Determination of relative enantiomer migration order using a racemic sample

Journal of Chromatography A, 1424 (2015) 139–143

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Short communication

Determination of relative enantiomer migration order using a racemic sample Ludmila Müllerová, Pavel Dubsky´ ∗ , Magda Ördögová, Bohuslav Gaˇs Charles University in Prague, Faculty of Science, Department of Physical and Macromolecular Chemistry, Prague, Czech Republic

a r t i c l e

i n f o

Article history: Received 27 May 2015 Received in revised form 14 October 2015 Accepted 15 October 2015 Available online 10 November 2015 Keywords: Dual selector system Cyclodextrin Electromigration order Model of electromigration Racemate

a b s t r a c t We developed a method that enables us to distinguish between the same or the opposite enantiomer migration order (EMO) of two enantiomers of a chiral compound with two different selectors. The method is applicable to racemic samples and thus a standard of the pure enantiomeric form(s) is not required. First, complexation constants and mobilities of complexes of the two enantiomers with the first and second selector are determined. However, for a racemic sample it is not possible to deduce whether the first migrating enantiomer with one selector is the same one as the first migrating enantiomer with the second selector. A specific mixture of the two selectors is designed to resolve this. In case the two enantiomers exhibit the same, respectively the opposite EMO in the two selectors, the mixture does, respectively does not separate the racemic sample. Thus two peaks are detected in the first case, while a single coalescent peak is recorded in the opposite case. We demonstrate the method on a racemic sample of amphetamine. Its relative EMO is determined with three cyclodextrins, heptakis(2,3,6-tri-O-methyl)-␤-cyclodextrin, (2-hydroxypropyl)-␤-cyclodextrin and heptakis(2,3-di-O-acetyl-6-O-sulfo)-␤-cyclodextrin. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Enantiomer migration order (EMO) in capillary electrophoresis (CE) plays an important role in optimizing enantioseparation methods [1–3]. Enantiomers of one chiral analyte may exhibit a certain enantiomer migration order (EMO) with one selector and either the same or the opposite EMO with another selector. Moreover, even with one single selector, the EMO may reverse when changing the selector concentration and/or pH of the background electrolyte (BGE) [4–6]. Relation between the structure of the enantiomerselector complexes and the EMO has been studied combining CE with other methods [7–9]. In the analytical practice, the separation is often achieved by using dual-selector mixtures [10–12]. The EMO and particularly its reversal in these systems have been investigated in several works [13–16] and we have recently summarized this topic in a review [17]. We have presented a dual-selector model [18,19] for predicting the EMO and the other separation characteristics in such systems. The model can be utilized for method optimizations [19]. To utilize this model, complexation constants and mobilities of

complexes must be known for both enantiomers with one and the other selector. Determining complexation constants and mobilities of complexes is generally an easy task [20,21]. However, without knowing the EMO, one cannot assign the complexation constants and mobilities of complexes to the proper enantiomeric forms of the analyte. To determine the EMO, the enantiomerically pure or enriched compound must be measured [13]. Unfortunately, pure enantiomers are often expensive or even not commercially available. Thus, we introduce a strategy that enables us to determine whether the EMO is the same or the opposite in two single-selector systems using a racemic analyte. This brings an advantage of being able to assign the complexation constants and mobilities of complexes to the proper enantiomeric forms of the analyte as measured in various selectors without having the pure enantiomers available. In this Short Communication, we present the proposed concept in a form as concise as possible. More detailed description and theory can be found in the Supplementary information. 2. Materials and methods 2.1. Chemicals

∗ Corresponding author at: Charles University in Prague, Faculty of Science, Albertov 2030, CZ-128 40 Prague 2, Czech Republic. ´ E-mail address: [email protected] (P. Dubsky). http://dx.doi.org/10.1016/j.chroma.2015.10.058 0021-9673/© 2015 Elsevier B.V. All rights reserved.

All chemicals were of analytical-grade purity: Racemic amphetamine (a generous gift from Prof. Dr. Martin Schmid,

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University of Graz, Austria), ortho-phosphoric acid (Lachema, Brno, Czech Republic), NaOH solution for rinsing the capillary (Agilent Technologies, Waldbronn, Germany). All other chemicals, including cyclodextrins, were purchased from Sigma–Aldrich, Prague, Czech Republic. Water was purified by Rowapur and Ultrapur, Watrex, San Francisco, USA. The IUPAC buffers, pH 1.679 and 4.005 (Radiometer, Copenhagen, Denmark), were used for calibration of the pH meter. 2.2. Instrumentation The experiments were performed using: Agilent 3D CE capillary electrophoresis equipped with a photometric diode array detector and operated by ChemStation software (Agilent Technologies, Waldbronn, Germany); fused-silica capillary of 50 ␮m id, 375 ␮m od, 50.3 cm length, and 41.8 cm to the detector (Polymicro Technologies, Phoenix, AZ, USA); pH meter PHM 240 pH/ION Meter (Radiometer analytical).

