Journal of Chromatography A, 1363 (2014) 331–337
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Fast-multivariate optimization of chiral separations in capillary electrophoresis: Anticipative strategies L. Escuder-Gilabert a , Y. Martín-Biosca a , S. Sagrado a,b , M.J. Medina-Hernández a,∗ a
Departamento de Química Analítica, Universidad de Valencia, Burjassot, Valencia, Spain Centro Interuniversitario de Reconocimiento Molecular y Desarrollo Tecnológico (IDM), Unidad Mixta Universidad Politécnica de Valencia-Universidad de Valencia, Spain b
a r t i c l e
i n f o
Article history: Received 16 April 2014 Received in revised form 23 June 2014 Accepted 29 June 2014 Available online 5 July 2014 Keywords: Capillary electrophoresis Enantioseparation optimization Design of experiments Steepest ascent Partial least squares Anticipative post-DOE strategy
a b s t r a c t The design of experiments (DOE) is a good option for rationally limiting the number of experiments required to achieve the enantioresolution (Rs) of a chiral compound in capillary electrophoresis. In some cases, the modeled Rs after DOE analysis can be unsatisfactory, maybe because the range of the explored factors (DOE domain) was not the adequate. In these cases, anticipative strategies can be an alternative to the repetition of the process (e.g. a new DOE), to save time and money. In this work, multiple linear regression (MLR)-steepest ascent and a new anticipative strategy based on a multiple response-partial least squares model (called PLS2-prediction) are examined as post-DOE strategies to anticipate new experimental conditions providing satisfactory Rs values. The new anticipative strategy allows to include the analysis time (At) and uncertainty limits into the decision making process. To demonstrate their efficiency, the chiral separation of hexaconazole and penconazole, as model compounds, is studied using highly sulfated--cyclodextrin (HS--CD) in electrokinetic chromatography (EKC). Box–Behnken DOE for three factors (background electrolyte pH, separation temperature and HS--CD concentration) and two responses (Rs and At) is used. Using commercially available software, the whole modeling and anticipative process is automatic, simple and requires minimal skills from the researcher. Both strategies studied have proven to successfully anticipate Rs values close to the experimental ones for EKC conditions outside the DOE domain for the two model compounds. The results in this work suggest that PLS2-prediction approach could be the strategy of choice to obtain secure anticipations in EKC. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Capillary electrophoresis (CE) is a powerful technique for enantiomer separations due to its intrinsic high separation efficiencies, speed of analysis, low reagent consumption and small sample requirements [1]. One of the most common modes of CE to perform chiral separations is electrokinetic chromatography (EKC), including a chiral selector in the background electrolyte (BGE) [2]. An alternative to the conventional EKC is the use of partial (PFT) and complete (CFT) filling techniques, in which, prior to injection of the analyte, the capillary is partially or completely filled with the chiral selector solution, respectively, while the while the inlet and outlet vials are free of chiral selector [2,3].
∗ Corresponding author at: Departamento de Química Analítica, Facultat de Farmacia, Universitat de Valencia, C/ Vicent Andrés Estellés s/n, E-46100 Burjassot, Valencia, Spain. Tel.: +34 963544899; fax: +34 963544953. E-mail address: [email protected] (M.J. Medina-Hernández). http://dx.doi.org/10.1016/j.chroma.2014.06.095 0021-9673/© 2014 Elsevier B.V. All rights reserved.
Among the different chiral selectors used in EKC, cyclodextrins (CDs) are the most widely employed due to their good enantiorecognition abilities, good water solubility, UV transparency, and the wide assortment of different neutral, cationic and anionic CDs with different functional groups that can be employed [4]. Highly sulfated--CD (HS--CD) is an anionic CD with an average content of 12 sulfate groups per molecule [5]. This CD has proven to be a powerful chiral selector for enantiomers of many basic and neutral organic compounds [6,7]. The enantioresolution (Rs) of compounds in EKC is the result of a delicate balance between different experimental variables such as chiral selector concentration, nature and concentration of electrophoretic buffer, BGE pH, temperature and applied voltage. Despite the fact that extensive research in the field of enantioseparations by CE using chiral selectors has been carried out, it is difficult to predict whether the separation of the enantiomers of a chiral compound is possible. Hence, experimental efforts are necessary to select appropriate experimental conditions (factors), usually by trial and error procedures. Thus, the enantioseparation of a chiral compound becomes a time- and money-consuming task.
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In most of the papers published on EKC, univariate optimization of experimental variables (factors) is still performed despite that multivariate optimization is strongly recommended to take into account possible interactions between factors [8]. The design of experiments (DOE) is the right systematic way to account with those interaction factors, limiting the number of experiments to obtain the proper information. Usually, the so called response surface model design is used in order to account with nonlinearities (e.g. squared factors). In DOE, factors are varied in a prefixed way to understand their effect on the response variable/-s and/or to model the relationships between the response variable/-s and the factors. The last feature allows to obtain the desirable, often optimal, experimental factors values that maximize (or minimize) the response variable/-s. For the case of a single response variable, the coefficients of the models are usually estimated by multiple linear regression (MLR) or partial least squares (PLS). For the case of multiple response variables, MLR (by using a ‘desirability’ function [8]) and PLS2 can be used. DOE requires an orderly and efficient mapping of the experimental space (DOE domain) to be cost-saving [9]. The selection of the factors is generally the first step in a DOE; then, one needs to properly define the extreme levels at which the factors will be studied. If boundaries are too wide, insufficient precision of the model is obtained. On the contrary, boundaries that are too narrow, can miss the desirable optimum [9]. The selection of a correct experimental domain is fundamental for a successful DOE and should be based on preliminary knowledge mostly gained by preliminary experiments. There is the possibility of running a screening DOE in order to fix the optimal values for some factors and to move the experimental domain of the remaining factors before being further studied by response surface methodology [8]. Sometimes, the initial DOE could be fixed according to the previous knowledge in separations with a given CD; just to save time and money, but with the risk to fail in finding adequate separation conditions. In this case, the recommended repetition of the process (new DOE), increasing the time and cost, is not the unique option. For instance, some experimental designs as Doehlert design can be moved to the zone leading to the best results, still maintaining the results of some experiments of the first DOE (although it still requires new experiments). Another post-DOE alternative could be to perform an extrapolation using the obtained response surface model in order to anticipate new experimental conditions that could provide convenient response variable/-s, requiring only one additional experiment, just to confirm the goodness of such anticipation, solving (or not) the problem. The steepest ascent (or descent) approach intends to provide locations of factors away from the initial DOE domain to find the optimal or desirable response. This strategy has been widely used in different scientific areas. However, its use in separation techniques has only been reported to optimize the mean resolution of biodiesel mixtures in liquid chromatography [10] and the resolution and analysis time (At) of two enantiomers, in supercritical fluid chromatography [11] and testosterone esters in micellar electrokinetic chromatography [12]. Recently, our research group has anticipated new desirable EKC conditions for bupivacaine enantiomers separation based on converting a multiple response-partial least squares model (PLS2) into linear-like equations (for Rs and At) and using them to extrapolate new results [13]. PLS2 was performed on the main factors, i.e. cross- and squared-terms to account for possible interactions between factors and nonlinearities, respectively, were not considered. A comparison with other alternatives was not performed. In this paper, MLR-steepest ascent and a new anticipative strategy (PLS2-prediction) are examined as post-DOE strategies to anticipate new experimental conditions providing satisfactory Rs (and At) for enantiomers separation in EKC. To demonstrate their
