* Department of Computational Science, National University of Singapore, Blk SOC1, Level 7, 3 Science Drive 2, Singapore 117543; Department of Applied Physics, Chongqing University, Chongqing 400044, P. R. China;
Department of Chemistry, Sichuan University, Chengdu 610064, P. R. China
Received December 17, 2003; accepted January 16, 2004
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ABSTRACT |
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Key Words: support vector machine; torsade de pointes; linear solvation energy relationship; prediction.
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INTRODUCTION |
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So far, attention has not been sufficiently paid to the development of methods for prediction of serious ADRs that occur less frequently. While these ADRs are tolerated to a certain extent for the approval of drugs used in serious diseases urgently needing effective or more treatment options such as AIDS and cancer (Somers et al., 1990), they are nonetheless important safety issues for the approval of drugs intended for minor illnesses with availability of alternative treatment options. Examples of these illnesses are rhinitis, cough, pain, inflammation, and hypertension. Therefore, there is a need to develop computational methods for facilitating the prediction of these ADRs.
One such ADR is torsade de pointes (TdP), which is an atypical rapid ventricular tachycardia with periodic waxing and waning of amplitude of the QRS complexes on the electrocardiogram as well as rotation of the complexes about the isoelectric line (Dorlands Illustrated Medical Dictionary, 2000). TdP may be self-limited or may progress to ventricular fibrillation (Dorlands Illustrated Medical Dictionary, 2000
). This ADR is uncommon (Darpo, 2001
) and thus difficult to detect during clinical trials. There are cases of TdP-causing drugs which were initially approved and later withdrawn after post-marketing surveillance revealed their TdP-causing potential (De Ponti et al., 2002
Layton et al., 2003
).
Not all mechanisms of TdP are completely understood (Moss, 1999). TdP is frequently associated with QT prolongation, which is the lengthening of the time between the start of ventricular depolarization and the end of ventricular repolarization. This arises from the disruption of the balance between inward and outward currents during the cardiac action potential repolarization phase (Malik and Camm, 2001
). Drugs that induce QT prolongation usually cause disruption of the outward potassium currents by blocking potassium ion channels, particularly HERG K+ channel (Vandenberg et al., 2001
). This correlation between QT prolongation and blockade of relevant channels had been exploited in the development of computational methods for the prediction of the QT prolongation risk of drugs using artificial neural network (Roche et al., 2002
) and pharmacophore models (Cavalli and Poluzzi, 2002
).
There is no definitive correlation between QT prolongation and TdP (Malik and Camm, 2001; Muzikant and Penland, 2002
). For instance, verapamil causes QT prolongation but does not induce TdP, whereas procainamide and disopyramide cause TdP but are not potent inhibitors of the HERG K+ channel (Muzikant and Penland, 2002
). Thus, it is desirable to develop a method capable of prediction of TdP of multiple mechanisms without complete knowledge of these mechanisms.
A useful method for classification of systems with multiple mechanisms without requiring their knowledge is the support vector machine (SVM), a relatively new and promising statistical learning algorithm for binary classification by means of supervised learning. SVM was originally developed by Vapnik and his coworkers (Burges, 1998; Vapnik, 1995
) and has been applied to a wide range of problems including drug blood-brain barrier penetration prediction (Doniger et al., 2002
Trotter et al., 2001
), cancer diagnosis (Guyon et al., 2002
Scridhar et al., 2001
Terrence et al., 2000
), microarray gene expression data analysis (Brown et al., 2000
), and protein function prediction (Cai et al., 2003a
). This work explores the use of SVM as a potential tool for TdP prediction.
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MATERIALS AND METHODS |
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Like in the case of other classification systems, training of a SVM system requires information about TdP agents. In this work, 243 TdP agents were obtained from the search of Micromedex, Drug Information Handbook, and American Hospital Formulary Service (AHFS) for agents with no reported case of TdP in humans. Thirty-nine of these agents were randomly selected and used as part of the independent validation set (Table 2 of Supplementary Data) to assess the prediction accuracy of the SVM system on TdP agents, while the rest were used in the training set (Table 1 of Supplementary Data).
