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

Reducing Cathodic Drift during Isoelectric Focusing Using Microscale Immobilized pH Gradient Gels

Microfluidic analytical tools play an important role in miniaturizing targeted proteomic assays for improved detection sensitivity, throughput, and automation. Microfluidic isoelectric focusing (IEF) can resolve proteoforms in lysate from low-to-single cell numbers. However, IEF assays often use carrier ampholytes (CAs) to establish a pH gradient for protein separation, presenting limitations like pH instability in the form of cathodic drift (migration of focused proteins toward the cathode). Immobilized pH gradient (IPG) gels reduce cathodic drift by covalently immobilizing the pH buffering components to a matrix. To our knowledge, efforts to implement IPG gels at the microscale have been limited to glass microdevices. To adapt IEF using IPGs to widely used microfluidic device materials, we introduce a polydimethylsiloxane (PDMS)-based microfluidic device and compare the microscale pH gradient stability of IEF established with IPGs, CAs, and a hybrid formulation of IPG gels and CAs (mixed-bed IEF). The PDMS-based IPG microfluidic device (μIPG) resolved analytes differing by 0.1 isoelectric point within a 3.5 mm separation lane over a 20 min focusing duration. During the 20 min duration, we observed markedly different cathodic drift velocities among the three formulations: 60.1 μm/min in CA-IEF, 2.5 μm/min in IPG-IEF (∼24-fold reduction versus CA-IEF), and 1.4 μm/min in mixed-bed IEF (∼43-fold reduction versus CA-IEF). Lastly, mixed-bed IEF in a PDMS device resolved green fluorescent protein (GFP) proteoforms from GFP-expressing human breast cancer cell lysate, thus establishing stability in lysate from complex biospecimens. μIPG is a promising and stable technique for studying proteoforms from small volumes.

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.

Evolution of the theoretical description of the isoelectric focusing experiment: III. Carrier ampholyte behavior in transient, bidirectional isotachophoresis

In modern isoelectric focusing (IEF) systems, where (i) convective mixing is prevented by gels or small cross-sectional area separation channels, (ii) current densities vary spatially due to the presence of electrode vessels with much larger cross-sectional areas than those of the gels or separation channels, and (iii) electrophoretic and diffusive fluxes do not balance each other, stationary, steady-state pH gradients cannot form (open-system IEF). Open-system IEF is currently described as a two-stage process: A rapid IEF process forms the pH gradient from the carrier ampholytes (CAs) in the first stage, then isotachophoretic processes degrade the pH gradient in the second stage as the extreme pI CAs are moved into the electrode vessels where they become diluted. Based on the ratios of the local effective mobilities and the local conductivities ( μ L eff ( x ) $\mu _{\rm{L}}^{{\rm{eff}}}( x )$ / κ ( x ) $\kappa ( x )$ values) of the anolyte, catholyte, and the CAs, we pointed out in the preceding paper (Vigh G, Gas B, Electrophoresis 2023, 44, x x x) that in open-system IEF, a single process, transient, bidirectional isotachophoresis (tbdITP) operates from the moment current is turned on. In this paper, we demonstrate some of the operational features of the tbdITP model using the new ITP/IEF version of Simul 6.

Recent progress in analytical capillary isotachophoresis (2018 - March 2022)

This review brings a survey of papers on analytical capillary and microchip isotachophoresis published since 2018 until the first quarter of 2022. Theoretical papers extending fundamental knowledge include those on computer simulations that remain an important research tool useful in the design of electrolyte systems. Many papers are focused on instrumental aspects where new media including microfluidic devices and their hyphenation to various detection techniques bring remarkable results. Papers reporting analytical applications demonstrate the potential of contemporary analytical isotachophoresis. Although it is not being used on a mass scale, its special features are attracting continued interest resulting in applications of isotachophoresis both as a stand-alone analytical method and as a part of multidimensional separation techniques.

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m 2 . We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.

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.