efficiency, the chiral separation of hexaconazole (HEX) and penconazole (PEN), as model compounds, is studied using HS--CD in EKC-CFT. The literature reports the separation of these compounds (together with other ones) using CD-modified micellar electrokinetic chromatography [14] and EKC with sulfated--cyclodextrin (a CD with lower degree of substitution than that used here) [15]. For each compound, in this work a Box–Behnken DOE for 3-factors (BGE pH, separation temperature and HS--CD concentration) and 2-responses (Rs and At), which requires 15 electrophoretic runs, is used. MLR and PLS2 response surface models are obtained, analyzed and in some cases, refined. Then, the steepest ascent and the PLS2prediction approaches are used to estimate the responses outside the original DOE domain. Finally, the outputs and their agreement with the experimental values of the two approaches are compared. 2. Materials and methods 2.1. Instrumentation A Beckman P/ACE MDQ Capillary Electrophoresis System equipped with a diode array detector (Beckman Coulter, Fullerton, CA, USA), and 32Karat software version 8.0 was used throughout. A 50 m inner diameter (id) uncoated fused-silica capillary with total and effective lengths of 60.2 and 50 cm, respectively, was employed (Beckman Coulter, Fullterton, CA, USA). Detection wavelength was fixed at 200 nm for all experiments. Electrophoretic solutions and samples were filtered through 0.45 m pore size nylon membranes (Micron Separation, Westboro, MA, USA) and degassed in an ultrasonic bath (JP Selecta, Barcelona, Spain) prior to use. A Crison Micro pH 2000 pH-meter from Crison Instruments (Barcelona, Spain) was employed to adjust the pH of buffer solutions. 2.2. Chemicals and reagents All reagents were of analytical grade. Sodium dihydrogen phosphate dihydrate was from Fluka (Buchs, Switzerland). Sodium hydroxide was from Scharlab S.L. (Barcelona, Spain). Racemic pesticides (HEX and PEN) were from Dr. Ehrenstofer (Augsburg, Germany) and HS--CD 20% w/v aqueous solution from Beckman Coulter (Fullerton, CA, USA). Ultra Clear TWF UV deionized water (SG Water, Barsbüttel, Germany) was used to prepare solutions. Background electrolytes (BGEs) containing phosphate 50 mM at different pH values were obtained by dissolving the appropriate amount of sodium dihydrogen phosphate dihydrate in water and adjusting the pH with 1 M NaOH. 1000 mg L−1 stock solutions of PEN and HEX were prepared in methanol and kept at 4 ◦ C. Working solutions (100 mg L−1 ) were prepared by dilution of the stock ones. HS--CD solutions at different concentrations were prepared by dilution in the corresponding BGE. 2.3. Capillary electrophoresis methodology New capillary was conditioned by rinsing with 1 M NaOH at 60 ◦ C during 15 min. Then, it was rinsed for 5 min with deionized water and 10 min with separation buffer at 25 ◦ C. In order to obtain good peak shapes and repeatable migration data, the capillary was conditioned prior to each injection. In all cases, the conditioning run included the following steps: (i) 1 min rinse with deionized water; (ii) 1 min rinse with 1 M NaOH; (iii) 1 min rinse with deionized water and (iv) 2 min rinse with the BGE solution. All steps were carried out at 20 psi. The solutions of the model compounds were injected hydrodynamically at 0.5 psi for 5 s. Before compounds injection, the capillary was completely filled with the HS--CD solution; by applying 20 psi during 1 min. No HS--CD was included in the BGE
L. Escuder-Gilabert et al. / J. Chromatogr. A 1363 (2014) 331–337
inlet and outlet vials (CFT mode). This operative mode was tested experimentally in our laboratory checking the consistence of electropherograms at injection times higher than 1 min at 20 psi. This is a counter current technique since the CD plug moves in the opposite direction to the EOF allowing the interaction with cationic or neutral compounds. Separation was performed in normal polarity by applying 15 kV. Different capillary temperatures were tested. 2.4. Box–Behnken DOE Box–Behnken DOEs for three factors (with two levels and three replicates of a center point) distributed in 15 experiments (identified by a number, Ne) were used for optimization of separation of HEX and PEN enantiomers (Table S1 in Supplementary data). For both compounds, main factors considered were: BGE pH (pH), separation temperature (T) and HS--CD concentration (CD). Their corresponding experimental values were set from the extreme levels at which they were going to be studied (CD: 0.5–2.5% w/v, T: 15–40 ◦ C and pH 6.5–8.5). 2.5. Software and calculations Enantioresolution (Rs) values were calculated using 32Karat software v. 8.0 (Beckman Coulter) by means of the following expression: Rs = 1.18
t2 − t1 w1 + w2
(1)
where t1 and t2 are, respectively, the migration times of the first and second eluted enantiomers, and w1 and w2 are the peak widths at 50% peak height. t2 is used along the text as analysis time (At). Statgraphics Plus® 5.1 (Statpoint Technologies, Warrenton, VA, USA) was used for Box–Benhken DOE analysis (MLR-response surface module) and to anticipate new response values by the steepest ascent strategy outside the DOE domain (here called MLR-steepest ascent strategy). The Unscrambler® v.9.2 multivariate analysis software (CAMO Software AS, Oslo, Norway) [16] was used for PLS2 modeling and to anticipate new responses values outside the DOE domain (here called PLS2-prediction strategy). For PLS2 autoscaled data were used. Leave-one-out cross-validation was used as validation strategy in PLS2 modeling. Note that anticipated results are simply predictions from MLR or PLS2 regression models outside the modeled domain. Further details on the modeling and prediction approaches are provided in the Supplementary data. 3. Results and discussion In this paper, to demonstrate the efficiency of the anticipative strategies studied for multivariate optimization of enantioseparations in EKC, HEX and PEN were used as model compounds and HS--CD was used as chiral selector. According to our laboratory experience in EKC enantioseparations using this CD, three EKC experimental conditions affecting Rs (and also At) were selected as main DOE factors: pH, T and CD (with a priori reasonable limits; Section 2.4). The levels of the factors for each experiment were set according to Box–Behnken DOE (Table S1 in Supplementary data). Although at the pH range used the neutral forms of HEX and PEN predominate (see Fig. S1 in Supplementary data), BGE pH can be an important factor on Rs since it strongly affects electroosmotic flow mobility and compounds apparent mobilities. Lower pH values would favor the compound ionization, and therefore, the interaction with the anionic HS--CD but also would decrease or even cancel the EOF. This fact could yield longer analysis times or make necessary the use of negative polarity (which implies to reverse the EOF and the especial use of injection configuration to allow the plug interaction in the CFT mode).
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The other factors, buffer concentration and applied voltage, were prefixed as indicated in Sections 2.2 and 2.3, respectively. They are in general important factors, which can help tuning the selectivity of the separation and analysis time. However, according to our experience working with this CD, their effect is much lower than that of the selected DOE variables. All these decisions are consistent with the aim of this work, which is to explore a fast (and inexpensive) optimization; assuming the risk of finding an unsatisfactory DOE result, but obtaining the sufficient information to make a further anticipation. In our laboratory, excellent enantioseparations have been achieved for a wide range of compounds with the above criteria, which agrees with the aim (a 16-experiment strategy). Therefore, alternatives such as previous screening-experiments, more complex DOE (e.g. more factors, levels or designs with more experiments) and/or more complex post-DOE strategies, although recommendable in general, were not considered in this work. Considering the errors/uncertainties involved in the overall process (experimental, modeling, possible extrapolation if necessary, among others), but also a trouble-free future work (e.g. quantitative EKC determination of both enantiomers), some goals were established. The attainment of anticipated Rs values close to 2 (or narrow Rs uncertainty intervals including this value) was prefixed as requisite (primary goal). When possible, At estimations were also anticipated, although considered as a secondary goal. To reach the primary goal, MLR-steepest ascent on Rs was used. A new anticipative post-DOE strategy (called here PLS2-prediction) involving Rs and At responses simultaneously, was intended to reach the two goals. Initially, modeling and anticipated estimates were obtained considering all the experiments as well as the three main factors (pH, T and CD) and their six extended terms (pH × T, pH × CD, T × CD, pH2 , T2 and CD2 ); just for simplicity, we will refer to all these factors and terms as ‘variables’. However, the elimination of the less reliable data (variables and/or experiments after model analysis), in order to refine the model, was considered as alternative scenarios for comparison purposes. On the other hand, all studies were restricted to automatic calculations allowed by the software to keep the simplicity of the tools. Table 1 summarizes the main features of the proposed PLS2prediction approach compared with the MLR-steepest ascent one. Such features are related to the options available in the particular software (and version) used here and they should not be interpreted as general for other software or algorithms published in the literature. As can be seen, several advantages are possible from the new approach. 