System peaks and non-linearity in capillary electrophoresis and high-performance liquid chromatography

Sample plug induced peak splitting in capillary electrophoresis studied using dual backscattered interferometry and fluorescence detection

The appearance of unexpected peaks in capillary electrophoresis (CE) is common and can lengthen the time of method development as assay conditions and experimental parameters are varied to understand and mitigate the effects of the additional peaks. Additional peaks can arise when a single-analyte zone is split into multiple zones. Understanding the underlying mechanism of these phenomena, recognizing conditions that favor its presence, and knowing how to confirm and eliminate the effect are important for efficient method optimization. In this study, we examine how the overlap of analyte zones with the sample plug can lead to peak splitting. This is explored experimentally using dual detection CE, which enables both the sample plug and analyte zones to be independently and simultaneously measured from the same detection volume. Simulations performed via COMSOL Multiphysics confirm the origin of the splitting and help guide experiments to reduce and eliminate the effect. Our findings show that this peak splitting mechanism can arise in separations of both small and large molecules but is, especially, prevalent in separations of slowly migrating macromolecules. This effect is also more prevalent when using a short length-to-detector, as is commonly found in microfluidic applications. A simple diffusion-less model is introduced to develop strategies for reducing peak splitting that avoids modifying the apparatus, such as by lengthening the separation length, which can be difficult. Decreasing the sample plug length and slowing the electroosmotic flow can both reduce this effect, which is confirmed experimentally.

Calibration-free quantitation in microchip zone electrophoresis with conductivity detection

The relationship between electrophoretic mobility and molar conductivity has previously led to speculation on achieving quantitation in zone electrophoresis without calibration curves when using conductivity detection. However, little work in this area has been pursued, possibly because of the breakdown of simple sensitivity-mobility relationships when working with partially protonated species. This topic is revisited with the aid of electrophoretic simulation software that produces facile predictions of analyte sensitivity relative to an internal standard. Calibration curve slopes for over 50 analyte/internal standard/BGE combinations were measured with both unbiased and electrokinetically biased injections using microchip electrophoresis with conductivity detection. The results were compared to theoretical expectations as computed with PeakMaster software. Good agreement was observed, with some systems being predicted with quantitative accuracy while others showed significant deviations. Some mechanisms that can lead to deviations from theory are demonstrated, but the causes for some discrepancies are still not understood. Overall, this work exhibits another useful application for simulation software, particularly for disposable devices where device-specific calibration curves cannot be collected. It also serves as quantitative validation for some outputs of PeakMaster simulation software.

Nonlinear waves in capillary electrophoresis

Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care, and forensics. In capillary electrophoresis, the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration "shocks." In this paper, we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single coion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity. If the analyte concentration is sufficiently low in a suitable nondimensional sense, Burgers' equation is recovered, and thus the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity, either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width, and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments.

Complexation of tauro- and glyco-conjugated bile salts with three neutral β-CDs studied by ACE

Complexation of the bile salts (BS) taurocholate, tauro-beta-muricholate, taurodeoxycholate, taurochenodeoxycholate, glycocholate, glycodeoxycholate, and glycochenodeoxycholate common in rat, dog, and man with natural beta-CD and the chemically modified beta-CDs 2-hydroxypropyl-beta-CD and 2-O-methyl-beta-CD was studied using mobility shift ACE. The CDs were selected due to their frequent use in preformulation and drug formulation as oral excipients for the solubilization of drug substances with low aqueous solubility. ACE was demonstrated to be a feasible and efficient technique for investigation of the interactions between BS and beta-CDs. All the investigated BS possessed affinity for the three CDs with stability constants ranging from 2x10(3) to 4x10(5) M(-) (1). The requirements and assumptions related to the use of ACE for estimating high affinity stability constants were discussed. The extent and pattern of hydroxylation significantly influenced the affinity of the glyco- and tauro-conjugated BS toward the beta-CDs (chenodeoxycholates >> deoxycholates > cholates) whereas the nature of the beta-CD derivatization and BS conjugation played a minor role only. The results indicate that displacement of drug substances from beta-CD inclusion complexes is likely to occur in the small intestine where BS are present potentially influencing drug bioavailability.

