Computer simulation and experimental validation of isoelectric focusing in ampholine-free systems

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.

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.

Capacitively coupled contactless conductivity detection for microfluidic capillary isoelectric focusing

We report capacitively coupled contactless conductivity detection (C4D) of proteins separated by microfluidic capillary isoelectric focusing (μCIEF). To elucidate the evolution of negative conductivity peaks during focusing and seek IEF conditions for sensitive conductivity detection, numerical simulation was performed using a model protein GFP (green fluorescence protein) and hypothetical carrier ampholytes (CAs). C4D was successfully applied to the μCIEF by optimizing assay conditions using a simple and effective pressure-mobilization approach. The conductivity and fluorescence signals of a focused GFP band were co-detected, confirming that the obtained negative C4D peak could be attributed to the actual protein, not the non-uniform background conductivity profile of the focused CAs. GFP concentrations of 10 nM-30 μM was quantified with a detection limit of 10 nM. Finally, the resolving power was analyzed by separating a mixture of R-phycoerythrin (pI 5.01), GFP-F64L (pI 5.48), and RK-GFP (pI 6.02). The conductivities of the three separated fluorescence proteins were measured with average separation resolution of 2.06. We expect the newly developed label-free μCIEF-C4D technique to be widely adopted as a portable, electronics-only protein-analysis tool.

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.

Stochastic simulation of reactive separations in capillary electrophoresis

A stochastic (Monte Carlo) simulation is used to investigate thermodynamic and kinetic contributions from the reversible A <--> B reaction in capillary electrophoresis (CE). The effects of equilibrium constant, rate constant, and electrophoretic mobility on the molecular zone profiles and the corresponding statistical moments are evaluated. As the reaction approaches steady state, the velocity of the zone is governed by the equilibrium constant and the electrophoretic mobilities of the reacting molecules. When the equilibrium constant is less than unity, the mean zone velocity is more similar to that of the reactant A. Conversely, when the equilibrium constant is greater than unity, the velocity is more similar to that of the product B. The extent of zone-broadening and asymmetry at steady state is dependent upon the equilibrium constant, the characteristic reaction lifetime, and the electrophoretic mobility difference between reacting molecules. If all other parameters are held constant, the plate height is greatest and skew is least when the equilibrium constant is unity. The plate height increases linearly with the characteristic reaction lifetime and electrophoretic mobility difference, whereas the skew is independent of these parameters. These conclusions have important implications for the elucidation of thermodynamic and kinetic information from experimental data.

Protocol of capillary isoelectric focusing to separate extremely acidic and basic proteins

A new set-up was constructed for capillary isoelectric focusing (CIEF) involving a sampling capillary as a bypass fixed to the separation capillary. Sample solutions were subjected to a previously established pH gradient from the sample capillary. Besides performing conventional CIEF, the separation of ampholytic compounds with isoelectric points (p/s) beyond the pH gradient was carried out on this system. This method was termed as pH gradient driven electrophoresis (PGDE) and the basic mathematical expressions were derived to express the dynamic fundamentals. Proteins such as lysozyme, cytochrome C, and pepsin with p/s higher than 10 or below 3 were separated in a pH gradient provided by Pharmalyte (pH 3-10). Finally, this protocol convincingly exhibited its potential in the separation of a solution of chicken egg white.

The unvalidity of Kohlrausch' regulating function for Svensson's isoelectric focusing and stationary electrolysis at steady state

Kohlrausch' regulating function is of important significance in the field of electrophoresis. In this paper, the relative regulating function is defined from Kohlrausch' regulating function. The relative values, including the limited values, of the regulating function for the stationary electrolysis of salt, on which the classic isoelectric focusing (IEF) is based, are computed and compared with the computer program of the QBASIC written by us. The results directly demonstrate that, (1) in a few cases the regulating function is valid for the stationary electrolysis and IEF, whereas (2) the function is, in most of cases, not valid for the stationary electrolysis and IEF at steady-state. Those findings may be useful for the studies on the relationships between Kohlrausch' regulating function and IEF and for the classification of numerous electrophoretic techniques.

Steady-state electrolysis of an ampholyte solution and possibility of violation of the "law of pH monotony"

The problem of stationary electrolysis of a single-component ampholyte solution is analyzed. The effect of nonconstant relative mobility is taken into account. It is demonstrated that an incorrect dissociation model (i.e., expressing the resulting ampholyte flux by the arithmetic sum of the fluxes for "cationic" and "anionic" species) may lead to the violation of the so-called "law of pH monotony".

Amperometric pH regulation--a flexible tool for rapid and precise temporal control over the pH of an electrolyte solution

Temporal control over both pH and ionic strength of an electrolyte solution with high accuracy was achieved with a dynamic, computer feedback-controlled amperometric pH-stat device consisting of four pH-regulating electrodes placed in electrolyte reservoirs that are separated by dialysis membranes from a central compartment. Theoretical predictions of the behavior of this arrangement, obtained by computer simulation, were validated by running temporal pH programs such as step functions, oscillations, and linear pH gradients. Deviations from nominal values given by the computer program are within the limits of accuracy of the pH-measuring electrodes. No volume changes accompany a change of pH or conductivity since ions are forced to leave or enter the central compartment through the membranes by the electrical force applied between the pH-regulating electrodes. The device is flexible, easy to use and easily miniaturized. We discuss a wide range of possible applications in biochemistry and cell science. These include automated pH adjustment, isoelectric protein separation, amperometric measurement of enzyme kinetics and the response of cell cultures to well-defined pH changes.

