QSAR AND DRUG
DESIGN
Corwen Hansch developed a
workable
methodology
Quantitative
Structure
Activity Relationship.
In 1968, Crum-Brown and
Fraser published an equation
first general formulation of
QSAR’S.

The relationship b/w chemical
structure and biological activity
since before the turn of the century.
 On
different
alkaloids
the
alkylation of the basic nitrogen
atom
produced
different
biological effects
quarternery
ammonium compouns
 Biological activity is a function of
the chemical structure
BA = f ( C) ….. (1)
Richet discovered that the toxicity
of organic compounds inversely
proportional to water solubility.
So changing biological activity
(ΔBA ) corresponds to the change in
the chemical and physiochemical
properties.
ΔBA= f (ΔC ) ------ (2)



All the QSAR equation corresponds to eqn
2,because only difference in BA
quantitatively correlates with changes in
lipophilicity of the compound under
investigation.
QSAR involves the derivation of
mathematical formula which relates the
biological activities of a group of
compounds to their measurable
physiochemical parameters.
These parameters have major influence
on drug’s activity.
Biological activity= function(parameters)
Activity is expressed as log(1/c),c is the
minimum concentration required to cause
a defined biological response.
QSAR based on Hammet’s constant uses
eletronic properties as the descriptors of
structures.



The importance of lipophilicity
expressed as octanol-water partition
coefficient on biological activity.
This parameter provides a measure
of bioavailability to compounds
which will determine the amt of
compounds that reaches the target
site.


All these reveal that biological
activity of a drug is a function of
chemicalfeatures(lipophilicity,electro
nic and steric) of the substituents
and skeleton of the molecule.
Lipophilicity is the major factor
governing transport,distribution and
metabolism of the drug in biological
system.


Electronic and steric features
influence the metabolism and
pharmacodynamic process of the
drug.
A major problem in QSAR studies
arise because
hydrophobic,electronic and steric
effect overlaps and cannot be
separated.
Parameters


Parameters assigned to various
chemical grps that can be used to
modify the structure of a drug.
The parameter is a measure of the
potential contribution of chemical
group to a particular property of the
parent drug.
Various parameters used are
1)Lipophilic parameters
Partitioncoefficient,
Chromatographic parameters and
π – Substitution constant.

ii)Polarizability parameters:
Molar refractivity(MR),Molarvolume,
Parachor.
iii)Electronic parameters:
Hammett Constant, Field and resonance
parameters, parameters derived from
spectroscopic
data,
Charge-transfer
constant, Dipole moment, Quantum
chemical parameters.


iv)Steric parameters:
Taft’s steric constant,Vanderwaal’s
radii.
v) Miscellaneous parameters :
Molecular weight,Geometric
parameters,Conformational
entropies,Connectivity indices and
other topological parameters.



Lipophilic parameters
Lipophilicity is defined as the
partitioning of a compound between
an aqueous and a nonqueous phase
Partition coefficient (p) and
lipophilic substituent(π).
Partition Coefficient
A drug passes through a no of
biological membranes to reach its
site of action.
The movement of drug through these
membranes measured by
P= COrganic/ Caqueous……..(3)


It is the ratio of concentration of the
substance in organic and aqueous
phase of a two compartment system
under equillibrium conditions.
For easily ionisable drug
P= COrganic/ Caqueous(1-α )
Alpha is
the degree of ionisation.
The acuracy of correlation of drug
activity wit coefficient will depend
on the solvent system used as a
model for the membrane.
 Both pure and buffered soln used
for the aqueous soln.
The n-octanol
water system is
frequently
chosen,because
it
appears to be a good mimic of lipid
polarity.

n-octanol
more constistent results for drugs
absorbed in GI tract
less polar solvents such as olive oil
give more consistent correlation of
drugs crossing the blood brain
barrier.



n-octanol
has
a
low
vapour
pressure,allowing
reproducible
measurements.
N-octanol is a UV transaparent over
a
large
range
making
the
quantitative detemination of a
compound very easy.