Prediction and understanding system peaks in capillary zone electrophoresis

Introduction of a sample into the separation column (microchip channel) in capillary zone electrophoresis (microchip electrophoresis) will cause a disturbance in the originally uniform composition of the background electrolyte. The disturbance, a system zone, can move in some electrolyte systems along the separation channel and, on reaching the position of the detector, cause a system peak. As shown by the linear theory of electromigration based on linearized continuity equations formulated in matrix form, the mobility of the system zone--the system eigenmobility--can be obtained as the eigenvalue of the matrix. Progress in the theory of electromigration allows us to predict the existence and mobilities of the system zones, even in very complex electrolyte systems consisting of several multivalent weak electrolytes, or in micellar systems (systems with SDS micelles) used for protein sizing in microchips. The theory is implemented in PeakMaster software, which is available as freeware (www.natur.cuni.cz/gas). The linearized theory also predicts background electrolytes having no stationary injection zone (water zone, water gap, water dip, EO zone) or unstable electrolyte systems exhibiting oscillations and creating periodic structures. The oscillating systems have complex system eigenmobilities (eigenvalues of the matrix are complex). This paper reviews the theoretical background of the system peaks (system eigenpeaks) and gives practical hints for their prediction and for preparing background electrolytes not perturbed by the occurrence of system peaks and by excessive peak broadening.

Simultaneous contactless conductivity detection and UV detection for the study of separation of tamsulosin enantiomers in discontinuous electrolyte systems by CE

This work shows the potential of using discontinuous electrolyte systems for the separation of tamsulosin enantiomers by CE. Sulfated beta-cyclodextrin was used as a chiral selector. In acidic electrolytes, sulfated beta-cyclodextrin migrates as an anion and the analyte (tamsulosin) migrates as a cation. Due to this, four experimental arrangements were proposed. These arrangements differ in composition of electrolytes in the inlet compartment, in the capillary and in the outlet compartment. The separation of tamsulosin enantiomers in acetate buffers with sodium and Tris counterions was studied. Simultaneous contactless conductivity detection and UV detection were used for the study of the separation mechanism in these systems. Mobilities of sulfated beta-cyclodextrin were used for the calculation of the time when the analyte migrates through the BGE zone with the selector. The simulation program Simul 4.0 was used for the calculations of the concentration profiles of the electrolyte components dependent on the time of the separation. The mechanism of enantioseparation in these arrangements was suggested.

Eigenmobilities in background electrolytes for CZE. V. Intensity (amplitudes) of system peaks

We present a mathematical model of CZE based on the concept of eigenmobilities - the eigenvalues of matrix M tied to the linearized governing equations of electromigration, and the spectral decomposition of matrix M into matrices of amplitudes P(j). Any peak in an electropherogram, regardless of whether it is an analyte peak or a system peak (system zone), is matched with its matrix P(j). This enables calculation of the peak parameters, such as the transfer ratio and the molar conductivity detection response (which give the indirect detection signal and the conductivity detection signal, respectively), when the initial disturbance caused by the injection of the sample is known. We also introduce new quantities, such as the generalized transfer ratio and the conductivity response of system zones, and show how the amplitude (intensity, area) of the analyte peaks and the system peaks can be calculated. We offer a free software, PeakMaster (http://www.natur.cuni.cz/gas), which yields this information in a user-friendly way.

Capillary isotachophoresis from the student point of view – images and the reality

A review of some fundamental aspects of ITP from the student point of view, imaginations of some basic facts and laws, use of ITP, and the recent trends are presented. The results of theoretical computations of ITP separation processes are added for comparison of imaginations with the exact mathematical description.

