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different molecules consistently. During the development of new compounds with de-
sired biological activity, STERIMOL parameters can guide the structural modification
process. By analyzing the effect of changes in substituents on the STERIMOL parame-
ters, researchers can make informed decisions about which modifications might be
most beneficial.
3.1.3.4 Other steric parameters
With more explorations in QSAR, certain other steric parameters evolved through the
passage of research. Some important steric parameters used in QSAR studies include:
– Steric hindrance: Steric hindrance refers to the obstruction of molecular interac-
tions due to bulky groups or atoms in close proximity. It affects the accessibility
of a molecule’s functional groups and can influence the molecule’s reactivity and
binding affinity [34].
(a) (b)
Fig. 3.7: (a) A surface diagram is drawn around the substituent of an imaginary drug molecule.
(b) Length of the substituent along all the axis from the center of the surface of the substituent.
Tab. 3.5: Verlopp/STERIMOL parameters of some of the substituents.
S. no. Substituent L (Å) B
(Å) B
(Å) B
(Å) B
(Å)
H . . . . .
CH
. . . . .
CH
OH . . ...
CF
. . . . .
OH . . . . .
OCH
. . . . .
NO
. . . . .
3.1 Physicochemical parameters and QSAR 49
– Steric bulk: Steric bulk measures the spatial size of a substituent or functional
group attached to the molecule. It is usually quantified by the volume occupied
by the substituent and helps in understanding how the size of different groups
impacts the molecular properties [35].
– Van der Waals volume: The Van der Waals volume represents the space occu-
pied by a molecule due to the attractive and repulsive forces between atoms. It
considers the effective size of atoms or groups in a molecule [36].
– Molecular surface area (MSA): MSA calculates the accessible surface area of a
molecule, taking into account the shape and size of the molecule. It can be useful
in predicting interactions with enzymes or receptors that depend on surface com-
plementarity [37].
– Steric energy: Steric energy is the energy associated with the repulsion or over-
lap of electron clouds between atoms or groups in a molecule. High steric energy
may lead to instability or unfavorable interactions [35].
– Shape index: The shape index is a numerical value that characterizes the three-
dimensional shape of a molecule. It can be used to compare the shapes of differ-
ent molecules and assess their structural similarity [38].
Steric parameters are often combined with other physicochemical properties in QSAR
models to gain a comprehensive understanding of how molecular structure relates to
biological or chemical activity. By considering these steric factors, researchers can de-
sign and modify molecules to optimize their properties for specific applications, such
as drug design, toxicity prediction, and environmental studies.
References
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50 Chapter 3 Physicochemical parameters and QSAR
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References 51
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Pesticide Chemistry: Human Welfare and Environment. Pergamon, 1983, 339–44.
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[34] Kubinyi H. What is QSAR? JACS, 1964, 86, 1616.
[35] Williford CJ, Stevens EP. Strain energies as a steric descriptor in QSAR calculations. QSAR &
Combinatorial Science, 2004, 23(7), 495–505.
[36] Roy K, Narayan Das R. A review on principles, theory and practices of 2D-QSAR. Current Drug
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[37] Prasanna S, Doerksen RJ. Topological polar surface area: A useful descriptor in 2D-QSAR. Current
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52 Chapter 3 Physicochemical parameters and QSAR
Chapter 4
Quantitative models in QSAR
In the realm of Quantitative Structure-Activity Relationships, data becomes the brush, and mod-
els the canvas, painting a picture of molecular behavior – Alexander Tropsha
4.1 Introduction
Quantitative structure–activity relationship (QSAR) models are mathematical and
computational models that aim to establish a quantitative relationship betwee n the
structural features of chemical compounds and their corresponding biological activi-
ties or properties [1]. These models provide a way to predict the activity of new com-
pounds based on their structural characteristics, which is particularly valuable in
drug discovery, environmental chemistry, toxicology, and related fields [2]. Quantita-
tive models in QSAR involve the following key components:
– Molecular descriptors: These are numerical representations of the structural fea-
tures of chemical compounds. Descriptors can include information about atom types,
bond lengths, molecular weight, electronic properties, and more. These descriptors
capture the molecular characteristics that may influence biological activity.
