Consensus kNN QSAR: A Versatile Method for Predicting the

Nov 3, 2004 - ... for screening the activities of untested molecules, producing valuable information on which compounds should be tested more thorough...
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Environ. Sci. Technol. 2004, 38, 6724-6729

Consensus kNN QSAR: A Versatile Method for Predicting the Estrogenic Activity of Organic Compounds In Silico. A Comparative Study with Five Estrogen Receptors and a Large, Diverse Set of Ligands A R J A H . A S I K A I N E N , * ,† JUHANI RUUSKANEN,† AND KARI A. TUPPURAINEN‡ Department of Environmental Sciences and Department of Chemistry, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland

Quantitative structure-activity relationships (QSARs) have proved increasingly useful for predicting the biological activities of molecules (e.g., their binding affinities to different receptors) and can be used in environmental chemistry as a preliminary tool for screening the activities of untested molecules, producing valuable information on which compounds should be tested more thoroughly with experimental affinity assays or in animals. The predictive ability of the consensus kNN QSAR method is corroborated here using a diverse set of 245 compounds, which have been assayed for their relative binding affinities to the estrogen receptor of four species: human (ERR and ERβ), calf, mouse, and rat. Leave-one-out cross-validation (LOO-CV) and y-randomization tests were applied to the QSAR models for internal validation, and separate training and test sets were used for external validation. The internal predictive abilities of the consensus models for all five data sets were convincing, with cross-validated correlation coefficients (LOO-CV q2 values) varying from 0.69 (human ERβ data) to 0.79 (human ERR data). The external predictive abilities were also encouraging, as the predictive r2 scores (pr-r2 values) varied from 0.62 (human ERβ data) to 0.77 (calf and mouse data). The results indicate that consensus kNN QSAR is a feasible method for rapid screening of the estrogenic activity of organic compounds.

Introduction Endocrine-disrupting chemicals (EDCs) have been under comprehensive study in recent years as they disturb the normal functions of the nuclear receptors (NRs), which transmit the action of steroidal hormones such as estrogen (estradiol-17β). Among the NRs, the estrogen receptor (ER) is distinctively promiscuous (i.e., it binds a plethora of ligands with some degree of affinity). At least two isoforms of ER have been identified, ERR and ERβ, showing different responses to the same chemicals (1). A large number of synthetic and natural compounds with a broad diversity of * Corresponding author phone: +358-17-162893; fax: +358-17163191; e-mail: [email protected]. † Department of Environmental Sciences. ‡ Department of Chemistry. 6724

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chemical structures, commonly known as xenoestrogens, have been found to mimic estrogen by binding to the ER as either an agonist or antagonist (2-4). The main risks posed by xenoestrogens for humans and wildlife are due to problems they may cause by disturbing reproductive processes and promoting the growth of cancer cells (5-7). There are several experimental methods available for screening the estrogenic activity of chemicals (e.g., in vivo and in vitro assay tests), and these have been carried out using receptors and other biological materials of human, rat, mouse, and calf origin at least (8-14). As it is not possible (for financial reasons alone) to test experimentally all chemicals that may possess estrogenic activity, the harmful estrogenic effects of a chemical for humans and wildlife may remain hidden. This has meant that the development of computational methods as an alternative tool for predicting the estrogenic activity of chemicals has been a subject of intensive study. Among these computational methods, quantitative structure-activity relationships (QSARs) have been widely used on xenoestrogens [for recent comprehensive reviews, see Fang et al. (15) and Schmieder et al. (16)]. The basic idea behind QSARs is to find mathematical relationships between descriptors that reflect the structure and physicochemical properties of molecules and their relative binding affinities (RBAs). These relationships can then be used to predict the activities of untested chemicals. The physical background of the QSAR methods applied to xenoestrogens so far such as CoMFA (17), SOMFA (18), CoSA (18), kNN (19), COREPA (20), HQSAR (21), and CODESSA (21) is highly diverse, and thus the models provide different perspectives on the interactions between the estrogen receptor and its ligands. In general terms, QSARs can be interpreted as quantifications of the similarity-analogy principle of physical organic chemistry: like substances react or behave similarly and similar changes in structure produce similar changes in reactivity and other chemical properties. As far as mathematical implementations of this general principle are concerned, the k-nearest-neighbors (kNN) method should be particularly well-suited for QSAR studies, as it is robust, conceptually simple, and easy to implement. In our preliminary study, we tested the kNN method on a data set of 142 compounds with RBA values measured for rat uterine cytosol (22). We also applied a method called consensus kNN in which the basic idea is to use the average of several kNN models as a final model in an attempt to produce more robust and reliable predictions. The aim of the work reported here was to test the performance of this latter consensus kNN method with five subsets of compounds and to evaluate its applicability as a fast screening method for large data sets.

