Journal of Chromatography A, 1381 (2015) 219–228
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Possibilities of retention modeling and computer assisted method development in supercritical fluid chromatography Eva Tyteca a,1 , Vincent Desfontaine b,1 , Gert Desmet a , Davy Guillarme b,∗ a b
Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium School of Pharmaceutical Sciences, University of Geneva, University of Lausanne, Switzerland
a r t i c l e
i n f o
Article history: Received 28 August 2014 Received in revised form 16 December 2014 Accepted 26 December 2014 Available online 7 January 2015 Keywords: SFC UHPSFC Method development Retention modeling Retention prediction
a b s t r a c t The multi-modal retention mechanism in supercritical fluid chromatography (SFC) results in a non-linear dependency of log(k) on the fraction of organic solvent ϕ and log(ϕ). In the present study, the possibility of retention modeling for method development purposes in SFC was investigated, considering several non-linear isocratic relationships. Therefore, both isocratic and gradient runs were performed, involving different column chemistries and analytes possessing diverse physico-chemical properties. The isocratic retention data of these compounds could be described accurately using the non-linear retention models typically used in HILIC and reversed-phase LC. The interconversion between isocratic and gradient retention data was found to be less straightforward than in RPLC and HILIC because of pressure effects. The possibility of gradient predictions using gradient scouting runs to estimate the retention parameters was investigated as well, showing that predictions for other gradients with the same starting conditions were acceptable (always below 5%), whereas prediction errors for gradients with a different starting condition were found to be highly dependent on the compound. The second part of the study consisted of the gradient optimization of two pharmaceutical mixtures (one involving atorvastatin and four related impurities, and one involving a 16 components mixture including eight drugs and their main phase I metabolites). This could be done via individual retention modeling based on gradient scouting runs. The best linear gradient was found via a grid search and the best multi-segment gradient via the previously published one-segment-per-component search. The latter improved the resolution between the critical pairs for both mixtures, while still giving accurate prediction errors (using the same starting concentrations as the gradient scouting runs used to build the model). The optimized separations were found in less than 3 h and 8 h of analysis time (including equilibration times), respectively. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) is gaining in importance as a chromatographic technique, to analyze a wide range of compounds from relatively hydrophilic to highly lipophilic [1–4]. In SFC, the retention mechanism is multi-modal, combining different interaction mechanisms, and highly dependent on the nature of the stationary phase and the type of organic modifier [5,6]. In SFC, the mobile phase generally consists of a mixture of apolar CO2 and a limited proportion of methanol (typically up to 30%). In this case, normal phase retention behavior takes place using a polar stationary phase (such as silica, diol, amino, cyano, amide). On the other hand, using an apolar stationary phase (such as C8 ,
∗ Corresponding author. Tel.: +41 22 379 34 63. E-mail address: [email protected] (D. Guillarme). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.chroma.2014.12.077 0021-9673/© 2015 Elsevier B.V. All rights reserved.
C18 , phenylhexyl), reversed-phase retention behavior is expected, as in the absence of H2 O, the interactions between the compounds and the stationary phase are favored, limiting the contribution of the apolar CO2 in the mobile phase. When other stationary phases (such as alkyl bonded phases with hydrophilic end-capping or polar embedded group) are used, intermediate behavior can be expected [7]. The use of MeOH in the mobile phase introduces other interactions such as H-bonding, dipole–dipole interactions and solvent adsorption [7,8]. Solvent adsorption is also playing a major role in hydrophilic interaction chromatography (HILIC) [9]. The multi-modal retention mechanism results in a non-linear dependency of the logarithm of the retention factor log(k) on the fraction of organic solvent ϕ and log(ϕ). As such, the linear solvent strength (LSS) model, widely used to model reversed-phase retention, can no longer be applied in SFC. Also in HILIC, a multi-modal retention mechanism exists, combining partitioning, adsorption through H-bonding and electrostatic and ionic interactions [10], and non-linear retention models have been reported [11–13].
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Therefore, the non-linear retention models that have proven to be successful in HILIC retention modeling could also be of interest for the SFC retention modeling: ln(k) = ln(kw ) + S1 + S2 ln()
(1)
ln(k) = ln(kw ) + S1 + S2 2
(2)
ln(k) = ln(kw ) + 2 · ln(1 + S2 ) −
S1 1 + S2
(3)
where is the fraction of water, kw the extrapolated value of k for = 0 (i.e., pure CO2 ), S1 the slope and S2 the curvature coefficient [14]. The expression for the gradient retention factor can be found by solving the fundamental gradient equation:
tR −t0
t0 =
dts k()
(4)
0
where t0 is the column dead time and tR is the total retention time. For multi-segment gradients, the fundamental gradient equation becomes a sum of integrals, each describing the retention during one segment of the gradient [15]. This sum of integrals can still be solved in a straightforward way, to obtain an analytical expression for the effective retention factor keff = (tR − t0 )/t0 . In reversed-phase method development (MD) schemes, isocratic and gradient data are measured and interpolated, then isocratic and gradient retention results can be interconverted (e.g. prediction of isocratic retention based on gradient scouting runs). This is possible because the retention relationships in reversedphase behave rather “gently”, with only relatively small deviations from the LSS-behavior, i.e. linear relationship between ln(k) and . In reversed-phase, the retention behavior of a component can therefore in general be examined with a set of well-chosen experiments that cover the entire intended experimental space. The retention space between experimental data points is then modeled, and computer predictions, based on these models, are used in MD processes [15–18]. Based on the accuracy of the retention models, different MD strategies can be applied. If accurate retention time predictions are possible, individual retention modeling can be used to optimize the gradient conditions. This approach was developed for reversed-phase separations [16]. In addition, HILIC separations for which an accurate retention model exists have also been optimized using this approach [13]. When the modeling is very accurate, the separation power can be increased, using multisegments gradients. However, smart algorithms are needed to find out the optimal gradient conditions among the innumerous combinations [15]. On the other hand, if no accurate retention modeling is possible, a hybrid method called the predictive elution window shifting and stretching approach (PEWS2 ) can be used for the gradient optimization in both RPLC and the HILIC mode [13,18]. Design of Experiments is another strategy that can be used to optimize a separation, without the need for retention models such as Eqs. (1)–(3). This approach was recently proposed to optimize SFC gradient conditions by Dispas et al. who reported on the optimization of tiso , tG and %MeOHstart for the separation of six antibiotic drugs and caffeine [19]. In the present study, the possibilities of retention modeling and gradient optimization in SFC were investigated, using the non-linear retention models of Eqs. (1)–(3). To the best of the authors’ knowledge, the isocratic retention models proposed in this study have not yet been applied in SFC. Moreover, gradient retention prediction and optimization of the gradient conditions via individual retention modeling have not been reported in SFC. For this purpose, a range of mobile phase compositions %B
