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Introduction
Paclitaxel (taxol, Bristol_Myers Squibb, New York, New
York, USA[1]) and docetaxel (taxotere, Sanofi_Aventis, Paris,
Paris, France[2]; Figure 1) are arguably two of the most
effective and clinically successful anticancer agents widely used
for the administration of several solid tumors, such as breast
and ovarian cancers. Both agents have a unique anticancer
mechanism known as microtubule-stabilizing activity. They
act by accelerating the polymerization of tubulin and
inhibiting the depolymerization of microtubules, thus leading to
cell apoptosis[3_5]. Although both drugs possess strong
antitumor activity, chemotherapy is usually limited by the
presence of multidrug resistance (MDR). MDR is the
cross-resistance of tumor cell lines to several structurally and
functionally unrelated chemotherapeutic agents after exposure
to a single cytotoxic drug[6,7]. Therefore, it is urgent to
develop a new generation of anti-MDR taxoids.
Extensive research has been conducted to better
understand the mechanism of MDR, and until now, several targets
have been recognized to be associated with MDR, such as
the overexpression of the ATP-binding cassette (ABC)
transporter proteins and the mutations on
tubulin[8,9]. The ABC transporter proteins include (but are not limited to) the
P-glycoprotein, the multidrug resistance protein (MRP) 1,
MRP2, and the breast cancer resistance
protein[8]. For tubulin, it has been proven that the point
mutation at the β-tubulin within or near the paclitaxel binding site and the
expression of the β-tubulin isotypes, which are less sensitive
to taxoid inhibition, usually lead to
MDR[10]. For the complexity of the receptor targets relative to MDR, it is difficult
to make use of receptor-based methods in exploring MDR
problems. Since the last decade, a lot of taxoids have been
synthesized, and their cytotoxicity activities to different cell
lines have been evaluated, so we can now explore the
problem of MDR from the perspective of ligands, that is,
exploring the quantitative structure_activity relationship (QSAR)
of taxoids and their anti-MDR activities. An important
parameter in evaluating the anti-MDR activity of compounds
is the resistance index (RI), which is the ratio of
IC50 of the resistance cell lines to that of the sensitive ones.
Since the last decade, there has been a lot QSAR-based
research about taxoids[11-15]. Most of these studies made
use of 3-D methods, such as the comparative molecular field
analysis (COMFA) or the comparative molecular similarity
indices analysis (COMSIA); another character of these
researches is that the activity they adopted is
IC50 of taxoids to inhibit the disassembly of microtubule or growth of tumor
cell lines instead of the RI of anti-MDR properties. MDR is
a common and serious problem that hinders the application
of taxoids; good IC50 activity alone can not satisfy the
clinical demand. The next generation of taxoids should conquer
the problem of MDR. Until now, we have found only 1
article that depicts the QSAR model of the RI. In this study,
Monti et al adopted multilinear regression (MLR) to mimic
the relationship between the RI and the structure of
cis-platinum complexes. Four descriptors were adopted in their final
models, and there are 16 compounds in the whole
dataset[16]. As for taxoids, until now, there is no such model to predict
the RI, so to obtain the RI, many cytotoxicity evaluation
experiments should be conducted. Experimental methods
are usually time and money consuming and they are not
consistent with the basic drug development strategy of "fail
early, fail cheap"[17,18], especially to millions of candidate
molecules. So it is necessary for us to build a QSAR model
to predict the RI for taxoids.
Molecular descriptors are one of the key factors to a
successful QSAR model, and they should encode the most
useful physicochemical information on structure features that
are relative to the activities to be modeled. Electrotopological
state (E-state) indices are widely used in QSAR modeling,
including recent cancer-related
research[19,20]. The large amount of variables in E-state indices can fully represent the
structure characters of molecules, such as information about
non-covalent interactions, which may be important to the
occurrence of anti-MDR activity. The artificial neural
network (ANN), used as a modeling technique, has recently
become a popular and powerful chemometric
tool[21-23]. Compared with classical statistical methods, ANN-based
approaches do not require preliminary knowledge of the
mathematical form of the relationship between the
variables[24], which makes the ANN suitable for extrapolating the complex
and unsure relationships between the biological
phenomenon and the structure of the compounds. Several
successful QSAR models in our previous studies have proven the
feasibility of the combination of the E-state index and the
ANN[20,25] to build models.