Chemical descriptors.
In this work, linear solvation energy relationships (LSER) descriptors (Abraham, 1993; Kamlet et al., 1981
, 1987
) were used for the modeling of TdP-causing potential of compounds. LSER descriptors describe solvent-solute interactions and contain three main terms: a cavity term, a polar term, and hydrogen-bond term. The cavity term is a measure of the endoergic cavity-forming process, which is the free energy necessary to separate the solvent molecules, overcoming solvent-solvent cohesive interactions, and provides a suitably sized cavity for the solute. The polar term measures the exoergic balance of solute-solvent and solute-solute dipolarity/polarizability interactions and the hydrogen-bond term measures the exoergic effects of the complexation between solutes and solvents.
LSER was initially developed for the estimation of the effects of different solvents on properties of specific solutes or the solubilities, lipophilicities, or other properties of a set of different solutes in a specific solvent. It has since been extended for analysis of biological properties including toxicological properties of compounds (Dai et al., 2001He et al., 1995
Liu et al., 2003
Sixt et al., 1995
Wilson and Famini, 1991
; Yu et al., 2002
), cell permeation (Platts et al., 2000
), intestinal absorption (Zhao et al., 2001
), and blood-brain barrier penetration (Platts et al., 2001
). LSER descriptors encode the size, polarity, and hydrogen bonding capability of a chemical that has been found to be important for the passive transport of a chemical through biological membranes (Gratton et al., 1997
Kramer and Wunderli-Allenspach, 2001
). In addition, it has been shown that complex systems, such as receptor sites, can be approximately described as a solvent system and LSER methods provide useful insights into important binding features (Cramer and Truhlar, 1992
). Thus, the polar term may represent the binding action via dispersion forces of a chemical in the polar regions of a receptor molecule and the hydrogen bond term represents the hydrogen-bonding effect between the chemical and the receptor molecule (Liu et al., 2003
Lowrey et al., 1997
). Since toxicity of a compound involves the transport of the compound to a site and its interaction with a molecular target, LSER descriptors are thus likely to be useful for TdP modeling.
The LSER descriptors used in this study was calculated using our own developed software based on the method developed by Platts (1999) and are given in Tables 1 and 2 of Supplementary Data. The accuracy of these calculated descriptors for some of the compounds has been verified using the demo version of the software Absolv (Sirius, 2000). These descriptors are excess molar refraction, combined dipolarity/polarizability, overall solute hydrogen bond acidity, overall solute hydrogen bond basicity, and McGowans characteristic volume.
SVM algorithm.
The theory of SVM has been extensively described in literatures (Burges, 1998; Evgeniou and Pontil, 2001
; Vapnik, 1995
). Thus only a brief description is given here. SVM is based on the structural risk minimization (SRM) principle from statistical learning theory (Vapnik, 1995
). In linearly separable cases, SVM constructs a hyperplane that separates the two classes of vectors (TdP+ class and TdP class) with a maximum margin. Each TdP+ or TdP agent is represented by a vector xi, which is its LSER descriptors. This is accomplished by finding another vector w and a parameter b that minimizes ||w||2 and satisfies the following conditions:
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In nonlinearly separable cases, SVM maps the vectors into a high dimensional feature space using a kernel function K(xi, xj). An example of a kernel function is the Gaussian kernel, which has been extensively used in different studies with good results (Burbidge et al., 2001Czerminski et al., 2001
Trotter et al., 2001
).
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Validation of SVM classification system.
In this work, the SVM classification system was optimized and validated using leave-one-out (LOO) cross-validation. In LOO cross-validation, a compound is left out of the training set and the remaining compounds are used to derive a SVM classification system. The classification system is then used to classify the left-out compound. This process is repeated until every compound in the training set has been left out once. The TdP+, TdP and overall accuracies are calculated using the following equations:
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Y-randomization was also used to validate the trained SVM classification system. A portion of TdP+ agents in the training set is randomly exchanged with TdP agents in the training set, creating new training sets with false TdP+ and TdP agents. A SVM classification system is trained using this scrambled training set. The randomization is repeated 10 times and LOO accuracies of the new classification system from each run are compared to that of the original classification system. If the scrambled training set gives significantly lower LOO accuracies than the original training set, the original classification system is considered as not resulting from chance correlation.
