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Quantitative Structure Activity Relationships QSAR

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Title: Quantitative Structure Activity Relationships QSAR


1
Quantitative Structure- Activity Relationships
(QSAR)
2
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.

3
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.

4
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

5
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.

6
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.

7
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

8
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.

9
Definition of Hammett r
These sp values are obtained from the best fit
line having a slope 1
10
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.

11
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

12
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

13
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

14
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.

15
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.

16
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.

17
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
18
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

19
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)

20
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

21
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.

22
Neolignans
23
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.

24
Two Most Important Descriptors

25
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).
26
QSAR-Calculated Antifungal Activity
27
New Neolignans
28
Example of a Pharmacophore 2D Hypothesis and
Alignment
29
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
30
CoMFA of Testosterone
Blue means electronegative groups enhance, red
means Electng. grps reduce binding
Green means bulky groups enhance, yellow means
they reduce binding
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