Dynamics of capillary isoelectric focusing in the absence of fluid flow: high-resolution computer simulation and experimental validation with whole column optical imaging

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.

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.

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.

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.

Intact and middle-down CIEF of commercial therapeutic monoclonal antibody products under non-denaturing conditions

A two‐step CIEF with chemical mobilization was developed for charge profiling of the therapeutic mAb rituximab under non‐denaturing separation conditions. CIEF of the intact mAb was combined with a middle‐down approach analyzing Fc/2 and F(ab´)₂ fragments after digest with a commercial cysteine protease (IdeS). CIEF methods were optimized separately for the intact mAb and its fragments due to their divergent pIs. Best resolution was achieved by combining Pharmalyte (PL) 8–10.5 with PL 3–10 for variants of intact rituximab and of F(ab´)₂ fragments, respectively, whereas PL 6.7–7.7 in combination with PL 3–10 was used for Fc/2 variants. Charge heterogeneity in Fc/2 dominates over F(ab´)₂. In addition, a copy product of rituximab, and adalimumab were analyzed. Both mAbs contain additional alkaline C‐terminal lysine variants as confirmed by digest with carboxypeptidase B. The optimized CIEF methods for intact mAb and Fc/2 were tested for their potential as platform approaches for these mAbs. The CIEF method for Fc/2 was slightly adapted in this process. The pI values for major intact mAb variants were determined by adjacent pI markers resulting in 9.29 (rituximab) and 8.42 (adalimumab). In total, seven to eight charge variants could be distinguished for intact adalimumab and rituximab, respectively.

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.

Arrayed isoelectric focusing using photopatterned multi-domain hydrogels

Isoelectric focusing (IEF) is a powerful separation method, useful for resolving subtle changes in the isoelectric point of unlabeled proteins. While microfluidic IEF has reduced the separation times from hours in traditional benchtop IEF to minutes, the enclosed devices hinder post-separation access to the sample for downstream analysis. The two-layer open IEF device presented here comprises a photopatterned hydrogel lid layer containing the chemistries required for IEF and a thin polyacrylamide bottom layer in which the analytes are separated. The open IEF device produces comparable minimum resolvable difference in isoelectric point and gradient stability to enclosed microfluidic devices while providing post-separation sample access by simple removal of the lid layer. Further, using simulations, we determine that the material properties and the length of the separation lanes are the primary factors that affect the electric field magnitude in the separation region. Finally, we demonstrate self-indexed photomasks for alignment-free fabrication of multi-domain hydrogels. We leverage this approach to generate arrayed pH gradients with a total of 80 concurrent separation lanes, which to our knowledge is the first demonstration of multiple IEF separations in series addressed by a single pair of electrodes.

Microchip with an open tubular immobilized ph gradient for UV whole column imaging detection

This study reports a new method for establishing an open tubular IPG in a microchip coupled with a whole column image detection (WCID) system for protein separation applications. This method allows a wider range of immobilized pH (2.6-9.5) to be established in a PDMS/quartz channel by controlling the diffusion of acidic and basic polymer solutions into the channel through well-designed channel dimensions. The developed pH gradient was experimentally validated by performing the separation of a mixture of standard pI markers. It was further validated by the separation of the hemoglobin control AFSC sample. This method is advantageous over existing IPG methods because it has a wider range of pH and maintains the open tubular feature that matches the UV WCID to improve the sensitivity.

Cascaded free-flow isoelectric focusing for improved focusing speed and resolution

This work presents the first implementation of cascaded stages for a microfabricated free-flow isoelectric focusing (FF-IEF) device. Both analytical and computational models for IEF suggest device performance will be improved by utilizing multiple stages to reduce device residence time. These models are shown to be applicable by using focusing of small IEF markers as a demonstration. We also show focusing of fluorescently tagged proteins under different channel geometries, with the most efficient focusing occurring in the cascaded design, as predicted by theory. An additional aim of this work is to demonstrate the compatibility of cascaded FF-IEF with common bioanalytical tools. As an example, outlet fractions from cascaded FF-IEF were analyzed by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). Processing of whole cell lysate followed by immunoblotting for cell signaling markers demonstrates the reduction of albumin from samples, as well as the enrichment of apoptotic markers.

Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing

Our dynamic capillary electrophoresis model which uses material specific input data for estimation of electroosmosis was applied to investigate fundamental aspects of isoelectric focusing (IEF) in capillaries or microchannels made from bare fused-silica (FS), FS coated with a sulfonated polymer, polymethylmethacrylate (PMMA) and poly(dimethylsiloxane) (PDMS). Input data were generated via determination of the electroosmotic flow (EOF) using buffers with varying pH and ionic strength. Two models are distinguished, one that neglects changes of ionic strength and one that includes the dependence between electroosmotic mobility and ionic strength. For each configuration, the models provide insight into the magnitude and dynamics of electroosmosis. The contribution of each electrophoretic zone to the net EOF is thereby visualized and the amount of EOF required for the detection of the zone structures at a particular location along the capillary, including at its end for MS detection, is predicted. For bare FS, PDMS and PMMA, simulations reveal that EOF is decreasing with time and that the entire IEF process is characterized by the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic transport and electroosmotic zone displacement are opposite and of equal magnitude. The location of immobilization of the boundary between anolyte and most acidic carrier ampholyte is dependent on EOF, i.e. capillary material and anolyte. Overall time intervals for reaching this state in microchannels produced by PDMS and PMMA are predicted to be similar and about twice as long compared to uncoated FS. Additional mobilization for the detection of the entire pH gradient at the capillary end is required. Using concomitant electrophoretic mobilization with an acid as coanion in the catholyte is shown to provide sufficient additional cathodic transport for that purpose. FS capillaries dynamically double coated with polybrene and poly(vinylsulfonate) are predicted to provide sufficient electroosmotic pumping for detection of the entire IEF gradient at the cathodic column end.

Modeling and simulation of IEF in 2-D microgeometries

A 2-D finite-volume model is developed to simulate nonlinear IEF in complex microgeometries. This mathematical model is formulated based on the mass conservation and ionic dissociation relations of amphoteric macromolecules, charge conservation, and the electroneutrality condition. Based on the 2-D model, three different separation cases are studied: an IPG in a planar channel, an ampholyte-based pH gradient in a planar channel, and an ampholyte-based pH gradient in a contraction-expansion channel. In the IPG case, cacodylic acid (pK(1) = 6.21) and Tris (pK(1) = 8.3) are used as the acid and base, respectively, to validate the 2-D IEF model. In the ampholyte-based pH gradient cases, IEF is performed in the pH range, 6.21-8.3 using 10 ampholytes in the planar channel and 20 ampholytes in the contraction-expansion channel. The numerical results reveal different focusing efficiencies and resolution in the narrow and wide sections of the contraction-expansion channel. To explain this, the expressions for separation resolution and peak concentrations of separands in the contraction-expansion channel are presented in terms of the channel shape factor. In a 2-D planar channel, a focused band remains straight all the time. However, in a contraction-expansion channel, initially straight bands take on a crescent profile as they pass through the trapezoidal sections joining the contraction and expansion sections.

High-resolution computer simulation of the dynamics of isoelectric focusing using carrier ampholytes: Focusing with concurrent electrophoretic mobilization is an isotachophoretic process

Focusing of four hemoglobins with concurrent electrophoretic mobilization was studied by computer simulation. A dynamic electrophoresis simulator was first used to provide a detailed description of focusing in a 100-carrier component, pH 6-8 gradient using phosphoric acid as anolyte and NaOH as catholyte. These results are compared to an identical simulation except that the catholyte contained both NaOH and NaCl. A stationary, steady-state distribution of carrier components and hemoglobins is produced in the first configuration. In the second, the chloride ion migrates into and through the separation space. It is shown that even under these conditions of chloride ion flux a pH gradient forms. All amphoteric species acquire a slight positive charge upon focusing and the whole pattern is mobilized towards the cathode. The cathodic gradient end is stable whereas the anodic end is gradually degrading due to the continuous accumulation of chloride. The data illustrate that the mobilization is a cationic isotachophoretic process with the sodium ion being the leading cation. The peak height of the hemoglobin zones decreases somewhat upon mobilization, but the zones retain a relatively sharp profile, thus facilitating detection. The electropherograms that would be produced by whole column imaging and by a single detector placed at different locations along the focusing column are presented and show that focusing can be commenced with NaCl present in the catholyte at the beginning of the experiment. However, this may require detector placement on the cathodic side of the catholyte/sample mixture interface.

