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.     

Simulation of the effects of complex- formation equilibria in electrophoresis: I. mathematical model

Simul 5 Complex is a one-dimensional dynamic simulation software designed for electrophoresis, and it is based on a numerical solution of the governing equations, which include electromigration, diffusion and acid-base equilibria. A new mathematical model has been derived and implemented that extends the simulation capabilities of the program by complexation equilibria. The simulation can be set up with any number of constituents (analytes), which are complexed by one complex-forming agent (ligand). The complexation stoichiometry is 1:1, which is typical for systems containing cyclodextrins as the ligand. Both the analytes and the ligand can have multiple dissociation states. Simul 5 Complex with the complexation mode runs under Windows and can be freely downloaded from our web page http://natur.cuni.cz/gas. The article has two separate parts. Here, the mathematical model is derived and tested by simulating the published results obtained by several methods used for the determination of complexation equilibrium constants: affinity capillary electrophoresis, vacancy affinity capillary electrophoresis, Hummel-Dreyer method, vacancy peak method, frontal analysis, and frontal analysis continuous capillary electrophoresis. In the second part of the paper, the agreement of the simulated and the experimental data is shown and discussed.     

Conductivity detection in capillary zone electrophoresis: inspection by PeakMaster

A simple rule stating that the signal in conductivity detection in capillary zone electrophoresis is proportional to the difference between the analyte mobility and mobility of the background electrolyte (BGE) co-ion is valid only for systems with fully ionized electrolytes. In zone electrophoresis systems with weak electrolytes both conductivity signal and electromigration dispersion of analyte peaks depend on the conductivity and pH effects. This allows optimization of the composition of BGEs to give a good conductivity signal of analytes while still keeping electromigration dispersion near zero, regardless of the injected amount of sample. The demands to achieve minimum electromigration dispersion and high sensitivity in conductivity detection can be accomplished at the same time. PeakMaster software is used for inspection of BGEs commonly used for separation of sugars (carbohydrates, saccharides) at highly alkaline pH. It is shown that the terms direct and indirect conductivity detection are misleading and should not be used.     

Electromigration peak dispersion of isotachophoretic protein zones during capillary zone electrophoresis

The relationships between electromigration dispersion (EMD) and on-line isotachophoresis-capillary zone electrophoresis (ITP-CZE) are described for several basic model proteins and interleukin-6 (rhIL-6). During CZE separation of the highly concentrated analyte zones which were generated during the initial ITP step EMD evolves from intrinsic differences in conductivity between the focused ITP zones and the leading electrolyte. Nearly triangular peaks with a sharp front and diffuse rear side were observed. An electromigration dispersion factor (F_EMD) was introduced to measure peak asymmetry. EMD of individual peaks was shown to increase with the absolute amount of the respective analyte injected and with analyte mobility. Good linearity was observed when F_EMD was plotted against protein mobility (r > 0.95). The slope of the graphs describing this relationship increased with the amount of analyte injected. The influence of EMD on the separation efficiency of neighboring peaks appeared to be less pronounced than expected. Consecutive release from the ITP-stack during transition from ITP to CZE might be an explanation for this observation.     

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.     

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/ .     

Optimization of background electrolytes for capillary electrophoresis I. Mathematical and computational model

A mathematical and computational model is introduced for optimization of background electrolyte systems for capillary zone electrophoresis of anions. The model takes into account mono- or di- or trivalent ions and allows also for modeling of highly acidic or alkaline electrolytes, where a presence of hydrogen and hydroxide ions is significant. At maximum, the electrolyte can contain two co-anions and two counter-cations. The mathematical relations of the model are formulated to enable an easy algorithmization and programming in a computer language. The model assesses the composition of the background electrolyte in the analyte zone, which enables prediction of the parameters of the system that are experimentally available, like the transfer ratio, which is a measure of the sensitivity in the indirect photometric detection or the molar conductivity detection response, which expresses the sensitivity of the conductivity detection. Furthermore, the model also enables the evaluation of a tendency of the analyte to undergo electromigration dispersion and allows the optimization of the composition of the background electrolyte to reach a good sensitivity of detection while still having the dispersion properties in the acceptable range. Although the model presented is aimed towards the separation of anions, it can be straightforwardly rearranged to serve for simulation of electromigration of cationic analytes. The suitability of the model is checked by inspecting the behavior of a phosphate buffer for analysis of anions. It is shown that parameters of the phosphate buffer when used at neutral and alkaline pH values possess singularities that indicate a possible occurrence of system peaks. Moreover, if the mobility of any analyte of the sample is close to the mobilities of the system peaks, the indirect detector signals following the background electrolyte properties will be heavily amplified and distorted. When a specific detector sensitive on presence of the analyte were used, the signal would be almost lost due to the excessive dispersion of the peak.     

