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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5728_Библиотеки_им_академика_М_И_Перельмана
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quately cover the chemical space or the diversity of the compounds being studied,
the model’s predictive ability may be compromised.
– Extrapolation issues: CoMSIA models are often less accurate when extrapolating
predictions to compounds that significantly differ from those in the training set
in terms of structure and properties.
– Assumption of additivity: CoMSIA assumes that the effects of molecular fields
are additive, mea ning that the contribu tions from different fields are indepen-
dent. This assumption might not always hold true for all molecular interactions.
– Computational complexity: CoMSIA calculations can be computationally intensive,
especially when dealing with larger datasets or more complex molecules. This com-
plexity can limit the practicality of the method for high-throughput applications.
– Model overfitting: Like any QSAR model, CoMSIA models can overfit the noise
present in the training data, leading to poor generalization performance on new,
unseen compounds.
– Lack of mechanistic insights: While CoMSIA can provide correlations between
molecular properties and activity, it might not offer deep mechanistic insights
into the underlying biological processes.
5.10 Other 3D-QSAR approaches
After the introduction of CoMFA and CoMSIA approaches for drug discovery, which
remained the flag-bearer of 3D-QSAR, numerous 3D-QSAR approaches have emerged.
A brief description of these approaches is given in Tab. 5.1 for the other alignment-
based 3D-QSAR methods.
Tab. 5.1: Description of important alignment-based 3D-QSAR methodologies.
Alignment-based D-QSAR models
S. no. Method Description and basic steps involved
Molecular surface analysis (MSA) – The dataset of the molecules is selected
– Conformations of each molecule are generated along with
the energy minimization
– A bioactive conformer is hypothesized based on the global
minima
– A shape reference compound is selected, generally the
most bioactive one
– Pair-wise alignment of the molecules is performed
– Calculation of molecular shape-based descriptors is done
– Incorporation of other parameters is done if required
– Generation of a trial QSAR [19]
5.10 Other 3D-QSAR approaches 99
Tab. 5.1 (continued)
Alignment-based D-QSAR models
S. no. Method Description and basic steps involved
Receptor surface analysis (RSA) – Molecules are optimized and conformers are generated
with the determination of their bioactive conformations
– Alignment of the bioactive conformations is done
– Generation of receptor surface based on the aligned
molecules is performed
– Calculation of the descriptors based on the properties of
the receptor surface
– Development of the QSAR model [20]
Self-organizing molecular field
analysis (SOMFA)
– The major difference is the calculation of the “mean
centered activity” (MCE) of each molecule
– Each biological activity is subtracted from the mean of the
biological activities, which represents molecules with
positive values of MCE as active and those having
negative values as inactive
– Aligned molecules are placed inside the grid, and steric
and electrostatic field values are multiplied by MCE
– Calculation of SOMFA descriptors performed and
correlated with the biological activity
– Instead of contour maps, master grids are generated for
the visualization [21]
Genetically evolved receptor
modeling (GERM)
– Aligned conformation of the molecules is taken as the
starting point
– The unique thing about the model is it derives a receptor
cavity around the aligned conformations using the genetic
algorithm approach
– Interaction energies of each conformer are calculated
around this generated receptor cavity using chemistry at
Harvard molecular mechanics (CHARMM) force field
– These interaction energies are correlated with the
biological activity [22]
HINT interaction field analysis
(HIFA)
– Considered a hybrid or extension of the traditional CoMFA
model
– Hydrophobic field parameters of the aligned molecules
placed inside the grid and calculated
– HINT intermolecular interaction maps are generated to
visualize the effect of hydrophobicity on the biological
activity [23]
100 Chapter 5 3D-QSAR in drug designing
Besides the alignment-based 3 D-QSAR models, many other models have been pro-
posed for 3D-QSAR. which are independent of the alignment criteria and are briefly
discussed in Tab. 5.2.
