1930 Angelo Antonio D’Archivio1 Maria Anna Maggi2 Fabrizio Ruggieri1 1 Dipartimento
di Scienze Fisiche e Chimiche, Universita` degli Studi dell’Aquila, L’Aquila, Italy 2 Hortus Novus, L’Aquila, Italy Received April 3, 2014 Revised April 29, 2014 Accepted May 5, 2014
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Research Article
Prediction of the retention of s-triazines in reversed-phase high-performance liquid chromatography under linear gradient-elution conditions In this paper, a multilayer artificial neural network is used to model simultaneously the effect of solute structure and eluent concentration profile on the retention of s-triazines in reversed-phase high-performance liquid chromatography under linear gradient elution. The retention data of 24 triazines, including common herbicides and their metabolites, are collected under 13 different elution modes, covering the following experimental domain: starting acetonitrile volume fraction ranging between 40 and 60% and gradient slope ranging between 0 and 1% acetonitrile/min. The gradient parameters together with five selected molecular descriptors, identified by quantitative structure-retention relationship modelling applied to individual separation conditions, are the network inputs. Predictive performance of this model is evaluated on six external triazines and four unseen separation conditions. For comparison, retention of triazines is modelled by both quantitative structure–retention relationships and response surface methodology, which describe separately the effect of molecular structure and gradient parameters on the retention. Although applied to a wider variable domain, the network provides a performance comparable to that of the above “local” models and retention times of triazines are modelled with accuracy generally better than 7%. Keywords: Gradient elution / Molecular descriptors / Multivariate modelling / Reversed-phase high-performance liquid chromatography / Triazines DOI 10.1002/jssc.201400346
Additional supporting information may be found in the online version of this article at the publisher’s web-site
1 Introduction Several models [1–7] have been proposed to predict retention in RP-HPLC. Quantitative structure–retention relationships (QSRRs) [8, 9], in particular, relate the retention to descriptors of the solute chemical structure and, once established for a given separation system, can be used to deduce the chromatographic behaviour of unseen analytes. Response surface methodology (RSM) is also potentially useful in chromatographic optimisation [2, 10–12]. This method defines a mulCorrespondence: Professor Angelo Antonio D’Archivio, Dipartimento di Scienze Fisiche e Chimiche, Universita` degli Studi dell’Aquila, Via Vetoio, 67100 Coppito, L’Aquila, Italy E-mail: [email protected] Fax: +39-0862-433033.
Abbreviations: ANN, artificial neural network; GA, genetic algorithm; QSERR, quantitative structure/eluent–retention relationship; QSRR, quantitative structure-retention relationship; PCA, principal component analysis; PC, principal component; RSM, response surface methodology; MLR, multilinear regression; SEC, standard error in calibration; SEP, standard error in prediction C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
tivariable response surface y = f(x1 , x2 , . . . ,xn ) describing the effect of various factors xi on a parameter y of chromatographic interest. The chromatographic resolution of a target mixture is the most common response, while the factors are various instrumental variables, such as mobile phase composition and pH, gradient profile, eluent flux and temperature [13–18]. Application domains of conventional QSRR and RSM methods can be considered complementary, as the first approach describes the effect of molecular structure on the retention under fixed separation conditions, while the latter method describes the influence of parameters related with the separation mode for a target analyte or mixture. Various comprehensive models in terms of both structural descriptors of solutes and descriptors of column and/or eluent have been developed [4–7]. A basic multivariable predictive approach contemplates, together with variability related with the solute structure, the effect of composition of binary hydro-organic eluents, which is the operational variable usually optimised in isocratic RP-HPLC analyses. Generation of mixed models in terms of molecular descriptors and eluent composition, hereafter indicated as quantitative structure/eluent–retention relationships (QSERRs), even
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under isocratic elution is more difficult than conventional QSRR modelling, because of the increased complexity of the searched relationship due to non-linear effects and interactions between the eluent and solute descriptors. It has been shown that artificial neural network (ANN) regression, which does not require prior definition of the equation relating the retention to the independent variables, can be helpful to overcome the above problems [19–22]. A great effort has been devoted to predict RP-HPLC retention in gradient elution mode [21, 23–29], which is preferred to isocratic elution for the separation of analytes with very different polarity and/or mass. However, only a few approaches [21, 23–25] explicitly consider as independent variables the descriptors of the molecular structure together with descriptors of the gradient profile, which is an essential requisite if retention of new solutes under external elution conditions has to be predicted. In this paper, we simultaneously model by ANN the effects of molecular structure and mobile phase characteristics on RP-HPLC retention of s-triazines under linear gradient-elution conditions. Predictive performance of the built QSERR is compared with results of QSRR modelling for representative (local) conditions within the calibration domain and RSM relating the retention of each triazine to the starting eluent composition and the slope of the linear gradient.
2 Materials and methods 2.1 Chemicals and solvents Triazine standards (purity better than 99%) were obtained from Labor Dr. Ehrenstorfer-Schafers (Augsburg, Germany). HPLC-grade acetonitrile (Carlo Erba Reagenti, Milano, Italy), double-deionised water, obtained from a Milli-Q filtration/purification system (Millipore, Bedford, MA, USA), sodium acetate and acetic acid (Carlo Erba Reagenti) of analytical reagent grade were used for the preparation of mobile phases.