More polar solvents such as
chloroform gives more consistent
value for buccal absorption.
It is a suitable model of the lipid
constituents
of
biological
membrane due to its long alkyl
chain and the polar hydroxyl grp.
The former parameter refers to the whole
molecule while the latter related to
substituted groups.
 Chromatographic Parameters
When the solubility of a solute is
considerably greater in 1st phase than the
other
,partition
coefficient
becomes
difficult to determine experimentally.
Chromatographic parameters obtained from
RP thin layer chromatography are
occassionaly used as substitutes for
partition coefficient.

Silica gel plate coated with
hydrophobic phase is eluted with
aqueous/organic solvent system of
increasing water content.
 Rf values are converted to Rm values
which are the true measure of
lipophilicity from the following
equation
Rm = Log(1/Rf-1)

The Rm values offer advantages compared to log P
values.
 Used as substitute for partition coefficient in
QSAR investigations.
a)Compounds need not be pure.
b) Only traces of materials needed
c) A wide range of hydrophilic and hydrophobic
congeners can be investigated
d) The measurement of practicaly insoluble
analogs possess no problem
e) No quantitative method for concentration
determination needed
f)
Several
compounds
can
be
estimated
simultaneously


The main disadvantages are
a) Lack of precision and
reproducibility
b) Use of different organic solvent
system renders the derivation of π
and f related scales impossible.
Π Substituent constant/Lipophilic
Substituent constant
Lipophilic substituent constant are also
known as hydrophobic constants (Π)
The Π substituent constant defined by
Hansch and Co-workers by the equation
Π= log PRH- log PRX
Where PRH and PRX are the partition
coefficient of the std compound and its
monosubstituted derivative respectively.
Calculation of Log P value of mchlorotoluene is given as
log P= log P benzene + π Cl + π me
= 2.13+0.71+0.56=3.40
log P= log P toluene + π me- Cl
= 2.69+0.76 =3.45
log P= log P chlorobenzene + π meta- Me
= 2.84+0.51=3.35
logP exp = 3.28

Polarizability parameters
Molar Refractivity(MR)
It is a measure of both the volume of a
compound and how easily it is polarized
It is expressed as
MR = (n2-1)Mw
(n2-1) d
Where n is the refractive iondex
M is the molecular weight
d is the density



The term Mw/d define a volume
,while the term (n2-1) / (n2+ 2)
indicates a correction factor by
indicating how easily the
substituent can be polarised.
This is particularly significant if the
substituent has a π electron or lone
pair of electrons.
Ligand –enzyme inter

The significance of molar refractivity
terms in QSAR equation of ligandenzyme
interaction
could
be
interpreted with the help of 3D
structure.The investigation shows
that substituent modelled by MR
bind in polar areas while π,bind in
hydrophobic space.

The positive sign of MR in QSAR
equation indicates that substituent
binds to polar surface while a – ve
sign or nonlinear relationship
indicates steric hindrance at the
binding sites.

Electronic Parameters
The distribution of electron in a
drug molecule has considerable
influence on the distribution and
activity of the drug.
Polar and nonpolar drug unionized
form are transported through the
membrane than polar drugs in their
ionized form.


If the drug reaches the target site, the
distributed electron will control the type
of bond that it forms with the target
site,which inturn affects its biological
activity.
The Hammet Constant (σ)
He quantified the electronic effects of
groups on the physiochemical properties
of the cpd.
The distribution of the elecrons within a
molecule depends on the nature of the
electron withdrawing and donating group
found in the structure.
Hammett used this concept to
calculate Hammet constant(σ)for a
variety of monosubstituted benzoic
acids.
These constants were used to
calculate the equillibrium constants
for chemical reactions.
σ=log KBx

KB

ie., σx= log KBx-log KB
pka= -log Ka
σx=pKB-pKBx
Where KB and KBx are the equillibrium
constants for benzoic acids and
monosubstituted
benzoic
acids
respectively.

Hammett substituent const is a
measure
of
the
electron
withdrawing or donating ability of a
substituent and is determined by
comparing the dissociation of a
series of substituted acid with that
of the parent or unsubstituted acid


A negative value of σx indicates that
the substituent is acting as an
electron donor and the +ve value
indicates that it is acting as a
electron withdrawing group.
Hammett constant take into acount
both resonance and inductive effect



The values for σ for a particular
substituent varies depending on their
substitution meta or para.
The meta and para sigma value are
commonly used and indicated by a
subscript m or p after the symbol ,
The o – substituent are unreliable
due to steric hindrance and other
effects
such
as
intramolecular
hydrogen bonding.
3 Kinds of static or electical
influence states predominates
 Resonance or Mesomeric effect
Inductive effect.
 Electrical effect which is transmitted
by the polarization of electrons from
atom to another.

