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: II. An open system isoelectric focusing experiment is a transient, bidirectional isotachophoretic experiment.

The carrier ampholytes-based (CA-based) isoelectric focusing (IEF) experiment evolved from Svensson's closed system IEF (constant spatial current density, absence of convective mixing, counter-balancing electrophoretic and diffusive fluxes yielding a steady state pH gradient) to the contemporary open system IEF (absence of convective mixing, large cross-sectional area electrode vessels, lack of counter-balancing electrophoretic- and diffusive fluxes leading to transient pH gradients). Open system IEF currently is described by a two-stage model: In the first stage, a rapid IEF process forms the pH gradient which, in the second stage, is slowly degraded by isotachophoretic processes that move the most acidic and most basic CAs into the electrode vessels. An analysis of the effective mobilities and the effective mobility to conductivity ratios of the anolyte, catholyte, and the CAs indicates that in open system IEF experiments a single process, transient bidirectional isotachophoresis (tbdITP) operates from the moment current is turned on until it is turned off. In tbdITP, the anolyte and catholyte provide the leading ions and the pI 7 CA or the reactive boundary of the counter-migrating H3 O+ and OH- ions serves as the shared terminator. The outcome of the tbdITP process is determined by the ionic mobilities, pKa values, and loaded amounts of all ionic and ionizable components: It is constrained by both the transmitted amount of charge and the migration space available for the leading ions. tbdITP and the resulting pH gradient can never reach steady state with respect to the spatial coordinate of the separation channel.

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, 675-88) 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.

CE determination of the thermodynamic pKa values and limiting ionic mobilities of 14 low molecular mass UV absorbing ampholytes for accurate characterization of the pH gradient in carrier ampholytes-based IEF and its numeric simulation.

Fourteen low molecular mass UV absorbing ampholytes containing 1 or 2 weakly acidic and 1 or 2 weakly basic functional groups that best satisfy Rilbe's requirement for being good carrier ampholytes (ΔpKa = pKamonoanion - pKamonocation < 2) were selected from a large group of commercially readily available ampholytes in a computational study using two software packages (ChemSketch and SPARC). Their electrophoretic mobilities were measured in 10 mM ionic strength BGEs covering the 2 < pH < 12 range. Using our Debye-Hückel and Onsager-Fuoss laws-based new software, AnglerFish (freeware, https://echmet.natur.cuni.cz/software/download), the effective mobilities were recalculated to zero ionic strength from which the thermodynamic pKa values and limiting ionic mobilities of the ampholytes were directly calculated by Henderson-Hasselbalch equation-type nonlinear regression. The tabulated thermodynamic pKa values and limiting ionic mobilities of these ampholytes (pI markers) facilitate both the overall and the narrow-segment characterization of the pH gradients obtained in IEF in order to mitigate the errors of analyte ampholyte pI assignments caused by the usual (but rarely proven) assumption of pH gradient linearity. These thermodynamic pKa and limiting mobility values also enable the reality-based numeric simulation of the IEF process using, for example, Simul (freeware, https://echmet.natur.cuni.cz/software/download).

Determination of binding constants of multiple charged cyclodextrin complexes by ACE using uncorrected and ionic strength corrected actual mobilities of the species involved.

In this study, the apparent binding constants and limiting mobilities of the multiply charged complexes of the Δ- and Λ-enantiomers of Ru(II)- and Fe(II)-polypyridyl associates ([Ru(2,2'-bipyridine)3 ]2+ , [Ru(1,10-phenanthroline)3 ]2+ , and [Fe(1,10-phenanthroline)3 ]2+ ) with single-isomer 2,3-diacetylated-6-sulfated-cyclodextrins (CDs) (12Ac-6S-α-CD, 14Ac-7S-ß-CD, and 16Ac-8S-γ-CD) were determined by ACE using uncorrected and ionic strength corrected actual mobilities of the species involved. Two limiting models were tested for the ionic strength correction of the actual mobilities based on an empirical relation for the ionic strength correction of multivalent ionic species. In model 1, the nominal values of the charge numbers (zS,nom ) and analytical concentrations (cS,nom ) of the above CD selectors in the BGEs were applied for calculation of the BGE ionic strength, as usual. In model 2, the CD selectors were considered as singly charged species (zS  = -1) with |zS,nom |-times higher concentrations in the BGE than their analytical concentrations (cS  = |zS,nom | × cS,nom ) in the calculation of the BGE ionic strength. In all three cases-with uncorrected actual mobilities as well as with actual mobilities corrected according to the two limiting models-the measured effective mobilities of the above enantiomers fit well the theoretical curves of their mobility dependences on the CD selectors concentrations in the BGE, with high average coefficients of determination (R2  = 0.9890-0.9995). Nevertheless, the best physico-chemically meaningful values of the apparent binding constants and the limiting mobilities of the enantiomer-CDs complexes with low RSDs were obtained using the actual mobilities of the species involved corrected according to model 2.