(10 mM ammonium formate in 98% MeOH + 2% H2 O) were applied to various column chemistries (BEH, 2-EP and HSS) and several analytes possessing diverse physico-chemical properties (see Table 1) and the isocratic retention relationships were studied. Subsequently, we investigated the possibility to predict gradient retention from a limited number of isocratic or gradient runs and applied this approach to two real-life separation problems, with varying number of compounds (atorvastatin and four related impurities, a 16 component mixture including 8 drugs and their main phase I metabolites), using Eq. (3) (the Neue and Kussequation), as this gives the simplest expression for the gradient retention factor when solving the fundamental gradient equation (Eq. (4)), and hence requires the smallest computational effort during the optimization searches (e.g. the model in Eq. (1) requires a time-resolved numerical integration for each individual screening condition). Atorvastatin marketed as a calcium salt is a member of the drug class known as statins, which are used for lowering blood cholesterol and for prevention of events associated with cardiovascular disease [20]. From 1996 to 2012, atorvastatin became the world’s best-selling drug of all time, under the trade name Lipitor, with more than $125 billion in sales over approximately 14 years [21]. In the present study, a stability-indicating SFC method was developed for the determination of atorvastatin and four related pharmacopeia impurities. To evaluate the interaction potential of drugs, new chemical entities, toxic substances and phytochemicals, and account for the existing risks during co-exposure, in vitro drug metabolism assay has to be performed in the pharmaceutical industry during the drug development process. From an analytical point of view, there is a need to develop fast methods able to discriminate a significant number of substrates and metabolites, each corresponding to a given cytochrome P450 (CYP) subfamily [22]. In the present study, a SFC method was developed for the separation of eight probe substrates and eight CYP-specific metabolites, previously investigated in LC conditions [23]. 2. Material and methods 2.1. Chemicals and reagents Methanol (MeOH) HPLC grade was purchased from Fisher Scientific (Loughborough, UK), whereas isopropanol (IpOH), ethanol (EtOH) and heptane were purchased from VWR (Radnor, PA, USA). Pressurized liquid CO2 , 3.0 grade, (99.9%) was purchased from PanGas (Dagmerstellen, Switzerland). Ultrapure water was supplied by a Milli-Q Advantage A10 purification unit from Millipore (Bedford, MA, USA). Ammonium formate was purchased from Sigma-Fluka (Buchs, Switzerland). 2.2. Instrumentation and columns All the experiments were performed on a Waters Acquity UPC2 system (Waters, Milford, MA, USA) equipped with a binary solvent delivery pump, an autosampler that included a 10 L loop for partial loop injection, a column oven and a two-step (passive + active) backpressure regulator (BPR). The passive component maintains pressure higher than 104 bar, while the active component allows further back pressure increase and fine backpressure adjustments. The injection volume was 1 L and the measured dwell volume was 440 L. The Acquity UPC2 system was also combined with a benchtop single quadrupole, namely Waters Acquity QDa detector fitted with a Z-spray electrospray (ESI) ionization source. Make-up solvent delivered by a Waters Isocratic Solvent Manager (ISM) pump
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Table 1 The nine test compounds used for the initial evaluation of the isocratic and gradient retention modeling together with their physico-chemical properties. is the optimal detector wavelength. Molecule
Acidic pKa
Basic pKa
log P
(nm)
Caffeine Nikethamide Warfarin Papaverine Acetazolamide Prednisolone Propranolol Ethacrynic Acid Octopamine
– – 5.1 – 7.2 – – 2.8 9.6
– 3.6 – 6 – – 9.4 – 9
−0.55 0.77 2.74 3.03 −0.26 1.62 2.93 3.66 −0.32
280 254 280 254 254 254 280 280 220
was added and mixed to the chromatographic effluent prior to MS detection through a split interface purchased from Waters. The UHPSFC-MS hyphenation interface and splitter are described in [24]. Data acquisition, data handling and instrument control were performed by Empower v. 4.1 software (Waters). The UHPSFC columns employed in this study were purchased from Waters: Acquity UPC2 BEH (BEH), Acquity UPC2 BEH 2-EP (2EP), Acquity UPC2 HSS C18 SB (HSS) and Acquity UPC2 CSH FluoroPhenyl (PFP). The PFP column was used in section 3.3 to include as much orthogonality as possible during the first step of the method development, i.e. stationary phase screening, to make sure the best possible solution can be found. All the UHPSFC columns have dimensions of 100 × 3.0 mm, 1.7 m, except the last one which possesses particle sizes of 1.8 m. The organic modifier chosen for the whole study was prepared by adding 10 mM ammonium formate to a mixture of 98% methanol and 2% water. For all the experiments, flow rate, temperature and BPR pressure were kept constant at 2 mL/min (except for Acquity UPC2 CSH Fluoro-Phenyl which was used at 1.7 mL/min), 40 ◦ C and 150 bar, respectively. 2.3. Compounds 2.3.1. Test compounds A set of nine test compounds was chosen to evaluate the isocratic and gradient retention modeling in SFC. This set included basic, acidic and neutral compounds and covered a broad spectrum of structures, pKa and log P values, as shown in Table 1. All the compounds were purchased from Sigma-Fluka. Stock solutions of each sample compound were prepared at 1000 ppm in pure MeOH. For injection, the compounds were diluted with heptane/IpOH (7:3) to 100 ppm (Vinj = 1 L). The nine compounds were injected individually and detected at their optimal wavelength (Table 1). 2.3.2. Mixture of atorvastatin and impurities Atorvastatin calcium trihydrate and atorvastatin Pharmacopoeia impurities A, B, C and D were purchased from EDQM (Strasbourg, France). Stock solutions of atorvastatin and impurities A to D were prepared at 5000 and 1000 ppm, respectively, in MeOH and diluted in IpOH before injection (Vinj = 1 L). UV-detection was employed for this evaluation. The wavelength was set at 254 nm to have a good balance between a sufficient response for the detected compounds and a reduced interference of mobile phase organic modifier. 2.3.3. Mixture of 16 drugs and metabolites Chlorzoxazone (98%), 6-hydroxychlorzoxazone (97%), 4 -hydroxyflurbiprofen (98%), hydroxybupropion (95%), 5-hydroxyome
prazole sodium salt (98%) and omeprazole (98%) were purchased from Toronto Research Chemicals (Ontario, Canada). Dextromethorphan hydrobromide (99%), dextrorphan tartrate (98%), bupropion hydrochloride (98%), phenacetin (97%), acetaminophen (99%), flurbiprofen (99%), coumarin (99%), 7-hydroxycoumarin (99%) were obtained from Sigma-Fluka, whereas methanolic stock solutions of midazolam and 1-hydroxymidazolam were purchased from Lipomed (Arlesheim, Switzerland). A mixture of these 16 compounds was made at 1 ppm in heptane/IpOH (7:3) and the injection volume was 1 L. In this study, the Acquity QDa simple quadrupole detector was employed. The probe temperature was set at 600 ◦ C, whereas the capillary voltage was set at 1.0 kV and 0.8 kV in ESI positive and negative ionization mode, respectively. The cone voltages were optimized for each compound in the corresponding ESI polarity mode. Ethanol was used as make-up solvent and the flow rate of the ISM was set at 0.7 mL/min.
2.4. Software for data analysis Retention relationships were obtained with Matlab-software 2 R2009a using the lsqcurvefit routine. Radjusted - and Q2 -values (correlation coefficient measured from leave-one-out cross-validated error in predictions), retention time predictions, prediction errors (kpredicted − kexperimental )/kexperimental were calculated with an inhome written Matlab-routine.
2.5. Procedure for data analysis The column dead time t0 was estimated via the solvent peak (t0 = 0.35 min). Then, the effective gradient retention factor k = (tR − t0 )/t0 was calculated taking into account the column dead time. Finally, the isocratic k-values were used to fit the isocratic retention relationship (Eq. (3)), using the Matlab-routine lsqcurvefit, given the experimental conditions as input data and the observed k-values as output data. To assess the isocratic and gradient predictive ability of the retention relationships, the Q2 -values and the percentage errors (kpredicted − kexperimental )/kexperimental were calculated.
2.5.1. Linear gradient optimization The gradient optimization strategy consists of a grid search, scanning through all combinations of ϕ0 and ˇ (100 × 100 conditions with ln(ˇ) equally spaced between 0.001 and 0.5 and ϕ0 between 0.01 and 0.35). For all compounds, the retention time tR was predicted using either of the retention models in Eq. (1)–(3). From these retention times, the expected resolution Rs (Eq. (11), [25])
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each segment tG,n is no longer an explicit search variable, and it is mathematically implemented as follows: tG,n = t R,n − tD − t0 −
n−1
tG,i
(12)
i=1
where tR,n is the retention time of the nth eluting peak. For 0 , 100 conditions were scanned, equally spaced between 0.01 and 0.35, and for ln(ˇ), 20 conditions were scanned, equally spaced between 0.001 and 0.5. Similarly to the linear gradient optimization, the expected resolution Rs (Eq. (11)) of each peak pair was estimated under all the combinations and the best one-segmentper-component gradient corresponds to baseline separation within the shortest possible analysis time (tR,analysis = tR,last compound ). A calculation time in the order of one or two minutes was applied. 3. Results and discussion 2 Fig. 1. Radjusted (o) and Q2 -values () for all nine compounds on the three stationary
phases (HSS, 2-EP and BEH) for the non-linear models Eqs. (1)–(3).
of each peak pair was estimated under all the combinations of ϕ0 and ˇ using: √ Rs =
k N 4 1 + kelution
(11)
where kelution is the highest retention factor between the two consecutive compounds when eluting from the column, i.e. for ϕ = ϕelution . The best gradient conditions correspond to baseline separation (Rs,crit = 1.6) within the shortest possible analysis time (tR,analysis = tR,last compound ).