Tab. 5.1 (continued)
Alignment-based D-QSAR models
S. no. Method Description and basic steps involved
Adaption of the field for
molecular comparison (AFMoC)
– Also known as “reverse CoMFA” as the fields enumerated
are derived from the protein environment rather than the
ligands
– A grid is placed inside the binding site of the protein and
“potential fields” are calculated
– These potential fields are converted to “interaction field
values” by multiplying them by the distance-dependent
atom-type properties of the molecules docked inside the
cavity
– Interaction field values are correlated with the biological
activity [24]
Molecular quantum similarity
measures (MQSM)
– MQSM represents the degree of similarity between the
two molecules based on the electron densities
– Quantum mechanical calculations are performed for
calculating the MQSM between two molecules by using the
following integral: Z
AB
(Ω
α
)=∫∫ρ
A
(r
1
) Ω
α
(r
1
,r
2
) ρ
B
(r
2
) dr
1
dr
2
where ρ
A
(r
1
)andρ
B
(r
2
) represent the density functions and
Ω
α
(r
1
,r
2
) represents positive definite operator
– As the number of MQSM variables obtained is very large,
hence, the partial component analysis (PCA) is performed
to reduce the number of variables [25]
Voronoi field analysis (VFA) – Alignment of the dataset of the molecules performed
– New regions from the aligned molecules space are
defined, which are termed as Voronoi Polyhedrals that are
different from CoMFA where lattice points of grid are
defined
– The number of variables obtained is less as compared to
traditional CoMFA
– Steric and electrostatic parameters are obtained from the
aligned molecules and steric field parameters are
calculated based on the hard-sphere model instead of
Lennard-Jones potential [26]
5.10 Other 3D-QSAR approaches 101
Tab. 5.2: Description of important alignment-independent 3D-QSAR methodologies.
Alignment-independent D-QSAR models
S. no. Method Description and basic steps involved
Weighed holistic invariant
molecular (WHIM) descriptor
analysis
– A new set of descriptors named WHIM descriptors is
calculated, which defines the 3D structure of the
molecule in terms of its size, shape, conformation, and
distribution of the atoms
– These descriptors are calculated simply from the 3D
conformation of the molecule represented by x-, y-,
and z-coordinates
– Directional WHIM descriptors are calculated using a
principal component analysis (PCA) approach
– Nondirectional WHIM descriptors are derived from the
directional descriptors [27]
Molecular hologram QSAR (HQSAR) – A new set of descriptors known as molecular
holograms is calculated, which is based on the
fragment fingerprints of the molecules
– HQSAR model is generated by using the PLS statistical
method for correlating the biological activity with the
variables [28]
VolSurf – It is generated with the help of VolSurf descriptors,
which are obtained by relating the 3D molecular
interaction fields of the molecules to their
physicochemical properties
– This approach is very useful and widely used for ADME
prediction [29]
Comparative molecular moment
analysis (CoMMA)
– Molecular similarity descriptors are enumerated based
on the moments of the molecular mass and charge
distributions
– These descriptors contain information about the shape
and charge distribution of the molecules in 3D space
[30]
– The QSAR model is generated by employing a PLS
statistical approach
Comparative spectral analysis
(CoSA)
– This is the approach in which the spectra of the
molecules are employed as descriptors for the
establishment of correlation with biological activity
– 1H, 13C, infrared, and mass spectra employed for the
generation of descriptors
– A multivariate regression model (PLS) is used for the
generation of the mathematical equation [31]
102 Chapter 5 3D-QSAR in drug designing
References
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approaches to correlate inhibitor activity for a series of indole amide hydroxamic acids. QSAR &
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[5] Ivanciuc O. 3D QSAR models. QSPR/QSAR Studies by Molecular Descriptors, 2001, 233–80.
[6] Hopfinger AJ, Wang S, Tokarski JS, Jin B, Albuquerque M, Madhav PJ, Duraiswami C. Construction of
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[7] Kubinyi H. QSAR and 3D QSAR in drug design Part 1: Methodology. Drug Discovery Today, 1997,
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[8] Oprea TI. 3D QSAR modeling in drug design. Computational Medicinal Chemistry for Drug
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[9] Thareja S. Steroidal 5α-reductase inhibitors: A comparative 3D-QSAR study review. Chemical
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[10] Madhavan T. A review of 3D-QSAR in drug design. Journal of the Chosun Natural Science, 2012, 5(1),
1–5.
[11] Hillebrecht A, Klebe G. Use of 3D QSAR models for database screening: A feasibility study. Journal of
Chemical Information and Modeling, 2008, 48(2), 384–96.
[12] Cramer RD, Patterson DE, Bunce JD. Comparative molecular field analysis (CoMFA). 1. Effect of shape
on binding of steroids to carrier proteins. Journal of the American Chemical Society, 1988, 110(18),
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[13] SYBYL 8.1, Tripos International, St. Louis, USA.