Multi-cationic aminopyrene-based labeling tags for oligosaccharide analysis by capillary electrophoresis-mass spectrometry.

In this work, new multi-cationic aminopyrene-based labeling tags were designed and synthesized for oligosaccharide analysis by capillary electrophoresis-mass spectrometry (CE-MS). The starting compound, 8-aminopyrene-1,3,6-trisulfonic acid trisodium salt, was modified in order to form a sulfonamide derivative having three tertiary amines in the label structure. The sulfonamide derivative was further methylated to generate three permanently charged quaternary ammonium moieties on the label. The synthesized labels were characterized by NMR, IR, UV/Vis, fluorescence spectroscopy and mass spectrometry. Furthermore, the labels were applied for maltooligosaccharide standards as well as N-linked glycans labeling via reductive amination and followed by CE-MS analysis. The CE-MS analysis of maltooligosaccharides labeled by these newly synthesized labels provided the sub-micromolar limit of detection based on the extracted ion electropherogram signals.

Overcoming the aggregation problem: a new type of fluorescent ligand for ConA-based glucose sensing.

Competitive binding assays based on the lectin Concanavalin A (ConA) have displayed significant potential to serve in continuous glucose monitoring applications. However, to date, this type of fluorescent, affinity-based assay has yet to show the stable, glucose predictive capabilities that are required for such an application. This instability has been associated with the extensive crosslinking between traditionally-used fluorescent ligands (presenting multiple low-affinity moieties) and ConA (presenting multiple binding sites) in free solution. The work herein introduces the design and synthesis of a new type of fluorescent ligand that can avoid this aggregation and allow the assay to be sensitive across the physiologically relevant glucose concentration range. This fluorescent ligand (APTS-MT) presents a single high-affinity trimannose moiety that is recognized by ConA's full binding site and a fluorophore that can effectively track the ligand's equilibrium binding via fluorescent anisotropy. This is confirmed by comparing its measured fluorescent lifetime to experimentally-determined rotational correlation lifetimes of the free and bound populations. Using an assay comprised of 200 nM APTS-MT and 1 µM ConA, the fluorescence anisotropy capably tracks the concentration of monosaccharides that are known to bind to ConA's primary binding site, and the assay displays a MARD of 6.5% across physiologically relevant glucose concentrations. Ultimately, this rationally-designed fluorescent ligand can facilitate the realization of the full potential of ConA-based glucose sensing assays and provide the basis for a new set of competing ligands to be paired with ConA.

Equivalent peak resolution: characterization of the extent of separation for two components based on their relative peak overlap.

Although the classical formula of peak resolution was derived to characterize the extent of separation only for Gaussian peaks of equal areas, it is often used even when the peaks follow non-Gaussian distributions and/or have unequal areas. This practice can result in misleading information about the extent of separation in terms of the severity of peak overlap. We propose here the use of the equivalent peak resolution value, a term based on relative peak overlap, to characterize the extent of separation that had been achieved. The definition of equivalent peak resolution is not constrained either by the form(s) of the concentration distribution function(s) of the peaks (Gaussian or non-Gaussian) or the relative area of the peaks. The equivalent peak resolution value and the classically defined peak resolution value are numerically identical when the separated peaks are Gaussian and have identical areas and SDs. Using our new freeware program, Resolution Analyzer, one can calculate both the classically defined and the equivalent peak resolution values. With the help of this tool, we demonstrate here that the classical peak resolution values mischaracterize the extent of peak overlap even when the peaks are Gaussian but have different areas. We show that under ideal conditions of the separation process, the relative peak overlap value is easily accessible by fitting the overall peak profile as the sum of two Gaussian functions. The applicability of the new approach is demonstrated on real separations.

