Determination of thermodynamic acidity constants and limiting ionic mobilities of weak electrolytes by capillary electrophoresis using a new free software AnglerFish.

Thermodynamic acidity constants (acid or acid-base dissociation constants, sometimes called also as ionization constants) and limiting ionic mobilities (both of them at defined temperature, usually 25°C) are the fundamental physicochemical characteristics of a weak electrolyte, that is, weak acid or weak base or ampholyte. We introduce a novel method for determining the data of a weak electrolyte by the nonlinear regression of effective electrophoretic mobility versus buffer composition dependence when measured in a set of BGEs with various pH. To correct the experimental data for zero ionic strength we use the extended Debye-Hückel model and Onsager-Fuoss law with no simplifications. Contrary to contemporary approaches, the nonlinear regression is performed on limiting mobility data calculated by PeakMaster's correction engine, not on the raw experimental mobility data. Therefore, there is no requirement to perform all measurements at a constant ionic strength of the set of BGEs. We devised the computer program AnglerFish that performs the necessary calculations in a user-friendly fashion. All thermodynamic pKa values and limiting electrophoretic mobilities for arbitrarily charged substances having any number of ionic forms are calculated by one fit. The user input consists of the buffer composition of the set of BGEs and experimentally measured effective mobilities of the inspected weak electrolyte.

The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co-migrating analytes: The displacement and the tag-along effects.

Peak shapes in electrophoresis are often distorted from the ideal Gaussian shape due to disturbing phenomena, of which the most important is electromigration dispersion. For fully dissociated analytes, there is a tight analogy between nonlinear models describing a separation process in chromatography and electrophoresis. When the velocity of the separated analyte depends on the concentration of the co-analyte, the consequence is a mutual influence of the analytes couples, which distorts both analyte zones. In this paper, we introduce a nonlinear model of electromigration for the analysis of two co-migrating fully dissociated analytes. In the initial stages of separation, they influence each other, which causes much more complicated peak shapes. The analysis has revealed that the two most important phenomena-the displacement and the tag-along effects-are common both for nonlinear chromatography and electrophoresis, though their description is partly based on rather different phenomena. The comparison between the nonlinear model of electromigration we describe and the numerical computer solution of the original continuity equations has proven an almost perfect agreement. The predicted features in peak shapes in initial stages of separation have been fully confirmed by the experiments.

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Capillary zone electrophoretic systems with complex-forming equilibria.

We discuss several possible phenomena in electrophoretic systems with complexing agents present in the background electrolyte. In our previous work, we extended the linear theory of electromigration with the first-order nonlinear term, which originally applied to acid-base equilibria only, by generalizing it to any fast chemical equilibria. This extension provides us with a fresh insight into the well-established technique of elecktrokinetic chromatography (EKC). We combine mathematical analysis of the generalized model with its solution by means of the new version of our software PeakMaster 6, and experimental data. We re-examine the fundamental equations by Wren and Rowe and Tiselius in the frame of the generalized linear theory of electromigration. Besides, we show that selector concentration can increase inside the interacting-analyte zone due to its complexation with the analyte, which contradicts the generally accepted idea of a consumption of a portion of the selector inside the zone. Next, we focus our discussion on interacting buffers (i.e., buffer constituents that form a complex with the selector). We demonstrate how such side-interaction of the selector with another buffer constituent can influence measuring analyte-selector interactions. Finally, we describe occurrence and mobilities of system peaks in these EKC systems. We investigate systems with fully charged analytes and neutral cyclodextrins as selectors. Although the theory is not limited in terms of the charge and/or the degree of (de)protonation of any constituent, this setup allows us to find analytical solutions to generalized model under approximate, yet realistic, conditions and to demonstrate all important phenomena that may occur in EKC systems. An occurrence of system peaks in a system with fully charged selector is also investigated.

Influence of salt and acetonitrile on the capillary zone electrophoresis analysis of imatinib in plasma samples.

