Modelling the simultaneous chiral separation of a group of drugs by electrokinetic chromatography using mixtures of cyclodextrins

Journal of Chromatography A 1681 (2022) 463444

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Journal of Chromatography A
journal homepage: www.elsevier.com/locate/chroma

Modelling the simultaneous chiral separation of a group of drugs by
electrokinetic chromatography using mixtures of cyclodextrins
L. García-Cansino a,# , J.M. Saz a,# , M.A. García a,b , M.L. Marina a,b,∗
a

Universidad de Alcalá, Departamento de Química Analítica, Química Física e Ingeniería Química, Ctra. Madrid-Barcelona Km. 33.600, 28871 Alcalá de
Henares (Madrid), Spain
b
Universidad de Alcalá, Instituto de Investigación Química Andrés M. del Río, Ctra. Madrid-Barcelona Km. 33.600, 28871 Alcalá de Henares (Madrid), Spain

a r t i c l e

i n f o

Article history:
Received 26 July 2022
Revised 18 August 2022
Accepted 22 August 2022
Available online 27 August 2022
Keywords:
cyclodextrin-electrokinetic chromatography/
chiral separation/ dual systems/ Dubsky’s
model/ drugs/

a b s t r a c t
Two mixtures of neutral cyclodextrins (CDs) were used in Electrokinetic Chromatography (EKC) to model
and optimize the simultaneous enantiomeric separation of a group of seven drugs. Heptakis(2,6-di-Omethyl)-β -CD (DM-β -CD) combined with methyl-γ -CD (M-γ -CD) or with carboxyethyl-γ -CD (CE-γ -CD)
was employed in a 25 mM formate buffer at pH 3.0 to have the drugs studied positively charged. Dubsky’s model was applied to calculate the enantiomer effective electrophoretic mobilities for each combination of CDs at different averaged molar fractions and total CDs concentrations. The most adequate
averaged molar fraction and total CDs concentration in terms of the simultaneous enantiomeric separation of the drug mixture were predicted by the model and results were experimentally corroborated. The
model also foresaw interesting effects, derived from the combination of DM-β -CD with M-γ -CD or with
CE-γ -CD, on the individual chiral separation of some of the drugs studied. The observed reversal of the
migration order for some compounds when changing the total CDs concentration was also predicted and
the model showed its potential even at concentrations out of the experimental range of CD concentrations experimentally employed. The use of an averaged molar fraction of 0.8 for DM-β -CD at a total CDs
concentration of 40 mM in the DM-β -CD/CE-γ -CD system predicted by the model enabled the simultaneous enantiomeric separation of six of the drugs studied (except verapamil) with resolutions ranging
from 0.6 to 4.0.
© 2022 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license
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1. Introduction
Chiral analysis is a very interesting area in analytical chemistry due to the different properties that enantiomers may have.
These differences are a very relevant issue in the pharmaceutical,
food, environmental, cosmetic or agrochemical fields, among others [1]. This interest has originated that chiral separation methods have been developed enabling the individual determination of
enantiomers. Among the most employed chiral separation techniques, Capillary Electrophoresis has attracted a great attention
due to its inherent characteristics such as high efficiency, the possibility of changing very easily the chiral selector and the low consumption of reagents and samples, being considered an environ-

∗

#

Corresponding author: Tel.: (+34) 918854935; fax: (+34) 918854971.
E-mail address: (M.L. Marina).
These authors contributed equally to this work.

mentally friendly technique [2–4]. Numerous chiral selectors have

been employed in the separation medium in the so-called Electrokinetic Chromatography (EKC) mode, such as cyclodextrins (CDs)
[5], macrocyclic antibiotics, chiral surfactants, etc. Among all these
chiral selectors, CDs have been the most employed due to their
discrimination power and the big variety of derivatives commercially available. However, even when using powerful chiral selectors as CDs, sometimes the separation of the enantiomers of a chiral compound can be difficult. In these cases, one possibility that
has demonstrated to be very useful can be the use of a mixture
of two CDs that are combined to produce an enhancement in the
chiral separation. From the first pioneering works dealing with the
use of mixtures of CDs [6–12] for chiral separations by EKC, the
combination of CDs has received an increasing attention [13–16].
However, the use of these systems generally supposes a complex
process for optimizing the most adequate experimental conditions
to achieve a given enantiomeric separation. This complexity is even

/>0021-9673/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
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L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

higher when multicomponent mixtures of chiral compounds have
to be enantiomerically separated. From this point of view, the proposal of physical-chemical models to facilitate the optimization of
the chiral separation conditions has demonstrated to be an interesting tool.
For a single CD system, Eq. (1) proposed by Wren and Rowe
[17] for an analyte interacting with a chiral selector can be applied. This equation enables the calculation of the apparent complexation constants (KC ) and the electrophoretic mobilities of the
enantiomer-CD complexes (μC ) assuming a 1:1 stoichiometry for
these complexes:

μA,eff =

μA,f + μC KC [S]
1 + KC [S]

being Ki the apparent complexation constant of each enantiomer
with each CD separately (Ki is equivalent to KC in Eq. (1)).
The electrophoretic mobility of the complex formed by each
enantiomer with the hypothetical CD (resulting from the combination of two CDs) (μover
) would be obtained by Eq. (3):
C

μover
=
C

χi Ki

χi μi Ki
=
i χi Ki

i

χi μi Ki
KCover

(3)

where μi is the electrophoretic mobility of the complex formed by
each enantiomer with each CD separately (μi is equivalent to μC
in Eq. (1)).

Once these parameters are obtained (KCover and μover
) from
C
Eqs. (2) and (3), the effective electrophoretic mobility of each
enantiomer with the hypothetical CD (μA,eff ) would be obtained
by an equation similar to that of Wren and Rowe (Eq. (4)):