General theory of indirect detection in chromatography

Indirect detection is used in liquid chromatography to detect sample components that more or less lack detectable properties. A detectable component, the probe, is added to the mobile phase and the sample containing the components is injected. Every solute, even those not normally detectable, will give rise to detectable peaks due to the presence of the probe. The theory currently used to describe this situation is different for different adsorption isotherm models and also restrictions have to be imposed on the adsorption isotherm parameters. We present a general theory that describes both the retention times and areas of the detected peaks without making any a priori adsorption isotherm assumptions. Our general theory is compared with the current theory and validated by computer simulations. An alternative quantification method is suggested based on the measurement of the relative areas of the sample components without the requirement of having standard curves of known solutions of the sample components. Using this approach, the new theory is able to predict the solute concentrations in cases when the current theory did not, i.e., when the saturation capacities of the sample components and the probe differed from each other. In addition, a new application is proposed: the estimation of adsorption isotherm parameters.

Peak shape modeling by Haarhoff-Van der Linde function for the determination of correct migration times: A new insight into affinity capillary electrophoresis

Among the different experimental strategies available in capillary electrophoresis (CE) to determine binding parameters, affinity capillary electrophoresis (ACE) has been the most widely embraced due to its easiness of implementation and of data handling. Ligand-substrate binding constants are thus directly derived from the substrate migration time shifts resulting from the variation of ligand concentration introduced in a background electrolyte. Classically, the substrate migration time is measured on top of the electrophoretic peak, assuming symmetrical peak shape. Depending on both substrate and ligand concentrations that may be required to meet detection sensitivity or complexation conditions, zonal migrations in ACE may, however, produce triangular peak shape, most often due to pronounced electromigration dispersion (EMD), and this may result in positively or negatively erroneous migration time assessments. In this work, EMD distorted triangular peak shapes obtained in the course of host-guest complexation studies were fitted with the Haarhoff-Van der Linde function, allowing better estimation of migration time. The model systems studied were those of beta-cyclodextrin and naproxen, 2-naphthalenesulfonate, or 1-adamantanecarboxylate. The impact of this correction on binding isotherms and binding constant evaluation was exemplified. Furthermore, in situations where the substrate concentration injected by far overtakes that of the ligand in the electrolyte, the interest in this peak shape correction was discussed in connection with the question of whether the free ligand concentration can be still considered equal to the ligand concentration introduced, a question that still remains under debate nowadays.

On-column electroextraction and separation of antisense oligonucleotides in human plasma by capillary gel electrophoresis

A novel approach is presented for the direct injection, and subsequent separation, of antisense phosphorothioate oligonucleotides in human plasma by capillary gel electrophoresis. The plasma, spiked with the antisense, was simply diluted 1:1 with acidified water and inserted into the sample holder in the capillary electrophoresis instrument. The separation capillary, filled with a dextran solution (replaceable polymer) and a short zone of acidified water at the injection side, was dipped into the plasma sample vial and voltage applied for simultaneous electrokinetic extraction and injection of antisense. The sample vial was then exchanged for the buffer vial, separation voltage applied, and size-sieving separation achieved. Separation time is less than 9 min and total time per analysis cycle 20 min, including rinsing of the capillary, filling with polymer, electroextraction/injection, and separation. This automated method can handle small sample volumes (4 microl) and has a detection limit of 0.5 microgml(-1) for a 16-mer phosphorothioate employing UV-detection. The capillary is stable for about 50 analyses.

System zones in capillary zone electrophoresis

When working with capillary zone electrophoresis (CZE), the analyst has to be aware that the separation system is not homogeneous anymore as soon as a sample is brought into the background electrolyte (BGE). Upon injection, the analyte creates a disturbance in the concentration of the BGE, and the system retains a kind of memory for this inhomogeneity, which is propagated with time and leads to so-called system zones (or system eigenzones) migrating in an electric field with a certain eigenmobility. If recordable by the detector, they appear in the electropherogram as system peaks (or system eigenpeaks). However, although their appearance can not be forecasted and explained easily, they are inherent for the separation system. The progress in the theory of electromigration (accompanied by development of computer software) allows to treat the phenomenon of system zones and system peaks now also in very complex BGE systems, consisting of several multivalent weak electrolytes, and at all pH ranges. It also allows to predict the existence of BGEs having no stationary injection zone (or water zone, EO zone, gap, dip). Our paper reviews the theoretical background of the origin of the system zones (system peaks, system eigenpeaks), discusses the validity of the Kohlrausch regulating function, and gives practical hints for preparing BGEs with good separation ability not deteriorated by the occurrence of system peaks and by excessive peak-broadening.