A simple, sensitive, specific, and cost-effective analytical methodology was developed for the analysis of human plasma samples spiked with imatinib by CZE with on-line UV detection in the context of Therapeutic Drug Monitoring. Several analytical conditions such as the ionic strength (I) and the pH of the BGE composed of citric acid and ε-amino caproic acid were studied in regards of the presence of sodium chloride (NaCl) in plasma samples (1% m/v). Computer simulations (Simul software) were used to confirm the experimental results and to understand imatinib electrophoretic behavior in the presence of NaCl. Furthermore, the advantages of adding ACN to the sample containing NaCl to combine efficient protein precipitation and on-line CZE stacking of imatinib were demonstrated. LOD and LOQ values of 48 and 191 ng/mL were obtained from plasma sample supernatant after protein precipitation with ACN, which is much lower than mean imatinib plasma level observed for patients treated by imatinib mesylate (about 1000 ng/mL). Good linearity was obtained in the concentration range 191-5000 ng/mL (R2  > 0.997). RSD of less than 1.68% and 2.60% (n = 6) for migration times and corrected peak areas, respectively, were observed at the LOQ.

Chiral separation of lansoprazole and rabeprazole by capillary electrophoresis using dual cyclodextrin systems.

Novel capillary electrophoresis methods using CDs as chiral selectors were developed and validated for the chiral separation of lansoprazole and rabeprazole, two proton pump inhibitors. Fourteen different neutral and anionic CDs were screened at pH 4 and 7 in the preliminary analysis. Sulfobutyl-ether-ß-CD with a degree of substitution of 6.5 and 10 at neutral pH proved to be the most suitable chiral selector for both compounds. Various dual CD systems were also compared, and the possible mechanisms of enantiomer separation were investigated. A dual selector system containing sulfobutyl-ether-ß-CD degree of substitution 6.5 and native γ-CD proved to be the most adequate system for the separations. Method optimization was carried out using an experimental design approach, performing an initial fractional factorial screening design, followed by a central composite design to establish the optimal analytical conditions. The optimized methods (25 mM phosphate buffer, pH 7, 10 mM sulfobutyl-ether-ß-CD/20 mM γ-CD, +20 kV voltage; 17°C temperature; 50 mbar/3 s injection, detection at 210 nm for lansoprazole; 25 mM phosphate buffer, pH 7, 15 mM sulfobutyl-ether-ß-CD/30 mM γ-CD, +20 kV voltage; 18°C temperature; 50 mbar/3 s injection, detection at 210 nm for rabeprazole) provided baseline separation for lansoprazole (Rs = 2.91) and rabeprazole (Rs = 2.53) enantiomers with favorable migration order (in both cases the S-enantiomers migrates first). The optimized methods were validated according to current guidelines and proved to be reliable, linear, precise, and accurate for the determination of 0.15% distomer as chiral impurity in dexlansoprazole and dexrabeprazole samples.

The dynamics of band (peak) shape development in capillary zone electrophoresis in light of the linear theory of electromigration.

The continuity equations that describe the movement of ions in liquid solutions under the influence of an external stationary electric field, as it is utilized in electrophoresis, were introduced a long time ago starting with Kohlrausch in 1897. From that time on, there have been many attempts to solve the equations and to discuss the results. In electrophoresis, special attention has always been devoted to the peak shapes obtained by the detector since the shapes have a tight connection with the phenomena taking place during electromigration and influence the efficiency and selectivity of the separation. Among these phenomena, the most important is electromigration dispersion. In this commented review paper, we compare various models of electromigration, try to find points that connect them, and discuss the range of their validity in light of the linear and nonlinear theory of electromigration.

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6-Next Generation.

