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mechanisms responsible for a compound’s activity, providing valuable insights for me-
dicinal chemists to optimize molecular structures [14].
QSAR can be defined as a mathematical relationship that correlates the biological ac-
tivity of a series of compounds with their physicochemical properties, steric properties,
and sometimes certain structural features (combined all these are known as molecular
descriptors) [15]. QSAR approach is seen as an alternative when the 3D structure of the
target protein is not available for structure-based drug designing such as molecular dock-
ing [16]. The simplest representation of a QSAR model is given in the following equation:
Biological activity = fn descriptorsðÞ (2:1)
The QSAR equation generated can further be employed for predicting the biological
activity of the newly proposed ligands [17]. The biological activity of the ligands can
be predicted by calculating the values of the descriptors of the proposed ligands, fol-
lowed by putting these values in the generated QSAR equation. The workflow of the
steps involved in a QSAR study is given in Fig. 2.1.
2.2 Classification of QSAR methodologies
There are certain ways by which a QSAR methodology can be classified [18]. The most
common ways of classifying the QSAR methodologies are listed in Fig. 2.2:
2.2.1 Based on the dimensions of descriptors used in the QSAR model
This is the widely accepted classification of QSAR models to date. Based on this classi-
fication, a QSAR model is further divided into:
2.2.1.1 0D-QSAR
0D-QSAR is a computational approach used in chemoinformatics and drug discovery to
predict the biological activity of a molecule based on its chemical structure. The “0D”
refers to the fact that it does not consider the spatial arrangement of atoms in the mole-
cule (as opposed to higher-dimensional QSAR models like 2D- and 3D-QSAR). In a 0D-
QSAR model, molecular descriptors are used to represent the chemical structure of a
compound. Molecular descriptors are numerical values that capture various physico-
chemical properties of the molecule, such as molecular weight, hydrophobicity, hydro-
gen bond donor and acceptor counts, and various other structural features. It is
important to note that while 0D-QSAR models can provide valuable insights into the
relationship between chemical structure and biological activity, they have limitations.
These models do not consider the three-dimensional spatial arrangement of atoms in
the molecule, which can be critical for some biological activities. To address this limita-
2.2 Classification of QSAR methodologies 19
Fig. 2.2: Different approaches for the classification of the QSAR modeling.
20 Chapter 2 Quantitative structure–activity relationship
tion, higher-dimensional QSAR models, such as 2D- and 3D-QSAR, take into account ad-
ditional structural information, leading to potentially more accurate predictions.
2.2.1.2 1D-QSAR
1D-QSAR is a computational method used in cheminformatics and drug discovery to pre-
dict the biological activity of a molecule based on its chemical structure. The term “1D”
referstothefactthatitusesone-dimensionalmolecular descriptors to represent the mo-
lecular structure. Molecular descriptors are numerical representations of various physico-
chemical properties or structural characteristics of a molecule. These descriptors include
simple properties such as number of rings, number of certain functional groups, pKa
value, etc. This model is developed by considering the substructural properties of the li-
gands for correlation with the biological activity.
It is important to note that 1 D-QSAR has limitations, as it only considers one-
dimensional descriptors and does not take into account spatial arrangements or
three-dimensional interactions of atoms in the molecule. As a result, more advanced
QSAR methods, such as 2D-QSAR and 3D-QSAR, have been developed to incorporate
additional structural information and improve predictive accuracy. Nonetheless, 1D-
QSAR remains a valuable tool for preliminary assessments of biological activity and
can be computationally less demanding than more complex QSAR methods.
2.2.1.3 2D-QSAR
2D-QSAR models are based on those descriptors that can be calculated by the graphi-
cal representation of the structures of the compounds. Topological descriptors, con-
nectivity indices, and eigenvalue-based descriptors are among the most commonly
employed descriptors for this model generation. It is important to note that QSAR
models are highly dependent on the quality and diversity of the dataset and the
choice of molecular descriptors and modeling techniq ues. Additionally, while QSAR
models can be valuable tools in drug discovery and chemical design, they are not a
replacement for experimental validation and should be used as supportive tools in
the decision-making process [19].