The purpose of this article was to build a QSAR model
combining the E-state indices and the ANN to predict the RI
for taxoids. Structure and cytotoxicity data of 63 taxoids,
including paclitaxel and docetaxel, were collected from
published studies[26-30]. Compared with the RI model
of cis-platinum complexes, we enlarged the chemical space of our
models by collecting 63 compounds synthesized by different
laboratories at different times; moreover, more than 4
descriptors were adopted, and the ANN was used as a
modeling technique as it does not have to suppose a linear
relationship between structure and activity as in MLR. In order
to determine the optimal composition of compounds in the
training and validation sets, 5-fold cross-validation was
performed. The robustness and generalization of our
models were still evaluated by an external, independent testing
set. The final model was statistically proven to be stable and
predictive. This model will aid in filtering drug candidates
and accelerate the design and development of new
generation anti-MDR taxoids.
Material and methods
Dataset In order to build a reliable QSAR model, 63
taxoids with diverse structures were collected from published
studies[26-30], which represented most of the structure
modifications since the last decade to improve the clinical
performance of paclitaxel and docetaxel. According to the
modification positions, these compounds are categorized into 6
classes[31], as shown in Figure 2, and the substitution
information of the compounds in each class are listed in Table 1.
The data about the inhibitory effects
(IC50) of these compounds to drug-sensitive human breast carcinoma
(MCF-7S) and multidrug-resistant human breast carcinoma
(MCF-7R) cell lines were also collected to calculate the RI.
Cytotoxicity experiments were conducted following the
same in vitro assay protocol developed by
Skehan et al[32].The reason we chose
MCF-7(S and R) cell lines was because they
are widely used in biological activity evaluations of taxoids,
which will aid in the collection of compounds. All the
MCF-7R cell lines were induced by doxorubicin to ensure that
they had the same MDR mechanisms. The anti-MDR
activity of different taxoids was expressed as a relative value of
the RI (taxoid)/RI (paclitaxel), and the values of _log (RI
[taxoid]/RI [paclitaxel]) were used for analysis in the back
propagation neural network (BPNN) model, which covered a
large range, with nearly 3 orders of magnitude from _0.57 to
+2.28.
The most reliable way to validate the generalization
ability of a model is by external
validation[33], that is, to assess the adequacy of the model by the dataset, which is not used
in model building. So we randomly selected 14 compounds
as an independent external testing set. Five-fold
cross-validation was performed on the remaining 49 taxoids to
evaluate the internal stability of models and to optimize the
composition of compounds in the training and validation sets,
so 49 compounds were randomly categorized into 5 groups.
One group was selected as the validation set each time, and
the remaining 4 groups as the training set; 5 different
training and validation datasets could be used to construct
different models[19]. The detailed grouping information of the
datasets for each model together with the activities for each
compound was given as supporting information.
Descriptor generation We used the Molconn-z program
in the SYBYL software package (Tripos Associates, St Loius,
MO, USA) to calculate molecular structure descriptors known
as E-state indices, whose availability has been proven in a
lot of QSAR models[20,34]. In total, 248 standard descriptors
were calculated included in the molecular connectivity Chi
indices, Kappa shape indices, E-state indices, hydrogen
E-state indices, atom type and bond type E-state indices,
topological equivalence indices and total topological index,
counts of graph paths, atoms, atom types, bond types, and
so on (Molconn-Z manual), which can sufficiently represent
the structural characters of molecules. The E-state indices
are shown to contain information reflecting the
intermolecular accessibility of atoms and groups in a molecule,
especially the electron accessibility, which is encoded into a
numerical value. The advantage of these kinds of descriptors
is that they encode not only the topological environment of
an atom, but also the electronic interactions from other
atoms in the molecules, as depicted in its
formula[35]:
Si=Ii+δIi (1),
where Si is the E-state of atom i,
Ii is the intrinsic state, and
dIi is the perturbations due to the atoms around it.
Moreover, most of the descriptors have been proven to be
well associated with non-covalent interactions, which are
important for bioactivity[36]. Thus, E-state indices can
represent the structure information, which may also be relative to
the anti-MDR properties for taxoids.
Feature reduction Not all of the 248 descriptors
contribute to the bioactivity; some measures were taken to
eliminate the noise (uninformative descriptors): eliminating the
descriptors with constant values and more than 90% zero
values because they offered little discriminating information
for the construction of model. After this procedure, 84
descriptors remained, as shown in Table 2. In order to further
reduce the variable space and the chance of correlation
between the descriptors, a principle component analysis (PCA)
was performed on the remaining 84 variables. The 11
derived principle component vectors (PC) were used for model
building. The calculation of PCA was done by free data
mining software, Tanagra 1.1
(http://eric.univ-lyon2.fr/~ricco/tanagra/en/tanagra.html).
ANN In order to build reliable and predictive QSAR
models, we adopted the ANN technique, which has been
proven to have outstanding non-linear approximation
ability[22,23,37]. A typical ANN consists of an input layer, a hidden
layer, and an output layer. In the ANN, signals are
propagated from the input neurons through the hidden layer to
the output neuron, and then the error is calculated and back
propagated to iteratively adjust weights and biases in order
to minimize the error in prediction; this is the most distinct
character of typical back propagation (BP) algorithm.