The linear theory of electromigration, including the first-order nonlinear approximation, is generalized to systems with any equilibria fast enough to be considered instantaneous in comparison with the timescale of peak movement. For example, this theory is practically applied in the electrokinetic chromatography (EKC) mode of the CZE. The model enables the calculation of positions and shapes of analyte and system peaks without restricting the number of selectors, the complexation stoichiometry, or simultaneous acid-base equilibria. The latest version of our PeakMaster software, PeakMaster 6-Next Generation, implements the theory in a user-friendly way. It is a free and open-source software that performs all calculations and shows the properties of the background electrolyte and the expected electropherogram within a few seconds. In this paper, we mathematically derive the model, discuss its applicability to EKC systems, and introduce the PeakMaster 6 software.

Integrated internal standards: A sample prep-free method for better precision in microchip CE.

Point-of-care systems based on microchip capillary electrophoresis require single-use, disposable microchips prefilled with all necessary solutions so an untrained operator only needs to apply the sample and perform the analysis. While microchip fabrication can be (and has been) standardized, some manufacturing differences between microchips are unavoidable. To improve analyte precision without increasing device costs or introducing additional error sources, we recently proposed the use of integrated internal standards (ISTDs): ions added to the BGE in small concentrations which form system peaks in the electropherogram that can be used as a measurement reference. Here, we further expand this initial proof-of-principle test to study a clinically-relevant application of K ion concentrations in human blood; however, using a mock blood solution instead of real samples to avoid interference from other obstacles (e.g. cell lysis). Cs as an integrated ISTD improves repeatability of K ion migration times from 6.97% to 0.89% and the linear calibration correlation coefficient (R2 ) for K quantification from 0.851 to 0.967. Peak area repeatability improves from 11.6-13.3% to 4.75-5.04% at each K concentration above the LOQ. These results further validate the feasibility of using integrated ISTDs to improve imprecision in disposable microchip CE devices by demonstrating their application for physiological samples.

Using single-isomer octa(6-O-sulfo)-γ-cyclodextrin for fast capillary zone electrophoretic enantioseparation of pindolol: Determination of complexation constants, software-assisted optimization, and method validation.

The present study describes a rapid and effective capillary electrophoresis (CE) method for the enantioseparation of pindolol using single-isomer octa(6-O-sulfo)-γ-cyclodextrin. The complexation parameters were determined under neutral and high pH conditions to identify optimal separation conditions using a theoretical model. Baseline separation of pindolol enantiomers was achieved within 6 min in a sodium/MOPS buffer, pH 7.2, with a selector concentration of 6 mM. The method was validated according to the ICH guidelines using imidazole as an internal standard. Low limits of detection and quantification were found, specifically 1.2 µg/mL and 4 µg/mL (0.6 µg/mL and 2 µg/mL per enantiomer), respectively. The calibration curves showed good linearity, with a coefficient of determination R2 ≥ 0.999 over a 5 - 55 µg/mL concentration range and over a 50 - 300 µg/mL concentration range of the racemic mixture. The relative standard deviations (%RSD) of intra-day and inter-day precision were lower than 8% at LOQ level, lower than 3% at 50 µg/mL level and lower than 1.5% at 300 µg/mL level. Accuracy ranged from 95 to 103% (106% at LOQ level). The proposed method was successfully tested on a medical formulation of Visken® Sandoz intravenous solution and Visken® Teofarma pills for oral use.

Enhancement of the conductivity detection signal in capillary electrophoresis systems using neutral cyclodextrins as sweeping agents.

Conductivity detection is a universal detection technique often encountered in electrophoretic separation systems, especially in modern chip-electrophoresis based devices. On the other hand, it is sparsely combined with another contemporary trend of enhancing limits of detection by means of various preconcentration strategies. This can be attributed to the fact that a preconcentration experimental setup usually brings about disturbances in a conductivity baseline. Sweeping with a neutral sweeping agent seems a good candidate for overcoming this problem. A neutral sweeping agent does not hinder the conductivity detection while a charged analyte may preconcentrate on its boundary due to a decrease in its effective mobility. This study investigates such sweeping systems theoretically, by means of computer simulations, and experimentally. A formula is provided for the reliable estimation of the preconcentration factor. Additionally, it is demonstrated that the conductivity signal can significantly benefit from slowing down the analyte and thus the overall signal enhancement can easily overweight amplification caused solely by the sweeping process. The overall enhancement factor can be deduced a priori from the linearized theory of electrophoresis implemented in the PeakMaster freeware. Sweeping by neutral cyclodextrin is demonstrated on an amplification of a conductivity signal of flurbiprofen in a real drug sample. Finally, a possible formation of unexpected system peaks in systems with a neutral sweeping agent is revealed by the computer simulation and confirmed experimentally.