2.2.1.3.1 General steps involved in developing either of 0D-, 1D-,
or 2D-QSAR models
– Data collection: Obtain a dataset containing chemical structures and their corre-
sponding biological activities (e.g., biological assay data or experimental results).
– Molecular descriptors’ calculation: Calculate 2D molecular descriptors for each
compound in the dataset. These descriptors represent variou s properties of the
molecules, such as size, shape, electronic, and topological characteristics.
2.2 Classification of QSAR methodologies 21
– Data splitting: Divide the dataset into two parts: a training set and a test set. The
training set is used to build the QSAR model, while the test set is used to evaluate
its predictive performance.
– Model development: Select a suitable statistical or machine learning method to
build the QSAR model. Common approaches include multiple linear regression
(MLR), partial least squares (PLS), support vector machines (SVMs), and random for-
est (RF).
– Model validation: Assess the predictive performance of the model using the test
set. Metrics such as root mean squared error (RMSE), mean absolute error (MAE),
and correlation coefficient (r) are commonly used to evaluate the model’saccuracy.
– Model interpretation: Analyze the model to understand which molecular de-
scriptors are most influential in predicting biolo gical activity. This information
can provide insights into the structure-activity relationship and guide further
chemical design.
– Model application: Once validated, the QSAR model can be used to predict the
activity of new, unseen molecules with similar structural features to those in the
training set. This enables the identification of potential lead compounds with de-
sired biological activity.
2.2.1.4 3D-QSAR
3D-QSAR is a computational approach used in drug discovery, environmental chemis-
try, and other fields of chemistry and biology to analyze the relationship between the
three-dimensional (3D) structure of molecules and their biological activities. The main
goal of 3D-QSAR is to predict the biological activity or potency of a compound based on
its structural features and interactions with a target receptor or enzyme. These models
are generated by calculating those descriptors that exist by the 3D representations of
the compounds. Comparative molecular field analysis (CoMFA) and Comparative molec-
ular similarity index analysis (CoMSIA) are the two most widely employed methods of
3D-QSAR study. WHIM descriptors, autocorrelation 3D descriptors, charged PSA, and so
on are the common descriptors of 3D-QSAR [20–23].
The 3D-QSAR method builds upon the principles of traditional QSAR modeling,
which involves establishing correlations between the chemical structure and the bio-
logical activity of a set of compounds. However, in 3D-QSAR, the focus shifts to consid-
ering the spatial arrangement and conformational flexibility of molecules, allowing
for a more detailed understanding of the ligand-receptor interactions.
2.2.1.4.1 Overview of the key steps involved in 3D-QSAR
– Molecular alignment: The first step in 3D-QSAR involves aligning the 3D struc-
tures of a set of molecules. This alignment aims to superpose the molecules in a
way that maximizes the overlap of their active site or pharmacophoric features,
which are critical for binding to the target receptor.
22 Chapter 2 Quantitative structure–activity relationship
– Molecular representation: Once the molecules are aligned, they are typically
represented as 3D grids or point clouds, where various molecular properties,
such as electrostatic potential, lipophilicity, and steric hindrance, are calculated
for each grid point or data point.
– Grid-based analysis: The next step involves statistical analysis of the data points
to identify correlations between the molecular properties and the biological activ-
ities of the compounds. Techniques like PLS, principal component analysis (PCA),
or CoMFA are commonly used for this purpose.
– Model validation: It is crucial to validate the generated 3D-QSAR model to ensure
its predictive powe r. This validation can be achieved using methods like cross-
validation, external test set validation, and leave-one-out validation.
– Interpretation and visualization: After obtaining a reliable 3D-QSAR model, re-
searchers can use it to interpret the structure-activity relationship of the com-
pounds. Visualization tools can help in understanding how specific structural
features contribute to biological activity or binding affinity.