2.2 Instrumentation and experimental conditions The chromatographic system used in this work is composed of two Model 510 pumps (Waters, Milford, MA, USA), a Pump Control Module II (Waters), a Model 7725i sample injector (Rheodyne, Cotati, CA, USA) equipped with a 20 L loop and a Model 996 diode array detector (Waters). Chromatographic data management was automated using a Millennium32 data acquisition system (Waters). All the analyses were performed on the analytical column Spherisorb ODS2 (Waters), 250 mm length by 4.6 mm i.d. and 5 m particle size, connected to a 4.6 × 10 mm ODS2 Guard Cartridge (Waters) with 5 m particle size. The mobile phases were mixtures of acetonitrile and aqueous acetate buffer at pH 6 and concentration 10 mM, degassed by bubbling helium C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Table 1. List of the investigated s-triazines
Triazine (abbreviation)
R1
R2
R3
R4
Cyanazine (CYA) Simazine (SMZ) Propazine (PPZ) Trietazine (TTZ) Terbuthylazine (TBA) Sebuthylazine (SBA) Atrazine (ATZ) Desethylterbuthylazine (DTA) Desethylatrazine (DEA) Desisopropylatrazine (DIA) Desethyldesisopropylatrazine (DEI) Prometon (PMT) Secbumeton (SCB) Terbumeton (TRB) Atraton (ATT) Desisopropylatraton (DAT) Desethylterbumeton (DTB) Prometryn (PMN) Methoprotryne (MTP) Desmetryn (DMT) Terbutryn (TBN) Dimethametryn (DMN) Ametryn (AMN) Simetryn (SMN)
Cl Cl Cl Cl Cl Cl Cl Cl
CH2 CH3 CH2 CH3 CH(CH3 )2 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3 C(CH3 )3
H H H CH2 CH3 H H H H
C(CH3 )2 CN CH2 CH3 CH(CH3 )2 CH2 CH3 C(CH3 )3 CHCH3 CH2 CH3 CH(CH3 )2 H
Cl Cl
CH(CH3 )2 CH2 CH3
H H
H H
Cl
H
H
H
OCH3 OCH3 OCH3 OCH3 OCH3
CH(CH3 )2 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3
H H H H H
CH(CH3 )2 CHCH3 CH2 CH3 C(CH3 )3 CH(CH3 )2 H
OCH3
C(CH3 )3
H
H
SCH3 SCH3 SCH3 SCH3 SCH3 SCH3 SCH3
CH(CH3 )2 CH(CH3 )2 CH3 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3
H H H H H H H
CH(CH3 )2 (CH2 )3 OCH3 CH(CH3 )2 C(CH3 )3 CHCH3 CH(CH3 )2 CH(CH3 )2 CH2 CH3
and delivered at a flow rate of 1.0 mL/min. Retention time (tr ) values of s-triazines were collected by injecting 5 mg/L acetonitrile solutions. The wavelength selected for detection was 240 nm for all compounds.
2.3 Data set Table 1 displays the 24 symmetric triazines (s-triazines) investigated here, including common herbicides and some metabolites. Figure 1 displays the 13 separation conditions, defined by the starting composition of the acetonitrile/water www.jss-journal.com
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Figure 1. Experimental design used to collect retention data of s-triazines and partition of separation conditions between calibration and prediction.
mixture (ϕ0 ) and the slope of linear variation of acetonitrile content (K); three cases (K = 0 and ϕ0 = 40, 50 or 60) correspond to isocratic elution modes. The observed log tr values collected under the above conditions are listed in Supporting Information Table S1. The triazines and the experimental conditions are partitioned in two groups, the first required in calibration and the latter to test model prediction. In particular, six triazines (AMN, ATT, DEA, SMZ, SMN and TBA), representing the three subclasses, chloro-, methoxy- and methylthiotriazines, and the variation in the alkylation degree and kind of substituents of the two amino groups were assigned to the prediction (or test) set. As to the partition of separation conditions, calibration data samples were identified according to a three-level experimental design (Fig. 1), while the remaining four separation conditions surrounding the centre of the domain are considered for prediction.
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the 473 molecular descriptors, a small subset encoding the effect of triazine structure on their retention. After preliminary analyses, we decided to adopt log tr as the MLR response, because the selected models were better than those providing the unscaled tr value. The GA-MLR method [32, 33] is based on the evolution of a starting random population of models. Each model is represented by a chromosome, namely a binary vector in which each position (gene) encodes the presence or absence of a descriptor by 1 or 0, respectively. The starting population evolves through mutation and crossover, until an optimal or near optimal model is identified. The chance for a given chromosome of being preserved in the next generation is associated to the predictive performance of the related model, which is quantified by the determination coefficient in leave-one-out cross-validation (Q2 loo-cv ). Q2 loo-cv is defined as (SSY-PRESS)/SSY, where PRESS is the predictive residual error sum of squares and SSY is the sum of the squared deviations of the dependent variables from their mean. In this work, GA-MLR analysis was performed using the program package V-PARVUS 2010 [34]. For each separation condition, variable selection was carried out on the 18 triazines of the calibration set and predictive performance of the built QSRR model was tested on the six excluded molecules.
2.6 Response surface methodology (RSM) RSM was separately applied to each triazine to relate the retention with the gradient characteristics, according to the following general quadratic relationship: log tr = a + b0 + c K + d20 + e K 2 + f 0 K .
(1)
Starting geometries of the triazines were generated by means of the MacroModel 7.1 molecular modelling program package [30]. Using the MM2 force-field, a conformational search was carried out to identify the global energy minimum for each molecule. Software Dragon [31] was used to compute the molecular descriptors from the optimised geometries. The quantities with little variance were eliminated and only one descriptor was retained among groups of highly correlated ones (r > 0.95). 473 molecular descriptors belonging to various classes remained after this procedure.
The RSM models were established using the calibration cases defined by a three-level experimental design (Fig. 1) and applied to the four external conditions. Initially, all the parameters of equation (1) were considered; but if non-significant terms assuming a 95% confidence probability were detected, the data were successively refitted without including these quantities in the regression. The linear solvent strength model, developed by Dolan and Snyder [35], permits to predict the retention time in linear gradient elution when the logarithm of the isocratic retention factor is linearly related to the volume fraction of organic modifier in the binary eluent. In the experimental conditions analysed here, such condition holds only for some triazines. Therefore, the model (1), although disconnected from the gradient elution theory, seems more convenient because can be applied to both regular and irregular solutes.
2.5 QSRR modelling under fixed, isocratic or gradient, elution conditions
2.7 Development of a quantitative structure/eluent–retention relationship (QSERR)
A QSRR model was separately established for each separation condition by multilinear regression (MLR) coupled with genetic algorithm (GA) variable selection to extract, within
A multilayer ANN [32,36,37] was used to build the QSERR describing the simultaneous effect of triazine molecular structure and separation conditions on the retention. It consists
2.4 Molecular descriptors
C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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of one input layer which collects the independent variables (the triazine structure and eluent descriptors), one output neuron providing the network response (the log tr value) and one hidden layer with an adjustable number of neurons fully connected to both input and output neurons. The network was trained by a quasi-Newton method [38] that incorporates second-order information about the shape of error surface and exhibits fast convergence and a great probability of avoiding local minima. The training data samples (139) were extracted from the 162 available calibration data (corresponding to 18 triazines and nine elution modes, designed previously) by the Kennard–Stone algorithm [39] applied to the space of the auto-scaled variables, while the 23 unselected cases were put in a validation set. Minimum of validation error was the adopted criterion for stopping the network learning and selecting among alternative trained networks the one with the expected best generalisation capability. The real prediction capability of the final QSERR model was evaluated on the prediction (or test) set consisting of 96 data samples. These correspond to all the 24 triazines (six unknown and 18 already used in ANN calibration) analysed at the four external separation conditions. ANN analysis was carried out using software OpenNN [40].