Materials and Methods Biological Data. The activities (i.e., log RBA values) of the molecules were extracted from the National Center for Toxicological Research (NCTR) endocrine disruptor knowledge base (EDKB, a stand-alone version is freely available on the Internet at http://edkb.fda.gov/databasedoor.html; accessed February 2003), concentrating on a set of 245 compounds with RBA values available from tests conducted with four species. The set was divided into five subsets according to the estrogen receptor used, resulting in the subsets of calf (53 compounds), human ERR (61 compounds), human ERβ (61 compounds), mouse (68 compounds), and rat (130 compounds) data (i.e., some compounds were present in several of the subsets). 10.1021/es049665h CCC: $27.50

 2004 American Chemical Society Published on Web 11/03/2004

The log RBA values of the compounds varied from -2.0 to 2.0 in the calf data, from -2.0 to 2.48 in the human ERR data, from -2.0 to 2.61 in the human ERβ data, from -3.36 to 2.94 in the mouse data, and from -4.5 to 2.6 in the rat data. The variability of the range of activity values obtained for the assays is in general typical of xenoestrogens. If several RBA values were available for the same compound and the same receptor in the EDKB, the value used here was selected so that the same experimental source was preferred for each receptor as far as possible. The RBA values were uniformly distributed in all the data sets except for the calf data, in which only 13 out of the 53 compounds had values below zero, and it was also in this subset that the variation in the RBA values was smallest. The structural variation among the compounds was similarly smaller in the calf data than in the other data sets, which may detrimentally influence the statistical parameters of the models derived for this species. kNN QSAR. The kNN QSAR method has been described in detail by Zheng and Tropsha (19). The basic idea is to predict a compound’s biological activity by calculating the weighted average of the activities of the k most similar compounds. The compounds are represented by numerical quantities (descriptors), and similarity is defined by calculating the Euclidean distances between the descriptor vectors. The statistical validity of the models for internal prediction was assessed by the leave-one-out cross-validation (LOO-CV) method. This proceeds by omitting one compound from the input data, deriving the kNN QSAR model, and predicting the RBA value of the omitted compound, after which the cycle continues until all the activities have been predicted once. The predictive ability of the model was assessed using the cross-validated standard error of prediction (Spress). Alternatively, a cross-validated correlation coefficient (q2) can be used. The optimum number of neighbors (kopt) was chosen to give the smallest Spress value. For external test sets, the conventional squared correlation coefficient (r2ex), standard error of prediction (SDEP) and predictive r2 scores (pr-r2) were calculated. Molecular Modeling and Descriptors. The three-dimensional structures of the compounds were modeled with the HYPERCHEM program package (Hypercube, Inc.) and minimized with AM1 Hamiltonian (23) using the AMPAC program package (QCPE No. 506, version 2.11). The molecular descriptors were calculated with the DRAGON program package (version 3.0) (24), which provides 1497 molecular descriptors (25). However, after exclusion of those with zero or constant values, the numbers remaining were 1211 for the calf data, 1244 for the human ERR data, 1244 for the human ERβ data, 1242 for the mouse data, and 1261 for the rat data. The correlations between the descriptors and RBA values were calculated to test an alternative approach to the selection of variable (see Results). Selection of Variables. The variables were selected by simulated annealing (SA), as described in detail elsewhere (19, 26). The main steps were as follows: (i) select a random subset from the whole descriptor pool and derive an initial model; (ii) calculate the predictive ability of the model (Spress value); (iii) change a small number of the descriptors randomly and derive a new model; (iv) calculate the Spress value for the new model; (v) accept the new model (a) always, if it gives a better Spress value or (b) it has a probability satisfying the Metropolis Monte Carlo criterion (p < exp(-(Spress_old Spress_new)/T), where T is temperature [i.e., the probability to accept an “energetically” unfavorable model decreases (rapidly) with decreasing temperature]). Steps i-v are repeated until the convergence criteria of the SA algorithm are met. The initial temperature used was 250 K, and it was lowered by 10% if a new model was accepted or if a better model was not found by generating 100 new models. The calculation was terminated when the temperature is de-