Molecular interaction in capillary electrophoresis

At the present time, affinity capillary electrophoresis is a well-established method for the measurement of binding constants involving 1:1 interactions. Many recent applications of this technique have illustrated its versatility. If affinity capillary electrophoresis is to be widely applied to the study of all types of interactions it is imperative that we consider that higher order interactions may be present. Applying proper equations or developing new models appropriate to the description of such systems is essential to obtaining reliable binding information.

Position and intensity of system (eigen) peaks in capillary zone electrophoresis

The intensity of system (or eigen) peaks encountered in capillary zone electrophoresis (CZE) can be predicted by considering mass balances for each of the analyte constituents and each of the constituents in the background electrolyte (BGE). As a result of coherence, in each zone the proportions in which the constituent concentrations vary are fixed; they are determined by the composition of the BGE and the nature of the analyte constituent (if present) and described as eigenvectors of a transport matrix. Considering the effect of an injection, the mass balances for all constituents can be satisfied only via the intensity of each zone. This leads to an n-equations, n-unknowns problem, with the intensities as the unknowns and the mass balances as equations. The latter can be easily solved to obtain the intensities. of the zones, of analytes as well as of system peaks. In this work the approach has been applied to CZE systems with two co-ions in the BGE, and experimental results have been compared to the predictions obtained from the model. Agreement was seen to be reasonable, but the quantitative comparison often failed, probably due to experimental difficulties.

Eigenmobilities in background electrolytes for capillary zone electrophoresis. I. System eigenpeaks and resonance in systems with strong electrolytes

A background electrolyte system for capillary zone electrophoresis which is composed of three strong univalent ionic constituents is investigated. The ion 1 is considered as a counter-ion and two ions, 2 and 3, are considered as co-ions in relation to the analyte ion 4. We investigate the linearized model of electromigration in such a system and calculate the eigenvalues of a corresponding matrix. The model is formulated in such a way that the eigenvalues of the system are certain mobilities, which we call eigenmobilites, which characterize specific features of the electtrophoretic migration. One of the eigenmobilities is the system eigenmobility u(s) causing the rise of the system peak, called here the system eigenpeak. A situation when the analyte has the same mobility as the system eigenmobility, u(4) = u(s), is analyzed in detail. We show that it leads to the resonance-the mutual jump in the concentration profile of both co-ions, 2 and 3, has a shape of the spatial derivation of the originally sampled analyte profile and, moreover, it grows linearly with time. After a sufficiently long time it can be "amplified" to any value. The resonance has then a great impact on signals of indirect detection methods, like indirect UV detection or conductivity detection. In the framework of the linearized model the relative velocity slope S(x), a measure of electromigration dispersion, is expressed as S(x) = F(u(1) + u(4))(u(2) - u(4))(u(3) - u(4))/[u(4)(u(s) - u(4))], where u(i) is the mobility of the ith ion and F is the Faraday constant. As in practice the concentration of the analyte is not infinitely small and has a certain finite value, the analyte will be at the resonance severely dispersed to a much broader spatial interval. When a specific detector is used, the signal of such an analyte can apparently be missed without any notice.