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one could be found if GA-MLR selection was repeated several times for each eluent. Moreover, a QSRR established for a given separation condition in general was seen to work well even at the other conditions. This suggests that the different sets are substantially equivalent, since only strong correlations (r > 0.95) were removed in previous pre-selection, and some molecular descriptors duplicate chemical information encoded by others. 3.2 Results of RSM The RSM models developed for the 24 triazines exhibit an acceptable descriptive and a predictive performance (Supporting Information Table S4), as demonstrated by R2 values greater than 0.99 and Q2 generally greater than 0.93. In the case of DEI, which is the least retained triazine by the C18 column, although the prediction errors are relatively small and comparable to those of the other solutes, a low Q2 value (0.395) is observed. This is the consequence of the substantial constancy of the log tr values of the prediction data samples, which makes the total sum of squares comparable to the predictive error sum of squares. 3.3 QSERR modelling
3 Results and discussion 3.1 QSRR modelling for the various separation conditions A five-dimensional QSRR model was established for each isocratic- and gradient-elution mode. The model complexity was established after a preliminary GA-MLR exploration carried out to evaluate the trend of the Q2 loo-cv value with respect to the number of included descriptors. The QSRRs are presented in Supporting Information Table S2. The coefficient of determination in calibration, R2 , the adjusted R2 (R2 adj ), the coefficient of determination in prediction (Q2 ) and standard errors in calibration and prediction (SEC and SEP, respectively) are the conventional statistical indices adopted to evaluate the descriptive and predictive quality of the various models. Q2 , analogously to Q2 loo-cv , is related to the predictive residual error sum of squares for the external data samples. Descriptive performance of the various QSRRs was quite good, as witnessed by R2 values generally greater than 0.994. As to their predictive ability, only a slight deterioration is observed (Q2 ranges between 0.928 and 0.990) with the exception of the model established for ϕ0 = 60 and K = 0 that exhibits a moderate worsening in prediction (Q2 = 0.907) with respect to the QSRR descriptive performance. Supporting Information Table S3 displays the meaning of the selected molecular descriptors. With the exception of the Ghose-Crippen octanol-water partition coefficient (MLOGP), that is included in all the QSRR models, different descriptors are generally selected for each separation condition. However, we observed that a number of alternative models with a comparable performance to that of the best C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
To describe the combined effect of triazine structure and separation conditions on the retention, the molecular descriptors and the parameters defining the elution mode (ϕ0 and K) were simultaneously considered as the input variables of an ANN giving log tr as response. Both input and output variables were subjected to range scaling between 0 and 1, while the starting network weights were randomly generated between –0.1 and 0.1. To represent the triazine structure, an informative subset of molecular descriptors was extracted within the group of variables identified by QSRR modelling for the various eluents (Supporting Information Table S3). Preliminarily, we considered all these molecular descriptors together as ANN inputs. Successively, to simplify the molecular descriptor set, we carried out a sensitivity analysis based on the method of weight zeroing proposed by Nord and Jacobsson [41]. According to this approach, the importance of a given input variable to define the ANN response is related to the deterioration of the network performance when the effect of that variable is removed by zeroing the corresponding weights. After the relative influence of each starting input is established, the less important one is removed and the network is re-optimised. This procedure is repeated until elimination of a further input produces a worsening of the ANN validation performance. To optimise the starting and reduced networks, the validation error was minimised as a function of the number of hidden neurons, the kind of activation function (logistic or hyperbolic tangent) in the hidden layer and the number of learning epochs. The molecular descriptors finally identified are X0Av, SIC1, Vp, R4u+ and MLOGP. The final network had a 7–12–1 architecture with a hyperbolic tangent activation function operating in the hidden layer and was learned www.jss-journal.com
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Figure 2. Agreement between experimental retentions and calculated or predicted responses of the QSERR model.
for 80 epochs. To be sure that the obtained model was not too optimistic, namely did not result from a fortunate combination of starting weights, the network was retrained 100 times and the responses were finally averaged. The R2 (or Q2 ) and SEC (or SEP) values of the final ANN model are respectively 0.9982 and 0.012 for the training set, 0.9970 and 0.017 for the validation set, and 0.9945 and 0.018 for the test set. The agreement between the experimental retentions and the calculated or predicted ANN responses are displayed in Fig. 2, while Supporting Information Fig. S1 shows the error trend. This figure reveals a random distribution of both computed and predicted residuals around zero and shows errors falling within a ±0.03 log tr range for most of the data points. This implies that tr values can be modelled with accuracy generally better than 7%. The few residuals outside this range are not anyway excessively high and do not overcome 13% in the tr scale.
