 (2004).
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QSAR-Calculated Antifungal Activity
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New Neolignans
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Example of a Pharmacophore 2D Hypothesis and
Alignment
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3 Dimensional QSAR Methods

• Important regions of bioactive molecules are
  mapped in 3D space, such that regions of
  hydrophobicity, hydrophilicity, H-bonding
  acceptor, H-bond donor, p-donor, etc. are
  rendered so that they overlap, and a general 3D
  pattern of the functionally significant regions
  of a drug are determined.
• CoMFA (Comparative
  Molecular Field Analysis)
  is one such
  approach

testosterone
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CoMFA of Testosterone
Blue means electronegative groups enhance, red
means Electng. grps reduce binding
Green means bulky groups enhance, yellow means
they reduce binding