(1)

where μA,eff is the effective electrophoretic mobility of the enantiomer, μA,f the electrophoretic mobility of the free enantiomer (in
the absence of CD) and [S] is the concentration of the chiral selector (the concentration of CD that remains free in the complexation
equilibrium with the enantiomers).
When a mixture of CDs is employed as chiral selector, different
physical-chemical models were developed to describe and predict
the migration of enantiomeric compounds with different characteristics in EKC [7,12,18-23]. The fundamentals and potential of these
models were reviewed in some interesting articles [13,15,24,25].
Lurie et al. [7] proposed a model to describe the impact of mixtures of neutral and charged CDs on the migration behaviour and
chiral resolution of cationic analytes. This model was based on
considering the two equilibria taking place between each analyte
and each CD present in the mixture. A 1:1 stoichiometry has to
be assumed for enantiomer-CD complexes in this model and that
no mixed complexes were formed. Also based on the consideration
of two independent equilibria between the enantiomers and each
CD, Surapaneni et al. [18] developed a model for the chiral separation of neutral analytes with mixtures of neutral and charged CDs.
Equations for selectivity and resolution were given from the expressions of the enantiomers mobility. Kranack et al. [19] derived
equations describing the effect of derivatized CDs with different
substitution degrees on the migration behaviour of analytes. These
multicomponent mixtures were considered single-component additives if the fraction of each component remained constant. These
equations were used in the study of mixtures of charged and neutral CDs. From the equilibrium constants and mobilities for each
chiral selector and analyte, migration behaviour of analytes could

be predicted at various concentrations of mixtures of two chiral
selectors. Fillet et al. [12] proposed a mechanism to explain the
changes in selectivity observed with dual CDs systems based on
the effect of the chiral selector on the analyte mobility. The overall mobility difference between the enantiomers with a combination of CDs was expressed as the addition of the mobility difference originated by each CD corrected by their respective statistical
weights. Two ways to improve the separation selectivity could be
established. If the two chiral selectors employed affect in opposite
ways the analyte mobility, then the affinity pattern of both enantiomers for the two chiral selectors should also be opposite. On the
contrary, if both chiral selectors affect similarly the analyte mobility, enantiomers should have a similar affinity pattern for the chiral
selectors. Among the different models proposed, Dubsky’s model is
considered a very simple possibility to be applied from a practical
point of view [20].
Dubsky et al. [20] proposed a theoretical model where the
system is considered to behave as a single hypothetical CD for
each ratio at which the two CDs are mixed (molar fraction, Xi ).
In such case, the apparent complexation constant (KCover ) for each
enantiomer-CD complex would be calculated by Eq. (2):

KCover =

i

μA,eff =

over
μA,f + μover
ctot
C KC

1 + KCover ctot

(4)

being μA,f the free electrophoretic mobility of each enantiomer
in the absence of CDs and ctot the total concentration of the CD
mixture that would remain without forming a complex with the
enantiomers.
This model assumes that: i) the rate of the complexation reaction between the enantiomers and each of the CDs is higher than
the separation and interconversion rates, ii) the ratio at which each
enantiomer interacts with each CD is 1:1, and iii) the concentration
of free CDs remains constant since the concentration of each enantiomer is very low compared to that of each CD [7,12,20]. On the
contrary, the use of pure chiral selectors is not required as theoretically justified and experimentally demonstrated by Dubsky’s et al.
who showed the validity of the model when a commercial mixture
of CDs was employed [20,21].
Although Dubsky’s model has demonstrated its usefulness to
predict the non-enantiomeric separation of a mixture of ibuprofen
and flurbiprofen using a combination of heptakis(2,6-di-O-methyl)β -CD (DM-β -CD) and β -CD or a combination of DM-β -CD and
6-O-α -maltosyl-β -CD [26], its potential to model and optimize the
enantiomeric separation of chiral compounds has scarcely been
illustrated. In fact, just two articles reported the modelling of chiral separations by EKC using mixtures of CDs. Thus, the separation of lorazepam enantiomers was modelled when using a commercially available mixture of highly sulphated-β -CDs [21]. On
the other hand, our research team successfully applied Dubsky’s
model for the first time to model and rapidly optimize the simultaneous enantiomeric separation of a multicomponent mixture of six chiral phenoxy acid herbicides using a combination
of 2-hydroxypropyl-β -CD and heptakis(2,3,6-tri-O-methyl)-β -CD
[27].
The aim of this work was to apply Dubsky’s model to predict and optimize the simultaneous enantiomeric separation of a
multicomponent mixture of seven chiral drugs by EKC (sitagliptin,
ivabradine, clopidogrel, ibrutinib, bupivacaine, terbutaline, and verapamil). The enantiomers of some of these drugs were recently
separated by EKC due to their novelty (ivabradine [28] and ibrutinib [29]) and a single CD system was employed in both cases.
The chiral separation of the other drugs was reported before:
sitagliptin was separated using a mixture of CDs [30], clopidogrel
using a single CD system [31,32], and the separation of the enantiomers of bupivacaine [33–43], terbutaline [35,44-63] and verapamil [33,58,60,61,64-68] was described in different works under

a variety of experimental conditions. After a screening of different
CDs, two combinations of CDs were employed and compared in
this work to optimize the multicomponent mixture of the studied
drugs using Dubsky’s model.

(2)

i

2


L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

2. Materials and methods

2.3. CE conditions

2.1. Chemicals, reagents, and standards

All analyses were carried out at 25°C in positive-polarity
(20 kV) mode applying a pressure of 50 mbar for 5 s and a detection wavelength of 200 nm (band width 5 nm) was used. Conditioning of a new capillary was achieved by flushing 1 M NaOH
for 30 min, Milli-Q water for 15 min and buffer solution (25 mM
sodium formate at pH 3.0) for 60 min. At the beginning of each
working day, the capillary was flushed with 0.1 M NaOH for 5 min,
Milli-Q water for 5 min, 0.1 M HCl for 5 min, Milli-Q water for
5 min, buffer solution for 5 min, and BGE for 5 min. To ensure repeatability between injections, the capillary was conditioned with 0.1 M NaOH for 2 min, Milli-Q water for 2 min,
0.1 M HCl for 2 min, Milli-Q water for 2 min, buffer solution for

2 min, and, finally, with BGE for 2 min.