3.1. MLR-steepest ascent approach DOE data (Table S1) for both compounds were analyzed. The optimum estimated resolutions by classical MLR were: Rs = 1.53 and 1.64 (lower than the Rs requisite) for HEX and PEN, respectively; suggesting the necessity of a post-DOE stage. Fig. 1 shows the Statgraphics® ‘Main effects plot for Rs’ for both compounds. As can be observed, in both cases, CD has the highest impact on Rs. So, the expected Rs values when increasing CD could be anticipated by the proper steepest ascent strategy. The Statgtaphics® version (Plus 5.1) used performs these calculations automatically starting from the center of the DOE, allowing the user to decide the prefixed increments on the desired variable. Table 2 shows the anticipated results from the steepest ascent for Rs, obtained by changing CD in increments of 0.5 units from the center of the DOE (steps 1 to 7), when all variables are used in the MLR model. The path of the steepest ascent for HEX, indicates that step 4 (a) in Table 2 provides convenient EKC conditions satisfying the Rs ∼ 2 requisite (expected Rs = 2.11). Note that further steps
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Table 1 Features of the PLS2-prediction approach compared with the MLR-steepest ascent one, restricted to the two commercial computer programs used and the EKC optimization problem to be solved: three factors (pH, T and CD) and two response variables (Rs and At). See Supplementary data for further information on the models. Feature
PLS2-prediction (Unscrambler® )
MLR-steepest ascent (Statgraphics® )
Data analysis
DOE data is analyzed as in a conventional PLS2 problem with the exception that the option ‘Interaction and square effects selection’ is used to incorporate to the matrix of three factors the six cross- and squared-terms; [3 + 6] format as X Two response surface models to estimate Y (Rs and At simultaneously) are built. Normally, an optimum number of latent variables (k) lower than the number of X-variables is selected, so partial (filtered) information is used. Ideally, a k close to 2 (number of Y-variables) could indicate an adequate latent (inner) structure of the PLS2 model Scaled regression coefficients including cross-validated uncertainty limits allow to detect the important variables (i.e. high and certain coefficients) for both responses. The less important variables can be removed from X for model refinement
Identical analysis, except that MLR is used to create the model
Model details
Importance of the variables
Outliers detection
Anticipated results (prediction)
Only the response surface model for Rs is builta . All the information are used
Uncertainty estimates are not available for the coefficientsb (only for the effectsc ). The variables corresponding to the less important effects can be removed from X for model refinement Unclear (see Section 3.1 for details)
Ne-points too far from the ‘target line’ in the ‘validation plot’ (predicted vs. experimental Rs) are poorly modeled. Ne-points with a high difference between the predicted and cross-validated Rs estimates in the ‘validation plot’ alter the model. These Ne-points (potential outliers) can be removed from X and Y for model refinement Freely simulated EKC conditions (inside and/or outside the DOE domain) are used as X ‘test’ data, for which the model predict their corresponding Y-values (Rs and At). Uncertainty limits for the predictions are obtained, which can help in deciding the proper EKC conditions
New conditions ‘movements’ (steps) are restricted by the steepest ascent algorithm. Uncertainty is not available for the steepest ascent estimatesd
Acronyms: At: analysis time; Ne: number of DOE experiment; Rs: enantioresolution; X: matrix containing the values of the variables related to the EKC conditions. Y: matrix containing the values of the experimental responses, Rs and At. a The available alternative ‘desirability function’ (accounting for both response variables) does not allow to perform the steepest ascent stage (so, it was discarded). b To obtain confidence intervals for the coefficients, an independent MLR model with the X-Rs data must be calculated (using another module of Statgraphics® ). c The ‘Standardized Pareto Chart for Rs’ shows the standardized effects (as bars) and a threshold vertical line. Only bars that extend beyond this line are significant at the 95% confidence level. d To obtain confidence intervals for the estimates, a similar strategy as described for PLS2-prediction approach can be followed (see Section 3.4).
provide higher Rs values, but with the corresponding extra cost, and probably, higher uncertainty since their larger distance from the DOE domain. The convenient estimate for PEN (step 4 (d)) is higher than for HEX, Rs = 2.54. For model refinement (see Table 1), the elimination of the less important variables in the HEX DOE data was considered. The standardized Pareto chart for Rs (see Fig. S2 in Supplementary data) suggested that only CD, CD2 , pH and CD × pH (in this importance order) are the statistically significant variables at a 95% confidence level. The T main factor showed a higher standardized effect than
the other non-significant variables. It was retained into the MLR model, together with the significant variables, totaling five variables (Partial-1 data in Table 2). As can be observed, the impact of such simplification on the steepest ascent anticipations is negligible (compare Partial-1 data vs. all data in Table 2). However, the model refinement provided improved model statistics and predictive ability (see Fig. S2-footnote in Supplementary data), thus increasing the model reliability. In the case of PEN, the standardized Pareto chart for Rs (see Fig. S2 in Supplementary data) suggested that just CD and CD2 were significant, an output also suggested by Fig. 1b.
Table 2 Some anticipative results from MLR-steepest ascent (Rs as response variable) and PLS2-predictions (Rs and At as response variables). Analyte
DOE data
HEX
All
Partial-1 Partial-2 PEN
All
Partial-3
MLR-steepest ascent
PLS2-prediction
Step
pH
T
CD
Rs
1 2 3 4 (a) 5 6 7 4 (b) 4 (c)
7.50 7.28 7.24 7.27 7.33 7.43 7.53 7.31 7.29
27.50 26.76 26.47 26.31 26.19 26.09 26.00 25.80 27.26
1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.0 3.0
0.33 0.71 1.28 2.11 3.24 4.67 6.43 2.14 2.17
1 2 3 4 (d) 5 6 7 4 (e)
7.50 7.45 7.43 7.42 7.42 7.42 7.43 7.06
27.50 27.41 27.37 27.35 27.35 27.35 27.35 27.16
1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.00
0.53 0.97 1.64 2.54 3.68 5.06 6.67 2.19
Simulation
pH
T
CD
Rs (u)
At (u)
(a) (a)
7.0 7.5
27.5 27.5
3.0 3.0
2.08 (0.52) 2.19 (0.49)
11.89 (1.86) 11.96 (1.76)
(c)
7.5
27.5
3.0
1.81 (0.44)
12.61 (1.96)
(d)
7.5
27.5
3.0
2.56 (0.51)
11.67 (1.75)
(d)
7.5
27.5
3.0
2.01 (0.19)
11.07 (0.91)
Partial-1 data: five selected variables: CD, CD2 , pH and CD × pH (significant variables at 95% confidence level; in importance order of the effects) and T. Partial-2 data: selected variables as in Partial-1 data and eliminating experiments Ne = 5 and Ne = 12 (according to PLS2 suggestions). Partial-3 data—seven selected variables: all terms, except pH × T and T × CD cross-terms, and eliminating experiment Ne = 11 (according to PLS2 suggestions). Letters between brackets correspond to the simulated EKC conditions for MLR-steepest ascent fitting the Rs ∼ 2 requisite. Similar conditions have been simulated using the PLS2-prediction strategy for comparison. u: uncertainty values
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Fig. 1. Statgraphics® ‘main effects plot for Rs’: (a) HEX and (b) PEN results.