Simulation of the effects of complex-formation equilibria in electrophoresis: III. Simultaneous effects of chiral selector concentration and background electrolyte pH.

This paper describes the results of the second-level testing of the simulation program Simul 5 Complex. We compare the published experimental results with the simulated migration behavior of the enantiomers at different pH and chiral selector concentration values and use the same optimization object function, separation selectivity, as the original papers. Simul 5 Complex proved to be a suitable tool for the prediction of the effective mobilities, separation selectivities, and migration order reversals in these pH-dependent and CD concentration dependent enantiomer separations. In addition, by performing simulations of four different separations systems (both real and model systems), Simul 5 Complex revealed the existence of unexpected and hitherto unexplained electromigration dispersion effects that were caused by the complexation process itself and could significantly impair the quality of the separations.

Comparison of charge state distribution in commercially available sulfated cyclodextrins used as chiral resolving agents in capillary electrophoresis.

The charge state distributions of randomly sulfated cyclodextrins from Sigma-Aldrich and Beckman-Coulter, as well as single isomer sulfated cyclodextrins from TM Chemicals LP were investigated using hydrophilic interaction liquid chromatography (HILIC). A cross-linked diol phase and an unbonded silica phase were used as HILIC stationary phases. Groups of sulfated cyclodextrins with different charge states were resolved from each other, while regioisomers in a charge group were partially separated. A ladder of sulfated cyclodextrins having a charge state distribution from 1 to 14 was prepared and was used to determine the charge state heterogeneity of the commercially available sulfated cyclodextrin samples. Wide charge state and regioisomer distributions are seen for the randomly sulfated cyclodextrins, while HILIC analysis of every single isomer sulfated cyclodextrin sample indicates the presence of a single species.

Preparative-scale isoelectric trapping by recursive electrophoresis in a compartmentalized system having orthogonal primary and secondary pH gradients. Part 1--construction and standard operation.

The performance of the current preparative-scale isoelectric trapping systems is limited by the serial arrangement of the separation compartments. A new system has been developed that achieves trapping by recursive electrophoresis in a compartmentalized system (T-RECS). T-RECS features (i) parallel-connected elementary separation heads with independent electrode compartments, feed compartments, and harvest compartments, (ii) orthogonal primary pH gradients and secondary pH gradients, (iii) directionally controlled convective analyte transport along the primary (resolving) pH gradients, and (iv) electrophoretic analyte transport along the secondary (harvesting) pH gradients. The operation of T-RECS has been quantitatively characterized via separation of small molecule ampholytes.

Preparative-scale isoelectric trapping by recursive electrophoresis in a compartmentalized system having orthogonal primary and secondary pH gradients. Part 2--operation in cascade mode.

A parallel multicompartmental electrolyzer recently developed for preparative-scale isoelectric trapping separations, trapping by recursive electrophoresis in a compartmentalized system, was set up to operate as a cascade of binary separations to produce at least one pure target ampholyte (or more, with additional separation heads) without other ampholytes ever entering (even transiently) the harvest stream. This mode of operation avoids the need for exhaustive electrophoresis and the accompanying long separation times brought about by the exponentially decreasing concentrations over the course of batch separations. Continuous operation can be achieved in the cascade mode by continuously feeding the sample into the first separation head configured with three flow-through compartments and continuously harvesting one (or more) target components in additional separation heads configured with two flow-through compartments, attached to the respective branching points.

Synthesis, analytical characterization and initial capillary electrophoretic use in an acidic background electrolyte of a new, single-isomer chiral resolving agent: heptakis(2-O-sulfo-3-O-methyl-6-O-acetyl)-ß-cyclodextrin.