Isolation of human serum transferrin by free-fluid recycling electrophoresis in simple buffers

The isolation of human serum transferrin (Tf) using recycling isotachophoresis (RITP) and recycling isoelectric focusing (RIEF) with simple buffers is described. Serum fractionation, the first step in the protocol for Tf purification, is shown to be easily performed either by RITP of filtered serum using low molecular mass spacers or by RIEF of dialyzed serum employing a binary mixture of a well-defined buffer pair covering the pH range between 5.2 and 6.2, called RIEF-OptiFocus. For polishing, Tf-containing fractions are reprocessed by RITP or RIEF-OptiFocus. Other RIEF approaches based on the use of single amino acids at high concentration and ternary amino acid mixtures are shown to constitute less effective methods for Tf isolation. With a four-step protocol, comprising in turn RITP, RIEF-OptiFocus, ultrafiltration and again RITP, "single-band" purity (as assessed by two-dimensional gel electrophoresis) is obtained. Omission of the first step (RITP) and direct processing of dialyzed serum by RIEF-OptiFocus, ultrafiltration and RITP, is shown to provide remarkable results as well.

Differentiation by preparative continuous free flow-isoelectric focusing of cyclosporin A inhibitable peptidyl-prolyl cis/trans isomerase of human erythrocytes

Preparative continuous free flow-isoelectric focusing has been used to separate at least three different components of intrinsic peptidyl-prolyl cis/trans isomerase (PPIase) activity from erythrocytes lysate. By adding chemical spacer molecules like glycine and Bicine to commercial carrier ampholyte mixtures the resulting pH profile was predictably influenced. With an applied field strength of 125-170 V/cm a residence time of less than 15 min was sufficient for the separation of PPIases with isoelectric points of 5.4, 5.7 and 5.9 from the bulky hemoglobin. The recovery of the overall PPIase activities was about 100%. The purification factor has been determined as 20- to 100-fold. For each isoform of the enzyme the peptidyl-prolyl cis/trans isomerase activity of the separated proteins was inhibited by cyclosporin A but was resistant toward FK 506.

Recycling isoelectric focusing: use of simple buffers

Using the recycling free-flow focusing (RF3) apparatus, we have demonstrated that single ampholytes can be utilized to establish very stable pH regions, separating all proteins into three groups: a sharply resolved zone of proteins isoelectric at the prevailing pH, this "pH window" being bracketed by zones of more acidic and/or basic proteins. The ampholytes used are either amino acids or their dipeptides and other derivatives. Where necessary, because of lack of an ampholyte with the required pH, a binary mixture of ampholytes can be utilized. The closer their isoelectric points (pI), the narrower will be the pH window, i.e., the sharper the resolution of the bracketed proteins. This method overcomes the necessity of using ill-defined commercial carrier ampholytes, such as Ampholine, for preparative isoelectric focusing. It is recommended that the ampholytes be utilized at relatively high concentration, 100mM or higher, this contributing to pH stability and minimizing protein precipitation.

On the computational approach to immobilized pH gradients

The unified treatment for computing the pH of complex mixtures of mono- and polyprotic buffers, including ampholytes, as utilized in the gradient simulation program PGS, is presented. Its ability to compute pH, buffering power and ionic strength is shown by discussing a few simulations. The problems arising in the automatic formulation of optimal mixtures are presented, as well as the merits and limits of several target functions utilized in such optimizations. It is shown that no universal target function exists and that a proper optimization method should account for the fact that more than one formulation is possible for a given pH range.

Isoelectric membrane simulator: a computational approach for isoelectric immobiline membranes

Isoelectric membrane simulator (IMS) is a computer program meant for computation of pH, buffering power (beta), ionic strength (I) and dissociation degree (a) of a mixture of up to 3 buffering and 1 titrant Immobilines, for generating in a reproducible manner isoelectric membranes. Such membranes, of precise isoelectric point, are then used for large-scale protein purification by isoelectric focusing in multicompartment electrolyzers. IMS can be used, in a more general application, for titrating mixtures of buffers to a desired pH value. This versatile program is written in M.Q.BASIC rel. 2.5 and it runs on any IBM hardware or compatible machine supported by MS-DOS. An example of purification of superoxide dismutase in a multicompartment electrolyzer with a set of fixed pI membranes of widely differing composition is shown.

Steady state electrolysis and isoelectric focusing

The properties of pH gradients formed by stationary electrolysis of weak mobile or fixed electrolytes are analyzed. The model uses the appropriate balance equations and those of chemical equilibria. It is shown how the equation of the current density has to be modified for considering that fraction of current that is associated with the diffusion of neutral buffer molecules within a pH gradient. Furthermore it is shown that the pH gradients themselves give rise to water production within the gradient and that essential properties of the steady state are related to chemical reactions between the electrolyte constituents. The differential equations describing the gradients of the concentration of a given component, the pH, conductivity and potential are explicitly formulated in relation to those reactions. The equations are solved numerically and the significance of the results for isoelectric focusing is discussed. The experimental conditions to reach shallow and smooth pH gradients exhibiting sufficient ionic strength are formulated.