2.2.1.5 4D-QSAR
4D-QSAR goes a step further and incorporates the temporal dimension, meaning it con-
siders changes in molecular properties over time, especially in the context of molecular
dynamics simulations. This approach can be particularly valuable in situations where
the biological activity of a compound depends on its dynamic behavior and interactions
with a target over time. A fourth dimension, ensemble averaging, is incorporated in the
3D-QSAR model to convert it into a 4D-QSAR analysis. 4D-QSAR study provides confor-
mational and alignment freedom to a 3D-QSAR model. 4D-QSAR-based descriptors are
grid cell occupancy measures of the atoms.
4D-QSAR is still an active area of research, and its application may vary depending
on the specific problem and available data. It requires sophisticated computational
methods and access to molecular dynamics simulations, making it more resource-
intensive compared to traditional 2D- or even 3D-QSAR methods. Nonetheless, the in-
sights gained from 4D-QSAR models can provide a deeper understanding of the molecu-
lar mechanisms behind biological activity, which can be valuable in drug design and
optimization processes.
2.2.1.6 5D-QSAR
5D-QSAR is the further extension of the 4D-QSAR model by incorporating a fifth di-
mension, that is, an additional degree of freedom. Therefore 5D-QSAR represents dif-
ferent induced-fit models in 4D-QSAR.
2.2 Classification of QSAR methodologies 23
2.2.1.7 6D-QSAR
When solvation p arameters are incorporated in the 5D-QSAR descriptors it is con-
verted further into a 6D-QSAR model [24].
2.2.2 Based on the chemometric techniques employed for QSAR model generation
This classification is based on the meth od used for finding the correlation between
biological activity and the values of descriptors [25, 26]. They are further classified as:
2.2.2.1 Regression-based QSAR
As the name suggests, it is based on the correlation that is established based on re-
gression. Examples include MLR, PLS, and genetic function algorithm. Out of all these,
MLR models are the most widely used by scientists.
2.2.2.1.1 General overview of the working of regression-based QSAR
– Descriptor calculation: The first step in building a QSAR model is to calculate
molecular descriptors for a dataset of molecules. Descriptors are numerical repre-
sentations of various physicochemical, topological, or electronic properties of the
molecules.
– Data preparation: The dataset should be divided into two subsets: a training set
and a test set. The training set is used to build the QSAR model, while the test set
is used to evaluate the model’s predictive performance.
– Model building: Regression techniques such as MLR, PLS regression, support vec-
tor regression, or neural networks are commonly used to relate the molecular de-
scriptors to the corresponding biological activity or property.
– Model validation: The performance of the QSAR model is assessed using various
statistical metrics such as the coefficient of determination (R
2
), RMSE, and MAE.
Cross-validation techniques may also be used to assess the model’srobustness
and avoid overfitting.
– Model interpretation: After successfully building and validating the QSAR
model, the model’ s coefficients can be analyzed to identify the key descriptors
that contribute most to the biological activity or property of interest. This inter-
pretation can provide insights into the structure–activity relationship.
– Prediction: Once the QSAR model is established and validated, it can be used to
predict the activity or property of new molecules based on their descriptors. This
prediction can aid in drug discovery and development by identifying potentially
active compounds.
24 Chapter 2 Quantitative structure–activity relationship
2.2.2.2 Classification-based QSAR
This QSAR methodology is based on the principle that the correlation between the bio-
logical activity and descriptor is established in such a way that compounds employed
in the study are classified either as active or not active. Techniques such as linear dis-
criminant analysis (LDA), logistic regression, and cluster analysis are used for the
classification-based QSAR model generation [27].
2.2.2.2.1 General overview of the classification-based QSAR model generation
– Creating the dataset: This is the initial step of the generation of the classifica-
tion-based QSAR model. In this step, a group of molecules with known biological
activities is selected, and based on the biological activities, the selected molecules
are categorized or classified as active or inactive against that particul ar disease
or target.