The sodium salt of heptakis(2-O-sulfo-3-O-methyl-6-O-acetyl)cyclomaltoheptaose (HAMS), the first single-isomer sulfated ß-CD that carries the sulfo group exclusively at the C2 position, has been synthesized. The purity of each synthetic intermediate and of the final product was determined by hydrophilic interaction (HILIC) and reversed-phase HPLC. The structural identity of each intermediate and of the final product was verified by 1-D and 2-D NMR spectroscopy and MALDI-TOF MS. HAMS was used for the capillary electrophoretic separation of the enantiomers of a set of non-ionic and weak base analytes in pH 2.5 background electrolytes. Rapid separations with satisfactory peak resolution values were obtained for most enantiomers using low concentrations of HAMS. The effective mobilities and separation selectivities were dependent on the concentration of HAMS according to the predictions of the charged resolving agent migration model. The separation selectivities observed with HAMS, heptakis(2-O-methyl-3-O-acetyl-6-O-sulfo)cyclomaltoheptaose and heptakis(2-O-methyl-3,6-di-O-sulfo)cyclomaltoheptaose were different for some of the analytes studied in detail.

Studies of histidine as a suitable isoelectric buffer for tryptic digestion and isoelectric trapping fractionation followed by capillary electrophoresis-mass spectrometry for proteomic analysis.

The use of histidine as a protein digestion buffer followed by isoelectric trapping separations using "membrane separated wells for isoelectric focusing and trapping" (MSWIFT) and mass spectrometry (MS) analysis is described. Tryptic digestion of bovine serum albumin (BSA) performed in histidine buffered solutions yields similar amino acid sequence coverage values to those obtained using ammonium bicarbonate buffer. Time course studies suggest that histidine buffers provide faster migration of peptides from the loading compartment compared to digestions prepared in ammonium bicarbonate due to differences in conductivities of the two buffers. In addition, this sample preparation method and MSWIFT separations have been coupled with capillary electrophoresis (CE) and matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) as an alternative separation approach for proteomic studies. Tryptic peptides of ribosomal proteins in histidine are fractionated using MSWIFT followed by CE-MALDI-MS, which further illustrates the ability to couple fractions from a pI based separation device to CE-MS. Specifically, two-dimensional CE-MS plots provide a direct correlation between the numbers of basic residues within the peptide sequence displayed in charge-state trend lines. Combining MSWIFT and CE-MS provides added information regarding peptide sequence, specifically pI and in-solution charge state. Post-translational modifications can also be identified using this method.

Concentration and fractionation by isoelectric trapping in a micropreparative-scale multicompartmental electrolyzer having orthogonal pH gradients. Part 1.

A multicompartmental electrolyzer called ConFrac has been developed and tested for micropreparative-scale isoelectric trapping separations. ConFrac contains n separate, minimalistic isoelectric trapping core units, each with a separate anode compartment, anodic flow-through compartment, collection compartment, cathodic flow-through compartment and a shared cathode compartment. The collection compartments are all isolated from each other and have volumes of 100 µL each. The liquid held in the collection compartments is stagnant. The respective anodic and cathodic flow-through compartments are hydraulically serially connected to each other by flexible, minimum-length, narrow internal diameter tubes. The respective feed solutions whose volumes are larger and variable are recirculated through the serially connected flow-through compartments. Poly(vinyl alcohol)-based buffering membranes are placed between the anode compartments, anodic flow-through compartments, collection compartments, cathodic flow-through compartments and cathode compartment. The membranes establish two orthogonal pH gradients in ConFrac. The primary pH gradient is parallel with the direction of the recirculating flows and orthogonal to that of the electric field. The secondary pH gradient is parallel with the direction of the electric field and orthogonal to that of the recirculating flows. Since the recirculating liquids are kept in thermostated reservoirs and the residence times in the flow-through compartments are shorter than 2 s, ConFrac can tolerate power loads as high as 2 W without overheating the solutions. The operation and performance of ConFrac has been quantitatively characterized: four 25 µM ampholytic components were isolated from 5 mL of feed solution in 20 min and their concentration increased approximately 50-fold.

Concentration and fractionation by isoelectric trapping in a micropreparative-scale multicompartmental electrolyzer having orthogonal pH gradients. Part 2.

A micropreparative-scale multicompartmental electrolyzer called ConFrac has been developed and tested for isoelectric trapping separations. ConFrac can be operated in pass-by-pass mode or recirculating mode, using either asymmetrical feeding (feed enters only the anodic or the cathodic flow-through compartment) or symmetrical feeding (feed enters both the anodic and the cathodic flow-through compartment). Symmetrical feeding results in higher processing rates and is the preferred operation mode. Residence time in the flow-through compartments is set as a compromise between processing rate and temperature rise in the effluent. Ampholytic components have been isolated from 5 to 50 mL volumes of micromolar feed solutions and hundredfold concentrated into 100-µL collection compartments. Samples containing ampholytic analytes in highly conducting salt solutions were readily desalted and fractionated in ConFrac in one operation. pH transients formerly observed in other isoelectric trapping devices were observed in ConFrac as well. The pH transients were caused by the unequal ion transmission rates of the anodic- and cathodic-side buffering membranes.

