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

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.

Journal of Chromatography A 1681 (2022) 463444 Contents lists available at ScienceDirect 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 Qmica 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 (http://creativecommons.org/licenses/by-nc-nd/4.0/) 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: mluisa.marina@uah.es (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 https://doi.org/10.1016/j.chroma.2022.463444 0021-9673/© 2022 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 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] + 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 + 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 L García-Cansino, J.M Saz, M.A García et al Journal of Chromatography A 1681 (2022) 463444 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 s and a detection wavelength of 200 nm (band width nm) was used Conditioning of a new capillary was achieved by flushing M NaOH for 30 min, Milli-Q water for 15 and buffer solution (25 mM sodium formate at pH 3.0) for 60 At the beginning of each working day, the capillary was flushed with 0.1 M NaOH for min, Milli-Q water for min, 0.1 M HCl for min, Milli-Q water for min, buffer solution for min, and BGE for To ensure repeatability between injections, the capillary was conditioned with 0.1 M NaOH for min, Milli-Q water for min, 0.1 M HCl for min, Milli-Q water for min, buffer solution for min, and, finally, with BGE for 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 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 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 − 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) 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 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) L García-Cansino, J.M Saz, M.A García et al Journal of Chromatography A 1681 (2022) 463444 Table 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 Bupivacaine (S)-Sitagliptin (R)-Sitagliptin (R)-Ivabradine (S)-Ivabradine Terbutaline Terbutaline Verapamil Verapamil (S)-Clopidogrel (R)-Clopidogrel (S)-Ibrutinib (R)-Ibrutinib 4±6 10 ± 4±7 2±7 12 ± 12 ± 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 ± 0.06 ± 0.02 ± 14 0.02 ± 14 0.03 ± 13 0.03 ± 13 7±1 8±1 56 ± 16 76 ± 21 0.3 ± 0.2 ± 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 ± 0.9 ± 10 ± 10 ± 72 ± 11 72 ± 11 25 ± 25 ± 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 and Table 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 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 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 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 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 to 1) relative to DM-β CD Results are shown in Table 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 to 40 mM) and averaged molar fractions (from 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 DM-β-CD/M-γ -CD KC over μC over χDM Bupi Bupi (S)-Sitag (R)-Sitag (R)-Ivab (S)-Ivab Ter Ter Ver Ver (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 2 3 Bupi -408.67 -36.46 -19.19 -13.07 -9.94 -8.04 -6.76 -5.84 -5.15 -4.61 -4.18 0.06 10 Bupi -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 2 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 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 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 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 44 81 117 154 191 228 265 302 339 376 Ter -1.36 0.42 0.56 0.62 0.65 0.66 0.67 0.68 0.69 0.69 0.70 49 90 131 172 214 255 296 337 378 419 Ter -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 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 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 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 Bupi (S)-Sitag (R)-Sitag (R)-Ivab (S)-Ivab Ter Ter Ver Ver (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 Bupi -3.08 -3.18 -3.29 -3.39 -3.50 -3.61 -3.72 -3.83 -3.94 -4.06 -4.18 5 8 10 Bupi -6.35 -4.78 -3.78 -3.10 -2.59 -2.21 -1.91 -1.66 -1.46 -1.29 -1.15 1 2 2 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 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 - Ter - 72 109 146 183 220 257 294 331 368 405 442 Ver -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 -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 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 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 × s; λ: 200 nm ± 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 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 Experimental Bupivacaine Sitagliptin Ivabradine Terbutaline Verapamil Clopidogrel Ibrutinib 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 - mM -1.97 0.00 0.00 0.00 -4.45 0.00 -2.13 mM -1.97 0.00 0.00 0.00 -4.45 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 / mM -5.81 0.00 0.00 -4.55 0.00 -0.11 -0.85 20 / mM -6.52 -0.95 -0.79 -3.07 0.00 24 / 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 - mM -1.97 0.00 0.00 0.00 -4.45 0.00 -2.13 mM -1.97 0.00 0.00 0.00 -4.45 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 / mM -6.50 -0.30 -0.07 -3.36 -0.04 -3.06 -1.03 20 / mM -6.93 -0.56 -0.18 -3.15 -0.06 24 / 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 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 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 mg L−1 and (R)-sitagliptin 10 mg L−1 , (3) (R)-ivabradine mg L−1 and (S)-ivabradine mg L−1 , (4) racemic terbutaline 10 mg L−1 , (5) verapamil racemic mg L−1 , (6) (R)-clopidogrel mg L−1 and (S)-clopidogrel mg L−1 , (7) (S)-ibrutrinib mg L−1 and (R)-ibrutrinib 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 Fig 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 mg L−1 and (R)-sitagliptine 10 mg L−1 , (3) (R)-ivabradine mg L−1 and (S)-ivabradine mg L−1 , (4) racemic terbutaline 10 mg L−1 , (5) racemic verapamil mg L−1 , (6) (R)-clopidogrel mg L−1 and (S)-clopidogrel mg L−1 , (7) (S)-ibrutrinib mg L−1 and (R)-ibrutrinib 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 Table 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 shows, as an example, the separations obtained at total CDs concentrations of 20, 30 and 40 mM As shown in Fig 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 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 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 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 - mM 0.00 0.00 0.00 0.00 0.00 0.00 mM 0.00 0.00 0.00 0.00 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 / mM -6.39 -0.85 -0.77 0.00 -2.34 -1.42 20 / mM -6.50 -1.02 -0.80 0.00 24 / 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 - mM -0.04 0.00 0.00 0.00 0.00 0.05 mM -0.04 0.00 0.00 0.00 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 / mM -5.86 -0.34 -0.11 0.00 -2.80 -1.22 20 / mM -6.22 -0.62 -0.23 0.00 24 / 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 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 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 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 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- [1] G D’Orazio, C Fanali, C Dal Bosco, A Gentili, S Fanali, Chiral separation and analysis of 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