High-resolution electrophoretic simulations: Performance characteristics of one-dimensional simulators

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/.

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.

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.

Insights into head-column field-amplified sample stacking: Part II. Study of the behavior of the electrophoretic system after electrokinetic injection of cationic compounds across a short water plug

Part I on head-column field-amplified sample stacking comprised a detailed study of the electrokinetic injection of a weak base across a short water plug into a phosphate buffer at low pH. The water plug is converted into a low conductive acidic zone and cationic analytes become stacked at the interface between this and a newly formed phosphoric acid zone. The fundamentals of electrokinetic processes occurring thereafter were studied experimentally and with computer simulation and are presented as part II. The configuration analyzed represents a discontinuous buffer system. Computer simulation revealed that the phosphoric acid zone at the plug-buffer interface becomes converted into a migrating phosphate buffer plug which corresponds to the cationically migrating system zone of the phosphate buffer system. Its mobility is higher than that of the analytes such that they migrate behind the system zone in a phosphate buffer comparable to the applied background electrolyte. The temporal behaviour of the current and the conductivity across the water plug were monitored and found to reflect the changes in the low conductivity plug. Determination of the buffer flow in the capillary revealed increased pumping caused by the mismatch of electroosmosis within the low conductivity plug and the buffer. This effect becomes elevated with increasing water plug length. For plug lengths up to 1% of the total column length the flow quickly drops to the electroosmotic flow of the buffer and simulations with experimentally determined current and flow values predict negligible band dispersion and no loss of resolution for both low and large molecular mass components.

Insights into head-column field-amplified sample stacking: Part I. Detailed study of electrokinetic injection of a weak base across a short water plug

The fundamentals of electrokinetic injection of the weak base methadone across a short water plug into a phosphate buffer at low pH were studied experimentally and with computer simulation. The current during electrokinetic injection, the formation of the analyte zone, changes occurring within and around the water plug and mass transport of all compounds in the electric field were investigated. The impact of water plug length, plug injection velocity, and composition of sample, plug and background electrolyte are discussed. Experimental data revealed that properties of sample, water plug and stacking boundary are significantly and rapidly altered during electrokinetic injection. Simulation provided insight into these changes, including the nature of the migrating boundaries and the stacking of methadone at the interface to a newly formed phosphoric acid zone. The data confirm the role of the water plug to prevent contamination of the sample by components of the background electrolyte and suggest that mixing caused by electrohydrodynamic instabilities increases the water plug conductivity. The sample conductivity must be controlled by addition of an acid to prevent generation of reversed flow which removes the water plug and to create a buffering environment. Results revealed that a large increase in background electrolyte concentration is not accompanied with a significant increase in stacking.

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.

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.

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.