Besides the presence of non-important variables in the model, the occurrence of outliers able to artificially alter the MLR model could be another problem to be taken into account. Unfortunately, the MLR model is designed to minimize the residuals, i.e. to accommodate the response surface to fit well all the experimental results. In fact, the residual plots, including the residuals normal probability plot (see Fig. S2 in Supplementary data), which could help to detect outliers, indicated that the largest residuals were not far from the others, so they were not perceived as outliers. 3.2. PLS2-prediction approach Table 2 shows some selected results of the PLS2-prediction approach, close to the EKC conditions selected in Section 3.1 (identified by the same letter in parenthesis) to facilitate the comparison between strategies. As can be observed, when all the DOE data were used in the models, similar Rs estimates were obtained, suggesting the equivalence of both approaches (see conditions/results (a) and (d) in Table 2 for HEX and PEN, respectively). However, the PLS2 analysis revealed some deficiencies in the models for HEX and PEN (e.g. a high number of uncertain regression coefficients and low cross-validated explained response variance, suggesting poor predictive ability of the models) when the entire dataset was used, (see for instance Fig. S3 in Supplementary data for the case of HEX). This fact suggests the models refinement to avoid unreliable anticipated results. For HEX, model refinement by the elimination of the less important four variables for predicting Rs (the same as in MLR) was performed. T was retained for the same reasons as in MLR (see Section 3.1), but also because it is the most important variable for predicting At (see Fig. S3b in Supplementary data). Note that PLS2 model uses the same variables for predicting Rs and At; i.e., the elimination of a variable (model refinement) affects to both response variables (see Supplementary data for further details). After variables removal, two experiments, Ne = 5 and 12, appeared as possible outliers affecting the model (according to Table 1), in contrast to the MLR observations. Ne = 12 showed a relatively high
335
residual value. Ne = 5 exhibited a relatively high difference between the Rs predicted and cross-validated values; moreover, it showed an atypically high Rs value for the low CD tested (see Table S1). This result is, in fact, responsible for the curvature of the CD effect on Rs in the MLR model (Fig. 1a), which predicts an illogical increase of Rs at low CD values, even for CD = 0. Experiments, Ne = 5 and 12 were eliminated from the PLS2 model as an alternative scenario (Partial-2 data in Table 2), but also in the MLR case, just for comparison purposes. This table shows the anticipated results for the new scenario using both strategies. The impact of this model refinement can be seen by comparing the conditions/results (c) vs. (a) in Table 2. While the model refinement (variables and experiments elimination) had a negligible effect on the MLR-steepest ascent, it had a relative impact on the PLS2predictions providing a lower Rs estimation: Rs = 1.81 after the model refinement, compared with the previous one (Rs > 2). In the case of PEN, PLS2 model refinement was also performed. The two less important variables (pH × T and T × CD) respect to the Rs and At responses and the experiment Ne = 11 were eliminated (Partial-3 data in Table 2). This experiment showed a relatively high difference between the Rs predicted and cross-validated values; this difference was larger than in the case above commented for HEX, then with higher risk to alter the model (i.e. modify the response surface). Again, this experiment was not perceived as outlier in the MLR analysis. The same model refinement was applied to MLR for comparison purposes. As can be observed in Table 2, the model refinement in this case had a noticeable impact on the anticipated Rs results for both approaches, but higher for the PLS2-prediction one. Thus, Rs = 2.01 (Partial-3 data) is ∼0.5 units lower than before model refinement (all data). Moreover, in contrast to the HEX case, simplification of data for PEN changed the steepest ascent ‘movements’ providing different EKC conditions (mainly for pH) apart from a lower Rs estimate (see new conditions/results (e) compared with (d)). It could be provisionally concluded that PLS2 model refinement provides lower Rs estimates (as observed for HEX and PEN). However, this behavior cannot be assured in the case of the MLRsteepest ascent approach. From a practical point of view, it is safer to anticipate under-optimistic rather than over-optimistic Rs estimates. Fig. 2 shows Rs vs. At plots obtained from the PLS2-prediction approach using the refined models for HEX and PEN (Partial-2 and Partial-3 data, respectively). As can be observed, the models show reasonably good predictive ability inside the DOE domain; e.g. estimates for the DOE data (squares) are quite similar to the experimental ones (triangles) (see also Fig. S4 in Supplementary data for correlation plots and absolute and relative differences). On the other hand, the anticipated results outside the DOE domain (crosses), for CD = 3% and different pH and T values, satisfy the Rs ∼ 2 requisite. One of these anticipated results for HEX and PEN is shown in Table 2 (Partial-2 and Partial-3 conditions, respectively). Such kind of plot could help to select a desirable Rs–At combination.
3.3. Experimental versus anticipated results To check the real usefulness of the anticipative strategies tested, the anticipated results were compared with the experimental ones (see also Fig. S4 in Supplementary data). Fig. 3 shows the electropherograms obtained under EKC conditions close to those anticipated from Partial-2 and Partial-3 data for HEX and PEN, respectively (Table 2). For HEX, at pH = 7.5, T = 25 ◦ C and CD = 3%, the experimental outputs were: Rs = 2.1 and At = 13.5 min. The experimental Rs agrees well with the one anticipated by the MLR-steepest ascent approach (2.2 ± 0.5; Partial-2 data in Table 2; see Section 3.4 for details on the confidence interval). In the PLS2-prediction
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(a) 3 Absorbance (mAU)
3
(a)
2.5 2
Rs
1.5 1
2
1
0
0.5
10
11
14
15
13
14
15
5
10
15
20
3
2.5 2
Absorbance (mAU)
(b) 3 0
At (min)
(b)
13
t (min)
0 -0.5
12
2
1
Rs
0 10
1.5
11
12
t (min) 1 0.5 0 0
5
10
15
20
25
At (min) Fig. 2. Rs and At values for HEX (a) and PEN (b). Experimental () and predicted results from PLS2 models () corresponding to DOE domain. Anticipated results by the PLS2-prediction approach outside the DOE domain for CD = 3% and varying pH in the 6–9 range and T in the 15–40 ◦ C range (+).
approach, the anticipated uncertainty intervals include the experimental Rs (and At) values: Rs = 1.8 ± 0.4 (and At = 12 ± 2 min). Similarly, for PEN, at pH = 7.5, T = 27.5 ◦ C and CD = 3%, the experimental outputs were: Rs = 1.9 and At = 12.4 min. The experimental Rs is lower than the anticipated by the MLR-steepest ascent approach (2.2 ± 0.4: Partial-3 data, in Table 2; see Section 3.4 for details on the confidence interval), although in slightly different pH and T conditions (step 4 (e) in Table 2). As before, the experimental Rs (and At) are included within the PLS2-prediction intervals: Rs = 2.01 ± 0.19 (and At = 11.1 ± 0.9 min). It should be noted that the anticipated Rs values from unrefined models result too optimistic and then risky. In general, the uncertainty intervals should help in the decision making process (Table 1). For instance, the PLS2 anticipated uncertainty level for PEN as consequence of model refinement (±0.19; Partial-3 data; Table 2) is more reliable than without simplification (±0.5; all data). High differences between the uncertainties of anticipated results were obtained (see Fig. S5 in Supplementary data). 3.4. Additional remarks In PLS2, the use of just the main factors (pH, T and CD) without their corresponding extended variables, as performed in a recent paper [13], could be an apparently simpler possibility. However, this is just an approximation, i.e. an attempt to ‘linearize’ an originally curved response surface, based on the flexibility of the linear PLS algorithm to partially accommodate interactions and nonlinearities. However, if the crossed- or squared-terms are relatively important, such model can fail in their estimations, particularly to make anticipations (extrapolations). An additional problem could
Fig. 3. Electropherograms of 100 mg L−1 solutions of racemic model compounds obtained under the following experimental conditions: (a) HEX: 3% HS--CD, 25 ◦ C, pH 7.5; (b) PEN: 3% HS--CD, 27.5 ◦ C, pH 7.5. Further experimental details are indicated in Section 2.
be that the outlier character of an experimental result becomes ambiguous; e.g. it could be forced by this ‘linearization’ process. Just for comparison, as an example, the PLS2 estimations using the three main factors were also calculated for PEN. First of all, four apparent outliers were identified (Ne = 1, 6, 11 and 12), while in the proposed approach only one of them, Ne = 11, was detected (Section 3.2). Elimination of four experiments in a dataset of 15 designed experiments seems to be excessive (but necessary). The estimations using the same EKC conditions as in (d)-simulation in Table 2, were: Rs = 1.8 ± 0.2 (and At = 11.9 ± 1.1 min). Although in this case, the results could be considered acceptable, the elimination of four experiments provides less confidence on the anticipations. For HEX, even more experiments should be eliminated. The Statgraphics® steepest ascent algorithm does not provide the corresponding confidence intervals for anticipated results. However, the prior MLR model (another module of the software) is able to calculate them, just including the desired new EKC conditions into the datasheet (as in the PLS2-prediction approach). For comparison purposes, these calculations were performed. For instance, the MLR estimated 95% confidence intervals for HEX and PEN shown in Section 3.3 are larger than the corresponding uncertainty intervals from the PLS2-prediction approach. 4. Conclusions In this work, MLR-steepest ascent and PLS2-prediction approaches are explored as post-DOE anticipative strategies in enantioselective EKC to save experimental effort for achieving full enantioresolution after unsatisfactory DOE results. Rs ∼ 2 estimates, as requisite, and preferably, narrow Rs uncertainty intervals including this value, are suggested to avoid future practical troubles. Using commercially available software, the whole modeling and anticipative process is automatic, simple and requires minimal skills from the researcher. Both strategies studied have proven to successfully anticipate Rs values close to the experimental ones for EKC conditions outside the DOE domain, for two model compounds (hexaconazole
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and penconazole). Attending to the current results obtained in this work, some conclusions can be obtained: (i) Both approaches tend to provide similar, but relatively optimistic and uncertain, results when all the DOE data are included in the models. (ii) PLS2 allows to identify (then, to eliminate) both experiments which are inconsistent with the response surface model and irrelevant variables, thus, the model refinement (with some extra skills). (iii) DOE data simplification (i.e. model refinement) tends to provide less risky estimations, mainly in the PLS2-prediction approach. (iv) Only the PLS2-prediction approach offers the possibility of selecting appropriate/certain anticipated Rs–At combinations. These arguments suggest that the PLS2-prediction approach could be the strategy of choice to obtain a reliable anticipated EKC experiment, ready to be proved, with high possibilities of solving the optimization problem. Further cases of study would be necessary to confirm this statement. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2014.06.095.
