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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5486_Библиотеки_им_академика_М_И_Перельмана
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5.4.1.4 Setting up the grid and calculation of molecular energy fields
This is the next step after the alignment of the molecules and is divided into two
phases:
a. Setting up of the grid: In this step, a 3D grid space is identified and aligned mole-
cules are kept in the center of this grid (Fig. 5.3). The default grid space, that is,
the distance between the two grid points, is kept at 2 Å, however, it can be varied
as per the requirement. Generally low values of the grid space are desirable for a
more exhaustive search. Talking about the size of the grid, it should be larger by
3–4 Å compared to the union surface of the aligned molecule. The location of the
grid box also plays an important role and it is noticed that if not located properly
it can vary the result of the generated CoMFA model.
b. Calculations of molecular energy fields: All the aligned molecules inside the
grid box are represented in terms of molecular energy fields (steric and electro-
static fields). A probe atom, generally a sp
3
hybridized carbon or a proton, is used
for evaluating these fields. The value of these molecular fields between the probe
atom and each molecule is calculated at the regularly spaced point of the grid
box. In the CoMFA model, steric fields are represented by the Lennard-jones po-
tential (equation (5.1)), and the electrostatic field are represented by the Columbic
potential (equation (5.2)):
E
vdw
= Σ A
ij
r
−12
ij
− C
ij
r
−6
ij
(5:1)
where E
vdw
represents the Van der Waals energy, r
ij
depicts the distance between
the molecules at point i and the probe atom at point j, and A
ij
and C
ij
are the con-
stants obtained from the Van der Waals radii of the concerned atoms:
Fig. 5.3: A generated grid box for the
generation of the CoMFA model.
5.4 Comparative molecular field analysis (CoMFA) 89
E
c
=
Σ q
i
q
j
ϵr
ij
(5:2)
where E
c
is the coulomb interaction energy, r
ij
stands for the distance between
the molecule at point i and the probe atom at point j, q
i
is the charge of the atom i
of the molecule, q
j
represents the charge of probe atom, and ϵ is the dielectric
constant.
5.4.1.5 Statistical generation of the CoMFA model
Energy field values obtained in the previous step serve as the descriptors in CoMFA
analysis for correlating the biological activity values of the compounds. However, the
major issue here is that we get thousands of these steric and electric field parameters.
Multiple linear regression (MLR), which is the choice of the statistical parameter in
traditional QSAR, is not preferred for CoMFA as it can result in chance correlation as the
number of descriptors in CoMFA is very large compared to the number of compounds
in the study. Hence to overcome this hindrance, another statistical approach, the PLS
method developed in 1986 is used for CoMFA model generation. PLS is used in CoMFA to
reduce the number of descriptors to a smaller set of uncorrelated variants. This ap-
proach is considered a natural extension of the principal component analysis (PCA) of
statistics. The model of the CoMFA is a correlation equation between the biological activ-
ity and several latent variables (LVs) (Fig. 5.4). LVs are the variables obtained through
the linear combinations of the original independent molecular field parameters.
Fig. 5.4: Development of the CoMFA model equation by using partial least square (PLS) statistical approach.
90 Chapter 5 3D-QSAR in drug designing
5.4.1.6 Validation of the CoMFA model
The quality of a CoMFA or any QSAR model is validated through various statistical
parameters. CoMFA, like any QSAR model developed, is validated for its predictability
and robustness both internally and externally:
a. Internal valid ation of the CoMFA model: In this approach, the quality of the
developed model is assessed from the molecules used for its development, that is,
from the training dataset. The following two parameters are used for this purpose
in the internal validation:
– Goodness of fit (R
2
): This is used to assess the quality of the CoMFA model in
terms of its reproducibility but does not provide any information regarding
the robustness and predicting ability of the generated model. It is calculated
by the following equation:
R
2
= 1 −
RSS
TSS
(5:3)
where RSS is the residual sum of squares and TSS represents the total sum of
squares; both parameters are calculated as shown in the following equations:
RSS = Σ ðY − Y
pred
Þ
2
(5:4)
TSS = Σ ðY − Y
mean
Þ
2
(5:5)
where Y represents the observed biological activity value of the molecule,
Y
pred
is the value of the biological activity predicted by the model, and Y
mean
is the average value of the observed biological activity of all the molecules in
the training set. The value of R
2
should be greater than 0.7 for considerin g
the generated model acceptable.