The final SVM classification system was then tested by using the independent validation set to objectively assess its predictive capability. Prediction accuracy of the final SVM classification system using this independent validation was compared with those derived from three other classification methods useful for the prediction of multiple mechanisms. These methods are probabilistic neural network (PNN; Specht, 1990), k nearest neighbor (KNN; Fix and Hodges, 1951
), and C4.5 decision tree (Quinlan, 1993
). PNN is a form of neural network that is designed for classification through the use of Bayes optimal decision rule. Unlike traditional neural networks like feed-forward back-propagation neural network where there are multiple parameters and network architectures to be optimized, PNN only has a single adjustable parameter, a smoothing factor
for the radial basis function in the Parzens nonparameteric estimator (Parzen, 1962
). Thus PNN usually trains a system orders of magnitude faster than the traditional neural networks.
In KNN, the Euclidean distance between an unclassified point and each individual datum in the training data is measured (Fix and Hodges, 1951). A total of k number of data points which are nearest to the unclassified point are then used to determine the data class of the unclassified point. The data class making up the majority of the k nearest neighbors will be predicted data class of the unclassified point.
C4.5 decision tree is a classifier in the form of a decision tree where a leaf indicates a data class and a decision node specifies a test to be carried out on a single attribute value, with one branch and subtree for each possible outcome of the test (Quinlan, 1993). C4.5 decision tree uses recursive partitioning where each attribute of the data is examined in turn and ranked according to its ability to partition the remaining data to construct the decision tree. A case is classified by starting at the root of the tree and moving through it until a leaf is encountered. At each nonleaf decision node, the cases outcome for the test at the node is determined and attention shifts to the root of the subtree corresponding to this outcome. When this process finally leads to a leaf, the class of the case is predicted to be that recorded at the leaf.
The three classification systems were trained using the same training set, descriptors, and procedure as those used in SVM. They were tested using the same independent validation set. SVM was performed using SVM, which has recently been developed and tested for the classification of DNA-binding proteins (Cai et al., 2003b
). Gaussian kernel shown in Equation 4 was used by SVM
. PNN and KNN were conducted by using our own software and C4.5 decision tree was performed by using the code from Quinlan (1993).
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RESULTS |
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To determine whether it results from chance correlation, the SVM classification system was further tested by repeating y randomization 10 times. The average LOO TdP+ accuracy from these 10 scrambled classification systems is 21.2% and the average LOO TdP accuracy is 77.3%. Both of these accuracies are worse than that of the original SVM classification system, indicating that the SVM classification system is produced as a result of actual correlation between LSER descriptors and TdP-causing potential of the chemicals and not due to chance.
There has been no reported computational study of the TdP-causing potential of a compound. Thus to objectively assess the usefulness of SVM for TdP prediction, its prediction accuracy is compared with those obtained from three other classification methods, C4.5 decision tree, KNN, and PNN, using the same independent validation set. The optimum parameters, k for KNN and for PNN, were found by using LOO cross-validation. The optimum parameters for SVM, PNN, and KNN and the accuracy results are given in Table 1. SVM has the highest overall accuracy among the four classification methods. Its TdP+ accuracy of 97.4% is substantially higher than the other three classification methods that have TdP+ accuracies of 38.589.7%. Its TdP accuracy of 84.6% is comparable to the other three methods that have TdP accuracies of 84.692.3%. These results suggest that SVM is potentially useful for facilitating the prediction of TdP causing risk of investigative agents and likely other ADRs with multiple mechanisms.
In the training set, there are several aminoglycoside antibiotics grouped together in a cluster that does not overlap significantly with the main cluster of compounds. To examine whether this cluster of aminoglycoside antibiotics contributes in some way to the high TdP+ accuracy, a new SVM classification system was trained with all of the aminoglycoside antibiotics removed from the training set. The new SVM classification system gives the same TdP+ and TdP accuracies as the original system. This suggests that the aminoglycoside antibiotics are not responsible for the high TdP+ accuracy of the SVM classification system.