2.5.2. Multi-segment gradient optimization The best multi-segment gradient was obtained via the previously published one-segment-per-component search [15]. This gradient design strategy allows for an adjustment of the gradient slope after the elution of each individual component of the sample. In this way, the retention properties (kw -, S1 - and S2 -values from Eq. (3)) of the different analytes auto-guide the course of the gradient profile. The gradient steepness ˇ was optimized for every compound separately and each gradient segment was ended after the elution of the compound. As a consequence, the length of
3.1. Isocratic retention modeling In a first step, the isocratic retention relationship in SFC was investigated by studying nine compounds with different chemical properties (including basic, acidic and neutral compounds, see Table 1) on three different stationary phases (BEH, 2-EP, HSS). The experimental retention factors were fitted with Eqs. (1)–(3), i.e. k vs. , and the quality of the fitting was assessed by the goodness of fit 2 (Radjusted -values) and its prediction ability by the (cross-validated) goodness of prediction (Q2 -values, correlation coefficient measured from leave-one-out cross-validated error in predictions). 2 The Radjusted and Q2 -values are provided in Fig. 1. Given the high 2 -values (>0.999) for Eqs. (1) and (3), it can be concluded that Radjusted the isocratic retention data in SFC can be accurately described by the non-linear mixed mode HILIC retention model (Eq. (1)) and also by 2 the non-linear reversed phase model (Eq. (3)). The Radjusted -values for Eq. (2) were lower, especially for the least retained compounds, because of the presence of the asymptotic behavior in the SFC k vs. relationship (see Fig. 2). Also, the Q2 -values (Fig. 1) for all models (Eqs. (1)–(3)) were lower because of the difficult prediction of this asymptotic behavior. The established retention models using Eq. (3) on the BEH stationary phase are given in Fig. 3. As can be seen from Fig. 3B no perfect fit can be obtained for the least retained compounds at higher %B (from 20%B). The obtained retention relationships even show physically impossible extrapolations (Fig. 3B). However, these high %B are not of practical interest for
Fig. 2. Retention relationships (Eqs. (1)–(3)) for (A) the poorly retained compound caffeine and (B) the strongly retained octopamine, on the BEH stationary phase.
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Fig. 3. Retention relationships (Eq. (3)) for all nine test compounds (see Table 2) on the BEH stationary phase (A) k as a function of the fraction of eluting solvent B and (B) ln(k) as a function of the fraction of B.
these compounds as during a gradient they will always elute before “feeling” this region of high %B. The gradient modeling is therefore expected not to be influenced by these unrealistic extrapolations at high %B. 3.2. Gradient retention modeling In a second step, we investigated whether the isocratic retention data can be used to model the retention in gradient elution mode, using Eqs. (1)–(3). Eight gradient runs were performed with different starting concentrations and gradient times (2–50%B and 5–50%B in 2, 6 and 10 min, 5–30%B in 6 min, and 10–50%B in 4 min). The interconversion between isocratic and gradient retention data was found to be less straightforward than in RPLC and HILIC. This behavior is in agreement with our expectations since the pressure generated by the column may vary between the different isocratic and gradient conditions (different mobile phase viscosity, depending on the percentage of methanol) [2,26,27]. Considering that in SFC, pressure has a very strong impact on the mobile phase density and its eluent strength, the inevitable change in experienced pressure between an isocratic and a gradient run severely compromises retention prediction in SFC. The gradient percentage errors based on isocratic scouting runs, for all nine compounds on the three stationary phases using the three non-linear models Eqs. (1)–(3) are given in Fig. 4. For all three isocratic models (Eqs. (1)–(3)), more than half of the total data set showed prediction errors were below 5% (58% for Eq. (1), (55)% for Eq. (2) and (56)% for Eq. (3)). A few conditions showed prediction errors above 10% (5% for Eqs. (1)–(2)) and 6% for Eq. (3)). Two outliers are observed using Eqs. ((1)–(2)) for nikethamide on the 2-EP column and the gradient from 10 to 50%B in 6 min. This is not surprising as nikethamide is the least retained compound of the whole data set. No other significant differences in prediction errors were observed between the different non-linear models, compounds, stationary phases and gradient runs with 2, 5 or 10%B as starting mobile phase (see Fig. 5). As a third step, we also investigated the possibilities of using three gradient scouting runs to predict retention for any other gradient condition. In reversed-phase, typically two runs with gradient times tG,1 and tG,2 = 3 × tG,1 (and the same starting concentration) are performed to estimate the LSS-parameters. Using a non-linear model, such as Eq. (3), at least three gradient runs are needed to
estimate the retention parameters. We selected gradient times tG of 2, 4 and 8 minutes in order to maintain the similar rules as in RPLC while keeping the analysis times low (tG,2 = 2 × tG,1 and tG,3 = 2 × tG,2 ). Using the estimated parameters, other gradient runs (with varying tG and starting concentration) were predicted. In Fig. 6A and B, the predictions errors are given for the nine model compounds on the BEH column considering parameter scouting runs starting at 5% and 2%B, respectively. Note that the fitting of these parameter scouting runs is almost perfect (0% error). Also, the predictions for other gradients with the same starting conditions are acceptable (even for extrapolations to the slowest gradient with tG = 15 min the prediction errors were always below 5%). On the other hand, prediction errors for gradient with a different starting condition were highly dependent on the compound. The most retained compounds can still be predicted with prediction errors below 5%, while for the combination of least retained compounds and slowest gradient (with tG = 15 min), the prediction errors can go up to 40%. The same trends were observed on the 2-EP and the HSS column.
Fig. 4. Gradient predictions errors for all nine test compounds on the BEH, 2-EP and the HSS column, based on isocratic scouting runs using Eqs. (1)–(3). Percentage errors defined as (kpredicted − kexp )/kexp . The test conditions included gradients from 2 to 50%B in 2, 6 and 10 min, from 5 to 50%B in 2, 6 and 10 min, from 5 to 30%B in 6 min and from 10 to 50%B in 4 min.
