Modeling resistance index of taxoids to MCF-7 cell lines using ANN together with electrotopological state descriptors¹

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.

Figure 1 Structure of paclitaxel and docetaxel.

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.

Figure 2 Structure of 6 classes of taxoids.

Table 1 Substituent information for all 63 taxoids.
Full table

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]:

(1),

where S_i is the E-state of atom i, I_i is the intrinsic state, and dI_i 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).

Table 2 Electrotopological state indices used in this work.
Full table

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+α, where m is the number of neurons in hidden layer, n is the number of input variables, and α 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: Q²_cv (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 Q²_cv^[43] and RMSE^[33] are listed below:

(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 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 Q²_cv (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.

Table 3 Component score coefficient matrix of 84 descriptors to 11 PC^a.
Full table

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 Q²_cv and RMSE _{(T, V)} are summarized in Table 4.

Table 4 Statistical results of 5-fold cross-validation.
Full table

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 Q²_cv values of model 3 was >0.5, and both the values of RMSE_T and RMSE_V 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 Q²_cv and R², allowing us to determine the most stable and predictive model for the RI.

Table 5 Results for external testing set of each model.
Full table

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 (Table 6). 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.

Table 6 Predicted activities and residual information of taxoids^a.
Full table

Figure 3 Plot of predicted flog (activity) values versus experimentally-derived ones for all 63 taxoids. (□) training set; (?) validation set; (△) testing set.

Figure 4 Plot of predicted versus experimentally-derived –log (activity) for testing set.

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(Q²_cv>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 RMSE_P=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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