3.4 Comparison of the various models The calculated or predicted responses provided by the three alternative approaches investigated in this work are compared with the experimental log tr values in Supporting Information Table S1, while Fig. 3 shows a comparison of the residual trends for the 24 triazines. It should be reminded that predictive performance of QSRRs and RSM models is evaluated on external triazines and external eluents, respectively, while generalisation of QSERR model is tested on both known and unknown solutes analysed at unknown separation conditions. To simplify the graphical representation, training and validation errors of the QSERR model are not distinguished in Fig. 3, because the validation data, although did not contribute to the ANN weight update, were involved in the network optimisation. For this reason, we assimilate the validation data to the training set rather than to the prediction set. Figure 3 confirms a relatively good performance of all the three predictive approaches that provide computed and predicted errors generally within a ±0.03 log tr range (±7% for the unscaled tr ) with a relatively small number of exceptions. C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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RSM computed or predicted residuals of all triazines are randomly distributed around zero and slightly wider distributions are observed in the case of PMN, TBA, TBN and TBZ. By contrast, QSRR modelling produces a moderate overestimation or underestimation of all or most of the retentions of some triazines (PPZ, SMZ, SMN, and TBA). This is diagnostic of a less accurate description of the structure for these solutes. Such small inaccuracy is also incorporated within the QSERR model, because retention of the same molecules, in addition to that of AMN, is overestimated or underestimated for all the external separation conditions. However, these systematic effects result in relatively small predictive errors, comparable to those of local QSRR modelling and to those associated to the imprecision of RSM for some triazines. It is known that quality and predictive power of conventional QSRR modelling, which is the basic structure-related approach to retention prediction, depends on several factors, such as the explanatory ability of the selected molecular descriptors, the structural similarity/dissimilarity of the investigated solutes, and the regression algorithm [8, 9]. Therefore, a comparative evaluation of the QSRRs established for the same target solutes and within the same experimental domain seems a reasonable preliminary test to check reliability of the QSERR model. It must be noted that a different QSRR model was built here for each experimental condition by variable selection applied to a large number of molecular descriptors of different kinds. Under these conditions, QSRR modelling is quite accurate. The descriptive/predictive quality of QSRRs is substantially preserved in the QSERR model, although chemical information carried out by the validation data samples, required to optimise the network, did not contribute in fact to the optimisation of the ANN weights. Moreover, while a specific subset of molecular descriptors has been selected to maximise QSRR quality, a small portion of chemical information is probably lost in successive selection of the ANN inputs. In summary, despite the QSRRs have been established under more favourable calibration conditions, the QSERR model is able to provide a comparable predictive performance. Previously, Kaliszan and co-workers [23, 24] attempted to predict retention in linear gradient elution by combining the linear solvent strength model with a QSRR model based on three structural descriptors of computational origin, the total dipole moment, the electron excess charge of the most negatively charged atom and the water-accessible molecular surface area. This method permitted the prediction of the retention behaviour of new analytes only approximately. Predictive performance was improved in a successive work [42], where the logarithm of octanol/water partition coefficient calculated from the structural formula by three different commercially available softwares was adopted as molecular descriptor. The best results were obtained using the ACD (Advanced Chemistry Development, Toronto, Canada) program, but quality of retention prediction was still moderate, the mean error in the retention time being 6.4%. Fatemi et al. [21] combined the solvatochromic descriptors with the gradient time and the starting and final acetonitrile content in the binary www.jss-journal.com
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Figure 3. Comparison of calculated and predicted residuals of the various models.
mobile phase. The retention time of 20 benzene derivatives under linear gradient elution were modelled both by MLR and ANN. The ANN-based model gave better results than the MLR counterpart, but its quality was poorer as compared with performance of the QSRRs established for individual gradients. The mean prediction error in the retention time, evaluated on external data samples, was 12%. The model here generated for the triazines exhibits a better predictive ability than the above QSRR-based approaches, which proves the reliability of the adopted strategy and the good explanatory capability of the selected variables.
3.5 Interpretation of the molecular descriptors of the QSERR model To attempt an interpretation of the structural effects governing retention of s-triazines, we focus our attention on the molecular descriptors of the QSERR model (X0Av, SIC1, Vp, R4u+ and MLOGP). Among the selected variables, MLOGP is the computed value of the logarithm of the partition coefficient between n-octanol and water, which is a well-known hydrophobicity index, but the physical meaning of the other four descriptors is not immediately clear. To facilitate the qualitative interpretation of the structure–retention relationship governing the RP-HPLC behaviour of triazines we performed a principal component analysis (PCA) [43] on the space of the above descriptors and log tr in the centre of the experimental domain (ϕ0 = 50 and K = 0.5%/min), after variable autoscaling. The PCA results are presented in Fig. 4 showing the loadings and scores projected on the plane spanned by the first two principal components (PC1 and PC2, accounting for about 92% of total variance). It can be observed that PC1 substantially represents the retention on the C18 column, because log tr is almost collinear with this component. Along this component, the dealkilated triazines, the least retained analytes of the whole group, are clearly separated from the other compounds and triazines are ordered according to the alkylation degree of amino groups. All the five molecular descriptors contribute with appreciable but different loadings to PC1. MLOGP and X0Av, on the other side, describe the dif C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 4. Biplot (score and loadings) obtained from PCA of autoscaled descriptors of the QSERR model and log tr in the centre of the experimental domain. Chloro-, methoxy- and methylthiotriazines are indicated with different character fonts using the abbreviations reported in Table 1.
ferences between the methoxy- and the methylthio-trazines, whereas R4u+ is responsible for the almost complete separation of the chloro-triazines from the group of methoxyand the methylthio-trazines. Separation of the three triazine subclasses occurs along directions which are not parallel to log tr and, therefore, the nature of the R1 group has a minor effect on the retention as compared with the alkylation degree of the amino groups, which has a great influence on the hydrophobicity and the possibility that the triazine can interact by hydrogen bonding with the aqueous mobile phase.
4 Concluding remarks In this paper, we have compared the performance of three approaches to retention prediction of triazines in RP-HPLC under linear gradient elution. Two of these, QSRR and RSM, are conventional methods, and can be considered complementary, as the first contemplates only the effect of molecular structure, while the latter describes only the influence of the gradient profile for a fixed structure. The third approach, www.jss-journal.com
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based on ANN regression, simultaneously accounts for the effect of molecular structure and elution mode on the retention. In spite of greater complexity related to the larger variability domain covered by the model, its predictive performance is substantially comparable to that of the above local models. The authors have declared no conflict of interest.
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[16] Song, J.-Z., Qiao, C.-F., Li, S.-L., Zhou, Y., Hsieh, M.-T., Xu, H.-X., J. Chromatogr. A 2009, 1216, 7007–7012. [17] Sivakumar, T., Manavalan, R., Muralidharan, C., Valliappan, K., J. Sep. Sci. 2007, 30, 3143–3153. ´ N. D., Marici ˇ c, ´ B., Agbaba, D., J. Sep. [18] Nikolic, K., Filijovic, Sci. 2013, 36, 3165–3175. [19] D’Archivio, A. A., Maggi, M. A., Ruggieri, F., Anal. Chim. Acta 2011, 690, 35–46. [20] D’Archivio, A. A., Maggi, M. A., Mazzeo, P., Ruggieri, F., Anal. Chim. Acta 2009, 646, 47–61.