There are seven agents incorrectly classified by our SVM system, which are shown in Figure 2. These include one TdP causing agent (prenylamine) and six non-TdP causing agents (medroxyprogesterone, medrysone, metirosine, penicillamine, pyridoxine, rimexolone). Their location on the score plot of the training set is shown in Figure 1. Prenylamine is incorrectly classified by SVM, PNN, and C4.5 decision tree. Metirosine and pyridoxine are incorrectly classified by SVM, KNN, and PNN, while penicillamine is incorrectly classified by both SVM and PNN. Medroxyprogesterone, medrysone, and rimexolone have a common steroidal structure and are consistently misclassified by all the four classification methods. This may indicate that the LSER descriptors are unable to fully describe the properties of steroidal compounds thus resulting in their misclassifications by all the four classification methods.
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DISCUSSION |
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The possible reason for the usefulness of LSER descriptors for TdP prediction is that they roughly encode most of the essential characteristics related to the TdP causing capability of a compound. Excess molar refraction represents the tendency of a compound to interact with a receptor through n- and -electron pairs and thus is a measure of the hydrophobic interaction between the compound and receptor. The combined dipolarity/polarizability, on the other hand, represents the ability of electrons to move and be delocalized in the chemical and is a measure of the polar interaction between the compound and receptor.
The overall solute hydrogen bond acidity, overall solute hydrogen bond basicity represents the ability of the compound to form hydrogen bonds with the receptor. This, together with the hydrophobic and polar interactions encoded by the excess molar refraction and combined dipolarity/polarizability, determines the binding affinity of the chemical for the receptor.
The McGowans characteristic volume influences the passage of a chemical through biological membranes. A compound with a large volume may have difficulty passing through biological membranes and thus may not exhibit toxicity as it is unable to reach its toxicity receptor. In addition, the binding site of a receptor is usually a cavity that can accommodate compounds of a specific range of sizes and shapes.
Currently, with the exception of C4.5 decision tree, which is able to generate decision rules, the other three classification methods are unable to determine the relative importance of individual LSER descriptor. This limits the scope of the application of SVM classification systems in drug design to tasks such as high-throughput screening. With further improvement of SVM algorithm such as the introduction of weighting function to the descriptors (Chapelle et al., 2002), specific rules of the descriptors may be derived which in turn extend the application range of SVM classification systems.
As with all other in silico predictions of toxicological properties of chemical compounds, prediction of TdP-causing potential by SVM should be assessed together with pharmacokinetic and pharmacodynamic properties of the chemical compounds in order to determine their clinical significance. This is because a potential TdP-causing drug is not the sole factor in precipitating TdP in a patient. Variability in drug concentrations, drug/drug interactions, and individual patients susceptibility are some of the numerous factors that affect the occurrence of TdP in patients. Thus a positive TdP-causing risk of a drug-like molecule may not preclude its use in the clinical setting (Malik and Camm, 2001). For example, both halofantrine and terfenadine can potentially cause TdP. However, halofantrine is still in use whereas terfenadine has been withdrawn from the U.S. market as halofantrine is useful for resistant malaria treatment but for terfenadine, there are other safer alternatives, like fexofenadine, available (Malik and Camm, 2001
). Despite the limitations of in silico prediction of TdP, it may be used as part of the overall risk-benefit analysis of investigative drugs to evaluate their usefulness in the clinical setting.
As a statistical learning method for the prediction of systems with multiple mechanisms, SVM is potentially useful for facilitating the prediction of TdP causing risk of investigative agents. The availability of more extensive information about various ADR-causing agents and associated mechanisms and more comprehensive descriptors for toxicity prediction will enable the development of SVM and other computational methods into useful tools for facilitating the prediction of different types of ADRs in the early stage of drug development.
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NOTES |
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1 To whom correspondence should be addressed. Fax: 65-6774-6756. E-mail: yzchen{at}cz3.nus.edu.sg
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