[14] Kubinyi H. Comparative molecular field analysis (CoMFA). The Encyclopedia of Computational
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[15] Akamatsu M. Current state and perspectives of 3D-QSAR. Current Topics in Medicinal Chemistry,
2002, 2(12), 1381–94.
[16] Hopfinger AJ, Tokarski JS. Three-Dimensional Quantitative Structure-activity Relationship Analysis.
Marcel Dekker, Inc., New York, USA, 1997.
[17] Oprea TI. 3D QSAR modeling in drug design. Computational Medicinal Chemistry for Drug
Discovery, 2004, 571–616.
[18] Klebe G, Abraham U, Mietzner T. Molecular similarity indices in a comparative analysis (CoMSIA) of
drug molecules to correlate and predict their biological activity. Journal of Medicinal Chemistry,
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[19] Walters DE, Hopfinger AJ. Case studies of the application of molecular shape analysis to elucidate
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[20] Hahn M. Receptor surface models. 1. Definition and construction. Journal of Medicinal Chemistry,
1995, 38(12), 2080–90.
[21] Robinson DD, Winn PJ, Lyne PD, Richards WG. Self-organizing molecular field analysis: A tool for
structure− activity studies. Journal of Medicinal Chemistry, 1999, 42(4), 573–83.
[22] Walters DE, Hinds RM. Genetically evolved receptor models: A computational approach to
construction of receptor models. Journal of Medicinal Chemistry, 1994, 37(16), 2527–36.
References 103
[23] Semus SF. A novel hydropathic intermolecular field analysis (HIFA) for the prediction of ligand-
receptor binding affinities. Medicinal Chemistry Research, 1999, 9(7–8), 535–47.
[24] Gohlke H, Klebe G. DrugScore meets CoMFA: Adaptation of fields for molecular comparison (AFMoC)
or how to tailor knowledge-based pair-potentials to a particular protein. Journal of Medicinal
Chemistry, 2002, 45(19), 4153–70.
[25] Gironés X, Amat L, Carbó-Dorca R. Using molecular quantum similarity measures as descriptors in
quantitative structure-toxicity relationships. SAR and QSAR in Environmental Research, 1999, 10(6),
545–56.
[26] Chuman H, Karasawa M, Fujita T. A novel three‐dimensional QSAR procedure: Voronoi field analysis.
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[27] Todeschini R, Gramatica P. New 3D molecular descriptors: The WHIM theory and QSAR applications.
Perspectives in Drug Discovery and Design, 1998, 9(0), 355–80.
[28] Lowis DR. HQSAR: A new, highly predictive QSAR technique. Tripos Technical Notes, 1997, 1(5), 17.
[29] Cruciani G, Pastor M, Guba W. VolSurf: A new tool for the pharmacokinetic optimization of lead
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molecular superposition. Journal of Medicinal Chemistry, 1996, 39(11), 2129–40.
[31] Bursi R, Dao T, van Wijk T, de Gooyer M, Kellenbach E, Verwer P. Comparative spectra analysis
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104 Chapter 5 3D-QSAR in drug designing
Chapter 6
Statistical approaches used in the QSAR
If your experiment needs statistics, you ought to have done a better experiment – Ernest Rutherford
6.1 Introduction
Statistics is the science of numerical data, which involves collection, analysis, inter-
pretation, representation, and inferring conclusions from these numerical data [1].
Statistics is employed at each step of the quantitative structure–activity relationship
(QSAR) model generation and hence, it becomes indispensable for anyone who wishes
to learn QSAR to have basic knowledge of statistics [2]. There are different statistical
approaches used in the QSAR depending upon the type of QSAR model being gener-
ated [3]. Statistical approaches in QSAR encompass a spectrum from linear to nonlin-
ear models, integrating various techniques to model intricate relationships between
molecular structures and activities, facilitating the efficient design of new compounds
for specific applications [4, 5]. Whether it is a traditional 2D-QSAR or 3D-QSAR, a cer-
tain statistical approach is employed in each of them for the generation of the QSAR
mathematical equation, which correlates the biological activity with the descriptors
of the molecules [6]. A brief overview of the statistical methods used for the genera-
tion of the QSAR model is given in Fig. 6.1.