– Biological activity data: Experimental data that quantifies the biological activity
or property of a set of compounds. This data serves as the basis for building and
validating QSAR models.
– Modeling algorithms: Various mathematical and statistical techniques are used
to establish the relationship between molecular descriptors and biological activ-
ity. These techniques can range from linear regression to more complex methods
like neural networks and support vector machines.
– Training and validation: QSAR models are developed using a training set of
compounds with known ac tivities. The model’s performance is then validated
using a separate set of compounds (validation set) that the model has not seen
before. This helps assess how well the model can predict the activity of new
compounds.
– Model evaluation: The performance of QSAR models is evaluated using metrics
such as correlation coefficients, root mean square error, and cross-validation
scores. A good QSAR model should accurately predict the activity of compounds
not included in the training data.
– Interpretation: QSAR models can provide insights into the relationship between
molecular structure and activity. By analyzing the model’s coefficients or feature
importance, researchers can identify which structural features contribute most to
the observed activity.
https://doi.org/10.1515/9783111434858-004
– Applicability domain: QSAR models often define a region in the descriptor space
where they are most accurate. This region is known as the applicability domain.
Predictions falling within this domain are considered reliable, while those outside
might be less trustworthy.
Quantitative models in QSAR help researchers prioritize compounds for further test-
ing, design new molecules with desired properties, and m ake informed decisions
about the potential risks or benefits of chemical substances [3]. The development of
accurate and rob ust QSAR models requires careful consideration of data quality,
model complexity, and validation methods [4].
As already discussed, the real dawn of the QSAR is considered in the early 1960s
with the work of Hansch and Fujita. It was during this period that scientists started to
correlate the biological activity of the compounds with their structural properties
(now known as molecular descriptors) more rationally. There have been many meth-
ods or models presented by scientists after this period for the correlation between bi-
ological activity and molecular properties. The most important methods that still hold
validity in the current era are discussed below in detail.
4.2 Hansch analysis
Hansch analysis, a cornerstone of QSAR studies, is a pioneering approach that eluci-
dates the relationship between chemical structure and biological activity by integrating
molecular properties and statistical modeling [5, 6]. Named after the chemist Corwin
Hansch, this method revolutionized drug design and predictive toxicology [7]. At it s
core, Hansch analysis involves constructing linear regression models that correlate the
biological activities of a set of compounds with their physicochemical properties or mo-
lecular descriptors. These descriptors encompass a range of attributes, including elec-
tronic, steric, and hydrophobic properties, which collectively characterize a molecule’s
structure [8]. The resulting quantitative equations reveal the quantitative contribution
of individual descriptors to the observed activity, thereby uncovering structure–activity
relationships.
Hansch analysis has proven particularly valuable in rational drug d esign, en-
abling researchers to tailor molecular structures to enhance or modify desired biolog-
ical activities [9]. The approach also offers insights into the underlying mechanisms
governing compound interactions with biological targets. While Hansch analysis origi-
nated as a linear model, its principles have been extended to nonlinear and more ad-
vanced methodologies, further enriching the predictive capabilities of QSAR models
[10]. Overall, Hansch analysis serves as a foundational framework in QSAR, empower-
ing researchers to decipher the intricate links between chemical structure and biolog-
ical response. Its historical significance and ongoing relevance in contemporary drug
54 Chapter 4 Quantitative models in QSAR
discovery and toxicological assessments underscore its enduring importance in the
field of computational chemistry [11].