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Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Fast-multivariate optimization of chiral separations in capillary electrophoresis: Anticipative strategies L. Escuder-Gilabert a , Y. Martín-Biosca a , S. Sagrado a,b , M.J. Medina-Hernández a,∗ a
Departamento de Química Analítica, Universidad de Valencia, Burjassot, Valencia, Spain Centro Interuniversitario de Reconocimiento Molecular y Desarrollo Tecnológico (IDM), Unidad Mixta Universidad Politécnica de Valencia-Universidad de Valencia, Spain b
a r t i c l e
i n f o
Article history: Received 16 April 2014 Received in revised form 23 June 2014 Accepted 29 June 2014 Available online 5 July 2014 Keywords: Capillary electrophoresis Enantioseparation optimization Design of experiments Steepest ascent Partial least squares Anticipative post-DOE strategy
a b s t r a c t The design of experiments (DOE) is a good option for rationally limiting the number of experiments required to achieve the enantioresolution (Rs) of a chiral compound in capillary electrophoresis. In some cases, the modeled Rs after DOE analysis can be unsatisfactory, maybe because the range of the explored factors (DOE domain) was not the adequate. In these cases, anticipative strategies can be an alternative to the repetition of the process (e.g. a new DOE), to save time and money. In this work, multiple linear regression (MLR)-steepest ascent and a new anticipative strategy based on a multiple response-partial least squares model (called PLS2-prediction) are examined as post-DOE strategies to anticipate new experimental conditions providing satisfactory Rs values. The new anticipative strategy allows to include the analysis time (At) and uncertainty limits into the decision making process. To demonstrate their efficiency, the chiral separation of hexaconazole and penconazole, as model compounds, is studied using highly sulfated--cyclodextrin (HS--CD) in electrokinetic chromatography (EKC). Box–Behnken DOE for three factors (background electrolyte pH, separation temperature and HS--CD concentration) and two responses (Rs and At) is used. Using commercially available software, the whole modeling and anticipative process is automatic, simple and requires minimal skills from the researcher. Both strategies studied have proven to successfully anticipate Rs values close to the experimental ones for EKC conditions outside the DOE domain for the two model compounds. The results in this work suggest that PLS2-prediction approach could be the strategy of choice to obtain secure anticipations in EKC. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Capillary electrophoresis (CE) is a powerful technique for enantiomer separations due to its intrinsic high separation efficiencies, speed of analysis, low reagent consumption and small sample requirements [1]. One of the most common modes of CE to perform chiral separations is electrokinetic chromatography (EKC), including a chiral selector in the background electrolyte (BGE) [2]. An alternative to the conventional EKC is the use of partial (PFT) and complete (CFT) filling techniques, in which, prior to injection of the analyte, the capillary is partially or completely filled with the chiral selector solution, respectively, while the while the inlet and outlet vials are free of chiral selector [2,3].
∗ Corresponding author at: Departamento de Química Analítica, Facultat de Farmacia, Universitat de Valencia, C/ Vicent Andrés Estellés s/n, E-46100 Burjassot, Valencia, Spain. Tel.: +34 963544899; fax: +34 963544953. E-mail address: [email protected] (M.J. Medina-Hernández). http://dx.doi.org/10.1016/j.chroma.2014.06.095 0021-9673/© 2014 Elsevier B.V. All rights reserved.
Among the different chiral selectors used in EKC, cyclodextrins (CDs) are the most widely employed due to their good enantiorecognition abilities, good water solubility, UV transparency, and the wide assortment of different neutral, cationic and anionic CDs with different functional groups that can be employed [4]. Highly sulfated--CD (HS--CD) is an anionic CD with an average content of 12 sulfate groups per molecule [5]. This CD has proven to be a powerful chiral selector for enantiomers of many basic and neutral organic compounds [6,7]. The enantioresolution (Rs) of compounds in EKC is the result of a delicate balance between different experimental variables such as chiral selector concentration, nature and concentration of electrophoretic buffer, BGE pH, temperature and applied voltage. Despite the fact that extensive research in the field of enantioseparations by CE using chiral selectors has been carried out, it is difficult to predict whether the separation of the enantiomers of a chiral compound is possible. Hence, experimental efforts are necessary to select appropriate experimental conditions (factors), usually by trial and error procedures. Thus, the enantioseparation of a chiral compound becomes a time- and money-consuming task.
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In most of the papers published on EKC, univariate optimization of experimental variables (factors) is still performed despite that multivariate optimization is strongly recommended to take into account possible interactions between factors [8]. The design of experiments (DOE) is the right systematic way to account with those interaction factors, limiting the number of experiments to obtain the proper information. Usually, the so called response surface model design is used in order to account with nonlinearities (e.g. squared factors). In DOE, factors are varied in a prefixed way to understand their effect on the response variable/-s and/or to model the relationships between the response variable/-s and the factors. The last feature allows to obtain the desirable, often optimal, experimental factors values that maximize (or minimize) the response variable/-s. For the case of a single response variable, the coefficients of the models are usually estimated by multiple linear regression (MLR) or partial least squares (PLS). For the case of multiple response variables, MLR (by using a ‘desirability’ function [8]) and PLS2 can be used. DOE requires an orderly and efficient mapping of the experimental space (DOE domain) to be cost-saving [9]. The selection of the factors is generally the first step in a DOE; then, one needs to properly define the extreme levels at which the factors will be studied. If boundaries are too wide, insufficient precision of the model is obtained. On the contrary, boundaries that are too narrow, can miss the desirable optimum [9]. The selection of a correct experimental domain is fundamental for a successful DOE and should be based on preliminary knowledge mostly gained by preliminary experiments. There is the possibility of running a screening DOE in order to fix the optimal values for some factors and to move the experimental domain of the remaining factors before being further studied by response surface methodology [8]. Sometimes, the initial DOE could be fixed according to the previous knowledge in separations with a given CD; just to save time and money, but with the risk to fail in finding adequate separation conditions. In this case, the recommended repetition of the process (new DOE), increasing the time and cost, is not the unique option. For instance, some experimental designs as Doehlert design can be moved to the zone leading to the best results, still maintaining the results of some experiments of the first DOE (although it still requires new experiments). Another post-DOE alternative could be to perform an extrapolation using the obtained response surface model in order to anticipate new experimental conditions that could provide convenient response variable/-s, requiring only one additional experiment, just to confirm the goodness of such anticipation, solving (or not) the problem. The steepest ascent (or descent) approach intends to provide locations of factors away from the initial DOE domain to find the optimal or desirable response. This strategy has been widely used in different scientific areas. However, its use in separation techniques has only been reported to optimize the mean resolution of biodiesel mixtures in liquid chromatography [10] and the resolution and analysis time (At) of two enantiomers, in supercritical fluid chromatography [11] and testosterone esters in micellar electrokinetic chromatography [12]. Recently, our research group has anticipated new desirable EKC conditions for bupivacaine enantiomers separation based on converting a multiple response-partial least squares model (PLS2) into linear-like equations (for Rs and At) and using them to extrapolate new results [13]. PLS2 was performed on the main factors, i.e. cross- and squared-terms to account for possible interactions between factors and nonlinearities, respectively, were not considered. A comparison with other alternatives was not performed. In this paper, MLR-steepest ascent and a new anticipative strategy (PLS2-prediction) are examined as post-DOE strategies to anticipate new experimental conditions providing satisfactory Rs (and At) for enantiomers separation in EKC. To demonstrate their
