Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

Mobilization in two-step capillary isoelectric focusing: Concepts assessed by computer simulation

The mobilization step in a two-step capillary isoelectric focusing protocol is discussed by means of dynamic computer simulation data for systems without and with spacer compounds that establish their zones at the beginning and end of the focusing column. After focusing in an electroosmosis-free environment (first step), mobilization (second step) can be induced electrophoretically, by the application of a hydrodynamic flow, or by a combination of both means. Dynamic simulations provide insight into the complexity of the various modes of electrophoretic mobilization and dispersion associated with hydrodynamic mobilization. The data are discussed together with the relevant literature.

Electric field-enhanced backscatter interferometry detection for capillary electrophoresis

Backscatter interferometry (BSI) is a refractive index (RI) detection method that is easily integrated with capillary electrophoresis (CE) and is capable of detecting species ranging from inorganic ions to proteins without additional labels or contrast agents. The BSI signal changes linearly with the square of the separation voltage which has been used to quantify sample injection, but has not been explored as a potential signal enhancement mechanism in CE. Here we develop a mathematical model that predicts a signal enhancement at high field strengths, where the BSI signal is dominated by the voltage dependent mechanism. This is confirmed in both simulation and experiment, which show that the analyte peak area grows linearly with separation voltage at high field strengths. This effect can be exploited by adjusting the background electrolyte (BGE) to increase the conductivity difference between the BGE and analyte zones, which is shown to improve BSI performance. We also show that this approach has utility in small bore capillaries where larger separation fields can be applied before excess Joule heating degrades the separation. Unlike other optical detection methods that generally degrade as the optical pathlength is reduced, the BSI signal-to-noise can improve in small bore capillaries as the larger separation fields enhance the signal.

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.

Evolution of the theoretical description of the isoelectric focusing experiment: I. The path from Svensson's steady-state model to the current two-stage model of isoelectric focusing

In 1961, Svensson described isoelectric focusing (IEF), the separation of ampholytic compounds in a stationary, natural pH gradient that was formed by passing current through a sucrose density gradient-stabilized ampholyte mixture in a constant cross-section apparatus, free of mixing. Stable pH gradients were formed as the electrophoretic transport built up a series of isoelectric ampholyte zones-the concentration of which decreased with their distance from the electrodes-and a diffusive flux which balanced the generating electrophoretic flux. When polyacrylamide gel replaced the sucrose density gradient as the stabilizing medium, the spatial and temporal stability of Svensson's pH gradient became lost, igniting a search for the explanation and mitigation of the loss. Over time, through a series of insightful suggestions, the currently held notion emerged that in the modern IEF experiment-where the carrier ampholyte (CA) mixture is placed between the anolyte- and catholyte-containing large-volume electrode vessels (open-system IEF)-a two-stage process operates that comprises a rapid first phase during which a linear pH gradient develops, and a subsequent slow, second stage, during which the pH gradient decays as isotachophoretic processes move the extreme pI CAs into the electrode vessels. Here we trace the development of the two-stage IEF model using quotes from the original publications and point out critical results that the IEF community should have embraced but missed. This manuscript sets the foundation for the companion papers, Parts 2 and 3, in which an alternative model, transient bidirectional isotachophoresis is presented to describe the open-system IEF experiment.

Isotachophoresis: Theory and Microfluidic Applications

Isotachophoresis (ITP) is a versatile electrophoretic technique that can be used for sample preconcentration, separation, purification, and mixing, and to control and accelerate chemical reactions. Although the basic technique is nearly a century old and widely used, there is a persistent need for an easily approachable, succinct, and rigorous review of ITP theory and analysis. This is important because the interest and adoption of the technique has grown over the last two decades, especially with its implementation in microfluidics and integration with on-chip chemical and biochemical assays. We here provide a review of ITP theory starting from physicochemical first-principles, including conservation of species, conservation of current, approximation of charge neutrality, pH equilibrium of weak electrolytes, and so-called regulating functions that govern transport dynamics, with a strong emphasis on steady and unsteady transport. We combine these generally applicable (to all types of ITP) theoretical discussions with applications of ITP in the field of microfluidic systems, particularly on-chip biochemical analyses. Our discussion includes principles that govern the ITP focusing of weak and strong electrolytes; ITP dynamics in peak and plateau modes; a review of simulation tools, experimental tools, and detection methods; applications of ITP for on-chip separations and trace analyte manipulation; and design considerations and challenges for microfluidic ITP systems. We conclude with remarks on possible future research directions. The intent of this review is to help make ITP analysis and design principles more accessible to the scientific and engineering communities and to provide a rigorous basis for the increased adoption of ITP in microfluidics.