In the initial development of QSAR, scientists tried to correlate the biological ac-
tivity of drug molecules with either their lipophilicity parameters or with the elec-
tronic parameters, respectively, as in the following equations [12, 13]:
log
1
C
= a log P + b (4:1)
log
1
C
= k
1
σ + k
2
(4:2)
where P is the partition coefficient representing the lipophilicity of the drug molecule
and σ is the Hammett constant affecting the electronic changes in the molecule due to
different substituents. A, b, k
1
, and k
2
are the constants. Both of the above equations
were able to correlate the biological activity with either of these parameters locally
but none applied to the broader range of molecules and other QSAR models for differ-
ent biological activities.
It was the year 1962 when Hansch and Fujito provided a breakthrough in QSAR stud-
ies [14]. The main idea behind their concept was that the site of drug administration is
different than its site of action [15, 16]. A drug has to pass through many phases to reach
thesiteofaction.Adsorptionanddesorption take place with lipid membranes and pro-
teins, whereas partitioning of drug molecules occurs between the different liquid systems
(Fig. 4.1). For any drug after reaching the site of action, interaction with the receptor is
essential to generate any biological effect. This drug-receptor interaction is governed by
the electronic parameters of the drug molecule. Hence, for defining any QSAR model, it is
important to correlate both lipophilic and electronic parameters with biological activity.
This gave birth to the famous model of the QSAR, popularly known as Hansch analysis.
The very first forms of the equation given by Hansch are given below:
Fig. 4.1: Movement of the drug inside the body. Partition/lipophilic parameters of the drug govern its
absorption whereas the electronic parameters determine its binding with the receptor.
4.2 Hansch analysis 55
log
1
C
= k
1
π + k
2
σ + k
3
(4:3)
log
1
C
= −k
1
π
2
+ k
2
π + k
3
σ + k
4
(4:4)
where π is the lipophilic/hydrophobic constant and σ represents the Hammett constant.
Equation(4.3)isapplicableonlywhenthestudyisdoneonsmallrangevaluesofπ;other-
wise equation (4.4) is applicable when the study is done on broader range values of π.
Hansch analysis is also known as the “extra-thermodynamic approach” or “linear
free energy-related approach” as the physicochemical parameters used in the Hansch
analysis are derived from the rate or equilibrium constants.
Lateron,anotherparameter,Taft’s steric parameter (E
s
) was included in the Hansch
analysis. It quantifies the steric hindrance or spatial bulkiness of substituents attached to
a molecule [12]. This parameter is named after the American chemist Robert W. Taft. The
steric parameter is crucial in understanding how the three-dimensional arrangement of
atomsaffectsamolecule’s interactions with other molecules or biological receptors. In
QSAR, it helps predict how changes in the size or shape of substituents on a molecule
can influence its biological activity. The resulting modified equations are depicted in the
following equations:
log
1
C
= k
1
π + k
2
σ + k
3
E
s
+ k
4
(4:5)
log
1
C
= −k
1
π
2
+ k
2
π + k
3
σ + k
4
E
s
+ k
5
(4:6)
Equation (4.5) is applicable when the studyisdoneonsmallrangevaluesofπ and equation
(4.6) is applicable when the study is done on broader range values of π.Theconstantsk
1
to
k
5
used in equations (4.3)–(4.6) are derived from the multiple linear regressions (MLRs).
The interesting fact of the Hansch analysis is that it originated from the studies
conducted on plants. The corr elation between the plant growth (biological activity)
with different lipophilicity and electronic parameters of substituted phenoxy acetic
acid was studied to develop the initial equations of Hansch analysis [16]. The effect on
the biological activity due to different substitutions at meta and para positions of phe-
noxy acetic acid was studied and the following QSAR equation was developed:
log
1
C
= −2.14 π
2
+ 4.08 π + 2.78 σ + 3.36 (4:7)
From the above equation, it is evident that plant growth is enhanced with an increase
in the value of σ and also, initially, with the increase in the value of π (by keeping σ
constant) plant growth increases. However, for a very high value of π the biological
activity becomes 0. The values of parameters used in this QSAR model along with ob-
served and calculated biological activity are given in Tab. 4.1.