efficiency, the chiral separation of hexaconazole (HEX) and penconazole (PEN), as model compounds, is studied using HS--CD in EKC-CFT. The literature reports the separation of these compounds (together with other ones) using CD-modified micellar electrokinetic chromatography [14] and EKC with sulfated--cyclodextrin (a CD with lower degree of substitution than that used here) [15]. For each compound, in this work a Box–Behnken DOE for 3-factors (BGE pH, separation temperature and HS--CD concentration) and 2-responses (Rs and At), which requires 15 electrophoretic runs, is used. MLR and PLS2 response surface models are obtained, analyzed and in some cases, refined. Then, the steepest ascent and the PLS2prediction approaches are used to estimate the responses outside the original DOE domain. Finally, the outputs and their agreement with the experimental values of the two approaches are compared. 2. Materials and methods 2.1. Instrumentation A Beckman P/ACE MDQ Capillary Electrophoresis System equipped with a diode array detector (Beckman Coulter, Fullerton, CA, USA), and 32Karat software version 8.0 was used throughout. A 50 m inner diameter (id) uncoated fused-silica capillary with total and effective lengths of 60.2 and 50 cm, respectively, was employed (Beckman Coulter, Fullterton, CA, USA). Detection wavelength was fixed at 200 nm for all experiments. Electrophoretic solutions and samples were filtered through 0.45 m pore size nylon membranes (Micron Separation, Westboro, MA, USA) and degassed in an ultrasonic bath (JP Selecta, Barcelona, Spain) prior to use. A Crison Micro pH 2000 pH-meter from Crison Instruments (Barcelona, Spain) was employed to adjust the pH of buffer solutions. 2.2. Chemicals and reagents All reagents were of analytical grade. Sodium dihydrogen phosphate dihydrate was from Fluka (Buchs, Switzerland). Sodium hydroxide was from Scharlab S.L. (Barcelona, Spain). Racemic pesticides (HEX and PEN) were from Dr. Ehrenstofer (Augsburg, Germany) and HS--CD 20% w/v aqueous solution from Beckman Coulter (Fullerton, CA, USA). Ultra Clear TWF UV deionized water (SG Water, Barsbüttel, Germany) was used to prepare solutions. Background electrolytes (BGEs) containing phosphate 50 mM at different pH values were obtained by dissolving the appropriate amount of sodium dihydrogen phosphate dihydrate in water and adjusting the pH with 1 M NaOH. 1000 mg L−1 stock solutions of PEN and HEX were prepared in methanol and kept at 4 ◦ C. Working solutions (100 mg L−1 ) were prepared by dilution of the stock ones. HS--CD solutions at different concentrations were prepared by dilution in the corresponding BGE. 2.3. Capillary electrophoresis methodology New capillary was conditioned by rinsing with 1 M NaOH at 60 ◦ C during 15 min. Then, it was rinsed for 5 min with deionized water and 10 min with separation buffer at 25 ◦ C. In order to obtain good peak shapes and repeatable migration data, the capillary was conditioned prior to each injection. In all cases, the conditioning run included the following steps: (i) 1 min rinse with deionized water; (ii) 1 min rinse with 1 M NaOH; (iii) 1 min rinse with deionized water and (iv) 2 min rinse with the BGE solution. All steps were carried out at 20 psi. The solutions of the model compounds were injected hydrodynamically at 0.5 psi for 5 s. Before compounds injection, the capillary was completely filled with the HS--CD solution; by applying 20 psi during 1 min. No HS--CD was included in the BGE
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inlet and outlet vials (CFT mode). This operative mode was tested experimentally in our laboratory checking the consistence of electropherograms at injection times higher than 1 min at 20 psi. This is a counter current technique since the CD plug moves in the opposite direction to the EOF allowing the interaction with cationic or neutral compounds. Separation was performed in normal polarity by applying 15 kV. Different capillary temperatures were tested. 2.4. Box–Behnken DOE Box–Behnken DOEs for three factors (with two levels and three replicates of a center point) distributed in 15 experiments (identified by a number, Ne) were used for optimization of separation of HEX and PEN enantiomers (Table S1 in Supplementary data). For both compounds, main factors considered were: BGE pH (pH), separation temperature (T) and HS--CD concentration (CD). Their corresponding experimental values were set from the extreme levels at which they were going to be studied (CD: 0.5–2.5% w/v, T: 15–40 ◦ C and pH 6.5–8.5). 2.5. Software and calculations Enantioresolution (Rs) values were calculated using 32Karat software v. 8.0 (Beckman Coulter) by means of the following expression: Rs = 1.18
t2 − t1 w1 + w2
(1)
where t1 and t2 are, respectively, the migration times of the first and second eluted enantiomers, and w1 and w2 are the peak widths at 50% peak height. t2 is used along the text as analysis time (At). Statgraphics Plus® 5.1 (Statpoint Technologies, Warrenton, VA, USA) was used for Box–Benhken DOE analysis (MLR-response surface module) and to anticipate new response values by the steepest ascent strategy outside the DOE domain (here called MLR-steepest ascent strategy). The Unscrambler® v.9.2 multivariate analysis software (CAMO Software AS, Oslo, Norway) [16] was used for PLS2 modeling and to anticipate new responses values outside the DOE domain (here called PLS2-prediction strategy). For PLS2 autoscaled data were used. Leave-one-out cross-validation was used as validation strategy in PLS2 modeling. Note that anticipated results are simply predictions from MLR or PLS2 regression models outside the modeled domain. Further details on the modeling and prediction approaches are provided in the Supplementary data. 3. Results and discussion In this paper, to demonstrate the efficiency of the anticipative strategies studied for multivariate optimization of enantioseparations in EKC, HEX and PEN were used as model compounds and HS--CD was used as chiral selector. According to our laboratory experience in EKC enantioseparations using this CD, three EKC experimental conditions affecting Rs (and also At) were selected as main DOE factors: pH, T and CD (with a priori reasonable limits; Section 2.4). The levels of the factors for each experiment were set according to Box–Behnken DOE (Table S1 in Supplementary data). Although at the pH range used the neutral forms of HEX and PEN predominate (see Fig. S1 in Supplementary data), BGE pH can be an important factor on Rs since it strongly affects electroosmotic flow mobility and compounds apparent mobilities. Lower pH values would favor the compound ionization, and therefore, the interaction with the anionic HS--CD but also would decrease or even cancel the EOF. This fact could yield longer analysis times or make necessary the use of negative polarity (which implies to reverse the EOF and the especial use of injection configuration to allow the plug interaction in the CFT mode).