The effect of pH adjusted electrolytes on capillary isoelectric focusing assessed by high-resolution dynamic computer simulation

The effect of the composition of electrolytes on capillary IEF is assessed for systems with carrier ampholytes covering two pH units and with catholytes of decreased pH, anolytes of increased pH, and both electrode solutions with adjusted pH values. For electrolytes composed of formic acid as anolyte and ammonium hydroxide as catholyte, simulation is demonstrated to provide the expected IEF system in which analytes with pI values within the formed pH gradient are focused and become immobile. Addition of formic acid to the catholyte results in the formation of an isotachophoretic zone structure that migrates toward the cathode. With ammonium hydroxide added to the anolyte migration occurs toward the anode. In the two cases, all carrier components and amphoteric analytes migrate isotachophoretically as cations or anions, respectively. The data reveal that millimolar amounts of a counter ion are sufficient to convert an IEF pattern into an ITP system. With increasing amounts of the added counter ion, the overall length of the migrating zone structure shrinks, the range of the pH gradient changes, and the migration rate increases. The studied examples indicate that systems of this type reported in the literature should be classified as ITP and not IEF. When both electrolytes are titrated, a non-uniform background electrolyte composed of formic acid and ammonium hydroxide is established in which analytes migrate according to local pH and conductivity without forming IEF or ITP zone structures. Simulation data are in qualitative agreement with previously published experimental data.

Dynamic computer simulations of electrophoresis: 2010-2020

The transport of components in liquid media under the influence of an applied electric field can be described with the continuity equation. It represents a nonlinear conservation law that is based upon the balance laws of continuous transport processes and can be solved in time and space numerically. This procedure is referred to as dynamic computer simulation. Since its inception four decades ago, the state of dynamic computer simulation software and its use has progressed significantly. Dynamic models are the most versatile tools to explore the fundamentals of electrokinetic separations and provide insights into the behavior of buffer systems and sample components of all electrophoretic separation methods, including moving boundary electrophoresis, CZE, CGE, ITP, IEF, EKC, ACE, and CEC. This article is a continuation of previous reviews (Electrophoresis 2009, 30, S16–S26 and Electrophoresis 2010, 31, 726–754) and summarizes the progress and achievements made during the 2010 to 2020 time period in which some of the existing dynamic simulators were extended and new simulation packages were developed. This review presents the basics and extensions of the three most used one‐dimensional simulators, provides a survey of new one‐dimensional simulators, outlines an overview of multi‐dimensional models, and mentions models that were briefly reported in the literature. A comprehensive discussion of simulation applications and achievements of the 2010 to 2020 time period is also included.

Simul 6: A fast dynamic simulator of electromigration

Simul 6 is a 1D dynamic simulator of electromigration based on the mathematical model of electromigration in free solutions. The model consists of continuity equations for the movement of electrolytes in a separation channel, acid-base equilibria of weak electrolytes, and the electroneutrality condition. It accounts for any number of multivalent electrolytes or ampholytes and provides a complete picture about dynamics of electromigration and diffusion in the separation channel. The equations are solved numerically using software means which allow for parallelization and multithreaded computation. Simul 6 has a user-friendly graphical interface. It is typically used for inspection of system peaks (zones) in electrophoresis, stacking and preconcentrating analytes, optimization of separation conditions, method development in either capillary zone electrophoresis, isotachophoresis, and isoelectric focusing. Simul 6 is the successor of Simul 5, and has been launched as a free software available for download at https://simul6.app/.