The ANN program used was the neural network software
package of MATLAB 7.0.1 developed by Math Works (Natick, MA, USA). Some fully connected 3-layer BP neural
networks with sigmoid transfer function were constructed.
The number of neurons in the input layer equaled the
number of PC. Before the net training, all of the input and output
values were normalized to between _1 and 1, and the
outputs were transferred back to the same units as the original
outputs for comparison purpose. The Levenberg_Marquardt
algorithm was adopted to optimize weights and biases
because it was significantly faster than other algorithms based
on gradient descent[38]. In each of the 5 different datasets,
the training sets were used to determine the architecture of
the ANN model; the validation sets were adopted to tune the
ANN parameters to prevent
overtraining[39], and the independent external testing set was used to evaluate the
predictive ability of the models. In order to determine the optimal
number of neurons in the hidden layer, we adopted some
empirical rules. For example, the number of neurons in the
hidden layer can be confirmed by the formula:
m=log2 n+a, where m is the number of neurons in hidden
layer, n is the number of input variables, and
a is the integer between 0 and
10[40_42]. The early-stopping method was adopted to
help prevent overtraining. For the 5 datasets with different
compounds in the training and validation sets, we
trained the models separately.
Model evaluation The following parameters were
calculated to evaluate the performance of the ANN and the
predictive ability of the model:
Q2cv (cross-validation
correlation coefficient), RMSE (residual mean square
error), R2 (square correlation coefficients for the regression line for
calculated and experimentally-derived activity of the
external testing set),
R02 (square correlation coefficients for the
regression line through the origin for calculated and
experimentally-derived activity of the external testing set), and
K (the slope of regression line through the origin for testing
sets). The residuals between the predicted and
experimentally-derived activities were also calculated for the best model.
The definitions of
Q2cv[43] and
RMSE[33] are listed below:
Q2cv =1-PRESS/SD (2)
 (3),
where PRESS is the sum of squared deviations between
the predicted and measured biological activity values for
each compound in the validation set, and SD is the sum of
the squared deviations between the measured activities of
the compounds in the validation set and the mean activity of
the training set compounds.  and yi are the predicted and actual
activities, respectively, and  corresponds to the equation of
regression  . The propositional criteria necessary for the high
predictive ability of a model are high
Q2cv (at least >0.5), high
R2 for the external testing set (at least >0.6),
(R2-R02
)/R2<0.1, and 0.85
£K £1.15[33, 47].
Results
Molecular descriptors The remaining 84 molecular
descriptors after the feature reduction were compressed and
analyzed by PCA, resulting in 11 PC for network building.
The number of components was determined by the maximum
variance described by the PC and the eigenvalues. Eleven
PC were sufficient to explain nearly 95% of the variance, and
all of their eigenvalues were greater than 1. The coefficients
of variables to each PC are described in Table 3. PC1 and
PC2 explained 23% and 19% of the total variance, respectively. In each, the molecular connectivity and
molecular shape indices played important parts. The PC2 mainly
consists of the E-state descriptors, which encode the
topological and the electronic information about each atom and
the interaction deriving from the environment. PC3, with
10% of the variances explained, represents the information
of the H-bond interaction derived from the information about
the H-bond donor and acceptors. PC4 was dominated by
the information about the atom type aaCH:, that is, :CH:,
including the number of atoms of this kind, number of H on
these atoms, and the total E-state values and HE-state values,
and it encodes 9.23% of the variance. The most important
descriptor in PC5 is the ndssC, which counts the number of
atoms of this kind =C<. Interestingly, the atom O descriptor
also accounts for a large part in PC5, which totally depicted
8.4% of the total variance. Although only 6.6% of the
variance was explained, PC6 contained important descriptors,
mainly about the atom N, such as NH_ and the group NC
(=O) OR. The remaining 5 PC can contribute to 16.6% of the
total variance and each one was dominated by important
descriptors.
QSAR modeling As for the 5 different training and
validation sets, 5 QSAR models were built separately. Eleven
PC served as input variables for each model. There are no
rigorous theoretical principles for determining the structure
for ANN, so different numbers of neurons in the hidden layer
and various numbers of epochs were tried in order to
prevent overfitting and overtraining. As weights and biases are
optimized by the back propagation iterative procedure,
training errors typically decrease, but validation errors first
decrease and subsequently begin to rise, revealing a
progressive worsening of the generalization ability of the network.