TABLE 1. Statistical Parameters for Internal Predictions for Consensus kNN Models of All the Data Setsa data set

Spress

q2

r2

human ERR mouse rat calf human ERβ

0.65 0.79 0.89 0.45 0.74

0.79 0.77 0.75 0.73 0.69

0.89 0.88 0.87 0.86 0.83

a S press ) x(PRESS/(n-2)) is the cross-validated standard error of prediction; PRESS ) ∑(yobs - ypred)2 is the residual sum of squares; q2 ) 1 - (PRESS/∑(yobs - ymean)2) is the cross-validated correlation coefficient; and r2 is the conventional correlation coefficient.

creased below 1 K. It should be emphasized that SA is a stochastic process that produces a plethora of individual kNN models with almost equal statistical properties but with different variables. All the calculations were performed with the MATLAB program package (MathWorks, Inc., version 5.3) in a PC environment using in-house scripts written by the authors. To achieve a high computational speed, the LIGHTSPEED toolbox (27), a collection of highly optimized functions for efficient MATLAB programming, was employed. All variables were autoscaled before statistical modeling.

Results Model Building and Internal Prediction. Different models were constructed to achieve the best predictive ability, and different approaches were adopted to test the reliability of the results. First, since it has been found that the kNN method may be sensitive to the number of descriptors (19), we derived models with different dimensionalities, one of which included all the variables. However, as in our previous study (22), it appeared that the number of variables did not have any significant effect on the predictive abilities of the models, and the number of variables was therefore set at 250, of which 11 were changed in every step of the simulated annealing. For every five data subsets, 50 individual models were built, from which the consensus kNN models were constructed. The statistical parameters representing the predictive ability of the consensus models are given in Table 1. The internal predictive abilities of all the models are broadly speaking good. The low Spress value for the calf data is a consequence of the small variation in the original RBA values, while conversely, the rather large Spress value for the rat data is the results of greater variation in the RBA values. Second, we compared the consensus kNN results with those of some previous QSAR studies that employed the same data sets. The calf data set had been employed earlier by Tong et al. in their CoMFA and CODESSA studies (28), and the rat data set was employed by Shi et al. in a CoMFA study (29). Furthermore, a part of the mouse data set (58 compounds) had been employed by Waller in CoMFA, FRED/ SKEYS, and HQSAR (30) studies and by Zheng and Tropsha in a kNN study (19). The results obtained here with the consensus kNN method are presented in Table 2 together with the previous results. Interestingly, this method seems to outperform all the others as far as the cross-validated correlation coefficient is concerned. Third, the reliability of the models was assessed using the y-randomization test (i.e., the RBA values were mixed so that the activities were no longer assigned to the right descriptors) to exclude the possibility of chance correlations. It appeared that no random combination yielded PLS statistics even close to the correct one. Usually q2 < 0, and only in very few cases were the q2 values above zero, which proves that the predictive ability of the actual models is real. Fourth, a different approach to the selection of variables was tested in which only those variables that correlated VOL. 38, NO. 24, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Comparison of Statistical Performance between Consensus kNN Method (in bold) and Other QSAR Methods for Selected Data Setsa q2 data set calf rat mouse

other methods 0.54b,

r2 consensus kNN

0.61c

0.73 0.75 0.84

0.71d 0.59e, 0.70f, 0.58g, 0.77h

other methods 0.68b,

0.97c

0.90d 0.88e, 0.78f, 0.81g, -h

consensus kNN

N

0.86 0.87 0.92

53 130 58

a q2 is the cross-validated correlation coefficient (for definition, see Table 1); r2 is the conventional correlation coefficient; and N is the number of compounds. The previous studies were as follows: bCoMFA by Tong et al. (28); cCODESSA by Tong et al. (28); dCoMFA (with an indicator variable added for the presence of phenol groups) by Shi et al. (29); eCoMFA by Waller (30); fFRED/SKEYS by Waller (30); gHQSAR by Waller (30); hkNN by Zheng and Tropsha (19); h-, not reported.