Fig. 6.1: Different statistical approaches employed in the development of different QSAR models.
https://doi.org/10.1515/9783111434858-006
6.2 Linear regression analysis
Linear regression analysis is considered the true mathematical approach for develop-
ing a correlation of biological activity with the descriptors of the molecules [7, 8]. In
this approach, the biological activity of the molecules is the response, outcome, or de-
pendent variable and the physicochemical parameters or descriptors are termed as
predictor, explanatory, or independent variables [9]. The number of independent var-
iables employed for the generation of a mathematical equation of correlation further
classifies this approach into simple linear regression (SLR) or multiple linear regres-
sion (MLR). Linear regression quantifies this relationship by fitting a linear equation
to the data, estimating coefficients that define the influence of molecular descriptors
on the acti vity. Utilizing various molecular f eatures, it predicts the activity of new
compounds. QSAR’s linear regression enables rational drug design, environmental im-
pact assessment, and toxicity prediction, playing a vital role in optimizing compound
properties and accelerating chemical and pharmaceutical research [10].
6.2.1 Simple linear regression (SLR)
In QSAR drug discovery, SLR analysis is a fundamental statistical approach [11]. It aims
to establish a relationship between the chemical structure of molecules and their bio-
logical activities [12]. By plotting and analyzing the data, this method identifies a linear
equation that best fits the relationship between molecular descriptors and activity val-
ues [13]. The slope and intercept of the line provide insights into the correlation and
predictive power of the model. SLR aids in understanding how changes in molecular
features impact activity, assisting researchers in designing and optimizing drug candi-
dates with desired properties. In this method, biological activity is correlated with only
one dependent variable (one physicochemical property) [14].
The equation of the SLR follows the simple equation of a straight line as in the
following equation:
Y = mX + C (6:1)
where Y is the dependent variable, X is the independent variable, m is the slope, and
C represents the intercept of the line.
Let us try to understand this with a hypothetical example as shown in Tab. 6.1.
Suppose there is a series of 10 hypothetical compounds numbered from 1 to 10 along
with their hypothetically experimental values of the biological activity and log P. For
developing a correlation between biological activity and log P, we will use an SLR ap-
proach. Here, our dependent variable will be biological activity (y) and the indepen-
dent variable will be log P (x).
106 Chapter 6 Statistical approaches used in the QSAR
The correlation equation between the biological activity and log P from the SLR
should be as in the following equation:
Biological activity = m log P + C (6:2)
where m represents the slope of the line and C represents the intercept of the line.
Both of them can be calculated mathematically with the following equation:
m = R
SD
X
var
SD
Y
var
(6:3)
where R is the Pearson correlation coefficient and SD represents the standard devia-
tion of X and Y variables. R can be calculated from the following equation:
R = Σ
ðX − X
mean
Þ Y − Y
mean
ðÞ
p
Σ ðX − X
mean
Þ
2
Σ ðY − Y
mean
Þ
2
!
(6:4)
where X variable is the value of log P and X
mean
is its average. Y variable represents
biological activity and Y
mean
is its average value. The values of SD
Xvar
and SD
Yvar
can
be calculated with the help of the following equations, respectively:
SD
X
var
=
p
Σ
ðX − X
mean
Þ
2
ffiffiffiffiffiffi
Σ n
p
− 1
!
(6:5)
SD
Y
var
=
p
Σ
ðY − Y
mean
Þ
2
ffiffiffiffiffiffi
Σ n
p
− 1
!
(6:6)
where n depicts the number of observations in this case.
The other parameter C, representing the intercept of the equation, can be calcu-
lated from the slope value with the help of the following equation:
Tab. 6.1: The hypothetical values of biological activity and the log P
of 10 hypothetical compounds.
Compound Biological activity value
(negative log of IC
)
Log P value
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
6.2 Linear regression analysis 107
Tab. 6.2: Calculated parameters from the values obtained from Tab. 6.1 of 10 hypothetical compounds.
Compound Biological activity value
(negative log of IC
)
Log P value (Y–Y
mean
)(X–X
mean
)(X–X
mean
)(Y–Y
mean
)(Y–Y
mean
)
(X–X
mean
)
. . −. −. . . .
. . .. . . .
. . . . . . .
. . −. −. . . .
. . .. . . .
. . −. −. . . .
. . −. −. . . .
. . . . . . .
. . −. −. . . .
. . . . . . .
Y
mean
= . X
mean
= . Σ = . Σ = . Σ = .
108 Chapter 6 Statistical approaches used in the QSAR
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