Into the theory of the partial-filling affinity capillary electrophoresis and the determination of apparent stability constants of analyte-ligand complexes.

The partial-filling affinity capillary electrophoresis (pf-ACE) works with a ligand present in a background electrolyte that forms a weak complex with an analyte. In contrast to a more popular mobility-shift affinity capillary electrophoresis, only a short plug of the ligand is introduced into a capillary in the pf-ACE. Both methods can serve for determining apparent stability constants of the formed complexes but this task is hindered in the pf-ACE by the fact that the analyte spends only a part of its migration time in a contact with the ligand. In 1998, Amini and Westerlund published a linearization strategy that allows for extracting an effective mobility of an analyte in the presence of a neutral ligand out of the pf-ACE data. The main purpose of this paper is to show that the original formula is only approximate. We derive a new formula and demonstrate its applicability by means of computer simulations. We further inspect several strategies of data processing in the pf-ACE regarding a risk of an error propagation. This establishes a good practice of determining apparent stability constants of analyte-ligand complexes by means of the pf-ACE.

Integrating Internal Standards into Disposable Capillary Electrophoresis Devices To Improve Quantification.

To improve point-of-care quantification using microchip capillary electrophoresis (MCE), the chip-to-chip variabilities inherent in disposable, single-use devices must be addressed. This work proposes to integrate an internal standard (ISTD) into the microchip by adding it to the background electrolyte (BGE) instead of the sample-thus eliminating the need for additional sample manipulation, microchip redesigns, and/or system expansions required for traditional ISTD usage. Cs and Li ions were added as integrated ISTDs to the BGE, and their effects on the reproducibility of Na quantification were explored. Results were then compared to the conclusions of our previous publication which used Cs and Li as traditional ISTDs. The in-house fabricated microchips, electrophoretic protocols, and solution matrixes were kept constant, allowing the proposed method to be reliably compared to the traditional method. Using the integrated ISTDs, both Cs and Li improved the Na peak area reproducibility approximately 2-fold, to final RSD values of 2.2-4.7% (n = 900). In contrast (to previous work), Cs as a traditional ISTD resulted in final RSDs of 2.5-8.8%, while the traditional Li ISTD performed poorly with RSDs of 6.3-14.2%. These findings suggest integrated ISTDs are a viable method to improve the precision of disposable MCE devices-giving matched or superior results to the traditional method in this study while neither increasing system cost nor complexity.

Affinity capillary electrophoresis: the theory of electromigration.

We focus on the state-of-the-art theory of electromigration under single and multiple complexation equilibrium. Only 1:1 complexation stoichiometry is discussed because of its unique status in the field of affinity capillary electrophoresis (ACE). First, we summarize the formulas for the effective mobility in various ACE systems as they appeared since the pioneering days in 1992 up to the most recent theories till 2015. Disturbing phenomena that do not alter the mobility of the analyte directly but cause an unexpected peak broadening have been studied only recently and are also discussed in this paper. Second, we turn our attention to the viscosity effects in ACE. Change in the background electrolyte viscosity is unavoidable in ACE but numerous observations scattered throughout the literature have not been reviewed previously. This leads to an uncritical employment of correction factors that may or may not be appropriate in practice. Finally, we consider the ionic strength effects in ACE, too. Limitations of the current theories are also discussed and the tasks identified where open problems still prevail. Graphical Abstract A weak base (A) undergoes an acidic-basic equilibria (in blue) and migrates with an electrophoretic mobility of [Formula: see text]. Simultaneously, it interacts with a selector (sel) while the analyte-selector complex migrates with an electrophoretic mobility of [Formula: see text]. The strength of the interaction (in orange) is governed by the binding constant, K A , and the concentration of the selector, c sel . This all gives the analyte an effective mobility of [Formula: see text] and moves it out of the zero position (EOF; right top insert). The interaction of the positively charged analyte with the neutral selector slows down the analyte with increasing selector concentration (right bottom insert).