High-resolution numerical simulations of electrophoresis using the Fourier pseudo-spectral method

We present the formulation, implementation, and performance evaluation of the Fourier pseudo-spectral method for performing fast and accurate simulations of electrophoresis. We demonstrate the applicability of this method for simulating a wide variety of electrophoretic processes such as capillary zone electrophoresis, transient-isotachophoresis, field amplified sample stacking, and oscillating electrolytes. Through these simulations, we show that the Fourier pseudo-spectral method yields accurate and stable solutions on coarser computational grids compared with other nondissipative spatial discretization schemes. Moreover, due to the use of coarser grids, the Fourier pseudo-spectral method requires lower computational time to achieve the same degree of accuracy. We have demonstrated the application of the Fourier pseudo-spectral method for simulating realistic electrophoresis problems with current densities as high as 5000 A/m² with over tenfold speed-up compared to the commonly used second-order central difference scheme, to achieve a given degree of accuracy. The Fourier pseudo-spectral method is also suitable for simulating electrophoretic processes involving a large number of concentration gradients, which render the adaptive grid-refinement techniques ineffective. We have integrated the numerical scheme in a new electrophoresis simulator named SPYCE, which we offer to the community as open-source code.

Instabilities of the pH gradient in carrier ampholyte-based isoelectric focusing: Elucidation of the contributing electrokinetic processes by computer simulation

Electrokinetic processes that lead to pH gradient instabilities in carrier ampholyte-based IEF are reviewed. In addition to electroosmosis, there are four of electrophoretic nature, namely (i) the stabilizing phase with the plateau phenomenon, (ii) the gradual isotachophoretic loss of carrier ampholytes at the two column ends in presence of electrode solutions, (iii) the inequality of the mobilities of positively and negatively charged species of ampholytes, and (iv) the continuous penetration of carbonate from the catholyte into the focusing column. The impact of these factors to cathodic and anodic drifts was analyzed by simulation of carrier ampholyte-based focusing in closed and open columns. Focusing under realistic conditions within a 5 cm long capillary in which three amphoteric low molecular mass dyes were focused in a pH 3-10 gradient formed by 140 carrier ampholytes was investigated. In open columns, electroosmosis displaces the entire gradient toward the cathode or anode whereas the electrophoretic processes act bidirectionally with a transition around pH 4 (drifts for pI > 4 and pI < 4 typically toward the cathode and anode, respectively). The data illustrate that focused zones of carrier ampholytes have an electrophoretic flux and that dynamic simulation can be effectively used to assess the magnitude of each of the electrokinetic destabilizing factors and the resulting drift for a combination of these effects. Predicted drifts of focused marker dyes are compared to those observed experimentally in a setup with coated capillary and whole column optical imaging.

Computer simulation of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers with a free or immobilized neutral chiral selector

A detailed computer simulation study of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers for cases with the neutral selector added to the leader, immobilized to the capillary wall or support, or partially present in the separation column is presented. The electrophoretic transport of the analytes from the sampling compartment into the separation medium with the selector, the formation of a transient mixed zone, the separation dynamics of the stereoisomers with a free or immobilized selector, the dependence of the leader pH, the ionic mobility of norpseudoephedrine, the complexation constant and selector immobilization on steady-state plateau zone properties, and zone changes occurring during the transition from the chiral environment into a selector free leader are thereby visualized in a hitherto unexplored way. For the case with the selector dissolved in the leading electrolyte, simulation data are compared to those observed in experimental setups with coated fused-silica capillaries that feature minimized electroosmosis and zone detection with conductivity and absorbance detectors.

