Hansch Constant (p)
Hansch derived constants for the contributions of
substituents to the partition coefficient. The lipophilicity
constant, π, is defined as:
π = log Px - log PH = log (Px/PH)
where Px is partition constant for the compound with X as
substituent and PH is the partition constant for the
parent.
Tables of values of π for other substituents are available.
p values for various substituents on
aromatic rings
CH3 t-Bu
0.5
2
OH
1.68 -0.67
CONH2 CF3
-1.49
Cl
Br
F
1.16 0.71 0.86 0.14
Theoretical Log P for chlorobenzene
= log P for benzene + p for Cl
= 2.13 + 0.71 = 2.84
p values for various substituents on
aromatic rings
CH3
t-Bu OH
CONH2
0.52 1.68 -0.67 -1.49
CF3
Cl
Br
F
1.16 0.71 0.86 0.14
Theoretical Log P for meta-chlorobenzamide
= log P for benzene + p for Cl + p for CONH2
= 2.13 + 0.71 - 1.49 = 1.35
The following are the p values for various substituents on an aromatic ring:
-CF3 (1.07), -Br (0.94), -OCH3 (-0.02), -CH2OH (-1.03). Which functional group
listed above will increase the water solubility of the following drug the most
(ie. we replace the R- group with one of the substituents).
A) -CF3 (1.07)
B) -Br (0.94)
C) -OCH3 (-0.02)
D) -CH2OH (-1.03)
E) They will all make the drug equally lipophilic
STERIC FACTORS
The bulk, size and shape of a drug will influence how easily it can
approach and interact with binding site.
A bulky substituents may act like a shield and hinder the ideal
interaction between a drug and its binding site.
Bulky substituent may help to orient a drug properly for
maximum binding and increase activity.
Steric Effects
much harder to quantitate
Examples are:
Taft’s steric factor (Es)
based on rate constants
(~1956), an experimental value
Molar refractivity (MR)--measure of the volume occupied
by an atom or group--equation includes the MW, density,
and the index of refraction—
Verloop steric parameter--computer program uses bond
angles, van der Waals radii, bond lengths
Steric Effects
The third major factor that often must be considered in
QSAR involves steric effects.
For studies involving reactivity of organic compounds,
a steric parameter, Es, was defined by Taft as :
where k is the rate constant for the acid hydrolysis of
esters of the type
Taft’s Steric Factor (Es)
•Measured by comparing the rates of hydrolysis of substituted
aliphatic esters against a standard ester under acidic conditions
kx represents the rate of hydrolysis of a substituted ester
ko represents the rate of hydrolysis of the parent ester
•Limited to substituents which interact sterically with the
tetrahedral transition state for the reaction
•Not by resonance or hydrogen bonding
Disadvantages
ES value measures intramolecular steric effect but drugs interact
with target binding site in intermolecular process (i.e. a drug
binding to a receptor)
Molar Refractivity (MR)
this is a measure of a substituent’s volume
MR =
(n 2 - 1)
(n 2 - 2)
Correction factor
for polarisation
(n=index of
refraction)
x
mol. wt.
density
Defines volume
This is perticularly significant if the substituent has π
electrons or lone pair of electrons
Verloop Steric Parameter
- calculated by software (STERIMOL)
- gives dimensions of a substituent from the standard
bond angle ,van der Waals radii, bond length and possible
conformations for the substituents
- can be used for any substituent
Example - Carboxylic acid
B4
O
B
3
B2
C
H
O
H
L
B3
B
4
O
C
O
B1
HANSCH EQUATION
•A QSAR equation relating various physicochemical properties
to the biological activity of a series of compounds
•Usually includes log P, electronic and steric factors
•Start with simple equations and elaborate as more structures
are synthesised
•Typical equation for a wide range of log P is parabolic
1
Log C =
- k1(logP)2 + k 2 logP + k 3 s + k 4 Es + k 5
Craig Plot
Craig plot shows values for 2 different physicochemical
properties for various substituents
.
.
..
. ..
. .
.
.
. ..
.
.
.
.
.
.
.
.
.
+
1.0
CF3SO 2
.75
CN
CH3SO2
SO 2NH2
NO2
.50
CH3CO
CONH2
OCF3
.25
CO2H
-2.0
-p
-1.6
-1.2
-.8
-.4
SF5
CF3
F
.4
I
Br
Cl
.8
1.2
1.6
CH3CONH
-.25
-.50
NMe 2
NH2
-.75
-1.0
-
Et
t-Butyl
OCH3
OH
Me
2.0
+p
•Allows an easy identification of suitable substituents for
a QSAR analysis which includes both relevant properties
•Choose a substituent from each quadrant to ensure
orthogonality
•Choose substituents with a range of values for each
property
– Assuming the electronic effects of substituent X can be
ignored, the size of X will affect the transition state and
hence the rate of reaction.