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[39] Kennard, R. W., Stone, L. A., Technometrics 1969, 11, 137–148. [40] Lopez R., OpenNN: Open Neural Networks Library (Version 0.9), 2012. [41] Nord, L. I., Jacobsson S. P., Chemom. Intell. Lab. Syst. 1998, 44, 153–160. [42] Baczek, T., Kaliszan, R., J. Chromatogr. A 2003, 987, ˛ 29–37. ¨ [43] Hardle, W., Simar, L., Applied Multivariate Statistical Analysis. Springer-Verlag, Berlin 2003.
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di Scienze Fisiche e Chimiche, Universita` degli Studi dell’Aquila, L’Aquila, Italy 2 Hortus Novus, L’Aquila, Italy Received April 3, 2014 Revised April 29, 2014 Accepted May 5, 2014
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Research Article
Prediction of the retention of s-triazines in reversed-phase high-performance liquid chromatography under linear gradient-elution conditions In this paper, a multilayer artificial neural network is used to model simultaneously the effect of solute structure and eluent concentration profile on the retention of s-triazines in reversed-phase high-performance liquid chromatography under linear gradient elution. The retention data of 24 triazines, including common herbicides and their metabolites, are collected under 13 different elution modes, covering the following experimental domain: starting acetonitrile volume fraction ranging between 40 and 60% and gradient slope ranging between 0 and 1% acetonitrile/min. The gradient parameters together with five selected molecular descriptors, identified by quantitative structure-retention relationship modelling applied to individual separation conditions, are the network inputs. Predictive performance of this model is evaluated on six external triazines and four unseen separation conditions. For comparison, retention of triazines is modelled by both quantitative structure–retention relationships and response surface methodology, which describe separately the effect of molecular structure and gradient parameters on the retention. Although applied to a wider variable domain, the network provides a performance comparable to that of the above “local” models and retention times of triazines are modelled with accuracy generally better than 7%. Keywords: Gradient elution / Molecular descriptors / Multivariate modelling / Reversed-phase high-performance liquid chromatography / Triazines DOI 10.1002/jssc.201400346
Additional supporting information may be found in the online version of this article at the publisher’s web-site
1 Introduction Several models [1–7] have been proposed to predict retention in RP-HPLC. Quantitative structure–retention relationships (QSRRs) [8, 9], in particular, relate the retention to descriptors of the solute chemical structure and, once established for a given separation system, can be used to deduce the chromatographic behaviour of unseen analytes. Response surface methodology (RSM) is also potentially useful in chromatographic optimisation [2, 10–12]. This method defines a mulCorrespondence: Professor Angelo Antonio D’Archivio, Dipartimento di Scienze Fisiche e Chimiche, Universita` degli Studi dell’Aquila, Via Vetoio, 67100 Coppito, L’Aquila, Italy E-mail: [email protected] Fax: +39-0862-433033.
Abbreviations: ANN, artificial neural network; GA, genetic algorithm; QSERR, quantitative structure/eluent–retention relationship; QSRR, quantitative structure-retention relationship; PCA, principal component analysis; PC, principal component; RSM, response surface methodology; MLR, multilinear regression; SEC, standard error in calibration; SEP, standard error in prediction C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
tivariable response surface y = f(x1 , x2 , . . . ,xn ) describing the effect of various factors xi on a parameter y of chromatographic interest. The chromatographic resolution of a target mixture is the most common response, while the factors are various instrumental variables, such as mobile phase composition and pH, gradient profile, eluent flux and temperature [13–18]. Application domains of conventional QSRR and RSM methods can be considered complementary, as the first approach describes the effect of molecular structure on the retention under fixed separation conditions, while the latter method describes the influence of parameters related with the separation mode for a target analyte or mixture. Various comprehensive models in terms of both structural descriptors of solutes and descriptors of column and/or eluent have been developed [4–7]. A basic multivariable predictive approach contemplates, together with variability related with the solute structure, the effect of composition of binary hydro-organic eluents, which is the operational variable usually optimised in isocratic RP-HPLC analyses. Generation of mixed models in terms of molecular descriptors and eluent composition, hereafter indicated as quantitative structure/eluent–retention relationships (QSERRs), even
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under isocratic elution is more difficult than conventional QSRR modelling, because of the increased complexity of the searched relationship due to non-linear effects and interactions between the eluent and solute descriptors. It has been shown that artificial neural network (ANN) regression, which does not require prior definition of the equation relating the retention to the independent variables, can be helpful to overcome the above problems [19–22]. A great effort has been devoted to predict RP-HPLC retention in gradient elution mode [21, 23–29], which is preferred to isocratic elution for the separation of analytes with very different polarity and/or mass. However, only a few approaches [21, 23–25] explicitly consider as independent variables the descriptors of the molecular structure together with descriptors of the gradient profile, which is an essential requisite if retention of new solutes under external elution conditions has to be predicted. In this paper, we simultaneously model by ANN the effects of molecular structure and mobile phase characteristics on RP-HPLC retention of s-triazines under linear gradient-elution conditions. Predictive performance of the built QSERR is compared with results of QSRR modelling for representative (local) conditions within the calibration domain and RSM relating the retention of each triazine to the starting eluent composition and the slope of the linear gradient.
2 Materials and methods 2.1 Chemicals and solvents Triazine standards (purity better than 99%) were obtained from Labor Dr. Ehrenstorfer-Schafers (Augsburg, Germany). HPLC-grade acetonitrile (Carlo Erba Reagenti, Milano, Italy), double-deionised water, obtained from a Milli-Q filtration/purification system (Millipore, Bedford, MA, USA), sodium acetate and acetic acid (Carlo Erba Reagenti) of analytical reagent grade were used for the preparation of mobile phases.