56 Chapter 4 Quantitative models in QSAR
From the above table, a noteworthy point to be studied is that meta- and para-fluorine-
substituted phenoxy acetic acid have remarkable differences in their biological activity
(log(1/C)).Hereinthiscase,thevalueofπ is similar for both of the substituents and this
change in the biological activity is attributed to the change in their value of σ at para
and meta substitutions. The value of σ of fluorine at the para substitution is 0.34, whereas
the same for the meta substitution is 0.06 producing a remarkable difference in the over-
all biological activity of the compound. This difference in the values of σ can be ex-
plained based on the electronic interactions as we all know fluorine exerts a+R effect
on the benzene ring and this effect is more predominant at the para position as com-
pared to the meta position. The same explanation can be sought for the difference in the
values of biological activity of para–chloro- and the meta-chloro-substitutions. From the
Tab. 4.1: Calculation of biological activity (log(1/C) from the σ and π values of different substituents of
substituted phenoxy acetic acid derivatives.
O
O
OH
meta
p
ara
Substituted phenoxy accetic acid
S. no. Substituent σ-Value π-Value Observed log (/C) Calculated log (/C)
. m-CF
. . ..
. p-Cl . . ..
. m-I . . ..
. p-F . . ..
. m-Br . . ..
. m-SF
. . ..
. m-Cl . . ..
. m-NO
. . ..
. m-SCH
−. . ..
. m-C
H
−. . ..
. m-n-C
H
−. . ..
. m-OCH
−. . ..
. m-CN . −. ..
. m-CH
−. . ..
. m-CH
CO . −. ..
. m-F . . ..
.H . . ..
. m-OH −. −. −..
. m-COOH . −. ..
. m-n-C
H
−. . ..
4.2 Hansch analysis 57
above table, it is evident that the value of π increases the size of the atom as it is lowest
for fluorine (0.20) and largest for iodine (1.08). The length of the alkyl group also affects
the value of π as the increase in the length results in the higher values of π.
4.2.1 Importance of Hansch analysis in drug discovery
It can be concluded that Hansch analysis holds significant importance in QSAR-driven
drug discovery due to its ability to elucidate the relationship between chemical struc-
ture and biological activity. This methodology provides valuab le insights that em-
power drug researchers to design more effective and efficient compounds. Here are
several reasons why Hansch analysis is crucial in QSAR for drug discovery:
– Rational drug design: Hansch analysis helps scientists understand how specific
structural features of molecules contribute to their biological activities. This in-
sight enables the rational design of new compounds with improved activity pro-
files by making targeted modifications to molecular structures.
– Efficient compound optimization: By identifying the key structural elements
that impact activity, Hansch analysis guides researchers in optimizing molecules
with minimal trial and error. This accelerates the drug discovery process by fo-
cusing efforts on compounds most likely to exhibit desired properties.
– Scaffold modification: The analysis aids in modifying existing molecular scaf-
folds to enhance desired activities. Substituent effects on biological interactions
can be quantified, leading to informed choices about where to introduce modifi-
cations for optimal outcomes.
– Lead compound selection: Hansch analysis aids in selecting lead compounds
with the highest likelihood of success. It allows researcher s to prioritize com-
pounds with favorable structural attributes, saving resources and time during the
lead identification phase.
– Mechanism of action understanding: By quantifying the relationship between
structural features and activity, Hansch’s analysis can shed light on the mecha-
nisms of action of bioactive compounds. This understanding contributes to the de-
velopment of more targeted therapies.
– Compound toxicity assessment: The analysis not only predicts activity but also
can offer insights into potential toxicity. This is vital for avoiding compounds
with unfavorable safety profiles early in the drug discovery process.
– Reduction of experimental efforts: Hansch analysis reduces the need for extensive
experimental testing of every compound by providing a computational framework
for predicting activity. This is especially valuable when dealing with large compound
libraries.
– Cost efficiency: By guiding compound design and prioritization, Hansch analysis
contributes to cost-effective drug development. It minimizes the wastage of resources
on compounds with poor potential.
58 Chapter 4 Quantitative models in QSAR
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