– Cross-validation coefficient (Q
2
cv
): This is the most popular and widely ac-
cepted method for the internal validation of the developed CoMFA model. In this
approach, a fixed amount of the molecules are omitted from the training set,
which is a leave-one-out method in which one molecule is omitted every time
from the training set till all the molecules are omitted one by one. The developed
CoMFA model is then utilized to predict the BA values of these omitted molecules
and Q
2
cv
of the model is calculated through the following equation:
Q
2
cv
= 1
PRESS
TSS
(5:6)
where PRESS represents the predictive error sum of squares and TSS repre-
sents the total sum of squares.
Let us assume that in a CoMFA model, we have n number of molecules in
the training set. The CoMFA model is generated from (n – 1) molecules leav-
ing one molecule at each time and predicting the biological activity of the
left-out molecule from this generated CoMFA model. If the actual biological
5.4 Comparative molecular field analysis (CoMFA) 91
activity of the left-out molecule is Y and Y
p
is its value predicted by the model
then the value of PRESS will be calculated from the following equation:
PRSS = Σ ðY − Y
p
Þ
2
(5:7)
PRESS is the total sum of the square of the difference between the actual and
predicted values of all the left-out molecules one by one. The Q
2
cv
value greater
than 0.7 indicates that the model developed can be robust and will have good
predictability.
b. External validation of the CoMFA model: The most widely used parameter for
the external validation of the developed CoMFA model is the coefficients of deter-
mination (R
2
pred
). It can be calculated from the following equation:
R
2
pred
= 1 −
Σ ðY − Y
pred
Þ
2
Σ ðY − Y
mean
Þ
2
!
(5:8)
where Y is the observed biological activity value of the test molecule, Y
pred
is the
value of biological activity predicted by the model of the test dataset molecule,
and the Y
mean
represents the average value of the observed biological activity of
the training set molecules. A value of R
2
pred
greater than 0.6 is considered accept-
able while assessing the robustness of the CoMFA model externally.
There is still a lot of debate amongst the scientific community on whether external
validation is required or not in any QSAR model, as some groups of scientists believe
that robust i nternal validation is sufficient for ass essing the model, whereas other
groups believe that external validation is a must.
5.4.1.7 Visualization and interpretation of the results
The information generated through the CoMFA model is assessed and interpreted
through contour maps and the PLS plots. Contour maps are the distinguished features of
a CoMFA model that differentiate it from the traditional QSAR model. Contour maps are
defined as the 3D space around the molecule, which tells us about the regions of high and
low activity due to steric and electrostatic effects (Fig. 5.5). Different colors in the contour
maps represent different effects of the groups in the contour map. In the steric contour
maps, the green color region represents the region where bulky groups are desired for
the biological activity and the yellow colors are the areas where the bulky groups will
decrease the biological activity. In the electrostatic contour maps, the blue area repre-
sents the requirement of electropositive groups for increasing the biological activity and
the red regions emphasize the requirement of the electronegative groups in that region
for increasing the biological activity. Besides contour maps useful information is also ex-
tracted from the PLS plots such as plots between the predicted and experimental values
of the biological activity of training and test datasets (Fig. 5.6).
92 Chapter 5 3D-QSAR in drug designing
Fig. 5.6: PLS plot of the CoMFA model plotted between the predicted and the actual biological activity of
the compounds employed for the generation of the CoMFA model.
Fig. 5.5: Contour maps obtained from the generated CoMFA model: (a) steric contour map where the
green color represents the sterically favorable region and yellow region represents the sterically
forbidden region; (b) electrostatic contour map where blue color is the electrostatically favorable region
and red region represents the electrostatically forbidden region.
5.4 Comparative molecular field analysis (CoMFA) 93
5.5 Advantages of the CoMFA model
– 3D structural information: CoMFA utilizes three-dimensional structural infor-
mation of molecules, capturing spatial interactions and alignment within the ac-
tive site of a protein. This leads to a more realistic represen tation of molecular
interactions compared to traditional 2D-QSAR.
– Spatial interaction analysis: CoMFA evaluates steric and electrostatic interac-
tions, which are critical for understanding binding interactions between a mole-
cule and its target protein. This detailed analysis aids in designing compounds
with optimal binding characteristics.
– Predictive power: CoMFA models can have high predictive accuracy, especially
when the alignment and grid parameters are carefully chosen. This accuracy
translates into the ability to predict the biological activity of new, untested com-
pounds, aiding in virtual screening and compound prioritization.
– Structure–activity relationship insights: CoMFAprovidesinsightsintothe
structure–activity rel ationships by highlighting how specific regions of a mole-
cule’s structure contribute to its biological activity. This information guides me-
dicinal chemists in modifying and optimizing compounds.
– Visual interpretation: CoMFA result s often include contour maps that visually
represent regions of favorable and unfavorable interactions within the active
site. These maps help chemists understand where modifications can lead to im-
proved binding affinities.