2.2 Instrumentation and experimental conditions The chromatographic system used in this work is composed of two Model 510 pumps (Waters, Milford, MA, USA), a Pump Control Module II (Waters), a Model 7725i sample injector (Rheodyne, Cotati, CA, USA) equipped with a 20 L loop and a Model 996 diode array detector (Waters). Chromatographic data management was automated using a Millennium32 data acquisition system (Waters). All the analyses were performed on the analytical column Spherisorb ODS2 (Waters), 250 mm length by 4.6 mm i.d. and 5 m particle size, connected to a 4.6 × 10 mm ODS2 Guard Cartridge (Waters) with 5 m particle size. The mobile phases were mixtures of acetonitrile and aqueous acetate buffer at pH 6 and concentration 10 mM, degassed by bubbling helium C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Table 1. List of the investigated s-triazines
Triazine (abbreviation)
R1
R2
R3
R4
Cyanazine (CYA) Simazine (SMZ) Propazine (PPZ) Trietazine (TTZ) Terbuthylazine (TBA) Sebuthylazine (SBA) Atrazine (ATZ) Desethylterbuthylazine (DTA) Desethylatrazine (DEA) Desisopropylatrazine (DIA) Desethyldesisopropylatrazine (DEI) Prometon (PMT) Secbumeton (SCB) Terbumeton (TRB) Atraton (ATT) Desisopropylatraton (DAT) Desethylterbumeton (DTB) Prometryn (PMN) Methoprotryne (MTP) Desmetryn (DMT) Terbutryn (TBN) Dimethametryn (DMN) Ametryn (AMN) Simetryn (SMN)
Cl Cl Cl Cl Cl Cl Cl Cl
CH2 CH3 CH2 CH3 CH(CH3 )2 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3 C(CH3 )3
H H H CH2 CH3 H H H H
C(CH3 )2 CN CH2 CH3 CH(CH3 )2 CH2 CH3 C(CH3 )3 CHCH3 CH2 CH3 CH(CH3 )2 H
Cl Cl
CH(CH3 )2 CH2 CH3
H H
H H
Cl
H
H
H
OCH3 OCH3 OCH3 OCH3 OCH3
CH(CH3 )2 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3
H H H H H
CH(CH3 )2 CHCH3 CH2 CH3 C(CH3 )3 CH(CH3 )2 H
OCH3
C(CH3 )3
H
H
SCH3 SCH3 SCH3 SCH3 SCH3 SCH3 SCH3
CH(CH3 )2 CH(CH3 )2 CH3 CH2 CH3 CH2 CH3 CH2 CH3 CH2 CH3
H H H H H H H
CH(CH3 )2 (CH2 )3 OCH3 CH(CH3 )2 C(CH3 )3 CHCH3 CH(CH3 )2 CH(CH3 )2 CH2 CH3
and delivered at a flow rate of 1.0 mL/min. Retention time (tr ) values of s-triazines were collected by injecting 5 mg/L acetonitrile solutions. The wavelength selected for detection was 240 nm for all compounds.
2.3 Data set Table 1 displays the 24 symmetric triazines (s-triazines) investigated here, including common herbicides and some metabolites. Figure 1 displays the 13 separation conditions, defined by the starting composition of the acetonitrile/water www.jss-journal.com
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Figure 1. Experimental design used to collect retention data of s-triazines and partition of separation conditions between calibration and prediction.
mixture (ϕ0 ) and the slope of linear variation of acetonitrile content (K); three cases (K = 0 and ϕ0 = 40, 50 or 60) correspond to isocratic elution modes. The observed log tr values collected under the above conditions are listed in Supporting Information Table S1. The triazines and the experimental conditions are partitioned in two groups, the first required in calibration and the latter to test model prediction. In particular, six triazines (AMN, ATT, DEA, SMZ, SMN and TBA), representing the three subclasses, chloro-, methoxy- and methylthiotriazines, and the variation in the alkylation degree and kind of substituents of the two amino groups were assigned to the prediction (or test) set. As to the partition of separation conditions, calibration data samples were identified according to a three-level experimental design (Fig. 1), while the remaining four separation conditions surrounding the centre of the domain are considered for prediction.
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the 473 molecular descriptors, a small subset encoding the effect of triazine structure on their retention. After preliminary analyses, we decided to adopt log tr as the MLR response, because the selected models were better than those providing the unscaled tr value. The GA-MLR method [32, 33] is based on the evolution of a starting random population of models. Each model is represented by a chromosome, namely a binary vector in which each position (gene) encodes the presence or absence of a descriptor by 1 or 0, respectively. The starting population evolves through mutation and crossover, until an optimal or near optimal model is identified. The chance for a given chromosome of being preserved in the next generation is associated to the predictive performance of the related model, which is quantified by the determination coefficient in leave-one-out cross-validation (Q2 loo-cv ). Q2 loo-cv is defined as (SSY-PRESS)/SSY, where PRESS is the predictive residual error sum of squares and SSY is the sum of the squared deviations of the dependent variables from their mean. In this work, GA-MLR analysis was performed using the program package V-PARVUS 2010 [34]. For each separation condition, variable selection was carried out on the 18 triazines of the calibration set and predictive performance of the built QSRR model was tested on the six excluded molecules.
2.6 Response surface methodology (RSM) RSM was separately applied to each triazine to relate the retention with the gradient characteristics, according to the following general quadratic relationship: log tr = a + b0 + c K + d20 + e K 2 + f 0 K .
(1)
Starting geometries of the triazines were generated by means of the MacroModel 7.1 molecular modelling program package [30]. Using the MM2 force-field, a conformational search was carried out to identify the global energy minimum for each molecule. Software Dragon [31] was used to compute the molecular descriptors from the optimised geometries. The quantities with little variance were eliminated and only one descriptor was retained among groups of highly correlated ones (r > 0.95). 473 molecular descriptors belonging to various classes remained after this procedure.
The RSM models were established using the calibration cases defined by a three-level experimental design (Fig. 1) and applied to the four external conditions. Initially, all the parameters of equation (1) were considered; but if non-significant terms assuming a 95% confidence probability were detected, the data were successively refitted without including these quantities in the regression. The linear solvent strength model, developed by Dolan and Snyder [35], permits to predict the retention time in linear gradient elution when the logarithm of the isocratic retention factor is linearly related to the volume fraction of organic modifier in the binary eluent. In the experimental conditions analysed here, such condition holds only for some triazines. Therefore, the model (1), although disconnected from the gradient elution theory, seems more convenient because can be applied to both regular and irregular solutes.