Campina Grande, Brazil) was used for fitting effective mobilities of the analyte to obtain the complexation parameters. Other calculations were performed using Microsoft Office Excel 2010. 3. Results and discussion In the proposed method we determine the relative EMO in two selectors when the chiral analyte is available only as a racemate. Amphetamine is used as a model analyte. At the selected pH (2.14), it is present exclusively as a monovalent cation. Cyclodextrins, TM-␤-CD (neutral), HP-␤-CD (neutral) and AS-␤-CD (negatively charged), were used as selectors. Most importantly, this information about the relative EMO is to be utilized in dual-selector systems, where the effective mobility of the analyte, eff,A , depends on the mixture composition and its total concentration according to the model presented by our group earlier [18,19]: eff,A =

2.3. Experimental conditions

over

Stock buffer contained 100 mM ortho-phosphoric acid and 50 mM tris(hydroxymethyl)aminomethane, pH was 2.14. Stock solutions of 50 mM heptakis(2,3,6-tri-O-methyl)-␤-cyclodextrin (TM-␤-CD) and of 50 mM (2-Hydroxypropyl)-␤-cyclodextrin (HP␤-CD) were prepared by dissolving the selector in the stock buffer. Stock solution of 5 mM heptakis(2,3-di-O-acetyl-6-O-sulfo)␤-cyclodextrin heptasodium salt (AS-␤-CD) contained 30 mM ortho-phosphoric acid, 15 mM Tris. The BGEs containing lower concentrations of the selectors were prepared by diluting the stock solution with the stock buffer (cf. Table 1). The BGEs containing two selectors were prepared by mixing the stock solutions of the two selectors and of the stock buffer (cf. Fig. 2). The racemic samples were prepared by mixing 8 ␮L of the stock solution of racemic amphetamine (0.29 mg/mL in the stock buffer), 30 ␮L of 1% (v/v) aqueous solution of nitromethane (EOF marker) and 112 ␮L of the stock buffer. The spiked samples were prepared in the same way but 2 ␮L of S-amphetamine solution (1 mg/mL in methanol) was added and 110 ␮L of the stock buffer used. The samples did not contain any selector. All the solutions were filtered using syringe filters, pore size 0.45 ␮m (Sigma–Aldrich, Prague, Czech Republic). Experimental conditions were as follows: temperature, 25 ◦ C; voltage, +15 kV; hydrodynamic injection, 80 mbar·s, 150 mbar·s (AS-␤-CD as a single selector only); pressure application due to low EOF, +10 mbar, +30 mbar (AS-␤-CD as a single selector only); new capillary was flushed, water, 5 min, 1 M NaOH, 5 min, water, 5 min twice; prior-to-run flush, BGE, 3 min at least. Each experiment was repeated at least four times. The software ChemStation (Agilent Technologies) was used for data collection and acquisition. The Origin 8.1 software (OriginLab Corporation, Northampton, USA) was used for fitting analyte peaks by the Haarhoff van der Linde (HVL) function [22,23] (analyte peaks in BGEs containing AS-␤-CD), the Gaussian function (marker peaks) and summation of two Gaussian functions (analyte peaks in BGEs containing HP-␤-CD or TM-␤-CD). The LAB Fit 7.2.48 software (Federal University of

K  AS

K  over 0 + over AS ctot AS

(1)

1 + K  over AS ctot

  = S1 KAS1 + (1 − S1 )KAS2

over AS =

 S1 AS1 KAS1

(2)