Contemporary chiral simulators for capillary zone electrophoresis

For separation of enantiomers in presence of a chiral selector, data obtained with the 1D dynamic simulators SIMUL5complex and GENTRANS are compared to data predicted by PeakMaster 6, a recently released generalized model of the linear theory of electromigration. Four electrophoretic systems with stereoisomers of weak bases were investigated. They deal with the estimation of input data for complexation together with the elucidation of the origin of observed system peaks, the interference of analyte and system peak migration, the change of enantiomer migration order as function of the selector concentration and the inversion of analyte migration direction in presence of a multiply negatively charged selector. For all systems, data predicted with PeakMaster 6 are in agreement with those of the dynamic simulators and simulation data compare well with experimental data that were monitored with setups featuring conductivity and/or UV absorbance detection along the capillary. SIMUL5complex and GENTRANS provide the full dynamics of any buffer and sample arrangement and require very long execution time intervals. PeakMaster 6 is restricted to conventional CZE, is based on an approximate solution of the transport equations, provides data for realistic experimental conditions within seconds and represents a practical tool for an experimentalist.

Inverse cationic ITP for separation of methadone enantiomers with sulfated β-cyclodextrin as chiral selector

Chiral ITP of the weak base methadone using inverse cationic configurations with H⁺ as leading component and multiple isomer sulfated β-CD (S-β-CD) as leading electrolyte (LE) additive, has been studied utilizing dynamic computer simulation, a calculation model based on steady-state values of the ITP zones, and capillary ITP. By varying the amount of acidic S-β-CD in the LE composed of 3-morpholino-2-hydroxypropanesulfonic acid and the chiral selector, and employing glycylglycine as terminating electrolyte (TE), inverse cationic ITP provides systems in which either both enantiomers, only the enantiomer with weaker complexation, or none of the two enantiomers form cationic ITP zones. For the configuration studied, the data reveal that only S-methadone migrates isotachophoretically when the S-β-CD concentration in the LE is between about 0.484 and 1.113 mM. Under these conditions, R-methadone migrates zone electrophoretically in the TE. An S-β-CD concentration between about 0.070 and 0.484 mM results in both S- and R-methadone forming ITP zones. With >1.113 mM and < about 0.050 mM of S-β-CD in the LE both enantiomers are migrating within the TE and LE, respectively. Chiral inverse cationic ITP with acidic S-β-CD in the LE is demonstrated to permit selective ITP trapping and concentration of the less interacting enantiomer of a weak base.

High-resolution dynamic computer simulation of electrophoresis using a multiphysics software platform

The modeling and simulation software COMSOL Multiphysics^® was recently extended with an electrophoretic transport interface. Its performance was investigated by comparison to results obtained using the 1D dynamic electrophoresis simulators GENTRANS and SIMUL5. Simulations of zone electrophoresis, isotachophoresis, isoelectric focusing and of an oscillating electrolyte system were performed. Smooth profiles were essentially identical indicating that the COMSOL electrophoretic transport interface is able to reproduce results of the 1D simulators. Differences in the way the respective numerical schemes handle steep concentration gradients and associated instabilities were observed. The COMSOL electrophoretic transport interface is expected to be useful as a general model for simulations in 1D, 2D or 3D geometries, as well as for simulations combining electrophoresis with other physical phenomena.

Modeling of formation and prevention of a pure water zone in capillary isoelectric focusing with narrow pH range carrier ampholytes

This paper comprises a continuation of computer simulation studies dealing with carrier ampholyte based CIEF in presence of narrow pH gradients. With this technique, amphoteric sample components with pI values outside the pH gradient are migrating isotachophoretically toward the cathode or anode whereas components with pI values within the gradient become focused. In order to understand the processes occurring in presence of the electric field, the behavior of both carrier ampholytes and amphoteric sample components is investigated by computer modeling. Characteristics of two pH unit gradients with end components having pI values at or around 7.00 and conditions that lead to the formation of a water zone at neutrality were investigated. Data obtained reveal that a zone of water is formed in focusing with carrier ampholytes when the applied pH range does not cover the neutral region, ends at pH 7.00 or begins at pH 7.00. The presence of additional amphoteric components that cover the neutrality region prevent water zone formation under current flow. This situation is met in experiments with narrow pH gradients that end or begin around neutrality. Simulation data reveal that no water zone evolves when atmospheric carbon dioxide dissolved in the catholyte causes the migration of carbonic acid (in the form of carbonate and/or hydrogen carbonate ions) from the catholyte through the focusing structure. An electrolyte change in the electrode solution does not have an impact on the focusing part but does change the isotachophoretic pattern migrating behind the leading ion.