2.5 QSRR modelling under fixed, isocratic or gradient, elution conditions
2.7 Development of a quantitative structure/eluent–retention relationship (QSERR)
A QSRR model was separately established for each separation condition by multilinear regression (MLR) coupled with genetic algorithm (GA) variable selection to extract, within
A multilayer ANN [32,36,37] was used to build the QSERR describing the simultaneous effect of triazine molecular structure and separation conditions on the retention. It consists
2.4 Molecular descriptors
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of one input layer which collects the independent variables (the triazine structure and eluent descriptors), one output neuron providing the network response (the log tr value) and one hidden layer with an adjustable number of neurons fully connected to both input and output neurons. The network was trained by a quasi-Newton method [38] that incorporates second-order information about the shape of error surface and exhibits fast convergence and a great probability of avoiding local minima. The training data samples (139) were extracted from the 162 available calibration data (corresponding to 18 triazines and nine elution modes, designed previously) by the Kennard–Stone algorithm [39] applied to the space of the auto-scaled variables, while the 23 unselected cases were put in a validation set. Minimum of validation error was the adopted criterion for stopping the network learning and selecting among alternative trained networks the one with the expected best generalisation capability. The real prediction capability of the final QSERR model was evaluated on the prediction (or test) set consisting of 96 data samples. These correspond to all the 24 triazines (six unknown and 18 already used in ANN calibration) analysed at the four external separation conditions. ANN analysis was carried out using software OpenNN [40].
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one could be found if GA-MLR selection was repeated several times for each eluent. Moreover, a QSRR established for a given separation condition in general was seen to work well even at the other conditions. This suggests that the different sets are substantially equivalent, since only strong correlations (r > 0.95) were removed in previous pre-selection, and some molecular descriptors duplicate chemical information encoded by others. 3.2 Results of RSM The RSM models developed for the 24 triazines exhibit an acceptable descriptive and a predictive performance (Supporting Information Table S4), as demonstrated by R2 values greater than 0.99 and Q2 generally greater than 0.93. In the case of DEI, which is the least retained triazine by the C18 column, although the prediction errors are relatively small and comparable to those of the other solutes, a low Q2 value (0.395) is observed. This is the consequence of the substantial constancy of the log tr values of the prediction data samples, which makes the total sum of squares comparable to the predictive error sum of squares. 3.3 QSERR modelling
3 Results and discussion 3.1 QSRR modelling for the various separation conditions A five-dimensional QSRR model was established for each isocratic- and gradient-elution mode. The model complexity was established after a preliminary GA-MLR exploration carried out to evaluate the trend of the Q2 loo-cv value with respect to the number of included descriptors. The QSRRs are presented in Supporting Information Table S2. The coefficient of determination in calibration, R2 , the adjusted R2 (R2 adj ), the coefficient of determination in prediction (Q2 ) and standard errors in calibration and prediction (SEC and SEP, respectively) are the conventional statistical indices adopted to evaluate the descriptive and predictive quality of the various models. Q2 , analogously to Q2 loo-cv , is related to the predictive residual error sum of squares for the external data samples. Descriptive performance of the various QSRRs was quite good, as witnessed by R2 values generally greater than 0.994. As to their predictive ability, only a slight deterioration is observed (Q2 ranges between 0.928 and 0.990) with the exception of the model established for ϕ0 = 60 and K = 0 that exhibits a moderate worsening in prediction (Q2 = 0.907) with respect to the QSRR descriptive performance. Supporting Information Table S3 displays the meaning of the selected molecular descriptors. With the exception of the Ghose-Crippen octanol-water partition coefficient (MLOGP), that is included in all the QSRR models, different descriptors are generally selected for each separation condition. However, we observed that a number of alternative models with a comparable performance to that of the best C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
To describe the combined effect of triazine structure and separation conditions on the retention, the molecular descriptors and the parameters defining the elution mode (ϕ0 and K) were simultaneously considered as the input variables of an ANN giving log tr as response. Both input and output variables were subjected to range scaling between 0 and 1, while the starting network weights were randomly generated between –0.1 and 0.1. To represent the triazine structure, an informative subset of molecular descriptors was extracted within the group of variables identified by QSRR modelling for the various eluents (Supporting Information Table S3). Preliminarily, we considered all these molecular descriptors together as ANN inputs. Successively, to simplify the molecular descriptor set, we carried out a sensitivity analysis based on the method of weight zeroing proposed by Nord and Jacobsson [41]. According to this approach, the importance of a given input variable to define the ANN response is related to the deterioration of the network performance when the effect of that variable is removed by zeroing the corresponding weights. After the relative influence of each starting input is established, the less important one is removed and the network is re-optimised. This procedure is repeated until elimination of a further input produces a worsening of the ANN validation performance. To optimise the starting and reduced networks, the validation error was minimised as a function of the number of hidden neurons, the kind of activation function (logistic or hyperbolic tangent) in the hidden layer and the number of learning epochs. The molecular descriptors finally identified are X0Av, SIC1, Vp, R4u+ and MLOGP. The final network had a 7–12–1 architecture with a hyperbolic tangent activation function operating in the hidden layer and was learned www.jss-journal.com
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Figure 2. Agreement between experimental retentions and calculated or predicted responses of the QSERR model.
for 80 epochs. To be sure that the obtained model was not too optimistic, namely did not result from a fortunate combination of starting weights, the network was retrained 100 times and the responses were finally averaged. The R2 (or Q2 ) and SEC (or SEP) values of the final ANN model are respectively 0.9982 and 0.012 for the training set, 0.9970 and 0.017 for the validation set, and 0.9945 and 0.018 for the test set. The agreement between the experimental retentions and the calculated or predicted ANN responses are displayed in Fig. 2, while Supporting Information Fig. S1 shows the error trend. This figure reveals a random distribution of both computed and predicted residuals around zero and shows errors falling within a ±0.03 log tr range for most of the data points. This implies that tr values can be modelled with accuracy generally better than 7%. The few residuals outside this range are not anyway excessively high and do not overcome 13% in the tr scale.