CEval: All-in-one software for data processing and statistical evaluations in affinity capillary electrophoresis.

We introduce CEval software (downloadable for free at echmet.natur.cuni.cz) that was developed for quicker and easier electrophoregram evaluation and further data processing in (affinity) capillary electrophoresis. This software allows for automatic peak detection and evaluation of common peak parameters, such as its migration time, area, width etc. Additionally, the software includes a nonlinear regression engine that performs peak fitting with the Haarhoff-van der Linde (HVL) function, including automated initial guess of the HVL function parameters. HVL is a fundamental peak-shape function in electrophoresis, based on which the correct effective mobility of the analyte represented by the peak is evaluated. Effective mobilities of an analyte at various concentrations of a selector can be further stored and plotted in an affinity CE mode. Consequently, the mobility of the free analyte, µA, mobility of the analyte-selector complex, µAS, and the apparent complexation constant, K('), are first guessed automatically from the linearized data plots and subsequently estimated by the means of nonlinear regression. An option that allows two complexation dependencies to be fitted at once is especially convenient for enantioseparations. Statistical processing of these data is also included, which allowed us to: i) express the 95% confidence intervals for the µA, µAS and K(') least-squares estimates, ii) do hypothesis testing on the estimated parameters for the first time. We demonstrate the benefits of the CEval software by inspecting complexation of tryptophan methyl ester with two cyclodextrins, neutral heptakis(2,6-di-O-methyl)-ß-CD and charged heptakis(6-O-sulfo)-ß-CD.

Determination of relative enantiomer migration order using a racemic sample.

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

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part II. Application to dual systems and experimental verification.

Interactions among analyte forms that undergo simultaneous dissociation/protonation and complexation with multiple selectors take the shape of a highly interconnected multi-equilibrium scheme. This makes it difficult to express the effective mobility of the analyte in these systems, which are often encountered in electrophoretical separations, unless a generalized model is introduced. In the first part of this series, we presented the theory of electromigration of a multivalent weakly acidic/basic/amphoteric analyte undergoing complexation with a mixture of an arbitrary number of selectors. In this work we demonstrate the validity of this concept experimentally. The theory leads to three useful perspectives, each of which is closely related to the one originally formulated for simpler systems. If pH, IS and the selector mixture composition are all kept constant, the system is treated as if only a single analyte form interacted with a single selector. If the pH changes at constant IS and mixture composition, the already well-established models of a weakly acidic/basic analyte interacting with a single selector can be employed. Varying the mixture composition at constant IS and pH leads to a situation where virtually a single analyte form interacts with a mixture of selectors. We show how to switch between the three perspectives in practice and confirm that they can be employed interchangeably according to the specific needs by measurements performed in single- and dual-selector systems at a pH where the analyte is fully dissociated, partly dissociated or fully protonated. Weak monoprotic analyte (R-flurbiprofen) and two selectors (native ß-cyclodextrin and monovalent positively charged 6-monodeoxy-6-monoamino-ß-cyclodextrin) serve as a model system.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part I. Theory.