Peak dispersion and contributions to plate height in nonaqueous capillary electrophoresis at high electric field strengths: propanol as background electrolyte solvent

Peak dispersion effects in nonaqueous capillary electrophoretic separations of aromatic anionic analytes were investigated in a propanolic background electrolyte solution. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone) coating was applied to the capillary to suppress the electroosmotic flow and to improve the repeatability of the migration times. Electrical field strengths up to 2000 Vcm(-1) were applied in separations and the separation efficiencies were compared with theoretical values calculated on the basis of plate height theory. The contributions to the total plate height were calculated for injection plug length, diffusion, Joule heating, electromigration dispersion, analyte adsorption to the capillary wall, and detector slit aperture length. Analyte diffusion coefficients were measured by Taylor dispersion method, while distribution constants were measured chromatographically. Agreement between the calculated and empirical results was fairly good even though some approximations were required. In most cases the longitudinal diffusion contribution governed the total plate height, while the contribution of Joule heating was insignificant even at exceptionally high field strengths used. The relatively long detection slit aperture was found to influence the separation efficiency strongly, while the other dispersion sources that were investigated were of minor importance, except for adsorption in the case of one analyte. With all analytes, the dispersive effect of longitudinal diffusion was reduced as the field strength was increased, leading to enhanced migration velocities and faster separations.     

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.     

Methods for determination of all binding parameters in systems with simultaneous borate and cyclodextrin complexation

Two novel methods for determination of binding constants in the systems with borate and cyclodextrin complexation were developed. The methods enable to determine all binding parameters in these systems and even the binding constants of interaction of a neutral analyte with a neutral cyclodextrin. The first method is based on nonlinear fitting of experimental data and further evaluation of fitting parameters. The second method requires a multiple regression. The methods provide identical results with low experimental error. Only one set of measurements is required for both methods. Thus the binding parameters can be mutually compared. The binding parameters for neutral analytes ((R,R)-(+)-hydrobenzoin and (S,S)-(-)-hydrobenzoin) and neutral cyclodextrin (heptakis(2,6-di-O-methyl)-β-cyclodextrin) were evaluated and the effect of individual types of interaction was revealed. The interaction of the analytes with cyclodextrin governs the chiral recognition, while the complexation of analyte with borate is responsible for electromigration. Very low values of the binding constants of mixed analyte-cyclodextrin-borate complexes indicate that this type of complexation has negligible effect on enantioseparation.     

Effect of urea on analyte complexation by 2,6‐dimethyl‐β‐CD in peptide enantioseparations by CE

The aim of the present study was the investigation of the effect of urea on analyte complexation in CD‐mediated separations of peptide enantiomers by CE in the pH range of about 2–5. pH‐independent complexation and mobility parameters in the absence and presence of 2 M urea were obtained by three‐dimensional, non‐linear curve fitting of the effective analyte mobility as a function of pH and heptakis‐(2,6‐di‐O‐methyl)‐β‐CD concentration. Urea led to decreased binding strength of the CD towards the protonated and neutral analyte enantiomers as well as to decreased mobilities of the free analytes. In contrast, mobilities of the fully protonated enantiomer–CD complexes as well as the pK_a values of the free and complexed analytes increased. The effect of urea on separation efficiency varied with pH and CD concentration. In the case of Ala‐Tyr and Ala‐Phe, separations improved in the presence of urea at pH 2.2. In contrast, separations were impaired by urea at pH 3.8 and low concentrations of the CD. Decreased separation efficiency was noted for Asp‐PheOMe and Glu‐PheNH₂ at low CD concentrations when urea was added but separations improved at higher CD concentrations over the entire pH range studied. The effect of urea on analyte complexation appeared to be primarily non‐stereoselective. Furthermore, the pH‐dependent reversal of the enantiomer migration order observed for Ala‐Tyr and Ala‐Phe can be rationalized by the complexation and mobility parameters.     

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6—Next Generation

The linear theory of electromigration, including the first‐order nonlinear approximation, is generalized to systems with any equilibria fast enough to be considered instantaneous in comparison with the timescale of peak movement. For example, this theory is practically applied in the electrokinetic chromatography (EKC) mode of the CZE. The model enables the calculation of positions and shapes of analyte and system peaks without restricting the number of selectors, the complexation stoichiometry, or simultaneous acid–base equilibria. The latest version of our PeakMaster software, PeakMaster 6—Next Generation, implements the theory in a user‐friendly way. It is a free and open‐source software that performs all calculations and shows the properties of the background electrolyte and the expected electropherogram within a few seconds. In this paper, we mathematically derive the model, discuss its applicability to EKC systems, and introduce the PeakMaster 6 software.     