– Molecular design: CoMFA allows for the design of new compounds with desired
activity profiles. By altering molecular structures to fit favorable contour regions,
chemists can rationally design analogs or derivatives for improved potency.
– Alignment flexibility: CoMFA provides a degree of alignment flexibility, accom-
modating variations in molecule conformations, which is particularly useful for
flexible ligands and proteins.
– Alignment-independent analysis: CoMFA can be used to analyze datasets with
structurally diver se molecules, as the alignment process can help identify com-
mon structural features across different molecules.
– Interpretability: CoMFA equations contain coefficients for each descriptor, pro-
viding a quantitative measure of their contribution to activity. This enhances the
understanding of the key molecular features influencing activity.
– Complementary to experimental methods: CoMFA can supplement experimen-
tal studies by suggesting hypotheses for binding modes and interactions, which
can guide subsequent experimental investigations.
– Time and cost-efficiency: CoMFA allows researchers to prioritize compounds for
synthesis and testing, potentially reducing the number of compounds needing ex-
perimental evaluation, and saving time and resources.
94 Chapter 5 3D-QSAR in drug designing
5.6 Limitations of the CoMFA model
Besides a lot of significant advantages over traditional QSAR, there are certain limita-
tions of the CoMFA that sh ould be addressed whenever this technique is applied to
model generation [16, 17]:
– Alignment sensitivity: CoMFA heavily relies on the accurate alignment of mole-
cules within the binding site. Slight variations in alignment can lead to different
results, making it sensitive to the chosen alignment method.
– Grid size and resolution: The choice of grid size and resolution can impact the
results significantly. An inappropriate grid can either miss important interactions
or introduce noise into the analysis.
– Sparse data regions: CoMFA is sensitive to areas in the active site with sparse
data points. If certain regions of the grid have insufficient data, the model’s accu-
racy can be compromised.
– Overfitting: Like any QSAR model, CoMFA can be prone to overfitting if not prop-
erly validated. Overfitting occurs when the model captures noise in the training
data rather than true underlying relationships.
– Descriptor limitations: CoMFA uses steric and electrostatic fields as descriptors,
which may not capture all the relevant molecular interactions and properties
that influence biological activity.
– Dependence on training set: The predictive power of a CoMFA model is heavily
reliant on t he quality and representativeness of the training dataset. A poorly
chosen dataset can lead to unreliable predictions.
– Applicability domain: CoMFA models are only valid within the applicability do-
main defined by the training data. Predictions for compounds that fall outside
this domain can be unreliable.
– Assumption of additivity: CoMFA assumes that the contributions of steric and
electrostatic fields are additive, which might not always hold true for complex
molecular interactions.
– Interpretability: While CoMFA provides insights into which regions of a mole-
cule contribute to its activity, the physical interpretation of the contour maps can
be challenging, limiting its usefulness for rational drug design.
– Variability in biological activity: Biological activity can be influenced by factors
beyond simple steric and electrostatic interactions, such as solvation effects, en-
tropy changes, and dynamic behavior, which CoMFA may not fully capture.
– Limited scope of interactions: CoMFA primarily considers steric and electro-
static interactions, potentially overlooking other crucial interactions like hydro-
gen bonding, π–π stacking, and metal coordination.
– Computational intensity: The calculations involved in generating CoMFA models
can be computationally intensive and time-consuming, particularly for larger da-
tasets or more complex molecular systems.
5.6 Limitations of the CoMFA model 95
5.7 Comparative molecular similar indices analysis (CoMSIA)
CoMSIA model was developed in 1994 by Klebe and coworkers and is considered the
natural extension of the CoMFA. CoMSIA is a computational method extensively uti-
lized in drug discovery to elucidate the quantitative relationship between molecular
structure and biological activity [18]. CoMSIA extends the principles of CoMFA by in-
corporating additional physicochemical properties beyond steric and electrostatic
fields. It considers fields like hydrophobicity, hydrogen bonding, and lipophilicity, en-
hancing the predictive accuracy of the model. CoMSIA operates by dividing the three-
dimensional space around molecules into grid points and calculating the interactions
of molecular probes at these points. These interactions are translated into numerical
descriptors that represent various physicochemical properties. Through statistical re-
gression, CoMSIA correlates these descriptors with biological activity data to construct
a predictive QSAR model. CoMSIA’s ability to encompass multiple molecular proper-
ties makes it a val uable tool for understanding complex structure–activity relation-
ships and guiding the design of novel drug candidates with improved potency and
selectivity.
Unlike the CoMFA model where we calculate the molecular field-based descrip-
tors (Lennard-Jones and Coulomb potentials), here some arbitrary descriptors are cal-
culated, which are based on the similarity and dissimilarity of the molecules in space.