Affinity capillary electrophoresis using a low-concentration additive with the consideration of relative mobilities

Most affinity studies in capillary electrophoresis assume that the analyte concentration is much smaller than the additive concentration so that the migration of the analyte has no effect on the concentration of the additive in the capillary. However, in most medium- to high-affinity interactions, the additive concentration has to be kept rather low to observe the changes in analyte mobility before saturation is reached. In this paper, a mathematical model is developed to describe the migration behavior of the analyte in a system where the complex formed becomes concentrated to levels much greater than the original concentration of the additive due to the differences in the mobilities of the analyte, additive, and complex. The analyte is flurbiprofen, the additive is transthyretin, and the stoichiometry of the reaction between the two is 1:2. This study also provides a new algorithm to determine medium- to high-affinity binding interaction constants by CE.

Applications of on-line weak affinity interactions in free solution capillary electrophoresis

The impressive selectivity offered by capillary electrophoresis can in some cases be further increased when ligands or additives that engage in weak affinity interactions with one or more of the separated analytes are added to the electrophoresis buffer. This on-line affinity capillary electrophoresis approach is feasible when the migration of complexed molecules is different from the migration of free molecules and when separation conditions are nondenaturing. In this review, we focus on applying weak interactions as tools to enhance the separation of closely related molecules, e.g., drug enantiomers and on using capillary electrophoresis to characterize such interactions quantitatively. We describe the equations for binding isotherms, illustrate how selectivity can be manipulated by varying the additive concentrations, and show how the methods may be used to estimate binding constants. On-line affinity capillary electrophoresis methods are especially valuable for enantiomeric separations and for functional characterization of the contents of biological samples that are only available in minute quantities.

Antigen-antibody interactions in capillary electrophoresis

Immunoreactions in combination with separations by capillary electrophoresis (CE) are increasingly being used to quantitate specific analytes in biological fluids. Both competitive and non-competitive approaches have been used for the purpose and, in selected cases, now compare favorably with conventional quantitative immunoassays with respect to concentration limits of detection. CE is also a useful method to evaluate antigen-antibody binding on-line and offers unique possibilities for binding constant estimates, also for weakly binding antibodies and antibody fragments. In this review we cover recent developments in the use of antigen-antibody interactions in conjunction with CE and conclude that continued development of miniaturization, on-line preconcentration and more sensitive detection schemes will contribute to the further dissemination of CE-based immunoassays building on already established affinity CE approaches.

Nonlinear analysis of dynamic binding in affinity capillary electrophoresis demonstrated for inclusion complexes of beta-cyclodextrin

The stability of the molecular host-guest inclusion complexes of beta-cyclodextrin with benzoate and four different hydroxybenzoates is investigated. For the measurement of the binding constants an experimental method is devised that is based on affinity capillary electrophoresis (ACE) with indirect UV absorbance detection. We derive an explicit equation for effective mobilities in ACE experiments without violation of rigorous mass balance. This equation is employed in the nonlinear least-squares analyses of the experimental data yielding binding constants of 48+/-2 M(-1) for benzoate, 299+/-38 M(-1) for 2-hydroxybenzoate, 37+/-1 M(-1) for 3-hydroxybenzoate, 228+/-9 M(-1) for 4-hydroxybenzoate, and 895+/-110 M(-1) in the case of 2,4-dihydroxybenzoate.

Identification, quantitation, and characterization of biomolecules by capillary electrophoretic analysis of binding interactions

The high resolving power of capillary electrophoresis combined with the specificity of binding interactions may be used with advantage to characterize the structure-function relationship of biomolecules, to quantitate specific analytes in complex sample matrices, and to determine the purity of pharmaceutical and other molecules. We here review recent and innovative methodologies and applications of high resolution affinity electrophoresis within the fields of binding constant determination, structure-activity studies, quantitative microassays, analysis of drug purity and protein conformation, and immobilized affinity ligands. Despite the virtues of these approaches with respect to applicability, resolving power, speed, and low sample consumption, problems remain with respect to analyte identification and low concentration limits of detection. The ongoing development of new detector technologies for capillary electrophoresis such as mass spectrometry, and possibly nuclear magnetic resonance and other spectroscopic methods, is therefore very promising for the continued increased use of affinity capillary electrophoresis.