Thus, when RMSE (transferred back) for training and
validation sets both reached comparatively small values, the
optimized number of neurons and epochs was confirmed. After
the structure of the ANN was chosen, repeated training was
done to optimize the weights and biases to find the best
predictive models. The architecture of each model and the
results of the cross-validation
Q2cv and RMSE (T, V)
are summarized in Table 4.
Model evaluation The external independent testing set
composing of 14 compounds was used to evaluate the
predictive ability of the 5 models with the results shown in Table
5. Although the Q2cv values of model 3 was >0.5, and both
the values of RMSET and
RMSEV were less (0.003), the generalization ability of this model is poor, as demonstrated by
the results of R02 and the values of
(R2_R02
)/R2. The statistical results of model 4 also did not satisfy the criteria for a
good model. Although the evaluation results of models 1, 2,
and 5 all satisfied the referred criteria necessary for
predictive models, we selected model 2 as our final model as it had
the highest value of
Q2cv and
R2, allowing us to determine the
most stable and predictive model for the RI.
The residuals between the predicted and
experimentally-derived activities for compounds in the training, validation,
and prediction sets by model 2 are shown in Table 1. We can
see that the activities of all 63 taxoids were predicted within
1.007 log units of their experimentally-derived activities with
an average absolute error of 0.213 log units. The predictive
results of all 63 compounds are plotted in Figure 3. The
statistical results of the testing set found that the greatest
deviation was 0.54 log units with an average absolute error
of 0.226 log units. The predicted results are also plotted in
Figure 4.
Discussion
A successful descriptor should represent the key structure
information of molecules, influences activity, and then can be
useful in the prediction of activity for unknown compounds.
According to some structure activity
studies[26_30], substitution by definite atoms or groups can influence anti-MDR
activity; for example, F-substituted taxoids at different
positions usually alter the anti-MDR activity differently, and the
_OH and groups including N atoms also play an important
part in the change of activity. As discussed earlier, the
E-state indices had fully encoded these kinds of structure
information; for example, F, N, =C< and :CH: descriptors were
all embodied in different PC. Moreover, the reported
mechanisms about MDR of taxoids are relative to ABC transporter
proteins and tubulin[10]. As for ABC transporter proteins,
intermolecular H bonds are key factors for the recognition of
taxoids by those proteins[25]. For tubulin, it has been proven
that specific conformation, such as the T- taxol for taxoids,
should be maintained, and taxoids can act on some definite
isotypes of tubulin, which are also relative to the
non-covalent interaction intra or inter
molecules[44_46]. So maybe the anti-MDR activities of taxoids have some relationship to
non-covalent interactions. Topological-based E-state indices
comprised H-bond descriptors for inter and intra molecules,
which represented the non-covalent interactions.
According to the above analysis, we can see that E-state indices
can represent important attributes of molecular structure,
especially those associated with the interaction between
taxoids and receptors. So it seems reasonable for us to
choose E-state indices as our descriptors for exploring the
relationship between the RI and the structure.
As for the statistical results of the 5 ANN models,
although each model was with the good internal
cross-validation results(
Q2cv>0.5), we can't conclude that all of them
have good generalization abilities. The results of model 3
indirectly indicated that only the independent external
testing rather than the internal validation could evaluate the
predictive ability of a model. The results of 5-fold
cross-validation and external testing also ensured that the
compound composition of the training and validation sets had
important influence on the architecture and performance of
models, especially on the predictive ability for the external
testing sets. Five-fold cross-validation could help us to find
out the optimal combination of compounds that may be
useful for obtaining the most predictive model.
According to the results of model 2, in Figure 3, all of the
samples distributed closely around the line, and the value
of R02 was 0.8936, together with the
K (the slope of regression line through the origin) was 1.0137, which further proved
the closeness of the predicted and experimentally-derived
activity. The results also indicated that the E-state indices
did correlate well with the _log (RI/P). The statistical results
of the testing set further confirmed the predictive ability of
this model.
As for the complexity of the receptor proteins associated
with MDR, we derived a ligand-based QSAR model to
predict the values of the RI for different taxoids. E-state indices
were used to represent the structure of molecules; BPNN
was used to explore the relationship between descriptors
and RI activity. During the construction of the models,
5-fold cross-validation was performed to determine the best
composition of compounds in the training and validation
sets. The predictive ability of the models was also evaluated
by an independent testing set. The best model had the
statistical results of R2=0.84,
R02=0.835, K=0.9933, and
RMSEP=0.014, indicating the excellent robustness and generalization of our
model. The results also proved that E-state indices have
some relationship to anti-MDR activity, and the BPNN
modeling technique can fully emulate this kind of non-linear
relationship. Our model can predict the values of the RI for
taxoids just from its structure even before it was synthesized,
so it will aid in the filter of anti-MDR drug candidates and
accelerate the design and development of taxoids with good
clinical performance to drug resistance cell lines.
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