Hammett Constant
Inductive effect
---- Intrinsic tendency of a
substituent to withdraw or release
electns.
For eg G releases e-ns ,disperses
charge and stabilises cation.
G
C+

G withdraws e-ns intensifies the
charge and destabilizes the cation.
G
C+
Disadvantage:
They only apply to substituent directly
attached to benzene ring.
If there is more than one substituent the
value are summarized as Σσ. This
constant was unsuccessful to relate
biological activity sine the electron
distribution is not the only factor
involved.
Inductive substituent Constant:
Hammett constant are a measure of both
inductive and mesomeric effect.
The para substituent constant (σp) has a
greater resonance component than the
equivalent meta constant (σm) and the
inductive const can be calculated from the
inductive substituent constant (σi)

σi= ½ (3 σp- σm)
It is used in aliphatic compound where
influencing and influenced form group do
not form a part of the conjugated system.
Taft’s substituent constant( σ*)
It is a measure of the polar effects of a
substituent in aliphatic compound.
They are based on the hydrolysis of ester
and calculated frm the following eqn

σ*= 1
log(k/ko)B - log(k/ko)A
2.48
ie, 0.403 log(k/ko)B - log(k/ko)A
Where k is the rate constants for the
hydrolysis of substituted compound.
Ko those of methyl derivative .
B represents basic hydrolysis and A
acid hydrolysis respectively.
The factor 1/2.48 is a constant
B is influenced by the polar effect so that
by substracting the acid term from the
basic term only the polar effect remain.
In taft’s substituent constant only the
methyl group is the standard for which
the constant is zero.


That can be compared with other
constant by writing the methyl
group in the form CH2-H and
identify it as the group for H.
Taft and Inductive substituent
constant are related as
σ*= 2.51 σi

Steric Substitution Constant
The drug approaches the binding site to
interact with the receptor.The bulk,size
and shape of the drug may influence on
this process.
A steric substitution constant is a measure
of the bulkiness of the grp it represents
and its effect on the closeness of the
group between the drug and receptor
site.
CHARTON’S STERIC CONSTANT

Corrected Vanderwaal’s radius U in
which the minimum Vanderwaal’s
radii of the substituent grp (rv(min) is
corrected for the corresponding
radius for hydrogen(rvH),
U= rv(min)-rvH= rv(min) -1.20

Other parameters
Molecular wt was used by Lien to
improve the fit of parabolic Hansch
equation .A more appropriate use of
MW was demonstrated in the QSAR
study of multidrug resistance of
tumour cells,where MW stands for
the
dependence
of
biological
activities on diffusion rate constant.


The relationship bw MW and volume
implies that 3√MW correponding to
linear dimension of size should be
better than log MW.
Indicator
variables
known
as
dummy
variables
or
de-nova
constant are used in linear multiple
regression analysis .It is used to
account for other structural features
1.Intramolecular
hydrogen
bonding,hydrogen donor & acceptor
properties,ortho
effects,cis/trans
isomers,diff parent skeleton,diff test
models etc.

Quantitative Models
This is the most popular mathematical approach to
QSAR introduced by Hansch.
a)
b)
Transport of drug to its site of action.
The binding of drug to its target site.
Each of these stages depends on the chemical and
physical properties of the drug and its target site.
In Hansch analysis these properties are described by
the parameters which correlates biological activity.

The
most
commonly
used
physiochemical
parameters
for
Hansch analysis are logp,Π, σ and
steric parameters are practically all
the parameters used in Hansch
analysis are linear free energy
related ,so it is known as linear free
energy
approach
or
extra
thermodynamical approach.
The relnship b/w P and drug activity
depends on P values.
If range is low,straight line is
obtained.
log1 /c = K1log p +K2
Where K1 and K2 are consts.


