Extra thermodynamic approach
Hansch analysis correlates biological activity values
with physicochemical properties by linear, linear
multiple, or non-linear regression analysis.
Thus Hansch analysis is indeed a property-property
Early attempts to correlate biological activity values
with lipophilicity expressed e.g. by solubility or
partition coefficients only explained nonspecific
structure activity relationships, the application of the
concept of a general biological hammett equation
The methodological breakthrough came from a
suggestion by Fujita, of that time working in hansch’s
Hansch and Fujita combined different physico-
chemical parameters in one equation.
Where, C – Molar concentration
k1, k2, k3, – Coefficients determined by least squares
For in vivo parabolic lipophilicity values in included in
above equation, hence it becomes
Later to this, steric parameters were added to this
general model and even latter molar refractivity
With such multiparameter equation it was
possible to describe much more complex
dependence of biological activities on physico-
In the last three decades nearly all conceivable
combinations of lipophilic, polarizability, electronic
and steric parameters with or without additional
indicator variables have been used and
correlated with biological activity values in linear,
parabolic and bilinear equation.
Hansch analysis can be used to describe
complex biological data, where several different
transport processes and equilibria contribute to
the overall structural activity relationship.
However, in industrial practice such relationships
and their quantitative description are of almost
Instead of wasting thousands of animals
nowadays enzyme inhibition, receptor binding
and cell culture data are used to derive the
activity profiles of large classes of compounds
and to predict the pharmacodynamic effects of
new drugs from simple and efficient in-vitro test
Application- Enzyme inhibition
Significant progress in QSAR resulted from
Hansch analyses of enzyme inhibitors, especially
from the systematic work of Hansch and his
group on dihydrofolate reductase and on cysteine
and serine protease.
Most of our current knowledge of the quantitative
aspects of ligand-protein interactions has been
derived from QSAR equations, aided by the
interpretation of the 3D structures of enzymes
and their inhibitor complexes with molecular
Application- Enzyme inhibition
3D structures of binary and tertiary DHFR
complexes from different bact. and vertibrates
have been published and an extremely large
number of QSAR equations have been derived
both for the isolated enzyme and for growth
inhibition of whole cells.
Due to the central role of DHFR in purine
biosynthesis, DHFR inhibitors are therapeutically
important as highly selective antibacterial
(trimethoprim) and antitumor agents
Application- Other in-vitro data
Hansch analysis provides the data for binding
affinities to the –
Hansch concluded that a change in the
membrane properties should be responsible for
the drug resistance.
So the multidrug resistance can be overcome by
Hansch quantitative models.
Pharmacokinetics describes the time dependence of
transport and distribution of a drug in the different
compartments of biological system.
Model simulations substantiate that the lipophilicity
dependence of the rate constants of drug transport
should follows bi-linear relationships.
Indeed, bi-linear equations have been derived for the
rate constant of drug transport in n-octanol/water
and for the rate constants of the transfer of various
barbiturates in a Sartorius absorption simulator from
an aqueous phase(pH-3) through an organic
membrane to another aqueous phase(pH-7.5)
modeling the gastric absorption of these compounds.
The additivity model
The version described by Fujita and Ban is a
straightforward application of the additivity concept of
group contributions to biological activity values.
logBA = contribution of unsubstituted parent
contribution of corresponding substituent
= µ + ∑aij
i-number of position at which substitution occurs
j-number of substituent at that position
BA = f(R) +f(R1) +f(R2) +f(R3) +µ
µ = biological activity of unsubstituted acetylenic
In comparison with classical version of the free-
Wilson analysis, the Fujita and Ban variant offers
a number of important advantages –
The table for regression analysis can easily be
The addition and elimination of compounds is
simple and does not change the values of the other
regression coefficients significantly.
Any compound may be chosen as the reference
Substituents which always occur together in two
different positions of the molecule can be combined
to a pseudo substituent.
The free-Wilson model is easy to apply.
Especially in the early phase of structure activity
analyses it is simple method to derive substituent
contributions and to have a first look on their
possible dependence on different physico-
It has some limitations-
Every substituent which only once occurs in the
data set, leads to a single point determination; the
corresponding group contribution contains the
whole experimental error of this one biological
Only a common activity contribution can be
derived for substituents which always occurs
together in two different positions of the
In most cases a large number of parameters is
needed to describe relatively few compounds,
sometimes leading to equations which are
statistically not significant.
Only a small number of new analogs can be
predicted from a Free-Wilson analysis .
Prediction for substituents which are not
included in the analysis are generally impossible.
It is limited to linear additive structure activity
Different sets of compounds were used in a Free Wilson
analysis of analgesic benzomorphans the first one
included all compounds (38 variables; n = 99; r = 0.893; s
= 0.466), a second one only contained racemic
compounds (36 variables; n = 86; r = 0.909; s = 0.457) and
a last one excluded all single point determinations (20
variables, n = 70; r = 0.879; s = 0.457).
The group contributions of the benzomorphans could be
used to predict the biological activity values of structurally
related morphinans, which are more active than the
benzomorphans by some orders of magnitude.
The simplest form of a Free Wilson analysis is presented
by describing the antibacterial activities of phenol and
isomeric chlorophenols (R = H, C1; one to five chlorine
atoms) us. Staphylococcus aureus; at least the linearity of
the structure-activity relationship can be derived from
below equation. On the other hand, although most
probably lipophilicity is responsible for the variance in the
biological activities, no Hansch equation can be derived,
because each other physicochemical property of the
chlorine atom will give identical results.
Free Wilson analyses may include far fewer variables than
substituents, if group contributions being not significant are
eliminated. Indicator variables for 28 different structural
features and different test models and 15 interaction terms
were investigated to describe the inhibition of dihydrofolate
reductase by 2,4-diaminopyrimidines; 9 indicator variables
and 2 interaction terms were selected and below equation
was derived out of the 2047 theoretically possible linear
combinations of any numbers of these variables.
This theoretical relationship between Hansch analysis and
the Free Wilson model was first recognized by Singer and
Free Wilson group contributions contain all possible
physicochemical contributions of a substituent;
correspondingly, a Free Wilson analysis always gives the
upper limit of correlation which can be achieved by a linear
A comparison of the results from Hansch and Free Wilson
analyses offers some information, whether a certain Hansch
model can be considered to be acceptable or not. In most
cases the Free Wilson analysis of a data set shows whether
a linear additive model is suited for the analysis; only in
certain cases is a good fit obtained for nonlinear
relationships, especially if there are only few degrees of
An example, how a Hansch equation can be
improved by comparing the group contributions
with those obtained from Free Wilson analysis, is
given below in equation was derived for the
antifungal activities of phenyl ethers (13, X, Y =
The Free Wilson analysis of the same data set indicates
that the smaller group contributions of the ortho-
substituents might be explained by a steric effect.
Due to the relationships between Hansch analysis and
the Free Wilson model, indicator variables have
relatively early been included in Hansch analyses. Both
models can be combined to a mixed approach, in a
linear and a nonlinear form, which offers the advantages
of both, Hansch analysis and Free Wilson analysis, and
widens their applicability in quantitative structure-activity
Kubinyi has presented the combination of Hansch
and Free –Wilson model as “Mixed approach”.
log 1c =K1 л+K2 б+K3Es +K………Hansch
log 1c=µ +∑aij………….Free-Wilson approach
Kj represent the coefficient of different physico-
Mixed approach was developed to find possible
interaction between Free-Wilson parameters and
physicochemical properties of substituents used.
QSAR: Hansch Analysis And Related
Approaches, By Hugo Kubinyi, VCH Publication.