– Calculating the molecular descriptors: Further, the selected molecules are sub-
jected to the calculation of their molecular descriptors. Descriptors can either be
0D, 1D, 2D, or 3D depending upon the requirement.
– Data preparation: The molecules selected for the model development are di-
vided into training and test dataset molecules. It is an unsaid rule that generally,
30% of the total molecules are put under the test dataset and the rest comes
under the training dataset.
– Development of the classification-based QSAR model: Genetic algorithm-LDA
and RF are the two most common approaches for the development of the QSAR
model in this type of classification.
– Model validation: There are certain parameters based on which a classification-
based QSAR model can be validated either internally or externally. Accuracy, sen-
sitivity, specificity, and precision are certain parameters based on which a new
classification-based QSAR model is validated.
– Prediction by model: Once our QSAR model is developed and validated, in the
last step it is employed for the prediction of the biological activity of the unknown
compounds. The most important thing in this type of QSAR model is that here pre-
diction of the unknown compounds is only done as active or inactive against a
particular disease or target.
There are certain machine learning algorithms of QSAR model development such as
artificial neural network, SVM, RF, and k-nearest neighbors which are gaining im-
mense popularity for the generation of both regression and classification-based QSAR
models.
2.2 Classification of QSAR methodologies 25
2.2.3 Based on the activity to be correlated in the QSAR model
This is another way of classifying the QSAR models, which is dependent on the type of
biological activity and how it is correlated with the descriptors of the series of com-
pounds. These models are further classified as:
2.2.3.1 Quantitative structure–toxicity relationship (QSTR)
These models are developed to correlate the toxicity values of the compounds with
their descriptor values [28].
2.2.3.2 Quantitative structure–metabolism relationship (QSMR)
These models are developed to correlate the parameters associated with the metabo-
lism of drugs and their structural features [29].
2.2.3.3 Quantitative structure–permeability relationship (QSPR)
These models are developed to correlate the drug permeability and the structural fea-
tures of the molecules [30].
2.2.3.4 Quantitative structure–bioavailability relationship (QSBR)
For any new hit/lead to become a successful drug candidate it is indispensable to
have good bioavailability. This is obtained by generating a correlation model between
the bioavailability parameters and descriptors of the series of compounds [31].
2.3 History and development of QSAR
Although the modern QSAR was considered to evolve in the early 1960s, this concept
was introduced way back in 1869 by the Edinburgh group’s pharmacologists Alexander
Crum Brown and Thomas R. Fraser in their research publication “On the connection
between chemical constitution & physiological action.” In this paper, they concluded
that “there can be no reasonable doubt but that a relation exists between the physio-
logic action of a substance (Φ) and its chemical composition and constitution (C).” They
suggested that physiologic action (Φ) must be a function of chemical structure (C)given
in the following equation, which is still considered the first generalized equation of the
QSAR [32]:
Φ = fC
ðÞ
(2:2)
where Φ represents the physiologic action and C represents the chemical structure of
the molecule.
26 Chapter 2 Quantitative structure–activity relationship
In the same context, Richardson in 1869 concluded that the narcotic effect of the
primary alcohols is proportional to their molecular weight [33]. In 1880, the famous Brit-
ish physician Lauder Brunton suggested in his book Pharmacology and Therapeutics,
or, Medicine Past and Present that soon physicians will be able to predict the biological
response of a drug through its chemical structure [34]. In an important finding, Richet
in 1893 discovered an inversely proportional relationship between the toxicity and mo-
lecular weight of the organic compounds [35]. The major advancement to this came
with the study of Overton [36] and Meyer [37], both of them working independently.
They postulated that the toxicity of narcotic compounds in tadpoles and other aquatic
species can be correlated to their oil-water partition coefficient (lipophilicity) [36, 37].
None of them could give a correlation equation for their work. The first attempt to cor-
relate the melting point with the structure of the atom was made by Longinescu in 1903
[38]. He derived the formula of the melting point by the following equation:
T
m
= 8.73D
p
n (2:3)
where D is the density and n is the number of atoms in the molecule.