Formic acid and sodium hydroxide (NaOH) were from SigmaAldrich (St. Louis, MO, USA). Dimethyl sulfoxide (DMSO) was from
Merck (Darmstadt, Germany) and hydrochloric acid (HCl) from
Scharlab S.L. (Barcelona, Spain). The water employed was purified
in a Millipore Milli-Q system (Bedford, MA, USA). To obtain the
25 mM formate buffer solution, the required volume of formic acid
was diluted with Milli-Q water and the pH was adjusted to 3.0
with 1 M NaOH before to reach the final volume.
CDs used in this work were: 2-hydroxypropyl-β -CD (HP-β CD, average degree of substitution (DS) 0.6) from Fluka (Buchs,
Switzerland), heptakis(2,6-di-O-methyl)-β -CD (DM-β -CD) from
Sigma-Aldrich, and methyl-γ -CD (M-γ -CD, DS 12), carboxyethylβ -CD (CE-β -CD, DS 3.5), carboxyethyl-γ -CD (CE-γ -CD, DS 3.3),
carboxymethyl-β -CD (CM-β -CD, DS 3.5), carboxymethyl-γ -CD
(CM-γ -CD, DS 3.5), and heptakis(2,3,6-tri-O-methyl)-β -CD (TM-β CD) from Cyclolab (Budapest, Hungary). When working with single
CD systems, the adequate amount of CD, to obtain the desired CD
concentration, was dissolved in the buffer solution. Regarding mixtures of CD systems, the corresponding amounts of the two CDs
to be combined were dissolved in the separation buffer to obtain
the desired individual and total CDs concentrations. Averaged molar fractions of each CD in the CDs mixture were calculated as if
the second component of the mixture, which is M-γ -CD (apparent
and averaged molecular weight 1476.00 g mol−1 ) or CE-γ -CD (apparent and averaged molecular weight 1535.13 g mol−1 ), were single chiral selectors. This was assumed since these CDs have a substitution degree as previously indicated. In these cases, the averaged molar mass indicated in the bottle of each CD was employed
for calculations.
(R)-ivabradine (505.05 g mol−1 ) was obtained from Toronto
Research Chemicals Canada (North York, ON, Canada); (S/R)bupivacaine (molecular weight 324.90 g mol−1 ), (S)- and (R)sitagliptin (molecular weight 505.31 g mol−1 ), (S)-ivabradine
(molecular weight 505.05 g mol−1 ), (S/R)-terbutaline (molecular
weight 274.30 g mol−1 ), (S/R)-verapamil (molecular weight 491.06
g mol−1 ), (S)-clopidogrel and (S/R)-clopidogrel (molecular weight
419.90 g mol−1 ) were purchased from Sigma-Aldrich; and (R)ibrutinib and (S/R)-ibrutinib (molecular weight 440.50 g mol−1 )
were from MedChem Express (Monmouth Junction, NJ, USA). All
standard compounds had a purity > 96 %. Stock standard solutions
(600 mg L−1 , except for (R)-ivabradine that had a concentration

of 10 0 0 mg L−1 ) were prepared dissolving the required amount
of each one analyte in DMSO as electroosmotic flow (EOF) marker
and stored at 4°C. Working standard solutions were obtained by
mixing the necessary volumes of each stock standard solution with
Milli-Q water until the desired concentrations were reached.

2.4. Data treatment
The values of migration times, and resolution values (Rs) were
obtained using the Chemstation software from Agilent Technologies. Excel Microsoft was employed for experimental data analysis
and to calculate all required parameters. Origin Pro8 was used for
the composition of graphs and to obtain the values of the apparent and averaged complexation constant KC and the electrophoretic
mobility μC for each enantiomer-CD complex using Eq. (1).
The experimental effective electrophoretic mobility (μA,eff ) was
calculated using Eq. (5):

μA,e f f =

Ld Lt
V

1
1
−
tm
t0

(5)

where Ld is the effective capillary length, Lt is the total capillary
length, V is the voltage, tm is the migration time and t0 is the EOF

time (determined with the EOF marker).
3. Results and discussion
Some preliminary experiments were carried out to select adequate CDs enabling the chiral separation of the compounds studied
when used as the sole chiral selectors in the separation medium.
With this aim, a screening with eight neutral CDs at a 10 mM
concentration was achieved (DM-β -CD, M-γ -CD, CM-β -CD, CMγ -CD, CE-β -CD, CE-γ -CD, HP-β -CD, TM-β -CD). A 25 mM formate
buffer (pH 3.0) was employed in order to have the drugs studied
positively charged. A temperature of 25°C and an applied voltage
of 20 kV were also chosen as initial experimental conditions. The
CDs presenting more advantages for the separation of a mixture of
the drugs studied in terms of number of peaks, analysis time, and
peak shape were DM-β -CD, M-γ -CD and CE-γ -CD. As DM-β -CD
enabled the enantiomeric separation of a higher number of compounds while M-γ -CD and CE-γ -CD had complementary selectivities, two mixtures of CDs consisting of DM-β -CD/M-γ -CD and DMβ -CD/CE-γ -CD were selected. These mixtures were employed to
evaluate the potential of the Dubsky’s model for the optimization
of the chiral separation of a mixture of the seven drugs as well as
to predict the individual separation of them under different experimental conditions. The variation of the temperature (15°C, 20°C,
25°C) and the applied voltage (20 kV, 25 kV) did not originate better results so a temperature of 25°C and an applied voltage of 20
kV were selected for further experiments.
Each drug was individually injected in CE using a single CD system based on DM-β -CD or M-γ -CD or CE-γ -CD as the sole chiral
selector in the separation buffer (25 mM formate buffer (pH 3.0)
at 25°C and a separation voltage of 20 kV). For each single system,
the CD concentration was varied from 5 to 25 mM. The experimental effective electrophoretic mobilities obtained for the enantiomers of each compound under these conditions using Eq. (5) are

2.2. Apparatus
An Agilent 7100 CE system from Agilent Technologies (Waldbronn, Germany) with a diode array detector (DAD) was employed.
The electrophoretic system was controlled with the HP 3D CE ChemStation software that included data collection and analysis. Separations were achieved in uncoated fused-silica capillaries of 50 μm
I.D. with a total length (Lt ) of 58.5 cm (50 cm effective length (Ld ))
from Polymicro Technologies (Phoenix, AZ, USA).
Reagents and standards were weighed using an OHAUS Adventurer Analytical Balance (Nänikon, Switzerland). pH measurements
were performed in a pHmeter model 744 from Metrohm (Herisau,

Switzerland). All solutions were sonicated with an ultrasonic bath
B200 from Branson Ultrasonic Corporation (Danbury, CO, USA).
3


L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

Table 1
Apparent and averaged association constants (KC ) and averaged electrophoretic mobilities (μC ) of the CD-enantiomer complexes for each individual CD obtained using
Eq. [1].
DM-β-CD
KC (L mol−1 ) ± SD
Bupivacaine 1
Bupivacaine 2
(S)-Sitagliptin
(R)-Sitagliptin
(R)-Ivabradine
(S)-Ivabradine
Terbutaline 1
Terbutaline 2
Verapamil 1
Verapamil 2
(S)-Clopidogrel
(R)-Clopidogrel
(S)-Ibrutinib
(R)-Ibrutinib

4±6

10 ± 6
4±7
2±7
12 ± 3
12 ± 3
376 ± 135
419 ± 129
442 ± 202
442 ± 202
137 ± 12
150 ± 13
1246 ± 182
1084 ± 193