– By definition Es = 0 for X=H.
– Tables of values of Es for other substituents are
available.
Hansch Approach
A drug's activity was really a function of two
processes:
1. its transportation from point of entry to receptor
site(s) (pharmacokinetics).
2. its
interaction
with
the
receptor
(pharmacodynamics).
– Hansch proposed that the ability of a drug to get
through a membrane might be modeled by its partition
coefficient between a lipid-type solvent and water
The suggested model for a drug traveling through the
body to its receptor site might be:
log 1/C = -k(log P)2 + k'(log P) + k"
where potency is expressed as log (1/C) and C is the
concentration of a drug that provides some standard
biological effect.
This equation has the format for a parabola
The significance of this observation is that an optimum
hydrophobicity may exist.
Log (1/C)
o
Log P
Log P
Optimum value of log P for anaesthetic activity = log Po
– Accordingly several membranes may have to be
traversed for compounds to get to the target site, and
compounds with the greatest hydrophobicity will
become localized in the membranes they encounter
initially, thereby slowing their transit to the target site.
– Hansch proposed also that there should be a linear free
energy relationship (like the Hammett equation) between
lipophilicity and drug activity and that this might be
indicated by the partition coefficient
Hansch Linear Free Energy Model
Hansch has derived a general equation based on linear
free-energy considerations.
In this equation is the ability to incorporate parameters
which encompass the full range of known biological
requirements for drug activity.
Among theses terms for biological transport,
drug/enzyme binding energies and substituent effects
(both electronic and steric).
The most general form of Hansch equation is:
log 1/C = -aπ2 + bπ + ρσ + c
Log 1/C = k1P - k2P2 + k3s + k4Es + k5
Where
activity expressed as 1/C, C = concentration,
π is the Hansch constant (measure of lipophilicty),
ρ is constant related to the given molecule,
ς is the Hammett substituent constant which is a measure of
the electronic effect.
Es Taft’s constant
Hansch Analysis
• Look at size and sign for each
component of the equation.
• Values of r <<0.9 indicate equation not
reliable
• Accuracy depends on using enough
analogs, accuracy of data, & choice of
parameters.
Examples for Hansch equations
log 1/C = 1.22 p – 1.59 s + 7.89
(n = 22; r = 0.918)
log 1/C = 0.398 p + 1.089 s + 1.03 Es + 4.541
(n = 9; r = 0.955)
Examples:
Adrenergic blocking activity of b-halo-b-arylamines
Y
X
CH CH2
1
Log C =
NRR'
1.22 p - 1.59 s + 7.89
Conclusions:
• Activity increases if p is + (i.e. hydrophobic substituents)
• Activity increases if s is negative (i.e. e-donating substituents)
For the antibacterial activity of substituted phenols
OH
X
log 1/C = 0.684 log P – 0.921σ + 0.268
For a series of phosphonate esters, cholinesterase inhibitors
O
O P OCH2CH3
R
O2N
log K = -0.152 π –1.68 σ + 4.053 Es + 7.212
Where
K is the inhibition constant,
σ is the Hammett substituent constant for aliphatic systems
Es is the Taft steric constant.
In this example steric effect of the substituents plays an important role.
The bulkier groups cause a decrease in cholinesterase inhibition.
一For the antibacterial effects on gram-negative bacteria of a series of diguanidines:
NH
(CH2)n
(NH-C-NH2)2
log 1/C = -0.081 π2 + 1.483 π – 1.578
Example: Antimalarial activity of phenanthrene aminocarbinols
CH2NHR'R"
(HO)HC
X
Y
1
Log C = - 0.015 (logP)2 + 0.14 logP + 0.27 SpX + 0.40 SpY + 0.65 SsX + 0.88 SsY + 2.34
Conclusions:
• Activity increases slightly as log P (hydrophobicity) increases
(note that the constant is only 0.14)
• Parabolic equation implies an optimum log Po value for activity
• Activity increases for hydrophobic substituents (esp. ring Y)
• Activity increases for e-withdrawing substituents (esp. ring Y)
Electronic effect
Lipophilicityt
Steric effect
3-D space formed by lipophilic, electronic and steric coordinates
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