These similarity indices are calculated for each of the aligned molecules using a com-
mon probe. Another major advantage of CoMSIA when compared with the CoMFA is
that it also incorporates the hydrophobic surface area (which explains the effect of
entropy on the binding affinity) and hydrogen bonding parameters in the generation
of the model. Therefore, CoMSIA enumerates five parameters using a probe, steric,
electrostatic, hydrophobic surface area, hydrogen bond donor, and hydrogen bond ac-
ceptor-based descriptors using a probe.
A probe atom, generally having a charge of +1, a radius of 1 Å, hydrophobicity of
+1, hydrogen bond acceptor value of 1, and having hydrogen donor value of 1, is used
in calculating the similarity indices in the CoMSIA model. Another major difference
from CoMFA is the visualization and interpretation of the contour maps. In CoMFA
we get those favorable or not favorable regions of the environment where aligned
molecules will interact; however, in the CoMSIA model, these regions are occupied by
the ligand that will like or dislike the presence of a particular group concerning a par-
ticular parameter. The rest of the methodology of CoMSIA, including generation of
conformations, alignment of molecules, and statistical approach (PLS), is similar to that
described above for the CoMFA model. A brief of steps used in the CoMSIA model gener-
ation is given in Fig. 5.7.
96 Chapter 5 3D-QSAR in drug designing
5.8 Advantages of the CoMSIA model
– Inclusion of multiple molecular fields: CoMSIA takes into account multiple mo-
lecular fields, such as steric, electrostatic, hydrophobic, and hydrogen-bonding
properties. This allows it to capture a more comprehensive picture of the interac-
tions between molecules and their targets.
– Enhanced predictive power: By incorporating multiple fields, CoMSIA can pro-
vide more accurate predictions of molecular activity. Different interactions contrib-
ute differently to the overall activity, and CoMSIA can highlight these contributions.
– Handling of steric effects: CoMSIA addresses steric hindrance, which is impor-
tant for accurately predicting molecular interactions. It considers the spatial ar-
rangement of atoms in addition to their electrostatic properties.
– Flexibility in descriptor calculations: CoMSIA allows flexibility in selecting and
calculating molec ular descriptors based on differen t properties. This versatilit y
enables researchers to tailor the analysis to their specific system.
Fig. 5.7: Basic workflow for the steps involved in the generation of a CoMSIA model.
5.8 Advantages of the CoMSIA model 97
– Alignment independence: CoMSIA is relatively less dependent on accurate mo-
lecular alignment compared to some other 3D-QSAR methods. This is beneficial
when working with flexible molecules or when experimental structural informa-
tion is limited.
– Overcoming traditional QSAR Limitations: Traditional 2D-QSAR methods often
struggle to predict activity for structurally diverse compounds with different substitu-
ents and conformations. CoMSIA’s 3D approach can better handle these challenges.
– Insight into molecular design: CoMSIA provides insights into how different mo-
lecular fields contribute to activity. This information can guide molecular design
efforts, helping researchers optimize compounds for desired interactions.
– Visualization of molecular interactions: CoMSIA generates maps that visualize
the regions of the molecule contributing positively or negatively to activity. This
aids in understanding how structural changes affect activity.
– Useful for lead optimization: CoMSIA is particularly valuable during lead opti-
mization phases, where understanding the impact of structural modifications on
activity is crucial.
– Application to diverse targets: CoMSIA can be applied to various types of molec-
ular targets, including enzymes, receptors, and other biomolecules, making it ver-
satile for different drug discovery projects.
5.9 Limitations of the CoMSIA model
– Sensitivity to alignment: CoMSIA heavily relies on the accurate alignment of
molecules in the dataset. Small variationsinalignmentcanleadtosignificant
changes in calculated descriptors, potentially affecting the model’s reliability and
predictive power.
– Descriptor selection and influence: The choice of descriptors used in CoMSIA
can significantly impact the results. Selecting an inappropriate set of descriptors
or ignoring important ones can lead to biased or inaccurate models. Additionally,
the influence of individual descriptors on the overall results may not always be
well understood.
– Sparse data: CoMSIA models can suffer from sparsity issues, especially when
dealing with limited data points or a small number of active compounds. This can
lead to overfitting and less reliable predictions.
– Descriptor interpretation: While CoMSIA provides molecular fields that corre-
late with activity, interpreting these fields in a mechanistic and actionable way
can be challenging. Understanding how specific field contributions relate to bio-
logical interactions is not always straightforward.
– Dependence on training set: CoMSIA models are highly dependent on the qual-
ity and representativeness of the training set. If the training set does not ade-
98 Chapter 5 3D-QSAR in drug designing
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