M-γ -CD

μC (m2 s−1 V−1 ) ± SD
−8

-(4 ± 9) x 10
-(1 ± 1) x 10−8
-(6 ± 14) x 10−8
-(9 ± 28) x 10−8
-(4 ± 4) x 10−9
-(5 ± 5) x 10−9
(7.0 ± 0.8) x 10−9
(6.8 ± 0.7) x 10−9
(5.3 ± 0.7) x 10−9
(5.3 ± 0.7) x 10−9
(2 ± 5) x 10−10

(2 ± 5) x 10−10
(3.94 ± 0.09) x 10−9
(3.8 ± 0.1) x 10−9

KC (L mol−1 ) ± SD
0.04 ± 9
0.06 ± 6
0.02 ± 14
0.02 ± 14
0.03 ± 13
0.03 ± 13
7±1
8±1
56 ± 16
76 ± 21
0.3 ± 4
0.2 ± 5
132 ± 11
141 ± 12

CE-γ -CD

μC (m2 s−1 V−1 ) ± SD
−6

-(4 ± 1080) x 10
-(3 ± 261) x 10−6
-(4 ± 3400) x 10−6
-(4 ± 3400) x 10−6
-(4 ± 2030) x 10−6

-(4 ± 2030) x 10−6
-(1.4 ± 0.5) x 10−8
-(9 ± 2) x 10−9
(4 ± 2) x 10−9
(5 ± 1) x 10−9
-(8 ± 121) x 10−7
-(1 ± 20) x 10−6
(2.1 ± 0.3) x 10−9
(2.0 ± 0.3) x 10−9

KC (L mol−1 ) ± SD

μC (m2 s−1 V−1 ) ± SD

4±6
2±6
0.9 ± 1
0.9 ± 1
10 ± 6
10 ± 6
72 ± 11
72 ± 11
25 ± 5
25 ± 5
401 ± 26
398 ± 25

-(3 ± 6) x 10−8
-(6 ± 18) x 10−8
-(1 ± 2) x 10−7

-(1 ± 2) x 10−7
-(1 ± 1) x 10−8
-(1 ± 1) x 10−8
-(2 ± 1) x 10−9
-(2 ± 1) x 10−9
-(6 ± 3) x 10−9
-(6 ± 3) x 10−9
-(3 ± 10) x 10−11
-(1 ± 10) x 10−11

0.8 relative to DM-β -CD, a total CDs concentration of 23 mM was
the optimum to achieve the simultaneous enantiomeric separation
of the drugs studied in the mixture. In fact, although at concentrations higher than 23 mM the model predicted an improvement
in the enantiomeric separation for sitagliptin and ivabradine, an
approaching between the peaks corresponding to clopidogrel and
ibrutinib was also predicted (Table S5). Even, a reversal in the migration order for both compounds was predicted at concentrations
higher than 30 mM (see Fig. 2A). This inversion could also be predicted by the model for other values of the molar fraction relative
to DM-β -CD such as 0.7 and 0.9 (Figs. 2B and 2C) but at different
total CDs concentrations (from 30 to 35 mM for a molar fraction
of 0.7 and from 25 to 30 mM for a molar fraction of 0.9).
In order to corroborate these predictions derived from the
model, a mixture of the seven drugs studied was injected under
the selected conditions (a molar fraction of 0.8 relative to DM-β CD and total CDs concentrations from 20 to 40 mM). Fig. 3 and
Table 3 show, as an example, the separations and resolutions obtained, respectively, at total CDs concentrations of 20, 23, 24, 25,
30 y 40 mM. As shown in Fig. 3, a total CD concentration of 23 mM
was observed to allow the best simultaneous enantiomeric separation of six drugs (except verapamil). These results agreed with the
predictions of the model including the fact that verapamil enantiomers were not separated at any of the total CD concentration
values assayed. Fig. 3 also shows that an inversion in the migration
order for clopidogrel and ibrutinib was experimentally observed
when increasing the total CDs concentration from 20 to 40 mM

according to the model predictions.
In addition to the optimization of the simultaneous enantiomeric separation of the mixture of the seven drugs derived from
the application of the model, some interesting effects could be observed at an individual level for some of the compounds investigated when using the mixture of CDs. Table 4 compares the differences between the enantiomer effective electrophoretic mobilities
calculated for the mixture of CDs ( μ3 ) with the sum of these
differences experimentally obtained with each single CD system
( μ1 + μ2 ) for all the compounds studied. As shown in Table 4,
the model predicted a loss in the chiral separation for bupivacaine
and verapamil when using the mixture of CDs at the three concentrations for which the results predicted by the model and the
experimental values observed could be compared (20, 25 and 30
mM). At these three concentrations, this loss in the enantiomeric
separation predicted by the model was experimentally corroborated through a decrease in the enantiomeric resolutions. The same
effect was observed for other compounds for some total CDs concentrations, e.g., terbutaline, clopidogrel and ibrutinib at 20 mM
(no individual data were obtained for other concentrations due

grouped in Table S1 in Supplementary Material for the three CDs
selected.
Data grouped in Table S1 enabled the calculation of the apparent and averaged association constants (KC ) for each enantiomer
and each CD as well as the averaged electrophoretic mobilities
for the enantiomer-chiral selector complexes (μC ) using Eq. (1).
Results obtained are grouped in Table 1. From data included in
Table 1, the effective electrophoretic mobilities were also theoretically calculated for all enantiomers with the three CDs using
Eq. (1) (Table S2). Fig. 1 shows, as an example, the good agreement observed between the values corresponding to the experimental effective electrophoretic mobilities and those calculated
by Eq. (1) for (R)-ibrutinib with DM-β -CD, M-γ -CD and CE-γ -CD
when used as the sole chiral selectors in the separation medium.
From the apparent and averaged association constants values for
each enantiomer and each CD as well as the electrophoretic mobilities for the enantiomer-chiral selector complexes included in
Table 1, Dubsky’s model was applied to calculate the values of
the global apparent and averaged association constants (KC over )
and global averaged electrophoretic mobilities (μC over ) of the complexes Eqs. (2) and ((3)) when using each combination of CDs at
different averaged molar fractions (from 0 to 1) relative to DM-β CD. Results are shown in Table 2. Using these global apparent and

averaged association constants and averaged electrophoretic mobilities for the complexes corresponding to the mixture of CDs, effective electrophoretic mobilities (μA,eff ) for the enantiomers of each
drug were calculated at different total CD concentrations (from 5
to 40 mM) and averaged molar fractions (from 0 to 1) values relative to DM-β -CD (Tables S3 and S4 in supplementary material)
(Eq. (4)).
3.1. DM-β -CD/M-γ -CD system
The results obtained for the DM-β -CD/M-γ -CD system allowed
to select the most appropriate averaged molar fraction and total CD
concentration as a compromise enabling the best possible simultaneous enantiomeric separation predicted by the model, based on
the calculated differences between the electrophoretic mobilities
for consecutive peaks in the mixture (Table S5). A value of 1×10−10
m2 s−1 V−1 was established as the minimum difference between
the electrophoretic mobilities to experimentally observe some chiral discrimination. An averaged molar fraction of 0.8 for DM-β -CD
and total CD concentrations ranging from 20 to 40 mM were considered the best option allowing the individual enantiomeric separation of each drug (except verapamil and ivabradine) as well as
the simultaneous enantiomeric separation of the mixture. In addition, the model predicted that, at an averaged molar fraction of
4