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Fig. 5. No significant difference in predictions errors is observed between different gradient conditions for all nine test compounds based on isocratic scouting runs using Eq. (3). Percentage errors defined as (kpredicted − kexp )/kexp . Grad 1–3 from 2 to 50%B in 2, 6 and 10 min, Grad 4–6 from 5 to 50%B in 2, 6 and 10 min, Grad 7 from 5 to 30%B in 6 min and Grad 8 from 10 to 50%B in 4 min. Black: BEH, Blue: 2-EP and Red: HSS stationary phase. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
3.3. Gradient optimization: examples 3.3.1. Mixture of atorvastatin and four related impurities In a first instance, the possibilities of gradient retention modeling based on gradient scouting runs were investigated, as done in section 3.2. Because Eq. (3) has the simplest expression for the gradient retention factor, and hence requires the smallest computational effort during the search procedures, this model was preferred for MD purposes. Because atorvastatin (AT) and all impurities were well retained, gradient runs starting from 5%B were performed with different gradient times tG (2, 3, 4, 6, 8 and 10 min). Four different stationary phases (2EP, BEH, HSS and PFP) were included to include as much orthogonality as possible, to make sure the best possible separation can be found. The retention parameters were estimated from runs with tG of 3, 6 and 10 min. We also performed one additional gradient run starting from a lower and one run starting from a higher concentration of eluting solvent B (from 2 to 30%B in 6 min and from 7 to 30%B in 6 min, respectively), to fully explore
the retention modeling possibilities for these compounds. Almost all prediction errors were below 2%, except for the least retained compound, impurity D, prediction errors between 13 and 46% were observed for the gradients with a starting concentration different from 5% (used in the gradient scouting runs for the parameters estimation). Because of these very good prediction errors for the closely eluting AT and impurities A, B and C, we subsequently investigated the possibility of gradient optimization via individual retention modeling. As Imp D was systematically eluting far before the other compounds and since the predictions at different starting concentrations were not reliable, this compound was left out of the optimization. The HSS-column was proposed by the algorithm to provide the best selectivity. In Fig. 7, the best linear gradient (Fig. 7A) and multi-segment gradient (Fig. 7B) are given for a mixture of equal concentrations of AT and the four impurities. Baseline separation was obtained in 3.6 min and 3.1 min, respectively. For both gradients, the retention time predictions were reasonable, with a maximal value of 1.7% and 3.4%, for the linear and the multisegment gradient, respectively (Table 2). Note that for the MD, only three scouting runs were required to obtain the retention parameters. The other gradient runs were solely incorporated in this study to show the possibilities and limitations of retention modeling in SFC. Finally, we tried to improve the resolution between AT and its impurities, to mimic a more realistic case in which AT is 100-times more concentrated than its impurities. For this purpose, a longer analysis time and a multi-segment gradient were required. The final chromatogram is shown in Fig. 7C. Acceptable Rs was obtained between the critical pair AT and Imp B. To further improve the Rs between AT and Imp B, a longer column would be required. However, some undesirable changes in selectivity could also occur because the column pressure drop would be different. Again, the retention time predictions were accurate in this case (maximal value of 1.7%, see Table 2). The final separation of AT and its related impurities was obtained in less than 3 h of instrument time, including equilibration times. 3.3.2. Mixture of 16 drugs and main phase I metabolites In a first instance, the possibilities of gradient retention modeling based on gradient scouting runs were investigated, similarly to what was done with the mixture of AT and related impurities. Gradients from 1 to 30%B in 2, 3, 4, 6, 8, 10 and 15 min were
Fig. 6. Gradient prediction errors for all nine compounds on the BEH column. Parameters estimated using three gradient scouting runs with the same starting concentration of eluting solvent B (see arrows). Gradient conditions from 2 to 50 and from 5 to 50%B in 2, 4, 6, 8, 10 and 15 min.
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Fig. 7. Separations of atorvastatin and four related impurities (A) best linear gradient (from 10.0 to 22.8%B in 4.25 min), (B) best multi-segment gradient (from 5.0 to 13.7%B in 0.43 min, to 17.7%B after 2.45 min, to 24.5%B after 2.58 min with an isocratic hold at 24.5%B until 3.58 min), (C) best multi-segment gradient (AT 100 times more concentrated) (from 3.0 to 9.0%B in 0.55 min, to 13.9%B after 5.47 min, to 14.2%B after 5.82 min, to 14.7%B after 6.32 min, to 15.1%B after 6.72 min, to 15.6%B in 7.50 min with an isocratic hold at 15.6%B until 7.50 min).
Table 2 Retention time predictions for the AT mixture (chromatograms A to C in Fig. 7). %Error is defined as (tR,pred − tR,exp )/tR,exp . tR,pred
tR,exp
%Error
(A)
Imp C AT Imp B Imp A
3.01 3.14 3.28 3.46
3.01 3.19 3.33 3.52
−0.2% −1.4% −1.6% −1.7%
(B)
Imp C AT Imp B Imp A
2.68 2.82 2.94 3.08
2.77 2.88 2.96 3.06
−3.4% −2.2% −0.9% 0.6%
(C)
Imp C AT Imp B Imp A
5.89 6.24 6.75 7.14
5.85 6.22 6.64 7.05
0.7% 0.3% 1.7% 1.3%
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Fig. 8. Separations of the 16 components mixture (8 drugs and their main phase I metabolites) (A) best possible linear gradient on BEH stationary phase (from 6.4 to 21.1%B in 6.63 min), (B) best possible linear gradient on 2-EP stationary phase (from 1 to 15.4%B in 6.7 min) and (C) optimized multi-segment gradient on the BEH column (from 1.0 to 6.9%B in 2.7 min, to 12.1%B after 4.32 min, to 28.6%B after 6.65 min).
performed and one gradient from 3 to 30%B in 6 min, on four different stationary phases (2EP, BEH, HSS and PFP). The parameters were obtained via the gradients with tG = 3, 6 and 10 min. For this mixture, the prediction errors for gradients with the same starting composition were again very good (mostly below 1%). On the other hand, for the gradient with a different starting composition, the prediction errors varied between 0 and more than 40%, depending on compounds retention. Similar prediction errors were found on the 2-EP and the HSS columns. The early eluting compounds coumarin, chlorzoxazone and bupropion were badly predicted, but as they elute separately from each other and from the other drugs and metabolites, the gradient optimization was made including the “unreliable” retention predictions of these compounds. The BEH column was proposed by the search algorithm to give the best selectivity. The experimental chromatogram corresponding to the best possible linear gradient is given in Fig. 8A. However, the predictions errors were unacceptable (Table 3), except for the last eluting compounds, including the critical pair. This can be understood from the high starting concentration of 6.4%B, compared to 1%B in the scouting runs (used to obtain the parameter values). Indeed, the prediction errors were already significantly larger for
the gradient starting from 3%B instead of 1%B. Even for the more retained compounds, prediction errors up to 8% were observed. For the 2-EP stationary phase, very different retentions and selectivities were achieved, compared to the BEH column. On the 2-EP, the best possible predicted linear gradient starts from 1%B, resulting in much more accurate retention time predictions (Table 3). However, the best possible linear gradients still gave resolution problems, between acetaminophen and OH-bupropion on the BEH stationary phase (Fig. 8A) and between phenacetin and midazolam, and OH-coumarin and OH-bupropion on the 2-EP stationary phase (Fig. 8B). The resolution was therefore further optimized via a multisegment gradient optimization, using the so-called one-segmentper-component optimization search (see section 2.6.2 and reference [15]). Using the BEH stationary phase, almost baseline separation was obtained between acetaminophen and OH-bupropion (Fig. 8C). Also note that more equal spacing of all 16 peaks was obtained. The optimized multi-segment gradient (starting from 1%B) again resulted in highly accurate retention time predictions (Fig. 3). The final separation was obtained in less than 8 h instrument time, including equilibration times.