Efficient electrophoretic method to remove neutral additives from protein solutions followed by mass spectrometry analysis.

A mass spectrometry (MS)-compatible, isoelectric point-based separation method for removal of neutral additives from protein solutions is described. The separation is performed by electrophoretic migration and trapping using a device referred to as membrane separated wells for isoelectric focusing and trapping (MSWIFT). Electrophoretic separation in the MSWIFT device is fast; the entire process can be carried out in a matter of minutes, and it does not require further sample cleanup prior to MS analysis. Proof-of-concept experiments in which neutral additives (e.g., Triton X-100, Tween 20, poly(ethylene glycol)) are removed from protein solutions using the MSWIFT device followed by MS analysis are described. Coupling the MSWIFT separation with ion mobility MS provides additional separation via the gas phase and assists in achieving higher quality ESI mass spectra when small amounts of additives remain in solution.

Combining isoelectric point-based fractionation, liquid chromatography and mass spectrometry to improve peptide detection and protein identification.

The off-line coupling of an isoelectric trapping device termed membrane separated wells for isoelectric focusing and trapping (MSWIFT) to mass spectrometry-based proteomic studies is described. The MSWIFT is a high capacity, high-throughput, mass spectrometry-compatible isoelectric trapping device that provides isoelectric point (pI)-based separations of complex mixtures of peptides. In MSWIFT, separation and analyte trapping are achieved by migrating the peptide ions through membranes having fixed pH values until the peptide pI is bracketed by the pH values of adjacent membranes. The pH values of the membranes can be tuned, thus affording a high degree of experimental flexibility. Specific advantages of using MSWIFT for sample prefractionation include: (1) small sample volumes (approximately 200 microL), (2) customized membranes over a large pH range, (3) flexibility in the number of desired fractions, (4) membrane compatibility with a variety of solvents systems, and (5) resulting fractions do not require sample cleanup before MS analysis. Here, we demonstrate the utility of MSWIFT for mass spectrometry-based detection of peptides in improving dynamic range and the reduction of ion suppression effects for high-throughput separations of tryptic peptides.

A systematic study in CIEF: defining and optimizing experimental parameters critical to method reproducibility and robustness.

A systematic study of two-step CIEF analysis was completed to identify key components that could be optimized to enhance the performance of mAb analysis by CIEF. Resolution between mAb isoforms was increased by selecting a narrow detector aperture, utilizing chemical rather than pressure mobilization, and improving protein solubility by incorporating urea into the carrier ampholyte (CA) solutions. Loss of the extreme pI CAs and sample components by the bidirectional ITP inherent to IEF was avoided by setting the concentration of the phosphoric acid anolyte to 200 mM and sodium hydroxide catholyte to 300 mM and by adding sufficient amounts of an acidic (pI<3) and basic (10

Simulation of desalting that occurs during isoelectric trapping separations.

Simul 5, the simulation program based on the 1-D model of electrophoresis has been extended to simulate isoelectric trapping (IET) separations that take place in recirculating multicompartmental electrolyzers (MCEs). In the extended Simul 5, the simulated separation space between the anode and cathode can be divided into multiple segments to represent the anode compartment, separation compartment(s) and the cathode compartment. The compartments may have identical or different cross sections. A new algorithm simulates convective mixing that occurs in the recirculating MCEs where the distances between the buffering membranes are short and the velocities of tangential flows through the compartments, orthogonal to the electric field, are high. The intensity of simulated mixing can be independently controlled in each compartment. pH transients that were reported to occur during the desalting step in IET separations were simulated with the extended Simul 5 program: the main features of the experimental results were reproduced by the simulations. The simulations shed light on the possible causes of uneven anion and cation removal rates, pH transients and the transient invasion of the separation compartment by components of the electrode solutions that might occur during the desalting step.