DM-β-CD/M-γ -CD

KC over

μC over

5

χDM

Bupi 1

Bupi 2

(S)-Sitag

(R)-Sitag

(R)-Ivab

(S)-Ivab

Ter 1

Ter 2

Ver 1

Ver 2

(S)-Clop

(R)-Clop

(S)-Ibrut

(R)-Ibrut

0.0
0.1
0.2
0.3
0.4

0.5
0.6
0.7
0.8
0.9
1.0

0.04
0.4
1
1
2
2
2
3
3
3
4
Bupi 1
-408.67
-36.46
-19.19
-13.07
-9.94
-8.04
-6.76
-5.84
-5.15
-4.61
-4.18

0.06
1
2
3
4
5
6
7
8
9
10
Bupi 2
-259.65
-15.77
-7.86
-5.11
-3.71
-2.86
-2.29
-1.89
-1.58
-1.34
-1.15

0.02
0.4
1
1
1

2
2
2
3
3
3
(S)-Sitag
-431.83
-24.47
-14.16
-10.60
-8.80
-7.71
-6.98
-6.46
-6.07
-5.77
-5.52

0.02
0.3
1
1
1
1
1
2
2
2
2

(R)-Sitag
-431.83
-34.81
-20.62
-15.66
-13.14
-11.61
-10.58
-9.85
-9.29
-8.86
-8.52

0.03
1
2
4
5
6
7
9
10
11
12
(R)-Ivab
-404.66
-8.05
-3.85
-2.43
-1.71

-1.28
-0.99
-0.79
-0.63
-0.51
-0.42

0.03
1
2
3
5
6
7
8
9
10
11
(S)-Ivab
-404.66
-8.74
-4.23
-2.70
-1.93
-1.47
-1.16
-0.94
-0.78
-0.65
-0.55

7
44
81
117
154
191
228
265
302
339
376
Ter 1
-1.36
0.42
0.56
0.62
0.65
0.66
0.67
0.68
0.69
0.69
0.70

8
49
90
131
172

214
255
296
337
378
419
Ter 2
-0.90
0.45
0.57
0.61
0.63
0.65
0.66
0.66
0.67
0.67
0.68

56
95
134
172
211
249
288
326
365
403
442

Ver 1
0.40
0.46
0.49
0.50
0.51
0.52
0.52
0.53
0.53
0.53
0.53

76
112
149
185
222
259
295
332
368
405
442
Ver 2
0.47
0.50
0.51
0.52
0.52

0.52
0.53
0.53
0.53
0.53
0.53

0.3
14
28
41
55
69
82
96
110
123
137
(S)-Clop
-84.87
-1.58
-0.70
-0.40
-0.25
-0.16
-0.10
-0.06
-0.03
-0.002
0.02

0.2
15
30
45
60
75
90
105
120
135
150
(R)-Clop
-105.13
-1.51
-0.66
-0.38
-0.23
-0.15
-0.09
-0.05
-0.02
0.01
0.02

132
244
355
466
578

689
800
912
1023
1135
1246
(S)-Ibrut
0.21
0.30
0.34
0.36
0.37
0.38
0.38
0.39
0.39
0.39
0.39

141
235
329
424
518
612
707
801
895
990
1084

(R)-Ibrut
0.20
0.28
0.32
0.34
0.35
0.36
0.36
0.37
0.37
0.38
0.38

χDM
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

L. García-Cansino, J.M. Saz, M.A. García et al.

Table 2
Global association constants (KC over ) and electrophoretic mobilities (μC over x 108 ) of each enantiomer-CD complex for the DM-β -CD/M-γ -CD and DM-β -CD/CE-γ -CD systems at different DM-β -CD averaged molar fractions (χ DM )

using Eqs. [2] and [3].

DM-β-CD/CE-γ -CD

KC over

Bupi 1

Bupi 2

(S)-Sitag

(R)-Sitag

(R)-Ivab

(S)-Ivab

Ter 1

Ter 2

Ver 1

Ver 2

(S)-Clop

(R)-Clop

(S)-Ibrut

(R)-Ibrut

0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

4
4
4
4
4
4
4
4
4
4
4
Bupi 1
-3.08
-3.18

-3.29
-3.39
-3.50
-3.61
-3.72
-3.83
-3.94
-4.06
-4.18

2
3
4
5
5
6
7
8
8
9
10
Bupi 2
-6.35
-4.78
-3.78
-3.10
-2.59
-2.21
-1.91
-1.66

-1.46
-1.29
-1.15

1
1
1
2
2
2
2
3
3
3
3
(S)-Sitag
-14.56
-11.89
-10.18
-8.98
-8.10
-7.42
-6.88
-6.44
-6.08
-5.78
-5.52

1
1

1
1
2
2
2
2
2
2
2
(R)-Sitag
-14.56
-13.19
-12.16
-11.35
-10.70
-10.17
-9.73
-9.36
-9.04
-8.76
-8.52

10
10
10
10
11
11
11
11

12
12
12
(R)-Ivab
-1.13
-1.04
-0.96
-0.88
-0.80
-0.73
-0.66
-0.60
-0.54
-0.48
-0.42

10
10
10
10
10
10
11
11
11
11
11
(S)-Ivab
-1.13
-1.06

-1.00
-0.93
-0.87
-0.81
-0.76
-0.70
-0.65
-0.60
-0.55

Ter 1
-

Ter 2
-

72
109
146
183
220
257
294
331
368
405
442
Ver 1
-0.16
0.12

0.26
0.34
0.40
0.44
0.46
0.49
0.51
0.52
0.53

72
109
146
183
220
257
294
331
368
405
442
Ver 2
-0.16
0.12
0.26
0.34
0.40
0.44
0.46
0.49