Simulation and experimental study of enzyme and reactant mixing in capillary electrophoresis based on-line methods

The establishment of an efficient reaction mixture represents a crucial part of capillary electrophoresis based on-line enzymatic assays. For ketamine N-demethylation to norketamine mediated by the cytochrome P450 3A4 enzyme, mixing of enzyme and reactants in the incubation buffer at physiological pH was studied by computer simulation. A dynamic electrophoretic simulator that encompasses Taylor-Aris diffusivity which accounts for dispersion due to the parabolic flow profile associated with pressure driven flow was utilized. The simulator in the diffusion mode was used to predict transverse diffusional reactant mixing occurring during hydrodynamic plug injection of configurations featuring four and seven plugs. The same simulator in the electrophoretic mode was applied to study electrophoretic reactant mixing caused by voltage application in absence of buffer flow. Resulting conclusions were experimentally verified with enantioselective analysis of norketamine in a background electrolyte at low pH. Furthermore, simulations visualize buffer changes that occur upon power application between incubation buffer and background electrolyte and have an influence on the reaction mixture.

Capture efficiency of dynamic pH junction focusing in capillary electrophoresis

Dynamic pH junction is one of the techniques used to overcome the issue of poor concentration sensitivity in CE. By introducing a long sample plug in the capillary and focusing the target molecules at the pH boundary between the sample plug and background electrolyte, this focusing technique can achieve a detection limit that is one to two orders of magnitude better than conventional CE. For quantification purposes, the capturing efficiency of the injected molecules should be scrutinized. Focusing of all target molecules inside the sample plug is desired to ensure good linearity across the whole dynamic range. To test the theoretical prediction with a real experiment, nicotine is used as the test molecule for two types of dynamic pH junctions. The first one is with acidic background electrolyte, and can accommodate both optical detection methods and positive-ion mode mass spectrometric detection, while the other is suitable for optical detection only due to the use of basic separation background electrolyte. With a theoretical simulation study, it is demonstrated that, for either of these dynamic pH junctions, focusing of at least 95% of target molecule injected into the capillary was easily achievable. More importantly, a longer sample plug could generate a high percentage of molecules captured by dynamic pH junction focusing. Sharp, symmetrical peaks and good linearity for calibration curve can be obtained. Real samples with complex matrixes were also used to demonstrate that nicotine can be selectively focused and quantified using CE-MS.

Validation of CE modeling with a contactless conductivity array detector

Dynamic computer simulation data are compared for the first time with CE data obtained with a laboratory made system comprising an array of 8 contactless conductivity detectors (C(4) Ds). The experimental setup featured a 50 μm id linear polyacrylamide (LPA) coated fused-silica capillary of 70 cm length and a purpose built sequential injection analysis manifold for fluid handling of continuous or discontinuous buffer configurations and sample injection. The LPA coated capillary exhibits a low EOF and the manifold allows the placement of the first detector at about 2.7 cm from the sample inlet. Agreement of simulated electropherograms with experimental data was obtained for the migration and separation of cationic and anionic analyte and system zones in CZE configurations in which EOF and other column properties are constant. For configurations with discontinuous buffer systems, including ITP, experimental data obtained with the array detector revealed that the EOF is not constant. Comparison of simulation and experimental data of ITP systems provided the insight that the EOF can be estimated with an ionic strength dependent model similar to that previously used to describe EOF in fused-silica capillaries dynamically double coated with Polybrene and poly(vinylsulfonate). For the LPA coated capillaries, the electroosmotic mobility was determined to be 17-fold smaller compared to the case with the charged double coating. Simulation and array detection provide means for quickly investigating electrophoretic transport and separation properties. Without realistic input parameters, modeling alone is not providing data that match CE results.