TABLE 3. Sizes of Training and Test Sets and Statistical Parameters for External Consensus Modelsa data set calf mouse human ERR rat human ERβ a

training/ testb 35/18 48/20 39/22 84/46 39/22

SDEP

pr-r2

r2

excludedc

0.50 (0.42) 0.84 (-) 0.66 (0.68) 0.89 (0.79) 0.78 (0.78)

0.77 (0.77) 0.77 (-) 0.76 (0.74) 0.73 (0.79) 0.62 (0.64)

0.91 (0.90) 0.89 (-) 0.88 (0.87) 0.88 (0.90) 0.79 (0.80)

151 73 19,26,39,51,73 70,72

Corresponding parameters for the models with some compounds excluded from the test set are presented in parentheses. SDEP )

x(PRESS/n) is the standard error of prediction, n is the number of test set compounds, pr-r2 ) 1 - (PRESS/∑(yobs - ymean)2) is the predictive r2

score (yobs refers to the test set compounds, and ymean refers to the mean activity of the training set compounds), r2 is the conventional correlation coefficient, (-) no model constructed. b Number of compounds in the training/test sets. c Numbers of the compounds excluded from the test set on the basis of the applicability domain tests (numbers correspond to the numbers in the Figure SI 1 and Table SI 1 in Supporting Information).

strongly with the RBA values, having either r > 0.5 or r < -0.5, were selected for the variable pool. This reduced the number of descriptors considerably, to 31 for the calf data, 185 for the human ERR data, 60 for the human ERβ data, 205 for the mouse data, and 176 for the rat data. kNN models were then derived using the reduced variable pools in their entirety and also by selecting some subsets by simulated annealing. In general, a slight improvement in the internal predictions was achieved with the models derived by the latter approach compared with the models presented in Table 1, although this was not the case with the rat and calf data. The number of variables obviously became too small for the calf data to be able to provide a highly predictive model, but the reason for the poorer performance with the rat data is somewhat unclear. It should be emphasized in this context, however, that there are no direct correlations between the descriptors and the activities in the kNN method, contrasting sharply with many other QSAR methods. This may explain why the variable reduction method based on the correlations does not necessarily lead to a better performance (see Discussion). External Prediction. The external predictive ability of a QSAR model is an important feature, particularly if the model is intended for the prediction of untested compounds. As internal tests do not necessarily guarantee the predictive ability of the models (31), external consensus models were derived for all five data sets. Compounds in the data sets were divided into training and test sets by selecting approximately two-thirds of them for the training set and placing the remaining ones in the test set. The compounds in the training set were selected so that the structural variation among the compounds and the variance in the RBA values were covered properly. The external models were constructed using the same adjustments as with the internal models, including models in which the variable pools were reduced on the basis of the correlations between the variables and RBA values. The applicability domains of the models were assessed using the similarity distance test (32), the details of the procedure adopted here being as described elsewhere (22). The aim of the applicability domain test was to exclude those test set compounds which differed too markedly from 6726

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the training set compoundssa situation that would be likely to lead to unreliable predictions. The numbers of compounds in the training and test sets and the statistical parameters for all the external consensus models are presented in Table 3. The values in parentheses represent external models from which some compounds were excluded on the basis of the applicability domain tests. Plots of calculated versus experimental log RBA values are presented in Figure 1. The external predictive abilities of the consensus kNN models are very encouraging. The predictive abilities of the models for the rat and human ERβ data sets were improved further by excluding some compounds from the test set, as these were judged to be too dissimilar from the compounds of the training set according to the applicability domain tests. On the other hand, the same operation did not have any positive effect on the predictive abilities of the models for the human ERR and calf data sets, possibly because the errors in the predictions of the excluded compounds in the human ERR and calf data sets were actually minimal, despite their obvious dissimilarity relative to the training set compounds (Figure 1). In contrast with the internal tests, reducing the number of variables on the basis of their correlations with the RBA values did not improve the predictive ability of the external consensus models (see Discussion). Predictions across Species. Shi et al. (29) have previously tested the performance of CoMFA for external predictions between RBA values taken from ER assays of different species. The training set consisted of compounds with the RBA values taken from rat ER assays (33, 34) and the two test sets obtained from mouse (35) and human R ER assays (36). Furthermore, the RBA values of the test set compounds were normalized to the rat data set using a correlation equation calculated by means of RBA values that were available for both data sets. The prediction across species was also tested with the consensus kNN method, obtaining the following statistical parameters (the parameters in parentheses were obtained using normalized RBA values for the compounds in the test sets): SDEP ) 1.32 (1.64) and pr-r2 ) 0.60 (0.54) for the mouse data and SDEP ) 0.83 (0.68) and pr-r2 ) 0.68 (0.71) for the human ERR data, respectively. As a whole, the consensus

kNN results were fully comparable to those obtained by Shi et al. with the best CoMFA model (pr-r2 ) 0.71 for the mouse data and pr-r2 ) 0.63 for the human ERR data). However, if QSAR methods are employed for predictions between species, the results should obviously be interpreted with due caution.