0.51
0.52
0.53

25
36
47
59
70
81
92
103
115
126
137
(S)-Clop
-0.63
-0.39
-0.26
-0.18
-0.12
-0.083
-0.053
-0.029
-0.011
0.005
0.018

25
38

50
63
75
88
100
113
125
138
150
(R)-Clop
-0.63
-0.37
-0.24
-0.16
-0.11
-0.069
-0.041
-0.019
-0.002
0.013
0.025

401
485
570
654
739
823
908
992

1077
1161
1246
(S)-Ibrut
0.0033
0.10
0.17
0.23
0.27
0.30
0.33
0.35
0.37
0.38
0.39

398
467
535
604
672
741
810
878
947
1015
1084
(R)-Ibrut
0.0013
0.089

0.15
0.20
0.24
0.28
0.30
0.33
0.35
0.36
0.38

χDM
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

Journal of Chromatography A 1681 (2022) 463444

μC over

χDM

L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

Fig. 2. Theoretical prediction of the inversion in the migration order of clopidogrel
((S)-clop (●) and (R)-clop (ο)) and ibrutinib ((S)-ibrut ( ) and (R)-ibrut ( )) when
a mixture of DM-β -CD/M-γ -CD was used at DM-β -CD averaged molar fractions of
0.8 (A), 0.7 (B) and 0.9 (C). Data were obtained from Table S3.

Fig. 1. Comparison between the experimental and theoretical effective electrophoretic mobilities of (R)-ibrutinib with each individual CD (DM-β -CD, M-γ -CD,
CE-γ -CD). Experimental ( ) and theoretical (ο) values. Experimental conditions:
uncoated fused-silica capillary, 58.5 cm (50 cm effective length) × 50 μm id; 25
mM formate buffer (pH 3.0); temperature: 25°C; voltage: 20 kV; hydrodynamic injection: 50 mbar × 5 s; λ: 200 nm ± 5 nm. Theoretical values were obtained using
Eq. (1).

to the comigration of ibrutinib with clopidogrel peaks). For these
five compounds, a different behavior was observed for each of the
CDs in the mixture which could justify the results obtained. No
chiral separation was observed for verapamil with DM-β -CD nor
for terbutaline with M-γ -CD. Likewise, bupivacaine and ibrutinib
showed a higher chiral discrimination with one of the CDs in the
mixture with respect to the other. An improvement of the chiral
separation was also predicted by the model and experimentally
demonstrated for ivabradine and terbutaline at 25 and 30 mM total CDs concentrations, in spite of the fact that terbutaline did not
show enantiomeric separation with M-γ -CD and that ivabradine
did not show chiral discrimination with any of the CDs in the mixture at 25 mM CDs concentration or with M-γ -CD at 30 mM total
CDs concentration. In the case of sitagliptine, the model only predicted correctly its behavior at a total CDs concentration of 25 mM
(a slight improvement was observed even if this drug did not show

Table 3

Enantiomeric resolution values obtained for all drugs studied with the DM-β -CD/Mγ -CD system for an averaged molar fraction of DM-β -CD of 0.8 (χ DM-β -CD = 0.8) and
different total CDs concentrations.
Drug

Bupivacaine
Sitagliptine
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutrinib

Resolution values
20 mM

23 mM

24 mM

25 mM

30 mM

40 mM

3.21
0.00
0.00
2.74
0.00

1.95
0.76

3.28
0.24
0.21
2.37
0.00
1.44
0.82

3.89
0.53
0.48
2.02
0.00
–
–

4.00
0.57
0.52
2.07
0.00
–
–

3.66
0.51
0.44

1.89
0.00
–
–

4.48
–
0.51
1.67
0.00
1.26
1.19

6


Experimental

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutinib
7

Bupivacaine
Sitagliptin
Ivabradine

Terbutaline
Verapamil
Clopidogrel
Ibrutinib

(a)

μ2
M-γ -CD

15 mM
-6.04
-0.20
0.00
-4.91
0.00
-3.20
-0.54
20 mM
-6.77
-0.40
0.00
-2.76
0.00
25 mM
-7.04
-0.93
-0.37
-2.29
0.00

-

5 mM
-1.97
0.00
0.00
0.00
-4.45
0.00
-2.13
5 mM
-1.97
0.00
0.00
0.00
-4.45
5 mM
-1.97
0.00
0.00
0.00
-4.45
-

μ1 + μ2

-8.01
-0.20
0.00
-4.91

-4.45
-3.20
-2.67
-8.74
-0.40
0.00
-2.76
-4.45
-9.01
-0.93
-0.37
-2.29
-4.45
-

μA,eff x 10
μ3

DM-β-CD/M-γ -CD

Theoretical
| μ3 | − (| μ1 +

16 / 4 mM
-5.81
0.00
0.00
-4.55
0.00
-0.11

-0.85
20 / 5 mM
-6.52
-0.95
-0.79
-3.07
0.00
24 / 6 mM
-6.63
-0.60
-0.75
-3.22
0.00
-

μ3 = μA,eff (enantiomer 1) - μA,eff (enantiomer 2) when using the DM-β -CD/M-γ -CD system;

-2.20
-0.20
0.00
-0.36
-4.45
-3.09
-1.82
-2.22
0.55
0.79
0.31
-4.45
-2.38

-0.33
0.38
0.93
-4.45
-

μ1 and

μ2 |)

μ1
DM-β-CD

μ2
M-γ -CD

15 mM
-6.11
-0.20
-0.02
-4.91
0.00
-3.21
-0.86
20 mM
-6.81
-0.48
-0.13
-2.76
0.00

25 mM
-7.02
-0.86
-0.28
-2.29
0.00
-

5 mM
-1.97
0.00
0.00
0.00
-4.45
0.00
-2.13
5 mM
-1.97
0.00
0.00
0.00
-4.45
5 mM
-1.97
0.00
0.00
0.00
-4.45
-

μ1 + μ2

-8.09
-0.20
-0.02
-4.91
-4.45
-3.21
-2.99
-8.78
-0.48
-0.13
-2.76
-4.45
-8.99
-0.86
-0.28
-2.29
-4.45
-

μ2 = μA,eff (enantiomer 1) - μA,eff (enantiomer 2) for each CD separately.

μA,eff x 10

μ2 )(a) .