 + (1 − S1 )AS2 KAS2 K  over AS

(3)

where S1 is a molar fraction of the first selector in the dualselector mixture (referred to as the mixture composition), ctot is   and KAS2 are the (ionic a total concentration of the selectors, KAS1 strength dependent) complexation constants and AS1 and AS2 are the mobilities of complexes with the first and the second selector, respectively. Knowing the dependence (1) for two analytes A and B, one can optimize the total selector concentration and the mixture composition with respect to the effective mobility difference, selectivity, resolution, as well as the EMO, as we summarized in a recent review paper [17]. First, the complexation parameters are determined in the singleselector systems. We have used affinity capillary electrophoresis (ACE) [20,21] for this purpose. All measurements were performed with a racemic sample of the amphetamine. At every selector concentration used, at least partial separation was observed. Therefore, it was possible to obtain migration times of both enantiomers, by fitting a suitable function (see Section 2.3) to the electropherogram data. The obtained complexation parameters are given in Table 1. Effective mobility of amphetamine in the selector-free buffer (inherently the same for both enantiomers) was also determined (25.7 × 10−9 m2 V−1 s−1 ). The measurement procedure and the related calculations are described in detail in the Supplementary information. At this point, individual values of the mobility of the free analyte, 0 , mobilities of the analyte-selector complexes with the first and the second migrating enantiomer, 1S ¯ and 2S ¯ , respectively, and the (ionic strength dependent) complexation constants with the first and the second migrating enantiomer, K ¯ , and K ¯ , 1S 2S respectively, are known for the two enantiomers in each selector.

Table 1 Complexation constants and mobilities of complexes of amphetamine enantiomers interacting with each single selector; subscripts 1¯ and 2¯ refer to the first and the second migrating enantiomer, respectively. Selector

K ¯ (mM−1 )

−9 1S m2 V−1 s−1 ) ¯ (10

K ¯ (mM−1 )

−9 2S m2 V−1 s−1 ) ¯ (10

Maximum cs (mM)

Number of concentration levels

TM-␤-CDa HP-␤-CD AS-␤-CDb

5.4 ± 1.6 28.7 ± 1.4 340 ± 4

12.7 ± 3.1 5.7 ± 0.5 −27.2 ± 0.3

6.6 ± 2.0 31.5 ± 1.4 426 ± 5

2S ¯ = 1S ¯ 5.9 ± 0.4 −27.7 ± 0.3

40 50 4.2

6 8 7

a b

1S

2S

In case of TM-␤-CD 2S ¯ = 1S ¯ = S had to be used (see Supplementary information details). Notice that the study finally revealed opposite enantiomer migration order in AS-␤-CD compared to the other two selectors.

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Fig. 1. Expected differences between effective mobilities of amphetamine enantiomers induced by dual-selector mixture of TM-␤-CD and HP-␤-CD for the EMO being the same (A) or opposite (B) in both single selectors; effective mobilities predicted by the model (1)–(4) utilizing the complexation parameters (Table 1) and mobility of free amphetamine 25.7 × 10−9 m2 V−1 s−1 .

¯ could However, until now the two amphetamine peaks, 1¯ and 2, not be attributed to its individual enantiomeric forms in any of ¯ in, e.g., the selectors. We may attribute the first migrating peak, 1, TM-␤-CD to an enantiomeric form A, and the second migrating ¯ to an enantiomeric form B. This would be adequate in peak, 2, single-selector systems as we do not need to know the absolute configuration of the enantiomers in order to optimize the separation system. To the contrary, when combining TM-␤-CD with another selector (e.g. HP-␤-CD) in a dual-selector system, incorrect overall parameters will result from the Eqs. (2) and (3) if we falsely assign {1¯ ≡ A; 2¯ ≡ B} in both selectors since the opposite EMO may apply with HP-␤-CD. To resolve this problem let’s have a closer look at the effective mobility difference eff = eff,A − eff,B

(4)

where eff,A and eff,B can be expressed for the two analytes, A and B, according to Eq. (1). First assign {1¯ TM-␤-CD ≡ A; 2¯ TM-␤-CD ≡ B} in the first-reference-selector, TM-␤-CD, by definition. Then map the expected effective mobility differences given by Eqs. (1)–(4) as a function of the two variables, ctot and TM-␤-CD , for the TM-␤-CD/HP-␤-CD dual-selector system. First do so under the assumption of {1¯ HP-␤-CD ≡ A; 2¯ HP-␤-CD ≡ B} (same EMO assumption). Second, perform the same mapping under the opposite assumption of {1¯ HP-␤-CD ≡ B; 2¯ HP-␤-CD ≡ A} (opposite EMO assumption). Finally find a dual-selector system so that its total concentration, ctot , and composition, TM-␤-CD , satisfy the following criteria: (i) If the EMO were opposite in HP-␤-CD compared to TM-␤-CD, a zero effective mobility difference would result in the dualselector system under the specified ctot and TM-␤-CD . (ii) If the EMO were the same in both single selectors, a distinguishably nonzero effective mobility difference would result under the same ctot and TM-␤-CD conditions. Thus a single peak would appear in the dual-selector system under the opposite-EMO assumption of {1¯ HP-␤-CD ≡ B; 2¯ HP-␤-CD ≡