The model of electromigration of a multivalent weak acidic/basic/amphoteric analyte that undergoes complexation with a mixture of selectors is introduced. The model provides an extension of the series of models starting with the single-selector model without dissociation by Wren and Rowe in 1992, continuing with the monovalent weak analyte/single-selector model by Rawjee, Williams and Vigh in 1993 and that by Lelièvre in 1994, and ending with the multi-selector overall model without dissociation developed by our group in 2008. The new multivalent analyte multi-selector model shows that the effective mobility of the analyte obeys the original Wren and Row's formula. The overall complexation constant, mobility of the free analyte and mobility of complex can be measured and used in a standard way. The mathematical expressions for the overall parameters are provided. We further demonstrate mathematically that the pH dependent parameters for weak analytes can be simply used as an input into the multi-selector overall model and, in reverse, the multi-selector overall parameters can serve as an input into the pH-dependent models for the weak analytes. These findings can greatly simplify the rationale method development in analytical electrophoresis, specifically enantioseparations.

Equivalent peak resolution: characterization of the extent of separation for two components based on their relative peak overlap.

Although the classical formula of peak resolution was derived to characterize the extent of separation only for Gaussian peaks of equal areas, it is often used even when the peaks follow non-Gaussian distributions and/or have unequal areas. This practice can result in misleading information about the extent of separation in terms of the severity of peak overlap. We propose here the use of the equivalent peak resolution value, a term based on relative peak overlap, to characterize the extent of separation that had been achieved. The definition of equivalent peak resolution is not constrained either by the form(s) of the concentration distribution function(s) of the peaks (Gaussian or non-Gaussian) or the relative area of the peaks. The equivalent peak resolution value and the classically defined peak resolution value are numerically identical when the separated peaks are Gaussian and have identical areas and SDs. Using our new freeware program, Resolution Analyzer, one can calculate both the classically defined and the equivalent peak resolution values. With the help of this tool, we demonstrate here that the classical peak resolution values mischaracterize the extent of peak overlap even when the peaks are Gaussian but have different areas. We show that under ideal conditions of the separation process, the relative peak overlap value is easily accessible by fitting the overall peak profile as the sum of two Gaussian functions. The applicability of the new approach is demonstrated on real separations.

A versatile electrophoresis-based self-test platform.

This paper reports on recent research creating a family of electrophoresis-based point of care devices for the determination of a wide range of ionic analytes in various sample matrices. These devices are based on a first version for the point-of-care measurement of Li(+), reported in 2010 by Floris et al. (Lab Chip 2010, 10, 1799-1806). With respect to this device, significant improvements in accuracy, precision, detection limit, and reliability have been obtained especially by the use of multiple injections of one sample on a single chip and integrated data analysis. Internal and external validation by clinical laboratories for the determination of analytes in real patients by a self-test is reported. For Li(+) in blood better precision than the standard clinical determination for Li(+) was achieved. For Na(+) in human urine the method was found to be within the clinical acceptability limits. In a veterinary application, Ca(2+) and Mg(2+) were determined in bovine blood by means of the same chip, but using a different platform. Finally, promising preliminary results are reported with the Medimate platform for the determination of creatinine in whole blood and quantification of both cations and anions through replicate measurements on the same sample with the same chip.

Determination of the correct migration time and other parameters of the Haarhoff-van der Linde function from the peak geometry characteristics.

For Gaussian peaks, the migration time of the analyte results as the position of the top of the peak and the zone variance is proportional to the peak width. Similar relations have not yet been derived for the Haarhoff-van der Linde (HVL) function, which appears as a fundamental peak-shape function in electrophoresis. We derive the relations between the geometrical measures of the HVL-shaped peak, that is the position of its maximum, its width and a measure of its asymmetry, and the respective parameters a1, a2, and a3, of the corresponding HVL function. Under the condition of the HVL-shaped peak, the a1 parameter reflects the true migration time of the analyte, which may differ from the peak top position significantly. Our procedure allows us to express the parameters without the need of any external data processing (nonlinear regression). We demonstrate our approach on simulated peaks and on experimental data integrated by the ChemStation software (delivered with the CE instrumentation by Agilent Technologies). A significant improvement is achieved reading the migration time of the experimental and simulated peaks, which draws the error of the HVL-shaped peak migration time evaluation down to the resolution of the data sampling rate.