10

μ3

DM-β-CD/M-γ -CD
16 / 4 mM
-6.50
-0.30
-0.07
-3.36
-0.04
-3.06
-1.03
20 / 5 mM
-6.93
-0.56
-0.18
-3.15
-0.06
24 / 6 mM
-7.02
-0.89
-0.31
-3.00
-0.07
-

| μ3 | − (| μ1 +

μ2 |)

-1.59
0.10

0.05
-1.55
-4.41
-0.15
-1.96
-1.85
0.08
0.05
0.39
-4.39
-1.97
0.03
0.04
0.71
-4.37
-

Journal of Chromatography A 1681 (2022) 463444

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutinib

μ1
DM-β-CD

10

L. García-Cansino, J.M. Saz, M.A. García et al.

Table 4
Experimental and theoretical differences between the electrophoretic mobilities of enantiomers when using the DM-β -CD/M-γ -CD system ( μ3 ) compared to the use of each CD separately ( μ1 and


L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

Fig. 4. Electropherograms corresponding to the separation of the enantiomers of
the drugs mixture in a standard solution containing (1) bupivacaine racemic 10 mg
L−1 , (2) (S)-sitagliptin 5 mg L−1 and (R)-sitagliptin 10 mg L−1 , (3) (R)-ivabradine
5 mg L−1 and (S)-ivabradine 7 mg L−1 , (4) racemic terbutaline 10 mg L−1 , (5) verapamil racemic 5 mg L−1 , (6) (R)-clopidogrel 5 mg L−1 and (S)-clopidogrel 7 mg
L−1 , (7) (S)-ibrutrinib 5 mg L−1 and (R)-ibrutrinib 7 mg L−1 , using 25 mM formate
buffer (pH 3.0) with a mixture of DM-β -CD/CE-γ -CD (χ DM-β -CD =0.8) at different total CDs concentration (A) 20 mM, (B) 30 mM, and (C) 40 mM. Other experimental
conditions as in Fig. 1.

Fig. 3. Electropherograms corresponding to the separation of the enantiomers of
the drugs mixture in a standard solution containing (1) racemic bupivacaine 10 mg
L−1 , (2) (S)-sitagliptine 5 mg L−1 and (R)-sitagliptine 10 mg L−1 , (3) (R)-ivabradine 5
mg L−1 and (S)-ivabradine 7 mg L−1 , (4) racemic terbutaline 10 mg L−1 , (5) racemic
verapamil 5 mg L−1 , (6) (R)-clopidogrel 5 mg L−1 and (S)-clopidogrel 7 mg L−1 , (7)
(S)-ibrutrinib 5 mg L−1 and (R)-ibrutrinib 7 mg L−1 , using 25 mM formate buffer
(pH 3.0) with DM-β -CD/M-γ -CD (χ DM-β -CD =0.8) as chiral selector at different total
CDs concentration (A) 20 mM, (B) 23 mM, (C) 24 mM, (D) 25 mM, (E) 30 mM, and
(F) 40 mM. Other experimental conditions as in Fig. 1.

Table 5
Enantiomeric resolution values obtained for all drugs studied with the DM-β CD/CE-γ -CD system for an averaged molar fraction of DM-β -CD of 0.8 (χ DM-β -CD =
0.8) and different total CDs concentrations.

chiral discrimination with M-γ -CD). As a result, out of a total of
17 cases (Table 4), 15 were correctly predicted by the model at a
qualitative level.

Resolution values
Drug

3.2. DM-β -CD/CE-γ -CD system

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutrinib

As in the case of the DM-β -CD/M-γ -CD system, the application
of the Dubsky’s model for the DM-β -CD/CE-γ -CD mixture allowed
to select the most appropriate averaged molar fraction relative to
DM-β -CD and total CDs concentration based on the calculated differences between the electrophoretic mobilities between consecutive peaks in the mixture (Table S6). An averaged molar fraction
of 0.8 for DM-β -CD and total CD concentrations ranging from 20
to 40 mM were considered the best option allowing the individual enantiomeric separation of each drug as well as the simultaneous enantiomeric separation of the mixture. The differences between the electrophoretic mobilities for the enantiomers could not
be calculated for terbutaline since it showed enantiomeric separation only with DM-β -CD as the sole chiral selector and no peaks
were observed for this drug with CE-γ -CD as the sole chiral selector. For verapamil, no differences between the electrophoretic mobilities for the enantiomers were predicted at any of the averaged
molar fraction and total CDs concentrations considered. In addition, the model predicted that, at an averaged molar fraction of 0.8,

a total CDs concentration of 40 mM was the optimum to achieve
the simultaneous enantiomeric separation of the drugs studied in
the mixture.
A mixture of the seven drugs studied was injected under the selected conditions (averaged molar fraction 0.8 relative to DM-β -CD
and total CDs concentration from 20 to 40 mM). Fig. 4 shows, as
an example, the separations obtained at total CDs concentrations
of 20, 30 and 40 mM. As shown in Fig. 4 and Table 5, a total CD
concentration of 40 mM was observed to allow the best simultaneous enantiomeric separation of six drugs (except verapamil). These
results agreed with those predicted by the model including the fact
that verapamil enantiomers were not separated at any of the total
CDs concentration values assayed. Fig. 4 also shows that an inver-

20 mM

30 mM

40 mM

3.54
0.50
0.47
2.30
0.00
1.79
0.92

3.51
0.54
0.49
1.87

0.00
–
–

3.98
0.82
0.62
1.80
0.00
1.44
1.28

sion in the migration order for clopidogrel and ibrutinib was experimentally observed when increasing the total CDs concentration
from 20 to 40 mM. This inversion in the migration order for these
two compounds was predicted by the model as shown in Fig. 5. It
can be observed that the model predicted that the inversion in the
migration order for clopidogrel and ibrutinib could be expected for
an averaged molar fraction of 0.8 at concentrations ranging from
30 to 35 mM (Fig. 5A). This inversion could also be predicted by
the model for other values of the averaged molar fraction such as
0.7 and 0.9 (Figs. 5B and 5C) but at different total CDs concentrations (from 35 to 40 mM for an averaged molar fraction of 0.7 and
from 25 to 30 mM for an averaged molar fraction of 0.9).
In addition to the optimization of the simultaneous enantiomeric separation of the mixture of the seven drugs derived from
the application of the model, some interesting effects could be observed at an individual level for some of the compounds investigated. In fact, improvements in the chiral separation of some compounds could be observed when using the mixture of the two CDs
with respect to the use of single CD systems. For example, the
model predicts for ivabradine, sitagliptin, and ibrutinib that the
difference between the electrophoretic mobilities for enantiomers
with the mixture of CDs should be higher than that obtained when
using a single CD system, and this fact was experimentally demonstrated (Table 6). In the case of clopidogrel and bupivacaine a de8