A}, while two peaks would be observed under the same-EMO assumption of {1¯ HP-␤-CD ≡ A; 2¯ HP-␤-CD ≡ B}. The easiest way of searching through the various S1 and ctot combinations is graphical analysis. We give a brief overview of the evaluation procedure in this paper, while a detailed description together with a calculation example can be found in the Supplementary information. We plotted the effective mobility differences as expected in the HP-␤-CD/TM-␤-CD dual-selector system under the assumptions of the same (Fig. 1A) or the opposite (Fig. 1B) EMOs. Various mixture constitutions fulfill the criteria (i) and (ii) and any of them can be chosen (by mixture constitution we mean here both its composition, S1 , and total concentration ctot ). Inspecting the graphs (see Supplementary information for details), we choose the dual-selector mixture constitution TM-␤-CD = 0.8 and ctot = 40 mM (light-colored lines in Fig. 1). The effective mobility differences of 0.006 × 10−9 m2 V−1 s−1 in Fig. 1B and 0.34 × 10−9 m2 V−1 s−1 in Fig. 1A, were predicted for the case of the opposite (i) and the same (ii) EMOs, respectively. Using analogous graphs (cf. Supplementary information), the selected testing constitution of the TM-␤-CD and AS-␤-CD mixture was TM-␤-CD = 0.997, ctot = 20 mM. Having these mixture constitutions selected, the same/opposite EMO assumption can be easily resolved in a single additional experiment per selector mixture. The obtained electropherograms are given in Fig. 2. We obtained two peaks of the amphetamine enantiomers in the system of TM␤-CD +HP-␤-CD, which means that the EMO is the same in the single-selector systems containing these two selectors. On the other hand, in the system of TM-␤-CD +AS-␤-CD only one peak was obtained, indicating the opposite EMO. Based on these results we can additionally conclude that the EMO in HP-␤-CD is opposite to that in AS-␤-CD without the need to make an extra measurement in the HP-␤-CD +AS-␤-CD dual-selector system. Nevertheless, the corresponding 2D-graphs can be found in the Supplementary information and the actual measurement that confirms this expectation is also seen in Fig. 2. This all enables us to assign the complexation parameters measured in the individual selectors, AS-␤-CD, HP-␤-CD and TM-␤-CD, to the proper enantiomeric forms, even though their

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Conflicts of interest All authors declare no conflicts of interest. Acknowledgements The authors acknowledge the financial support of this work from the Grant No. 15-18424Y of the Czech Science Foundation, from the Grant No. 510214 of the Grant Agency of Charles University, and from the Charles University grant UNCE204025/2012, and express their thanks to Prof. Dr. Martin Schmid for providing them with the sample. 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.2015.10. 058. Fig. 2. Electropherograms of racemic amphetamine obtained in the dual-selector mixtures (constitution given in the figure, see text for experimental details); symbols mark the migration time differences predicted under the same (shorter lines) or the opposite (longer lines) EMO assumption considering run-specific electroosmotic flow.

Fig. 3. Electropherograms of racemic amphetamine spiked with S-enantiomer in single-selector systems (selectors and concentrations given in the figure, see text for experimental details).

absolute configuration remains unknown. Specifically, it was concluded that if {1¯ TM-␤-CD ≡ A; 2¯ TM-␤-CD ≡ B} then {1¯ HP-␤-CD ≡ A; 2¯ HP-␤-CD ≡ B}, while {1¯ AS-␤-CD ≡ B; 2¯ AS-␤-CD ≡ A}. As a verification, electrophoretic experiments were performed in the singleselector systems using amphetamine samples spiked with the pure S-enantiomer. The results, which are in accordance with our expectation, are presented in Fig. 3. 4. Concluding remarks We proposed a method that allows us to conclude whether the EMO is the same or the opposite in various selectors using a racemic sample. The prime aim of this work is to supplement our previously published model for optimizing dual-selector mixtures. The same procedure can be applied when the absolute EMO in a new selector is unknown, while the EMO in a reference selector is determined in previous experiments or is obtained from the literature data.

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