Simul 5 – Free dynamic simulator of electrophoresis

We introduce the mathematical model of electromigration of electrolytes in free solution together with free software Simul, version 5, designed for simulation of electrophoresis. The mathematical model is based on principles of mass conservation, acid-base equilibria, and electroneutrality. It accounts for any number of multivalent electrolytes or ampholytes and yields a complete picture about dynamics of electromigration and diffusion in the separation channel. Additionally, the model accounts for the influence of ionic strength on ionic mobilities and electrolyte activities. The typical use of Simul is: inspection of system peaks (zones), stacking and preconcentrating analytes, resonance phenomena, and optimization of separation conditions, in either CZE, ITP, or IEF.

On-line chemiluminescence detection for isoelectric focusing of heme proteins on microchips

In this paper we present a sensitive chemiluminescence (CL) detection of heme proteins coupled with microchip IEF. The detection principle was based on the catalytic effects of the heme proteins on the CL reaction of luminol-H2O2 enhanced by para-iodophenol. The glass microchip and poly(dimethylsiloxane) (PDMS)/glass microchip for IEF were fabricated using micromachining technology in the laboratory. The modes of CL detection were investigated and two microchips (glass, PDMS/glass) were compared. Certain proteins, such as cytochrome c, myoglobin, and horseradish peroxidase, were focused by use of Pharmalyte pH 3-10 as ampholytes. Hydroxypropylmethylcellulose was added to the sample solution in order to easily reduce protein interactions with the channel wall as well as the EOF. The focused proteins were transported by salt mobilization to the CL detection window. Cytochrome c, myoglobin, and horseradish peroxidase were well separated within 10 min on a glass chip and the detection limits (S/N=3) were 1.2x10(-7), 1.6x10(-7), and 1.0x10(-10) M, respectively.

Salt removal during Off-Gel electrophoresis of protein samples

The Off-Gel technology was recently described for protein fractionation in a solution placed on top of an immobilized pH gradient gel. In addition, this process was found to remove salts from the biological samples to analyze. This desalting effect is studied experimentally in a conductometric prototype cell. A simplified analytical model is developed to understand this process and a good agreement is found with the conductivity measurements. To illustrate the desalting of a biological sample, a 1 mg.mL(-1) solution of beta-lactoglobulin A in 0.1 M NaCl is subjected to electrophoresis in a single compartment Off-Gel cell. The analysis of the resulting sample by ESI-MS demonstrates the effective removal of salt. A finite element diffusion-migration model is also used to illustrate how the nonuniformity of the electric field in the cell, associated with the salt migration, can slow down the desalting process.

Conductivity properties of carrier ampholyte pH gradients in isoelectric focusing

The conductivity properties of natural pH gradient created by carrier ampholytes were studied during the process of isoelectric focusing (IEF). IEF was performed in capillaries (10-30 mm long) or in microchips with the same channel length. A 10-30x reduction of the conductivity of the separation medium was observed during the establishment of pH gradient. Results obtained using different IEF voltages indicate that there is a nonlinear relationship between the conductivity of an established pH gradient and the applied electric field. Our theoretical analysis using a simplified model generated values that reasonably agree with the experimental data. In addition, we found that above a certain electric field ( approximately 300 V/cm), resolution does not increase with the applied voltage as predicated; we observed band-broadening and gel breakdown. The approach presented in this work can be used for optimization of the IEF separation and judicious selection of IEF conditions.

The transitional isoelectric focusing process

The transitional isoelectric focusing (IEF) process (the course of pH gradient formation by carrier ampholytes (CAs) and the correlation of the focusing time with CA concentration) were investigated using a whole-column detection capillary isoelectric focusing (CIEF) system. The transitional double-peak phenomenon in IEF was explained as a result of migration of protons from the anodic end and hydroxyl ions from the cathodic end into the separation channel and the higher electric field at both acidic and basic sides of the separation channel. It was observed that focusing times increase logarithmically with CA concentration under a constant applied voltage. The correlation of focusing time with CA concentration was explained by the dependence of the charge-transfer rate on the amount of charged CAs within the separation channel during focusing.

Capillary electrophoresis of proteins 1999-2001

This review article with 223 references describes recent developments in capillary electrophoresis (CE) of proteins and covers papers published during last two years, from the previous review (V. Dolnik, Electrophoresis 1999, 20, 3106-3115) through Spring 2001. It describes the topics related to CE of proteins including modeling of the electrophoretic properties of proteins, sample pretreatment, wall coatings, improving selectivity, detection, special electrophoretic techniques, and applications.