Analyte and system eigenpeaks in nonaqueous capillary zone electrophoresis: theoretical description and experimental confirmation with methanol as solvent

A mathematical model developed for aqueous solutions and adapted to methanol as solvent was applied to predict the electromigration characteristics of analytes and background electrolytes in capillary zone electrophoresis. These characteristics are the effective mobility, and the tendency of the analyte to undergo peak-broadening due to electromigration dispersion. The input parameters for calculation like limiting mobilities and dissociation constants were experimentally determined or taken from the literature. By the aid of the model, the molar response for conductivity detection was calculated as well as the transfer ratio when indirect UV detection was used. They allow depicting the electropherogram by computer simulation. An additional important program output is the prediction of the occurrence of system- or eigenpeaks that mimic peaks of analytes or electroosmotic flow markers. The measured electropherograms were in agreement with those theoretically predicted. Deviations were attributed to ion pairing in methanolic solutions, which was not implemented in the model.     

Peak dispersion and contributions to plate height in nonaqueous capillary electrophoresis at high electric field strengths: ethanol as background electrolyte solvent

Nonaqueous capillary electrophoretic separations were performed under high electric field strengths (up to 2000 Vcm(-1)) in ethanolic background electrolyte solution and the contributions of different band broadening effects to plate height were evaluated. Under optimum conditions, increasing the field strength will provide faster separations and increased separation efficiency. Decrease in the separation efficiency at high field strengths was, however, observed in a previous study and now in the present paper an attempt is made to quantify various band broadening effects by applying a plate height model, which included the contributions of the injection plug length, diffusion, electromigration dispersion, Joule heating, analyte adsorption to the capillary wall, and detector slit aperture length. Of special interest were the contributions of Joule heating and analyte adsorption to the capillary wall. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone)-coated fused-silica capillaries were used with internal diameters (ID) ranging from 30 to 75 microm. The separation efficiencies obtained experimentally were compared with the theoretically calculated efficiencies and fairly good agreement was observed for the 30 microm ID capillary. Relatively large deviation from the predictions of the model was found for the other capillary diameters especially at higher field strengths. The possible reasons for the deviation were discussed.     

Effects of partial/asymmetrical filling of micelles and chiral selectors on capillary electrophoresis enantiomeric separation: generation of a gradient

The effect of several experimental parameters on enantiomeric separations in micellar capillary electrophoresis (MCE) was studied. A model separation system was tested. It was composed of an acidic phosphate buffer with sodium dodecyl sulfate (SDS) and hydroxypropyl-beta-cyclodextrin (HP-beta-CD) as the chiral selector. A substituted angelicin was used as a chiral analyte. Changes in the concentration of SDS micelles/SDS monomers in the presence of HP-beta-CD and their impact on the enantioselective separation were investigated. Variation of the composition of electrolytes in the individual compartments of the separation system (inlet vial, capillary, and outlet vial) affected both the migration times and the resolution of the enantiomers. Current vs. time dependencies also were monitored during the separations. A mathematical model of electromigration in micellar systems with chiral selector present was proposed and a computer simulation was used to explain the observed phenomena and to confirm the generation of a CD/SDS-micelle concentration gradient under certain experimental conditions. This is the reported first attempt of a computer simulation of the complex, dynamic chiral environment of the CD-SDS-MCE system.     

Peak shapes in open tubular ion-exchange capillary electrochromatography of inorganic anions

An experimental study of parameters influencing peak shapes in ion-exchange open tubular (OT) capillary electrochromatography (CEC) was conducted using adsorbed quaternary aminated latex particles as the stationary phase. The combination of separation mechanisms from both capillary electrophoresis and ion-exchange chromatography results in peak broadening in OT-CEC arising from both these techniques. The sources of peak broadening that were considered included the relative electrophoretic mobilities of the eluent co-ion and analyte, and resistance to mass transfer in both the mobile and stationary phases. The parameters investigated were the mobility of the eluent co-ion, column diameter, separation temperature and secondary interactions between the analyte and the stationary phase. The electromigration dispersion was found to influence peak shapes to a minor extent, indicating that chromatographic retention was the dominant source of dispersion. Improving the resistance to mass transfer in the mobile phase by decreasing the capillary diameter improved peak shapes, with symmetrical peaks being obtained in a 25 microm I.D. column. However, an increase in temperature from 25 degrees C to 55 degrees C failed to show any significant improvement. The addition of p-cyanophenol to the mobile phase to suppress secondary interactions with the stationary phase did not result in the expected improvement in efficiency.