E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228 Table 3 Prediction errors optimized gradients (see Fig. 8). Critical pairs are denoted with an asterisk*. tR,pred
tR,exp
%Error
(A)
0.730 0.995 1.142 1.327 1.404 1.565 1.723 2.070 2.312 2.444 2.713 2.918 3.007 4.288 4.970 7.236
0.413 0.502 0.558 0.952 1.008 1.1 1.361 1.616 1.901 2.064 2.647* 2.701* 2.817 4.075 4.536 6.998
76.7% 98.1% 104.6% 39.3% 39.3% 42.3% 26.6% 28.1% 21.6% 18.4% 2.5% 8.0% 6.7% 5.2% 9.6% 3.4%
(B)
0.763 1.034 1.824 2.624 2.695 2.774 3.052 3.162 3.278 3.610 4.118 4.263 4.910 5.008 6.052 6.641
0.722 0.902 1.93 2.635 2.654 2.828 3.008 3.253 3.353 3.405 4.001 4.424 4.961 5.094 6.244 6.417
5.7% 14.6% −5.5% −0.4% 1.5% −1.9% 1.5% −2.8% −2.2% 6.0% 2.9% −3.6% −1.0% −1.7% −3.1% 3.5%
(C)
0.758 1.654 1.854 2.312 2.628 2.919 3.111 3.799 4.104 4.242 4.498 4.615 4.732 5.679 6.090 7.064
0.727 1.646 1.8 2.378 2.643 2.918 3.144 3.791 4.099 4.279 4.581 4.69 4.797 5.726 6.106 7.094
4.3% 0.5% 3.0% −2.8% −0.6% 0.0% −1.0% 0.2% 0.1% −0.9% −1.8% −1.6% −1.4% −0.8% −0.3% −0.4%
227
higher than 10%. No significant difference in prediction errors were observed between the different isocratic models, compounds, stationary phases and gradient conditions. We also investigated the possibilities of gradient scouting runs to estimate the retention parameters using Eq. (3), as this model requires the smallest computational effort for the effective retention factor keff . In this case, accurate retention time modeling was possible when the starting concentration of the gradient was kept constant and the gradient time was modified. Accurate predictions (
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Possibilities of retention modeling and computer assisted method development in supercritical fluid chromatography Eva Tyteca a,1 , Vincent Desfontaine b,1 , Gert Desmet a , Davy Guillarme b,∗ a b
Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium School of Pharmaceutical Sciences, University of Geneva, University of Lausanne, Switzerland
a r t i c l e
i n f o
Article history: Received 28 August 2014 Received in revised form 16 December 2014 Accepted 26 December 2014 Available online 7 January 2015 Keywords: SFC UHPSFC Method development Retention modeling Retention prediction
a b s t r a c t The multi-modal retention mechanism in supercritical fluid chromatography (SFC) results in a non-linear dependency of log(k) on the fraction of organic solvent ϕ and log(ϕ). In the present study, the possibility of retention modeling for method development purposes in SFC was investigated, considering several non-linear isocratic relationships. Therefore, both isocratic and gradient runs were performed, involving different column chemistries and analytes possessing diverse physico-chemical properties. The isocratic retention data of these compounds could be described accurately using the non-linear retention models typically used in HILIC and reversed-phase LC. The interconversion between isocratic and gradient retention data was found to be less straightforward than in RPLC and HILIC because of pressure effects. The possibility of gradient predictions using gradient scouting runs to estimate the retention parameters was investigated as well, showing that predictions for other gradients with the same starting conditions were acceptable (always below 5%), whereas prediction errors for gradients with a different starting condition were found to be highly dependent on the compound. The second part of the study consisted of the gradient optimization of two pharmaceutical mixtures (one involving atorvastatin and four related impurities, and one involving a 16 components mixture including eight drugs and their main phase I metabolites). This could be done via individual retention modeling based on gradient scouting runs. The best linear gradient was found via a grid search and the best multi-segment gradient via the previously published one-segment-per-component search. The latter improved the resolution between the critical pairs for both mixtures, while still giving accurate prediction errors (using the same starting concentrations as the gradient scouting runs used to build the model). The optimized separations were found in less than 3 h and 8 h of analysis time (including equilibration times), respectively. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) is gaining in importance as a chromatographic technique, to analyze a wide range of compounds from relatively hydrophilic to highly lipophilic [1–4]. In SFC, the retention mechanism is multi-modal, combining different interaction mechanisms, and highly dependent on the nature of the stationary phase and the type of organic modifier [5,6]. In SFC, the mobile phase generally consists of a mixture of apolar CO2 and a limited proportion of methanol (typically up to 30%). In this case, normal phase retention behavior takes place using a polar stationary phase (such as silica, diol, amino, cyano, amide). On the other hand, using an apolar stationary phase (such as C8 ,
∗ Corresponding author. Tel.: +41 22 379 34 63. E-mail address: [email protected] (D. Guillarme). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.chroma.2014.12.077 0021-9673/© 2015 Elsevier B.V. All rights reserved.
C18 , phenylhexyl), reversed-phase retention behavior is expected, as in the absence of H2 O, the interactions between the compounds and the stationary phase are favored, limiting the contribution of the apolar CO2 in the mobile phase. When other stationary phases (such as alkyl bonded phases with hydrophilic end-capping or polar embedded group) are used, intermediate behavior can be expected [7]. The use of MeOH in the mobile phase introduces other interactions such as H-bonding, dipole–dipole interactions and solvent adsorption [7,8]. Solvent adsorption is also playing a major role in hydrophilic interaction chromatography (HILIC) [9]. The multi-modal retention mechanism results in a non-linear dependency of the logarithm of the retention factor log(k) on the fraction of organic solvent ϕ and log(ϕ). As such, the linear solvent strength (LSS) model, widely used to model reversed-phase retention, can no longer be applied in SFC. Also in HILIC, a multi-modal retention mechanism exists, combining partitioning, adsorption through H-bonding and electrostatic and ionic interactions [10], and non-linear retention models have been reported [11–13].
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Therefore, the non-linear retention models that have proven to be successful in HILIC retention modeling could also be of interest for the SFC retention modeling: ln(k) = ln(kw ) + S1 + S2 ln()
(1)
ln(k) = ln(kw ) + S1 + S2 2
(2)
ln(k) = ln(kw ) + 2 · ln(1 + S2 ) −
S1 1 + S2
(3)
where is the fraction of water, kw the extrapolated value of k for = 0 (i.e., pure CO2 ), S1 the slope and S2 the curvature coefficient [14]. The expression for the gradient retention factor can be found by solving the fundamental gradient equation:
tR −t0
t0 =
dts k()
(4)
0
where t0 is the column dead time and tR is the total retention time. For multi-segment gradients, the fundamental gradient equation becomes a sum of integrals, each describing the retention during one segment of the gradient [15]. This sum of integrals can still be solved in a straightforward way, to obtain an analytical expression for the effective retention factor keff = (tR − t0 )/t0 . In reversed-phase method development (MD) schemes, isocratic and gradient data are measured and interpolated, then isocratic and gradient retention results can be interconverted (e.g. prediction of isocratic retention based on gradient scouting runs). This is possible because the retention relationships in reversedphase behave rather “gently”, with only relatively small deviations from the LSS-behavior, i.e. linear relationship between ln(k) and . In reversed-phase, the retention behavior of a component can therefore in general be examined with a set of well-chosen experiments that cover the entire intended experimental space. The retention space between experimental data points is then modeled, and computer predictions, based on these models, are used in MD processes [15–18]. Based on the accuracy of the retention models, different MD strategies can be applied. If accurate retention time predictions are possible, individual retention modeling can be used to optimize the gradient conditions. This approach was developed for reversed-phase separations [16]. In addition, HILIC separations for which an accurate retention model exists have also been optimized using this approach [13]. When the modeling is very accurate, the separation power can be increased, using multisegments gradients. However, smart algorithms are needed to find out the optimal gradient conditions among the innumerous combinations [15]. On the other hand, if no accurate retention modeling is possible, a hybrid method called the predictive elution window shifting and stretching approach (PEWS2 ) can be used for the gradient optimization in both RPLC and the HILIC mode [13,18]. Design of Experiments is another strategy that can be used to optimize a separation, without the need for retention models such as Eqs. (1)–(3). This approach was recently proposed to optimize SFC gradient conditions by Dispas et al. who reported on the optimization of tiso , tG and %MeOHstart for the separation of six antibiotic drugs and caffeine [19]. In the present study, the possibilities of retention modeling and gradient optimization in SFC were investigated, using the non-linear retention models of Eqs. (1)–(3). To the best of the authors’ knowledge, the isocratic retention models proposed in this study have not yet been applied in SFC. Moreover, gradient retention prediction and optimization of the gradient conditions via individual retention modeling have not been reported in SFC. For this purpose, a range of mobile phase compositions %B