333
The other factors, buffer concentration and applied voltage, were prefixed as indicated in Sections 2.2 and 2.3, respectively. They are in general important factors, which can help tuning the selectivity of the separation and analysis time. However, according to our experience working with this CD, their effect is much lower than that of the selected DOE variables. All these decisions are consistent with the aim of this work, which is to explore a fast (and inexpensive) optimization; assuming the risk of finding an unsatisfactory DOE result, but obtaining the sufficient information to make a further anticipation. In our laboratory, excellent enantioseparations have been achieved for a wide range of compounds with the above criteria, which agrees with the aim (a 16-experiment strategy). Therefore, alternatives such as previous screening-experiments, more complex DOE (e.g. more factors, levels or designs with more experiments) and/or more complex post-DOE strategies, although recommendable in general, were not considered in this work. Considering the errors/uncertainties involved in the overall process (experimental, modeling, possible extrapolation if necessary, among others), but also a trouble-free future work (e.g. quantitative EKC determination of both enantiomers), some goals were established. The attainment of anticipated Rs values close to 2 (or narrow Rs uncertainty intervals including this value) was prefixed as requisite (primary goal). When possible, At estimations were also anticipated, although considered as a secondary goal. To reach the primary goal, MLR-steepest ascent on Rs was used. A new anticipative post-DOE strategy (called here PLS2-prediction) involving Rs and At responses simultaneously, was intended to reach the two goals. Initially, modeling and anticipated estimates were obtained considering all the experiments as well as the three main factors (pH, T and CD) and their six extended terms (pH × T, pH × CD, T × CD, pH2 , T2 and CD2 ); just for simplicity, we will refer to all these factors and terms as ‘variables’. However, the elimination of the less reliable data (variables and/or experiments after model analysis), in order to refine the model, was considered as alternative scenarios for comparison purposes. On the other hand, all studies were restricted to automatic calculations allowed by the software to keep the simplicity of the tools. Table 1 summarizes the main features of the proposed PLS2prediction approach compared with the MLR-steepest ascent one. Such features are related to the options available in the particular software (and version) used here and they should not be interpreted as general for other software or algorithms published in the literature. As can be seen, several advantages are possible from the new approach. 3.1. MLR-steepest ascent approach DOE data (Table S1) for both compounds were analyzed. The optimum estimated resolutions by classical MLR were: Rs = 1.53 and 1.64 (lower than the Rs requisite) for HEX and PEN, respectively; suggesting the necessity of a post-DOE stage. Fig. 1 shows the Statgraphics® ‘Main effects plot for Rs’ for both compounds. As can be observed, in both cases, CD has the highest impact on Rs. So, the expected Rs values when increasing CD could be anticipated by the proper steepest ascent strategy. The Statgtaphics® version (Plus 5.1) used performs these calculations automatically starting from the center of the DOE, allowing the user to decide the prefixed increments on the desired variable. Table 2 shows the anticipated results from the steepest ascent for Rs, obtained by changing CD in increments of 0.5 units from the center of the DOE (steps 1 to 7), when all variables are used in the MLR model. The path of the steepest ascent for HEX, indicates that step 4 (a) in Table 2 provides convenient EKC conditions satisfying the Rs ∼ 2 requisite (expected Rs = 2.11). Note that further steps
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Table 1 Features of the PLS2-prediction approach compared with the MLR-steepest ascent one, restricted to the two commercial computer programs used and the EKC optimization problem to be solved: three factors (pH, T and CD) and two response variables (Rs and At). See Supplementary data for further information on the models. Feature
PLS2-prediction (Unscrambler® )
MLR-steepest ascent (Statgraphics® )
Data analysis
DOE data is analyzed as in a conventional PLS2 problem with the exception that the option ‘Interaction and square effects selection’ is used to incorporate to the matrix of three factors the six cross- and squared-terms; [3 + 6] format as X Two response surface models to estimate Y (Rs and At simultaneously) are built. Normally, an optimum number of latent variables (k) lower than the number of X-variables is selected, so partial (filtered) information is used. Ideally, a k close to 2 (number of Y-variables) could indicate an adequate latent (inner) structure of the PLS2 model Scaled regression coefficients including cross-validated uncertainty limits allow to detect the important variables (i.e. high and certain coefficients) for both responses. The less important variables can be removed from X for model refinement
Identical analysis, except that MLR is used to create the model
Model details
Importance of the variables
Outliers detection
Anticipated results (prediction)
Only the response surface model for Rs is builta . All the information are used
Uncertainty estimates are not available for the coefficientsb (only for the effectsc ). The variables corresponding to the less important effects can be removed from X for model refinement Unclear (see Section 3.1 for details)
Ne-points too far from the ‘target line’ in the ‘validation plot’ (predicted vs. experimental Rs) are poorly modeled. Ne-points with a high difference between the predicted and cross-validated Rs estimates in the ‘validation plot’ alter the model. These Ne-points (potential outliers) can be removed from X and Y for model refinement Freely simulated EKC conditions (inside and/or outside the DOE domain) are used as X ‘test’ data, for which the model predict their corresponding Y-values (Rs and At). Uncertainty limits for the predictions are obtained, which can help in deciding the proper EKC conditions
New conditions ‘movements’ (steps) are restricted by the steepest ascent algorithm. Uncertainty is not available for the steepest ascent estimatesd
Acronyms: At: analysis time; Ne: number of DOE experiment; Rs: enantioresolution; X: matrix containing the values of the variables related to the EKC conditions. Y: matrix containing the values of the experimental responses, Rs and At. a The available alternative ‘desirability function’ (accounting for both response variables) does not allow to perform the steepest ascent stage (so, it was discarded). b To obtain confidence intervals for the coefficients, an independent MLR model with the X-Rs data must be calculated (using another module of Statgraphics® ). c The ‘Standardized Pareto Chart for Rs’ shows the standardized effects (as bars) and a threshold vertical line. Only bars that extend beyond this line are significant at the 95% confidence level. d To obtain confidence intervals for the estimates, a similar strategy as described for PLS2-prediction approach can be followed (see Section 3.4).
provide higher Rs values, but with the corresponding extra cost, and probably, higher uncertainty since their larger distance from the DOE domain. The convenient estimate for PEN (step 4 (d)) is higher than for HEX, Rs = 2.54. For model refinement (see Table 1), the elimination of the less important variables in the HEX DOE data was considered. The standardized Pareto chart for Rs (see Fig. S2 in Supplementary data) suggested that only CD, CD2 , pH and CD × pH (in this importance order) are the statistically significant variables at a 95% confidence level. The T main factor showed a higher standardized effect than
the other non-significant variables. It was retained into the MLR model, together with the significant variables, totaling five variables (Partial-1 data in Table 2). As can be observed, the impact of such simplification on the steepest ascent anticipations is negligible (compare Partial-1 data vs. all data in Table 2). However, the model refinement provided improved model statistics and predictive ability (see Fig. S2-footnote in Supplementary data), thus increasing the model reliability. In the case of PEN, the standardized Pareto chart for Rs (see Fig. S2 in Supplementary data) suggested that just CD and CD2 were significant, an output also suggested by Fig. 1b.
Table 2 Some anticipative results from MLR-steepest ascent (Rs as response variable) and PLS2-predictions (Rs and At as response variables). Analyte
DOE data
HEX
All
Partial-1 Partial-2 PEN
All
Partial-3
MLR-steepest ascent
PLS2-prediction
Step
pH
T
CD
Rs
1 2 3 4 (a) 5 6 7 4 (b) 4 (c)
7.50 7.28 7.24 7.27 7.33 7.43 7.53 7.31 7.29
27.50 26.76 26.47 26.31 26.19 26.09 26.00 25.80 27.26
1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.0 3.0
0.33 0.71 1.28 2.11 3.24 4.67 6.43 2.14 2.17
1 2 3 4 (d) 5 6 7 4 (e)
7.50 7.45 7.43 7.42 7.42 7.42 7.43 7.06
27.50 27.41 27.37 27.35 27.35 27.35 27.35 27.16
1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.00
0.53 0.97 1.64 2.54 3.68 5.06 6.67 2.19
Simulation
pH
T
CD
Rs (u)
At (u)
(a) (a)
7.0 7.5
27.5 27.5
3.0 3.0
2.08 (0.52) 2.19 (0.49)
11.89 (1.86) 11.96 (1.76)
(c)
7.5
27.5
3.0
1.81 (0.44)
12.61 (1.96)
(d)
7.5
27.5
3.0
2.56 (0.51)
11.67 (1.75)
(d)
7.5
27.5
3.0
2.01 (0.19)
11.07 (0.91)
Partial-1 data: five selected variables: CD, CD2 , pH and CD × pH (significant variables at 95% confidence level; in importance order of the effects) and T. Partial-2 data: selected variables as in Partial-1 data and eliminating experiments Ne = 5 and Ne = 12 (according to PLS2 suggestions). Partial-3 data—seven selected variables: all terms, except pH × T and T × CD cross-terms, and eliminating experiment Ne = 11 (according to PLS2 suggestions). Letters between brackets correspond to the simulated EKC conditions for MLR-steepest ascent fitting the Rs ∼ 2 requisite. Similar conditions have been simulated using the PLS2-prediction strategy for comparison. u: uncertainty values
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Fig. 1. Statgraphics® ‘main effects plot for Rs’: (a) HEX and (b) PEN results.