In 1903 and 1904, Fuhner further established in a study on sea urchin eggs that
within the homologous series of the compounds, the narcotic toxicity follows a geo-
metric progression [39, 40]. In 1937, Hammet in his research developed a correlation
between the dissociation constant and substitution on the benzene ring [41]. A simple
equation was given by Hammet as follows:
log K = log K
∘
+ σρ (2:4)
where K is the rate constant, σ is a substituent constant, and ρ is a reaction constant.
The work done by various scientists from 1917 to 1935 on the correlation between
chemical or physical properties and their intensity of toxicity was quantified by Fer-
guson in 1939. In this study, thermodynamic interpretation is given by Ferguson for
the toxic effects of certain compounds when correlated with the chemical constitu-
tion [42].
The decade of 1950 had some great contributions to the development of QSAR
methodologies. From a series of research, Robert W. Taft Jr. has given a linear rela-
tionship between the log of the rate of hydrolysis of substituted benzamides and elec-
tronic steric factors in 1953 [43]. The following equation was given by them:
log k=k
o
= δE
s
(2:5)
where δ is a proportionality constant dependent only upon the nature of the reaction
series and E
s
is the steric substituent constant.
The first attempt to extend Hammet’s equation to the biological system was done
by Zahradnik in a series of research conducted from 1960 to 1962. The equation given
by them is considered a “biological Hammet equation”; however, this model has little
applicability within a specific homologous series [44]. The following equation was
given by them:
2.3 History and development of QSAR 27
log τ
i
, − log τ
ET
= αβ (2:6)
where τ
i
is the biological activity of the ith compound, τ
ET
is the biological activity of
the ethyl substituted compound of the series, α is the substituent constant, and β rep-
resents the constant dependent on the biological activity.
The work of Hansen in 1962 provided the real correlation between the toxicity of
substituents and their electronic constants (σ) and was considered a true extension of
the work of Hammet [45]. The year 1964 came with the real revolution in the field of
QSAR and is considered the dawn of modern QSAR. There were two major contribu-
tions this year, first by Hansch and Fujita, which provided the linear free energy rela-
tionship, also known as Hansch analysis [8], and second by Free and Wilson who gave
the molecular fragment-based QSAR study popularly known as the Free Wilson ap-
proach. Hansch further extended their research and provided a breakthrough by lin-
ear addition of the physicochemical parameters in correlation with the biological
activity [46]. The following equation was provided by them:
log 1=CðÞ= k1π + k2σ + k3(2:7)
where C is the molar concentration producing a standard response, π is the lipophilic-
ity parameter, and σ is the steric factor constant.
In 1971, another significant contribution was made by Fujita and Ban by giving a
mathematical expression to the Free Wilson approach [47] as follows:
log A = Σ G
i
X
i
+ C (2:8)
where A is the biological activity of the substituted compound, G
i
is the log activity
enhancement factor of the ith substituent relative to that of H, and X
i
is a parameter
that takes a value of 1 or 0 according to the presence or absence of the ith substituent.
Both Hansch and Free Wilson’s approaches are considered as a backbone of
QSAR studies, as in the next three decades much research was conducted based on
these two models. In 1977, another bilinear model for the nonlinear dependence of
biological activity on the hydrophobic character was proposed by Hugo Kubiyi, also
known as a mixed Hansch/Free Wilson model [48]. This equation is as follows:
log l=C = a log P − b log βP + IðÞ+ c (2:9)
where C is the molar concentration producing a standard response, P is the partition
coefficient of the molecule, and terms a, b, c, and β are constants.
The first 3D-QSAR model was generated in 1976 by James Y. Fukunaga for the in-
hibitionofthedihydrofolatereductaseenzyme[49].Thefieldof3D-QSARbecame
popular when the first linear 3D-QSAR model, CoMFA, was generated in 1988 by
Cramer and team [50]. Another modification to this, CoMSIA, was given by Klebe in
1994 [51].
28 Chapter 2 Quantitative structure–activity relationship
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