(10 mM ammonium formate in 98% MeOH + 2% H2 O) were applied to various column chemistries (BEH, 2-EP and HSS) and several analytes possessing diverse physico-chemical properties (see Table 1) and the isocratic retention relationships were studied. Subsequently, we investigated the possibility to predict gradient retention from a limited number of isocratic or gradient runs and applied this approach to two real-life separation problems, with varying number of compounds (atorvastatin and four related impurities, a 16 component mixture including 8 drugs and their main phase I metabolites), using Eq. (3) (the Neue and Kussequation), as this gives the simplest expression for the gradient retention factor when solving the fundamental gradient equation (Eq. (4)), and hence requires the smallest computational effort during the optimization searches (e.g. the model in Eq. (1) requires a time-resolved numerical integration for each individual screening condition). Atorvastatin marketed as a calcium salt is a member of the drug class known as statins, which are used for lowering blood cholesterol and for prevention of events associated with cardiovascular disease [20]. From 1996 to 2012, atorvastatin became the world’s best-selling drug of all time, under the trade name Lipitor, with more than $125 billion in sales over approximately 14 years [21]. In the present study, a stability-indicating SFC method was developed for the determination of atorvastatin and four related pharmacopeia impurities. To evaluate the interaction potential of drugs, new chemical entities, toxic substances and phytochemicals, and account for the existing risks during co-exposure, in vitro drug metabolism assay has to be performed in the pharmaceutical industry during the drug development process. From an analytical point of view, there is a need to develop fast methods able to discriminate a significant number of substrates and metabolites, each corresponding to a given cytochrome P450 (CYP) subfamily [22]. In the present study, a SFC method was developed for the separation of eight probe substrates and eight CYP-specific metabolites, previously investigated in LC conditions [23]. 2. Material and methods 2.1. Chemicals and reagents Methanol (MeOH) HPLC grade was purchased from Fisher Scientific (Loughborough, UK), whereas isopropanol (IpOH), ethanol (EtOH) and heptane were purchased from VWR (Radnor, PA, USA). Pressurized liquid CO2 , 3.0 grade, (99.9%) was purchased from PanGas (Dagmerstellen, Switzerland). Ultrapure water was supplied by a Milli-Q Advantage A10 purification unit from Millipore (Bedford, MA, USA). Ammonium formate was purchased from Sigma-Fluka (Buchs, Switzerland). 2.2. Instrumentation and columns All the experiments were performed on a Waters Acquity UPC2 system (Waters, Milford, MA, USA) equipped with a binary solvent delivery pump, an autosampler that included a 10 L loop for partial loop injection, a column oven and a two-step (passive + active) backpressure regulator (BPR). The passive component maintains pressure higher than 104 bar, while the active component allows further back pressure increase and fine backpressure adjustments. The injection volume was 1 L and the measured dwell volume was 440 L. The Acquity UPC2 system was also combined with a benchtop single quadrupole, namely Waters Acquity QDa detector fitted with a Z-spray electrospray (ESI) ionization source. Make-up solvent delivered by a Waters Isocratic Solvent Manager (ISM) pump
E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228
221
Table 1 The nine test compounds used for the initial evaluation of the isocratic and gradient retention modeling together with their physico-chemical properties. is the optimal detector wavelength. Molecule
Acidic pKa
Basic pKa
log P
(nm)
Caffeine Nikethamide Warfarin Papaverine Acetazolamide Prednisolone Propranolol Ethacrynic Acid Octopamine
– – 5.1 – 7.2 – – 2.8 9.6
– 3.6 – 6 – – 9.4 – 9
−0.55 0.77 2.74 3.03 −0.26 1.62 2.93 3.66 −0.32
280 254 280 254 254 254 280 280 220
was added and mixed to the chromatographic effluent prior to MS detection through a split interface purchased from Waters. The UHPSFC-MS hyphenation interface and splitter are described in [24]. Data acquisition, data handling and instrument control were performed by Empower v. 4.1 software (Waters). The UHPSFC columns employed in this study were purchased from Waters: Acquity UPC2 BEH (BEH), Acquity UPC2 BEH 2-EP (2EP), Acquity UPC2 HSS C18 SB (HSS) and Acquity UPC2 CSH FluoroPhenyl (PFP). The PFP column was used in section 3.3 to include as much orthogonality as possible during the first step of the method development, i.e. stationary phase screening, to make sure the best possible solution can be found. All the UHPSFC columns have dimensions of 100 × 3.0 mm, 1.7 m, except the last one which possesses particle sizes of 1.8 m. The organic modifier chosen for the whole study was prepared by adding 10 mM ammonium formate to a mixture of 98% methanol and 2% water. For all the experiments, flow rate, temperature and BPR pressure were kept constant at 2 mL/min (except for Acquity UPC2 CSH Fluoro-Phenyl which was used at 1.7 mL/min), 40 ◦ C and 150 bar, respectively. 2.3. Compounds 2.3.1. Test compounds A set of nine test compounds was chosen to evaluate the isocratic and gradient retention modeling in SFC. This set included basic, acidic and neutral compounds and covered a broad spectrum of structures, pKa and log P values, as shown in Table 1. All the compounds were purchased from Sigma-Fluka. Stock solutions of each sample compound were prepared at 1000 ppm in pure MeOH. For injection, the compounds were diluted with heptane/IpOH (7:3) to 100 ppm (Vinj = 1 L). The nine compounds were injected individually and detected at their optimal wavelength (Table 1). 2.3.2. Mixture of atorvastatin and impurities Atorvastatin calcium trihydrate and atorvastatin Pharmacopoeia impurities A, B, C and D were purchased from EDQM (Strasbourg, France). Stock solutions of atorvastatin and impurities A to D were prepared at 5000 and 1000 ppm, respectively, in MeOH and diluted in IpOH before injection (Vinj = 1 L). UV-detection was employed for this evaluation. The wavelength was set at 254 nm to have a good balance between a sufficient response for the detected compounds and a reduced interference of mobile phase organic modifier. 2.3.3. Mixture of 16 drugs and metabolites Chlorzoxazone (98%), 6-hydroxychlorzoxazone (97%), 4 -hydroxyflurbiprofen (98%), hydroxybupropion (95%), 5-hydroxyome
prazole sodium salt (98%) and omeprazole (98%) were purchased from Toronto Research Chemicals (Ontario, Canada). Dextromethorphan hydrobromide (99%), dextrorphan tartrate (98%), bupropion hydrochloride (98%), phenacetin (97%), acetaminophen (99%), flurbiprofen (99%), coumarin (99%), 7-hydroxycoumarin (99%) were obtained from Sigma-Fluka, whereas methanolic stock solutions of midazolam and 1-hydroxymidazolam were purchased from Lipomed (Arlesheim, Switzerland). A mixture of these 16 compounds was made at 1 ppm in heptane/IpOH (7:3) and the injection volume was 1 L. In this study, the Acquity QDa simple quadrupole detector was employed. The probe temperature was set at 600 ◦ C, whereas the capillary voltage was set at 1.0 kV and 0.8 kV in ESI positive and negative ionization mode, respectively. The cone voltages were optimized for each compound in the corresponding ESI polarity mode. Ethanol was used as make-up solvent and the flow rate of the ISM was set at 0.7 mL/min.
2.4. Software for data analysis Retention relationships were obtained with Matlab-software 2 R2009a using the lsqcurvefit routine. Radjusted - and Q2 -values (correlation coefficient measured from leave-one-out cross-validated error in predictions), retention time predictions, prediction errors (kpredicted − kexperimental )/kexperimental were calculated with an inhome written Matlab-routine.
2.5. Procedure for data analysis The column dead time t0 was estimated via the solvent peak (t0 = 0.35 min). Then, the effective gradient retention factor k = (tR − t0 )/t0 was calculated taking into account the column dead time. Finally, the isocratic k-values were used to fit the isocratic retention relationship (Eq. (3)), using the Matlab-routine lsqcurvefit, given the experimental conditions as input data and the observed k-values as output data. To assess the isocratic and gradient predictive ability of the retention relationships, the Q2 -values and the percentage errors (kpredicted − kexperimental )/kexperimental were calculated.
2.5.1. Linear gradient optimization The gradient optimization strategy consists of a grid search, scanning through all combinations of ϕ0 and ˇ (100 × 100 conditions with ln(ˇ) equally spaced between 0.001 and 0.5 and ϕ0 between 0.01 and 0.35). For all compounds, the retention time tR was predicted using either of the retention models in Eq. (1)–(3). From these retention times, the expected resolution Rs (Eq. (11), [25])
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each segment tG,n is no longer an explicit search variable, and it is mathematically implemented as follows: tG,n = t R,n − tD − t0 −
n−1
tG,i
(12)
i=1
where tR,n is the retention time of the nth eluting peak. For 0 , 100 conditions were scanned, equally spaced between 0.01 and 0.35, and for ln(ˇ), 20 conditions were scanned, equally spaced between 0.001 and 0.5. Similarly to the linear gradient optimization, the expected resolution Rs (Eq. (11)) of each peak pair was estimated under all the combinations and the best one-segmentper-component gradient corresponds to baseline separation within the shortest possible analysis time (tR,analysis = tR,last compound ). A calculation time in the order of one or two minutes was applied. 3. Results and discussion 2 Fig. 1. Radjusted (o) and Q2 -values () for all nine compounds on the three stationary
phases (HSS, 2-EP and BEH) for the non-linear models Eqs. (1)–(3).
of each peak pair was estimated under all the combinations of ϕ0 and ˇ using: √ Rs =
k N 4 1 + kelution
(11)
where kelution is the highest retention factor between the two consecutive compounds when eluting from the column, i.e. for ϕ = ϕelution . The best gradient conditions correspond to baseline separation (Rs,crit = 1.6) within the shortest possible analysis time (tR,analysis = tR,last compound ).