Experimental

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutinib
9

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutinib

(a)

μ2
CE-γ -CD

15 mM
-6.04
-0.20
0.00
0.00

-3.20
-0.54
20 mM
-6.77
-0.40
0.00
0.00
25 mM
-7.04
-0.93
-0.37
0.00
-

5 mM
0.00
0.00
0.00
0.00
0.00
0.00
5 mM
0.00
0.00
0.00
0.00
5 mM
0.00
0.00
0.00

0.00
-

μ1 + μ2

-6.04
-0.20
0.00
0.00
-3.20
-0.54
-6.77
-0.40
0.00
0.00
-7.04
-0.93
-0.37
0.00
-

μA,eff x 10
μ3

DM-β-CD/CE-γ -CD

Theoretical
| μ3 | − (| μ1 +

16 / 4 mM

-6.39
-0.85
-0.77
0.00
-2.34
-1.42
20 / 5 mM
-6.50
-1.02
-0.80
0.00
24 / 6 mM
-6.61
-1.05
-0.87
0.00
-

μ3 = μA,eff (enantiomer 1) - μA,eff (enantiomer 2) when using the DM-β -CD/CE-γ -CD system;

0.35
0.65
0.77
0.00
-0.86
0.88
-0.27
0.62
0.80
0.00

-0.43
0.12
0.50
0.00
-

μ1 and

μ2 |)

μ1
DM-β-CD

μ2
CE-γ -CD

15 mM
-6.11
-0.20
-0.02
0.00
-3.21
-0.86
20 mM
-6.81
-0.48
-0.13
0.00
25 mM
-7.02

-0.86
-0.28
0.00
-

5 mM
-0.04
0.00
0.00
0.00
0.00
0.05
5 mM
-0.04
0.00
0.00
0.00
5 mM
-0.04
0.00
0.00
0.00
-

μ1 + μ2

-6.16
-0.20
-0.02
0.00

-3.21
-0.82
-6.85
-0.48
-0.13
0.00
-7.06
-0.86
-0.28
0.00
-

μ2 = μA,eff (enantiomer 1) - μA,eff (enantiomer 2) for each CD separately.

μA,eff x 10

μ2 )(a) .

10

μ3

DM-β-CD/CE-γ -CD
16 / 4 mM
-5.86
-0.34
-0.11
0.00
-2.80
-1.22

20 / 5 mM
-6.22
-0.62
-0.23
0.00
24 / 6 mM
-6.27
-0.97
-0.37
0.00
-

| μ3 | − (| μ1 +

μ2 |)

-0.29
0.14
0.09
0.00
-0.41
0.40
-0.63
0.14
0.10
0.00
-0.79
0.11
0.09
0.00

-

Journal of Chromatography A 1681 (2022) 463444

Bupivacaine
Sitagliptin
Ivabradine
Terbutaline
Verapamil
Clopidogrel
Ibrutinib

μ1
DM-β-CD

10

L. García-Cansino, J.M. Saz, M.A. García et al.

Table 6
Experimental and theoretical differences between the electrophoretic mobilities of enantiomers when using the DM-β -CD/CE-γ -CD system ( μ3 ) compared to the use of each CD separately ( μ1 and


L. García-Cansino, J.M. Saz, M.A. García et al.

Journal of Chromatography A 1681 (2022) 463444

imental range of CD concentrations employed. Some interesting effects relative to the use of the CDs mixtures were also predicted by
the model and experimentally corroborated. In addition, the model
predicted the reversal in the migration order of some compounds

when changing the total CDs concentration according to the experimental observations. The combination of DM-β -CD with CE-γ -CD
at a 40 mM total CDs concentration showed to be the most appropriate conditions to achieve the simultaneous enantiomeric separation of the multicomponent mixture of drugs with resolutions
values ranging from 0.6 to 4.0.
This is the first time that Dubsky’s model is applied to predict
a simultaneous chiral separation of a mixture by extrapolating the
results to total CDs concentrations out of the experimental range
established to obtain the parameters of the model. Thus, it has
been shown that the model enabled to find interesting separation
conditions from a few initial experiments achieved with each pair
of enantiomers and each CD employed as the sole chiral selector.
Therefore, the model can be considered a powerful tool to help in
the optimization of chiral separations when mixtures of CDs are
employed in EKC.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
CRediT authorship contribution statement
L. García-Cansino: Investigation, Validation, Data curation, Visualization, Writing – original draft. J.M. Saz: Investigation, Formal
analysis, Validation, Data curation, Visualization, Writing – original
draft. M.A. García: Methodology, Visualization, Data curation, Resources, Supervision, Writing – original draft, Writing – review &
editing, Project administration, Funding acquisition. M.L. Marina:
Conceptualization, Methodology, Visualization, Data curation, Resources, Supervision, Writing – original draft, Writing – review &
editing, Project administration, Funding acquisition.
Data availability
Data will be made available on request.
Acknowledgments

Fig. 5. Theoretical prediction of the inversion in the migration order of clopidogrel
((S)-clop (●) and (R)-clop (ο)) and ibrutinib ((S)-ibrut ( ) and (R)-ibrut ( )) when
the mixture DM-β -CD/ CE-γ -CD was used at DM-β -CD averaged molar fractions of

0.8 (A), 0.7 (B) and 0.9 (C). Data were obtained from Table S4.

Authors thank financial support from the Spanish Ministry of Science and Innovation (research project PID2019104913GB-I00, Agencia Estatal de Investigación, Referencia del
Proyecto/AEI/10.13039/50110 0 011033), and the University of Alcalá
for research project CCG20/CC-023. L.G.C. thanks the University of
Alcalá for her predoctoral contract.

crease in the difference between the electrophoretic mobilities for
enantiomers with the mixture of CDs was predicted by the model
(for 25 and 30 mM total CDs concentrations for bupivacaine and
for 20 mM total CDs concentration for clopidogrel) and this fact
was also experimentally corroborated. Out of 14 cases, the model
correctly predicted 13 cases at a qualitative level (Table 6).

Supplementary materials
Supplementary material associated with this article can be
found, in the online version, at doi:10.1016/j.chroma.2022.463444.

4. Concluding remarks
References
The chiral separation of a mixture of seven drugs by EKC using two mixtures of CDs (DM-β -CD/M-γ -CD and DM-β -CD/CE-γ CD) was modelled using Dubsky’s model. A good agreement between the experimental results obtained and those predicted by
the model was observed. The model showed its potential to optimize the simultaneous enantiomeric separation of the mixture of
drugs studied in this work even at concentrations out of the exper-

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