If the hydrophobicity values are
limited to a small values then the
eqn will be linear.
log1 /c = k1log p +k2 σ+K3E3+ K4
Where
K1,K2,K3
are
constant
obtained by least square procedure.
C is the molar concentration that
produces biological action.
The molecule which are too hydrophilic
or lipophilic will not be able to cross
the lipophilic or hydrophilic barriers
respectively.
If the P value are higher range ,then
the equation will be parabolic and
given as


log1/c =-K1 (logp)2 +K2logP+
K3 σ+K4εS+K5
The constants K1-K5 are obtained by
least square method.
Here the graph of log 1/c against log P
Have max values logP0 ---- parabolic form

Below the P0 – drug reluctant to
enter the membrane.
 Above P0--- reluctant to leave the

membrane.
The analogues with partition coeff
near this optimum value ---- most
active and important to study.
HANCH RULES
Selection of independent variables
Different parameters
1. log P,Π, σ,MR, steric
2.Parameters should be
independent.
The intercorrelation coefficient should
not be larger than 0.6-0.7.


All the reasonable parameters must
be
validated
by
appropriate
statistical procedure ie either by a
step wise regression analysis or
cross validation.

The best equation is normally one
with lower standard deviation and
higher F value.



If all the equations are equal
simplest one is taken
Number of variable should be at least
5 or 6 data point per variable to
avoid chance correlations.
Model should be consistent with
the known physical.organic and
bio-medicinal chemistry of the
process
under
consider
consideration.

APPLICATIONS OF HANCH ANALYSIS
It is used to predict the activity
of an yet unsynthesised
analogue.
This enables the medicinal
chemist
to
synthesise
an
analogue which is worthy.
Eg; The adrenergic activity of a
series
of
analogues
of
βhaloarylamine was observed.
It was found that only pi and sigma
values only related to activity and
not the steric factor.
Log 1/c =1.78pi+1.674


Hansch analysis may also used
to give an indication of the
importance of the influence of
parameters on the mechanism
by which a drug acts.
The smaller the value of coefficient
of σ relative to that of Π in tha
above eqn shows that electronic
effect do not play an important role
in the action of the drug.
The accuracy of Hansch equation
depends on
1)The no of analogues used

2) The greater the number, the
higher the probability of obtaining
an accurate Hansch equation.
3)The accuracy of biological data used
in the derivation of the equation.
4)The choice of parameters.

Free Wilson Analysis
It is a true SAR model.This is an alternative
approach to Hamett model.
Free and Wilson used a series of substituent
constant which related biological activity
to the presence of a specific functional
group at a specific location on the parent
molecule.

The relationship between biological
activity and the presence or
absence
of
a
substituent
is
expressed by the following equation
Activity=A+Gij Xij
Where A is average biological activity
of the series,Gij is the contribution
of actiivity to the functional grp i in
the jth position and Xij the presence
or absence of functional grp i in the
jth position.
Whole molecular descriptors
Some of the natural

The method is based upon an
additive mathematical model in
which a particular substituent in a
particular molecular position is
assumed to make an additive and
constant contribution to biological
activity of a molecule in a series of
chemically related molecule.
Mathematical
model,Additive
model or denovo approach are
the
synonyms
for
free
wilsonmethod.
The substituent constant based on
activities are used rather than
physical properties

Introduction
of
a
particular
substituent at a particular molecular
position
always
lead
to
a
quantitatively similar effect on
biological potency of the whole
molecules and expressed by the eqn
as
BA=µ+Σaij

Where µ= contribution of unsubstituted
compounds
Σaij = contribution of substituted
compounds
i = number of position the substituent
occurs
j = number of substituent at that
position
APPLICATION
1)Easy to apply
2)Simple method to derive the
substituent contribution and to have
a first look on their possible
dependence
on
different
physiochemical properties


The substituent which cannot fulfill
the principle of additivity can be
recognized.
Substituent constants like σ and Π
were not considered and so this
method
is
effective
when
substituent
constants
are
not
available.
Disadvantages
The structural variation is necessary
in at least two different position of
the substitution.
Large no of parameter is necessary to
describe relatively few compounds.
Only a small no of new nalogues can
be predicted.