2.5.2. Multi-segment gradient optimization The best multi-segment gradient was obtained via the previously published one-segment-per-component search [15]. This gradient design strategy allows for an adjustment of the gradient slope after the elution of each individual component of the sample. In this way, the retention properties (kw -, S1 - and S2 -values from Eq. (3)) of the different analytes auto-guide the course of the gradient profile. The gradient steepness ˇ was optimized for every compound separately and each gradient segment was ended after the elution of the compound. As a consequence, the length of
3.1. Isocratic retention modeling In a first step, the isocratic retention relationship in SFC was investigated by studying nine compounds with different chemical properties (including basic, acidic and neutral compounds, see Table 1) on three different stationary phases (BEH, 2-EP, HSS). The experimental retention factors were fitted with Eqs. (1)–(3), i.e. k vs. , and the quality of the fitting was assessed by the goodness of fit 2 (Radjusted -values) and its prediction ability by the (cross-validated) goodness of prediction (Q2 -values, correlation coefficient measured from leave-one-out cross-validated error in predictions). 2 The Radjusted and Q2 -values are provided in Fig. 1. Given the high 2 -values (>0.999) for Eqs. (1) and (3), it can be concluded that Radjusted the isocratic retention data in SFC can be accurately described by the non-linear mixed mode HILIC retention model (Eq. (1)) and also by 2 the non-linear reversed phase model (Eq. (3)). The Radjusted -values for Eq. (2) were lower, especially for the least retained compounds, because of the presence of the asymptotic behavior in the SFC k vs. relationship (see Fig. 2). Also, the Q2 -values (Fig. 1) for all models (Eqs. (1)–(3)) were lower because of the difficult prediction of this asymptotic behavior. The established retention models using Eq. (3) on the BEH stationary phase are given in Fig. 3. As can be seen from Fig. 3B no perfect fit can be obtained for the least retained compounds at higher %B (from 20%B). The obtained retention relationships even show physically impossible extrapolations (Fig. 3B). However, these high %B are not of practical interest for
Fig. 2. Retention relationships (Eqs. (1)–(3)) for (A) the poorly retained compound caffeine and (B) the strongly retained octopamine, on the BEH stationary phase.
E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228
223
Fig. 3. Retention relationships (Eq. (3)) for all nine test compounds (see Table 2) on the BEH stationary phase (A) k as a function of the fraction of eluting solvent B and (B) ln(k) as a function of the fraction of B.
these compounds as during a gradient they will always elute before “feeling” this region of high %B. The gradient modeling is therefore expected not to be influenced by these unrealistic extrapolations at high %B. 3.2. Gradient retention modeling In a second step, we investigated whether the isocratic retention data can be used to model the retention in gradient elution mode, using Eqs. (1)–(3). Eight gradient runs were performed with different starting concentrations and gradient times (2–50%B and 5–50%B in 2, 6 and 10 min, 5–30%B in 6 min, and 10–50%B in 4 min). The interconversion between isocratic and gradient retention data was found to be less straightforward than in RPLC and HILIC. This behavior is in agreement with our expectations since the pressure generated by the column may vary between the different isocratic and gradient conditions (different mobile phase viscosity, depending on the percentage of methanol) [2,26,27]. Considering that in SFC, pressure has a very strong impact on the mobile phase density and its eluent strength, the inevitable change in experienced pressure between an isocratic and a gradient run severely compromises retention prediction in SFC. The gradient percentage errors based on isocratic scouting runs, for all nine compounds on the three stationary phases using the three non-linear models Eqs. (1)–(3) are given in Fig. 4. For all three isocratic models (Eqs. (1)–(3)), more than half of the total data set showed prediction errors were below 5% (58% for Eq. (1), (55)% for Eq. (2) and (56)% for Eq. (3)). A few conditions showed prediction errors above 10% (5% for Eqs. (1)–(2)) and 6% for Eq. (3)). Two outliers are observed using Eqs. ((1)–(2)) for nikethamide on the 2-EP column and the gradient from 10 to 50%B in 6 min. This is not surprising as nikethamide is the least retained compound of the whole data set. No other significant differences in prediction errors were observed between the different non-linear models, compounds, stationary phases and gradient runs with 2, 5 or 10%B as starting mobile phase (see Fig. 5). As a third step, we also investigated the possibilities of using three gradient scouting runs to predict retention for any other gradient condition. In reversed-phase, typically two runs with gradient times tG,1 and tG,2 = 3 × tG,1 (and the same starting concentration) are performed to estimate the LSS-parameters. Using a non-linear model, such as Eq. (3), at least three gradient runs are needed to
estimate the retention parameters. We selected gradient times tG of 2, 4 and 8 minutes in order to maintain the similar rules as in RPLC while keeping the analysis times low (tG,2 = 2 × tG,1 and tG,3 = 2 × tG,2 ). Using the estimated parameters, other gradient runs (with varying tG and starting concentration) were predicted. In Fig. 6A and B, the predictions errors are given for the nine model compounds on the BEH column considering parameter scouting runs starting at 5% and 2%B, respectively. Note that the fitting of these parameter scouting runs is almost perfect (0% error). Also, the predictions for other gradients with the same starting conditions are acceptable (even for extrapolations to the slowest gradient with tG = 15 min the prediction errors were always below 5%). On the other hand, prediction errors for gradient with a different starting condition were highly dependent on the compound. The most retained compounds can still be predicted with prediction errors below 5%, while for the combination of least retained compounds and slowest gradient (with tG = 15 min), the prediction errors can go up to 40%. The same trends were observed on the 2-EP and the HSS column.
Fig. 4. Gradient predictions errors for all nine test compounds on the BEH, 2-EP and the HSS column, based on isocratic scouting runs using Eqs. (1)–(3). Percentage errors defined as (kpredicted − kexp )/kexp . The test conditions included gradients from 2 to 50%B in 2, 6 and 10 min, from 5 to 50%B in 2, 6 and 10 min, from 5 to 30%B in 6 min and from 10 to 50%B in 4 min.
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Fig. 5. No significant difference in predictions errors is observed between different gradient conditions for all nine test compounds based on isocratic scouting runs using Eq. (3). Percentage errors defined as (kpredicted − kexp )/kexp . Grad 1–3 from 2 to 50%B in 2, 6 and 10 min, Grad 4–6 from 5 to 50%B in 2, 6 and 10 min, Grad 7 from 5 to 30%B in 6 min and Grad 8 from 10 to 50%B in 4 min. Black: BEH, Blue: 2-EP and Red: HSS stationary phase. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
3.3. Gradient optimization: examples 3.3.1. Mixture of atorvastatin and four related impurities In a first instance, the possibilities of gradient retention modeling based on gradient scouting runs were investigated, as done in section 3.2. Because Eq. (3) has the simplest expression for the gradient retention factor, and hence requires the smallest computational effort during the search procedures, this model was preferred for MD purposes. Because atorvastatin (AT) and all impurities were well retained, gradient runs starting from 5%B were performed with different gradient times tG (2, 3, 4, 6, 8 and 10 min). Four different stationary phases (2EP, BEH, HSS and PFP) were included to include as much orthogonality as possible, to make sure the best possible separation can be found. The retention parameters were estimated from runs with tG of 3, 6 and 10 min. We also performed one additional gradient run starting from a lower and one run starting from a higher concentration of eluting solvent B (from 2 to 30%B in 6 min and from 7 to 30%B in 6 min, respectively), to fully explore
the retention modeling possibilities for these compounds. Almost all prediction errors were below 2%, except for the least retained compound, impurity D, prediction errors between 13 and 46% were observed for the gradients with a starting concentration different from 5% (used in the gradient scouting runs for the parameters estimation). Because of these very good prediction errors for the closely eluting AT and impurities A, B and C, we subsequently investigated the possibility of gradient optimization via individual retention modeling. As Imp D was systematically eluting far before the other compounds and since the predictions at different starting concentrations were not reliable, this compound was left out of the optimization. The HSS-column was proposed by the algorithm to provide the best selectivity. In Fig. 7, the best linear gradient (Fig. 7A) and multi-segment gradient (Fig. 7B) are given for a mixture of equal concentrations of AT and the four impurities. Baseline separation was obtained in 3.6 min and 3.1 min, respectively. For both gradients, the retention time predictions were reasonable, with a maximal value of 1.7% and 3.4%, for the linear and the multisegment gradient, respectively (Table 2). Note that for the MD, only three scouting runs were required to obtain the retention parameters. The other gradient runs were solely incorporated in this study to show the possibilities and limitations of retention modeling in SFC. Finally, we tried to improve the resolution between AT and its impurities, to mimic a more realistic case in which AT is 100-times more concentrated than its impurities. For this purpose, a longer analysis time and a multi-segment gradient were required. The final chromatogram is shown in Fig. 7C. Acceptable Rs was obtained between the critical pair AT and Imp B. To further improve the Rs between AT and Imp B, a longer column would be required. However, some undesirable changes in selectivity could also occur because the column pressure drop would be different. Again, the retention time predictions were accurate in this case (maximal value of 1.7%, see Table 2). The final separation of AT and its related impurities was obtained in less than 3 h of instrument time, including equilibration times. 3.3.2. Mixture of 16 drugs and main phase I metabolites In a first instance, the possibilities of gradient retention modeling based on gradient scouting runs were investigated, similarly to what was done with the mixture of AT and related impurities. Gradients from 1 to 30%B in 2, 3, 4, 6, 8, 10 and 15 min were
Fig. 6. Gradient prediction errors for all nine compounds on the BEH column. Parameters estimated using three gradient scouting runs with the same starting concentration of eluting solvent B (see arrows). Gradient conditions from 2 to 50 and from 5 to 50%B in 2, 4, 6, 8, 10 and 15 min.