Computer simulations of sample preconcentration in carrier-free systems and isoelectric focusing in microchannels using simple ampholytes

In this work, electrophoretic preconcentration of protein and peptide samples in microchannels was studied theoretically using the 1D dynamic simulator GENTRANS, and experimentally combined with MS. In all configurations studied, the sample was uniformly distributed throughout the channel before power application, and driving electrodes were used as microchannel ends. In the first part, previously obtained experimental results from carrier-free systems are compared to simulation results, and the effects of atmospheric carbon dioxide and impurities in the sample solution are examined. Simulation provided insight into the dynamics of the transport of all components under the applied electric field and revealed the formation of a pure water zone in the channel center. In the second part, the use of an IEF procedure with simple well defined amphoteric carrier components, i.e. amino acids, for concentration and fractionation of peptides was investigated. By performing simulations a qualitative description of the analyte behavior in this system was obtained. Neurotensin and [Glu1]-Fibrinopeptide B were separated by IEF in microchannels featuring a liquid lid for simple sample handling and placement of the driving electrodes. Component distributions in the channel were detected using MALDI- and nano-ESI-MS and data were in agreement with those obtained by simulation. Dynamic simulations are demonstrated to represent an effective tool to investigate the electrophoretic behavior of all components in the microchannel.

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.

Impact of Taylor-Aris diffusivity on analyte and system zone dispersion in CZE assessed by computer simulation and experimental validation

Application of pressure-driven laminar flow has an impact on zone and boundary dispersion in open tubular CE. The GENTRANS dynamic simulator for electrophoresis was extended with Taylor-Aris diffusivity which accounts for dispersion due to the parabolic flow profile associated with pressure-driven flow. Effective diffusivity of analyte and system zones as functions of the capillary diameter and the amount of flow in comparison to molecular diffusion alone were studied for configurations with concomitant action of imposed hydrodynamic flow and electroosmosis. For selected examples under realistic experimental conditions, simulation data are compared with those monitored experimentally using modular CE setups featuring both capacitively coupled contactless conductivity and UV absorbance detection along a 50 μm id fused-silica capillary of 90 cm total length. The data presented indicate that inclusion of flow profile based Taylor-Aris diffusivity provides realistic simulation data for analyte and system peaks, particularly those monitored in CE with conductivity detection.

Computer simulation of electrophoretic aspects of enantiomer migration and separation in capillary electrochromatography with a neutral selector

A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.

Approximation of weak solution for the problem of a pH-gradient creation in isoelectrofocusing

The mathematical model describing the stationary natural pH -gradient arising under the action of an electric field in an aqueous solution of ampholytes is constructed and investigated. The model is a part of a more general model of the isoelectrofocusing process. Investigation is based on the approximation of a weak solution by the piecewise continuous non-smooth functions. The method can be used for solving classes of problems for ordinary differential equations with a small parameter at the highest derivatives and the turning points.

10,000-fold concentration increase in proteins in a cascade microchip using anionic ITP by a 3-D numerical simulation with experimental results

This paper describes both the experimental application and 3-D numerical simulation of isotachophoresis (ITP) in a 3.2 cm long "cascade" poly(methyl methacrylate) (PMMA) microfluidic chip. The microchip includes 10 × reductions in both the width and depth of the microchannel, which decreases the overall cross-sectional area by a factor of 100 between the inlet (cathode) and outlet (anode). A 3-D numerical simulation of ITP is outlined and is a first example of an ITP simulation in three dimensions. The 3-D numerical simulation uses COMSOL Multiphysics v4.0a to concentrate two generic proteins and monitor protein migration through the microchannel. In performing an ITP simulation on this microchip platform, we observe an increase in concentration by over a factor of more than 10,000 due to the combination of ITP stacking and the reduction in cross-sectional area. Two fluorescent proteins, green fluorescent protein and R-phycoerythrin, were used to experimentally visualize ITP through the fabricated microfluidic chip. The initial concentration of each protein in the sample was 1.995 μg/mL and, after preconcentration by ITP, the final concentrations of the two fluorescent proteins were 32.57 ± 3.63 and 22.81 ± 4.61 mg/mL, respectively. Thus, experimentally the two fluorescent proteins were concentrated by over a factor of 10,000 and show good qualitative agreement with our simulation results.