Discussion

FIGURE 1. Calculated vs observed log RBA values for the external consensus kNN models (9 represents the compounds that were judged to be too different from the training set compounds).

Taken overall, the performance of the consensus kNN method for the prediction of the estrogenic activities of diverse sets of compounds proved to be excellent. Its computational speed is high, as with a very fast rate for calculating a single kNN model, a consensus kNN model can be derived from 50 individual ones within a reasonable time. The computation times for the data sets varied from 1 to 6 h (using a PC with a 2.4 GHz processor and 1024 MB of memory), being greatly dependent on the number of compounds in the data set. Calculation of the DRAGON descriptors is a quick operation, taking about 1 h for all the data sets combined. The simplicity of the kNN QSAR method is also an important feature, especially when the main purpose is to provide a simple, fast method for screening a large set of compounds rather than to gain a detailed physical understanding of the ligandreceptor interactions. The selection of variables is a potential problem with kNNtype QSAR methods. Although simulated annealing worked properly in this case, some concerns were detected. For example, the difference in the statistical parameters for external prediction with the mouse data set between the poorest (SDEP ) 1.34, pr-r2 ) 0.41 and r2 ) 0.63) and the best individual model (SDEP ) 0.871, pr-r2 ) 0.83 and r2 ) 0.91) was considerable. It should be emphasized that this difference originates solely from the different variable pools. It was demonstrated, however, that consensus kNN could provide a highly predictive external model for the mouse data despite the poor performance of some of the individual models used for its construction. Reducing the size of the variable pool according to the correlations between the RBA values and the variables provided slightly better models for internal predictions but poorer models for external predictions. The number of variables decreased considerably in all the data sets when this was done and became extremely small for the calf data set. Simultaneously, the information content of the variable pool decreased remarkably, resulting in too small discriminating power among the remaining variables to produce reliable, predictive kNN models. This seems to justify large variable pools if used together with simulated annealing as a method for selecting variables. It should be remembered, however, that the lack of direct correlations between descriptors and activities is a distinctive feature of kNN modeling, in which the descriptors are used merely to quantify the similarities between molecules. Thus the kNN method can tolerate a large number of moderate or even poor correlations between activities and variables, provided that their discriminating power is large enough. It seems that it is the discriminating power of the variables rather than their modeling power that makes the (consensus) kNN method work. Outliers can cause problems in constructing QSAR models. There were some compounds present in our data sets that could have been judged to be outliers, but their actual effect on the predictive abilities of the consensus kNN models was minimal. Of course, compounds lying outside the applicability domain of the model have to be taken into account in the external tests, and there were some compounds in our test sets that were shown by the applicability domain tests to be too different from the training set compounds to produce reliable predictions. It appeared, however, that the consensus kNN method could also provide good predictions for these compounds (Figure 1), and thus it can be concluded VOL. 38, NO. 24, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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that the effect of possible outliers and dissimilar compounds may not be so significant for the predictive ability of the consensus kNN method as it evidently is for many other QSAR methods. Finally, it should be emphasized that the performance of the consensus kNN method will probably improve as an increasing number of molecules are tested experimentally, making it more attractive among the QSAR methods. The darker side of the kNN method is that the models are not particularly open to physicochemical interpretation, which may tip the balance in favor of conventional QSAR methods if a detailed description of the ligand-receptor interactions is required. The many obvious advantages of the consensus kNN method (i.e., that it is nonlinear, the descriptors can be calculated quickly, no alignment of compounds is needed, and the models are robust and simple to construct) make it a very promising alternative and supplement to more sophisticated but complex QSAR methods.

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Acknowledgments The Academy of Finland is gratefully acknowledged for funding this research (Grant 200978).

Supporting Information Available The structures of the compounds with their log RBA values and the numbers of training set compounds for external models. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review March 3, 2004. Revised manuscript received September 6, 2004. Accepted September 13, 2004. ES049665H

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