E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228
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Fig. 7. Separations of atorvastatin and four related impurities (A) best linear gradient (from 10.0 to 22.8%B in 4.25 min), (B) best multi-segment gradient (from 5.0 to 13.7%B in 0.43 min, to 17.7%B after 2.45 min, to 24.5%B after 2.58 min with an isocratic hold at 24.5%B until 3.58 min), (C) best multi-segment gradient (AT 100 times more concentrated) (from 3.0 to 9.0%B in 0.55 min, to 13.9%B after 5.47 min, to 14.2%B after 5.82 min, to 14.7%B after 6.32 min, to 15.1%B after 6.72 min, to 15.6%B in 7.50 min with an isocratic hold at 15.6%B until 7.50 min).
Table 2 Retention time predictions for the AT mixture (chromatograms A to C in Fig. 7). %Error is defined as (tR,pred − tR,exp )/tR,exp . tR,pred
tR,exp
%Error
(A)
Imp C AT Imp B Imp A
3.01 3.14 3.28 3.46
3.01 3.19 3.33 3.52
−0.2% −1.4% −1.6% −1.7%
(B)
Imp C AT Imp B Imp A
2.68 2.82 2.94 3.08
2.77 2.88 2.96 3.06
−3.4% −2.2% −0.9% 0.6%
(C)
Imp C AT Imp B Imp A
5.89 6.24 6.75 7.14
5.85 6.22 6.64 7.05
0.7% 0.3% 1.7% 1.3%
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E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228
Fig. 8. Separations of the 16 components mixture (8 drugs and their main phase I metabolites) (A) best possible linear gradient on BEH stationary phase (from 6.4 to 21.1%B in 6.63 min), (B) best possible linear gradient on 2-EP stationary phase (from 1 to 15.4%B in 6.7 min) and (C) optimized multi-segment gradient on the BEH column (from 1.0 to 6.9%B in 2.7 min, to 12.1%B after 4.32 min, to 28.6%B after 6.65 min).
performed and one gradient from 3 to 30%B in 6 min, on four different stationary phases (2EP, BEH, HSS and PFP). The parameters were obtained via the gradients with tG = 3, 6 and 10 min. For this mixture, the prediction errors for gradients with the same starting composition were again very good (mostly below 1%). On the other hand, for the gradient with a different starting composition, the prediction errors varied between 0 and more than 40%, depending on compounds retention. Similar prediction errors were found on the 2-EP and the HSS columns. The early eluting compounds coumarin, chlorzoxazone and bupropion were badly predicted, but as they elute separately from each other and from the other drugs and metabolites, the gradient optimization was made including the “unreliable” retention predictions of these compounds. The BEH column was proposed by the search algorithm to give the best selectivity. The experimental chromatogram corresponding to the best possible linear gradient is given in Fig. 8A. However, the predictions errors were unacceptable (Table 3), except for the last eluting compounds, including the critical pair. This can be understood from the high starting concentration of 6.4%B, compared to 1%B in the scouting runs (used to obtain the parameter values). Indeed, the prediction errors were already significantly larger for
the gradient starting from 3%B instead of 1%B. Even for the more retained compounds, prediction errors up to 8% were observed. For the 2-EP stationary phase, very different retentions and selectivities were achieved, compared to the BEH column. On the 2-EP, the best possible predicted linear gradient starts from 1%B, resulting in much more accurate retention time predictions (Table 3). However, the best possible linear gradients still gave resolution problems, between acetaminophen and OH-bupropion on the BEH stationary phase (Fig. 8A) and between phenacetin and midazolam, and OH-coumarin and OH-bupropion on the 2-EP stationary phase (Fig. 8B). The resolution was therefore further optimized via a multisegment gradient optimization, using the so-called one-segmentper-component optimization search (see section 2.6.2 and reference [15]). Using the BEH stationary phase, almost baseline separation was obtained between acetaminophen and OH-bupropion (Fig. 8C). Also note that more equal spacing of all 16 peaks was obtained. The optimized multi-segment gradient (starting from 1%B) again resulted in highly accurate retention time predictions (Fig. 3). The final separation was obtained in less than 8 h instrument time, including equilibration times.
E. Tyteca et al. / J. Chromatogr. A 1381 (2015) 219–228 Table 3 Prediction errors optimized gradients (see Fig. 8). Critical pairs are denoted with an asterisk*. tR,pred
tR,exp
%Error
(A)
0.730 0.995 1.142 1.327 1.404 1.565 1.723 2.070 2.312 2.444 2.713 2.918 3.007 4.288 4.970 7.236
0.413 0.502 0.558 0.952 1.008 1.1 1.361 1.616 1.901 2.064 2.647* 2.701* 2.817 4.075 4.536 6.998
76.7% 98.1% 104.6% 39.3% 39.3% 42.3% 26.6% 28.1% 21.6% 18.4% 2.5% 8.0% 6.7% 5.2% 9.6% 3.4%
(B)
0.763 1.034 1.824 2.624 2.695 2.774 3.052 3.162 3.278 3.610 4.118 4.263 4.910 5.008 6.052 6.641
0.722 0.902 1.93 2.635 2.654 2.828 3.008 3.253 3.353 3.405 4.001 4.424 4.961 5.094 6.244 6.417
5.7% 14.6% −5.5% −0.4% 1.5% −1.9% 1.5% −2.8% −2.2% 6.0% 2.9% −3.6% −1.0% −1.7% −3.1% 3.5%
(C)
0.758 1.654 1.854 2.312 2.628 2.919 3.111 3.799 4.104 4.242 4.498 4.615 4.732 5.679 6.090 7.064
0.727 1.646 1.8 2.378 2.643 2.918 3.144 3.791 4.099 4.279 4.581 4.69 4.797 5.726 6.106 7.094
4.3% 0.5% 3.0% −2.8% −0.6% 0.0% −1.0% 0.2% 0.1% −0.9% −1.8% −1.6% −1.4% −0.8% −0.3% −0.4%
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higher than 10%. No significant difference in prediction errors were observed between the different isocratic models, compounds, stationary phases and gradient conditions. We also investigated the possibilities of gradient scouting runs to estimate the retention parameters using Eq. (3), as this model requires the smallest computational effort for the effective retention factor keff . In this case, accurate retention time modeling was possible when the starting concentration of the gradient was kept constant and the gradient time was modified. Accurate predictions (