3.4 Comparison of the various models The calculated or predicted responses provided by the three alternative approaches investigated in this work are compared with the experimental log tr values in Supporting Information Table S1, while Fig. 3 shows a comparison of the residual trends for the 24 triazines. It should be reminded that predictive performance of QSRRs and RSM models is evaluated on external triazines and external eluents, respectively, while generalisation of QSERR model is tested on both known and unknown solutes analysed at unknown separation conditions. To simplify the graphical representation, training and validation errors of the QSERR model are not distinguished in Fig. 3, because the validation data, although did not contribute to the ANN weight update, were involved in the network optimisation. For this reason, we assimilate the validation data to the training set rather than to the prediction set. Figure 3 confirms a relatively good performance of all the three predictive approaches that provide computed and predicted errors generally within a ±0.03 log tr range (±7% for the unscaled tr ) with a relatively small number of exceptions. C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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RSM computed or predicted residuals of all triazines are randomly distributed around zero and slightly wider distributions are observed in the case of PMN, TBA, TBN and TBZ. By contrast, QSRR modelling produces a moderate overestimation or underestimation of all or most of the retentions of some triazines (PPZ, SMZ, SMN, and TBA). This is diagnostic of a less accurate description of the structure for these solutes. Such small inaccuracy is also incorporated within the QSERR model, because retention of the same molecules, in addition to that of AMN, is overestimated or underestimated for all the external separation conditions. However, these systematic effects result in relatively small predictive errors, comparable to those of local QSRR modelling and to those associated to the imprecision of RSM for some triazines. It is known that quality and predictive power of conventional QSRR modelling, which is the basic structure-related approach to retention prediction, depends on several factors, such as the explanatory ability of the selected molecular descriptors, the structural similarity/dissimilarity of the investigated solutes, and the regression algorithm [8, 9]. Therefore, a comparative evaluation of the QSRRs established for the same target solutes and within the same experimental domain seems a reasonable preliminary test to check reliability of the QSERR model. It must be noted that a different QSRR model was built here for each experimental condition by variable selection applied to a large number of molecular descriptors of different kinds. Under these conditions, QSRR modelling is quite accurate. The descriptive/predictive quality of QSRRs is substantially preserved in the QSERR model, although chemical information carried out by the validation data samples, required to optimise the network, did not contribute in fact to the optimisation of the ANN weights. Moreover, while a specific subset of molecular descriptors has been selected to maximise QSRR quality, a small portion of chemical information is probably lost in successive selection of the ANN inputs. In summary, despite the QSRRs have been established under more favourable calibration conditions, the QSERR model is able to provide a comparable predictive performance. Previously, Kaliszan and co-workers [23, 24] attempted to predict retention in linear gradient elution by combining the linear solvent strength model with a QSRR model based on three structural descriptors of computational origin, the total dipole moment, the electron excess charge of the most negatively charged atom and the water-accessible molecular surface area. This method permitted the prediction of the retention behaviour of new analytes only approximately. Predictive performance was improved in a successive work [42], where the logarithm of octanol/water partition coefficient calculated from the structural formula by three different commercially available softwares was adopted as molecular descriptor. The best results were obtained using the ACD (Advanced Chemistry Development, Toronto, Canada) program, but quality of retention prediction was still moderate, the mean error in the retention time being 6.4%. Fatemi et al. [21] combined the solvatochromic descriptors with the gradient time and the starting and final acetonitrile content in the binary www.jss-journal.com
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Figure 3. Comparison of calculated and predicted residuals of the various models.
mobile phase. The retention time of 20 benzene derivatives under linear gradient elution were modelled both by MLR and ANN. The ANN-based model gave better results than the MLR counterpart, but its quality was poorer as compared with performance of the QSRRs established for individual gradients. The mean prediction error in the retention time, evaluated on external data samples, was 12%. The model here generated for the triazines exhibits a better predictive ability than the above QSRR-based approaches, which proves the reliability of the adopted strategy and the good explanatory capability of the selected variables.
3.5 Interpretation of the molecular descriptors of the QSERR model To attempt an interpretation of the structural effects governing retention of s-triazines, we focus our attention on the molecular descriptors of the QSERR model (X0Av, SIC1, Vp, R4u+ and MLOGP). Among the selected variables, MLOGP is the computed value of the logarithm of the partition coefficient between n-octanol and water, which is a well-known hydrophobicity index, but the physical meaning of the other four descriptors is not immediately clear. To facilitate the qualitative interpretation of the structure–retention relationship governing the RP-HPLC behaviour of triazines we performed a principal component analysis (PCA) [43] on the space of the above descriptors and log tr in the centre of the experimental domain (ϕ0 = 50 and K = 0.5%/min), after variable autoscaling. The PCA results are presented in Fig. 4 showing the loadings and scores projected on the plane spanned by the first two principal components (PC1 and PC2, accounting for about 92% of total variance). It can be observed that PC1 substantially represents the retention on the C18 column, because log tr is almost collinear with this component. Along this component, the dealkilated triazines, the least retained analytes of the whole group, are clearly separated from the other compounds and triazines are ordered according to the alkylation degree of amino groups. All the five molecular descriptors contribute with appreciable but different loadings to PC1. MLOGP and X0Av, on the other side, describe the dif C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 4. Biplot (score and loadings) obtained from PCA of autoscaled descriptors of the QSERR model and log tr in the centre of the experimental domain. Chloro-, methoxy- and methylthiotriazines are indicated with different character fonts using the abbreviations reported in Table 1.
ferences between the methoxy- and the methylthio-trazines, whereas R4u+ is responsible for the almost complete separation of the chloro-triazines from the group of methoxyand the methylthio-trazines. Separation of the three triazine subclasses occurs along directions which are not parallel to log tr and, therefore, the nature of the R1 group has a minor effect on the retention as compared with the alkylation degree of the amino groups, which has a great influence on the hydrophobicity and the possibility that the triazine can interact by hydrogen bonding with the aqueous mobile phase.
4 Concluding remarks In this paper, we have compared the performance of three approaches to retention prediction of triazines in RP-HPLC under linear gradient elution. Two of these, QSRR and RSM, are conventional methods, and can be considered complementary, as the first contemplates only the effect of molecular structure, while the latter describes only the influence of the gradient profile for a fixed structure. The third approach, www.jss-journal.com
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based on ANN regression, simultaneously accounts for the effect of molecular structure and elution mode on the retention. In spite of greater complexity related to the larger variability domain covered by the model, its predictive performance is substantially comparable to that of the above local models. The authors have declared no conflict of interest.
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