Besides the presence of non-important variables in the model, the occurrence of outliers able to artificially alter the MLR model could be another problem to be taken into account. Unfortunately, the MLR model is designed to minimize the residuals, i.e. to accommodate the response surface to fit well all the experimental results. In fact, the residual plots, including the residuals normal probability plot (see Fig. S2 in Supplementary data), which could help to detect outliers, indicated that the largest residuals were not far from the others, so they were not perceived as outliers. 3.2. PLS2-prediction approach Table 2 shows some selected results of the PLS2-prediction approach, close to the EKC conditions selected in Section 3.1 (identified by the same letter in parenthesis) to facilitate the comparison between strategies. As can be observed, when all the DOE data were used in the models, similar Rs estimates were obtained, suggesting the equivalence of both approaches (see conditions/results (a) and (d) in Table 2 for HEX and PEN, respectively). However, the PLS2 analysis revealed some deficiencies in the models for HEX and PEN (e.g. a high number of uncertain regression coefficients and low cross-validated explained response variance, suggesting poor predictive ability of the models) when the entire dataset was used, (see for instance Fig. S3 in Supplementary data for the case of HEX). This fact suggests the models refinement to avoid unreliable anticipated results. For HEX, model refinement by the elimination of the less important four variables for predicting Rs (the same as in MLR) was performed. T was retained for the same reasons as in MLR (see Section 3.1), but also because it is the most important variable for predicting At (see Fig. S3b in Supplementary data). Note that PLS2 model uses the same variables for predicting Rs and At; i.e., the elimination of a variable (model refinement) affects to both response variables (see Supplementary data for further details). After variables removal, two experiments, Ne = 5 and 12, appeared as possible outliers affecting the model (according to Table 1), in contrast to the MLR observations. Ne = 12 showed a relatively high
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residual value. Ne = 5 exhibited a relatively high difference between the Rs predicted and cross-validated values; moreover, it showed an atypically high Rs value for the low CD tested (see Table S1). This result is, in fact, responsible for the curvature of the CD effect on Rs in the MLR model (Fig. 1a), which predicts an illogical increase of Rs at low CD values, even for CD = 0. Experiments, Ne = 5 and 12 were eliminated from the PLS2 model as an alternative scenario (Partial-2 data in Table 2), but also in the MLR case, just for comparison purposes. This table shows the anticipated results for the new scenario using both strategies. The impact of this model refinement can be seen by comparing the conditions/results (c) vs. (a) in Table 2. While the model refinement (variables and experiments elimination) had a negligible effect on the MLR-steepest ascent, it had a relative impact on the PLS2predictions providing a lower Rs estimation: Rs = 1.81 after the model refinement, compared with the previous one (Rs > 2). In the case of PEN, PLS2 model refinement was also performed. The two less important variables (pH × T and T × CD) respect to the Rs and At responses and the experiment Ne = 11 were eliminated (Partial-3 data in Table 2). This experiment showed a relatively high difference between the Rs predicted and cross-validated values; this difference was larger than in the case above commented for HEX, then with higher risk to alter the model (i.e. modify the response surface). Again, this experiment was not perceived as outlier in the MLR analysis. The same model refinement was applied to MLR for comparison purposes. As can be observed in Table 2, the model refinement in this case had a noticeable impact on the anticipated Rs results for both approaches, but higher for the PLS2-prediction one. Thus, Rs = 2.01 (Partial-3 data) is ∼0.5 units lower than before model refinement (all data). Moreover, in contrast to the HEX case, simplification of data for PEN changed the steepest ascent ‘movements’ providing different EKC conditions (mainly for pH) apart from a lower Rs estimate (see new conditions/results (e) compared with (d)). It could be provisionally concluded that PLS2 model refinement provides lower Rs estimates (as observed for HEX and PEN). However, this behavior cannot be assured in the case of the MLRsteepest ascent approach. From a practical point of view, it is safer to anticipate under-optimistic rather than over-optimistic Rs estimates. Fig. 2 shows Rs vs. At plots obtained from the PLS2-prediction approach using the refined models for HEX and PEN (Partial-2 and Partial-3 data, respectively). As can be observed, the models show reasonably good predictive ability inside the DOE domain; e.g. estimates for the DOE data (squares) are quite similar to the experimental ones (triangles) (see also Fig. S4 in Supplementary data for correlation plots and absolute and relative differences). On the other hand, the anticipated results outside the DOE domain (crosses), for CD = 3% and different pH and T values, satisfy the Rs ∼ 2 requisite. One of these anticipated results for HEX and PEN is shown in Table 2 (Partial-2 and Partial-3 conditions, respectively). Such kind of plot could help to select a desirable Rs–At combination.
3.3. Experimental versus anticipated results To check the real usefulness of the anticipative strategies tested, the anticipated results were compared with the experimental ones (see also Fig. S4 in Supplementary data). Fig. 3 shows the electropherograms obtained under EKC conditions close to those anticipated from Partial-2 and Partial-3 data for HEX and PEN, respectively (Table 2). For HEX, at pH = 7.5, T = 25 ◦ C and CD = 3%, the experimental outputs were: Rs = 2.1 and At = 13.5 min. The experimental Rs agrees well with the one anticipated by the MLR-steepest ascent approach (2.2 ± 0.5; Partial-2 data in Table 2; see Section 3.4 for details on the confidence interval). In the PLS2-prediction
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approach, the anticipated uncertainty intervals include the experimental Rs (and At) values: Rs = 1.8 ± 0.4 (and At = 12 ± 2 min). Similarly, for PEN, at pH = 7.5, T = 27.5 ◦ C and CD = 3%, the experimental outputs were: Rs = 1.9 and At = 12.4 min. The experimental Rs is lower than the anticipated by the MLR-steepest ascent approach (2.2 ± 0.4: Partial-3 data, in Table 2; see Section 3.4 for details on the confidence interval), although in slightly different pH and T conditions (step 4 (e) in Table 2). As before, the experimental Rs (and At) are included within the PLS2-prediction intervals: Rs = 2.01 ± 0.19 (and At = 11.1 ± 0.9 min). It should be noted that the anticipated Rs values from unrefined models result too optimistic and then risky. In general, the uncertainty intervals should help in the decision making process (Table 1). For instance, the PLS2 anticipated uncertainty level for PEN as consequence of model refinement (±0.19; Partial-3 data; Table 2) is more reliable than without simplification (±0.5; all data). High differences between the uncertainties of anticipated results were obtained (see Fig. S5 in Supplementary data). 3.4. Additional remarks In PLS2, the use of just the main factors (pH, T and CD) without their corresponding extended variables, as performed in a recent paper [13], could be an apparently simpler possibility. However, this is just an approximation, i.e. an attempt to ‘linearize’ an originally curved response surface, based on the flexibility of the linear PLS algorithm to partially accommodate interactions and nonlinearities. However, if the crossed- or squared-terms are relatively important, such model can fail in their estimations, particularly to make anticipations (extrapolations). An additional problem could
Fig. 3. Electropherograms of 100 mg L−1 solutions of racemic model compounds obtained under the following experimental conditions: (a) HEX: 3% HS--CD, 25 ◦ C, pH 7.5; (b) PEN: 3% HS--CD, 27.5 ◦ C, pH 7.5. Further experimental details are indicated in Section 2.
be that the outlier character of an experimental result becomes ambiguous; e.g. it could be forced by this ‘linearization’ process. Just for comparison, as an example, the PLS2 estimations using the three main factors were also calculated for PEN. First of all, four apparent outliers were identified (Ne = 1, 6, 11 and 12), while in the proposed approach only one of them, Ne = 11, was detected (Section 3.2). Elimination of four experiments in a dataset of 15 designed experiments seems to be excessive (but necessary). The estimations using the same EKC conditions as in (d)-simulation in Table 2, were: Rs = 1.8 ± 0.2 (and At = 11.9 ± 1.1 min). Although in this case, the results could be considered acceptable, the elimination of four experiments provides less confidence on the anticipations. For HEX, even more experiments should be eliminated. The Statgraphics® steepest ascent algorithm does not provide the corresponding confidence intervals for anticipated results. However, the prior MLR model (another module of the software) is able to calculate them, just including the desired new EKC conditions into the datasheet (as in the PLS2-prediction approach). For comparison purposes, these calculations were performed. For instance, the MLR estimated 95% confidence intervals for HEX and PEN shown in Section 3.3 are larger than the corresponding uncertainty intervals from the PLS2-prediction approach. 4. Conclusions In this work, MLR-steepest ascent and PLS2-prediction approaches are explored as post-DOE anticipative strategies in enantioselective EKC to save experimental effort for achieving full enantioresolution after unsatisfactory DOE results. Rs ∼ 2 estimates, as requisite, and preferably, narrow Rs uncertainty intervals including this value, are suggested to avoid future practical troubles. Using commercially available software, the whole modeling and anticipative process is automatic, simple and requires minimal skills from the researcher. Both strategies studied have proven to successfully anticipate Rs values close to the experimental ones for EKC conditions outside the DOE domain, for two model compounds (hexaconazole
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and penconazole). Attending to the current results obtained in this work, some conclusions can be obtained: (i) Both approaches tend to provide similar, but relatively optimistic and uncertain, results when all the DOE data are included in the models. (ii) PLS2 allows to identify (then, to eliminate) both experiments which are inconsistent with the response surface model and irrelevant variables, thus, the model refinement (with some extra skills). (iii) DOE data simplification (i.e. model refinement) tends to provide less risky estimations, mainly in the PLS2-prediction approach. (iv) Only the PLS2-prediction approach offers the possibility of selecting appropriate/certain anticipated Rs–At combinations. These arguments suggest that the PLS2-prediction approach could be the strategy of choice to obtain a reliable anticipated EKC experiment, ready to be proved, with high possibilities of solving the optimization problem. Further cases of study would be necessary to confirm this statement. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2014.06.095.
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