Dynamic high-resolution computer simulation of electrophoretic enantiomer separations with neutral cyclodextrins as chiral selectors

Isotachophoresis: Theory and Microfluidic Applications

Isotachophoresis (ITP) is a versatile electrophoretic technique that can be used for sample preconcentration, separation, purification, and mixing, and to control and accelerate chemical reactions. Although the basic technique is nearly a century old and widely used, there is a persistent need for an easily approachable, succinct, and rigorous review of ITP theory and analysis. This is important because the interest and adoption of the technique has grown over the last two decades, especially with its implementation in microfluidics and integration with on-chip chemical and biochemical assays. We here provide a review of ITP theory starting from physicochemical first-principles, including conservation of species, conservation of current, approximation of charge neutrality, pH equilibrium of weak electrolytes, and so-called regulating functions that govern transport dynamics, with a strong emphasis on steady and unsteady transport. We combine these generally applicable (to all types of ITP) theoretical discussions with applications of ITP in the field of microfluidic systems, particularly on-chip biochemical analyses. Our discussion includes principles that govern the ITP focusing of weak and strong electrolytes; ITP dynamics in peak and plateau modes; a review of simulation tools, experimental tools, and detection methods; applications of ITP for on-chip separations and trace analyte manipulation; and design considerations and challenges for microfluidic ITP systems. We conclude with remarks on possible future research directions. The intent of this review is to help make ITP analysis and design principles more accessible to the scientific and engineering communities and to provide a rigorous basis for the increased adoption of ITP in microfluidics.

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.

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/.

Computer simulation of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers with a free or immobilized neutral chiral selector

A detailed computer simulation study of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers for cases with the neutral selector added to the leader, immobilized to the capillary wall or support, or partially present in the separation column is presented. The electrophoretic transport of the analytes from the sampling compartment into the separation medium with the selector, the formation of a transient mixed zone, the separation dynamics of the stereoisomers with a free or immobilized selector, the dependence of the leader pH, the ionic mobility of norpseudoephedrine, the complexation constant and selector immobilization on steady-state plateau zone properties, and zone changes occurring during the transition from the chiral environment into a selector free leader are thereby visualized in a hitherto unexplored way. For the case with the selector dissolved in the leading electrolyte, simulation data are compared to those observed in experimental setups with coated fused-silica capillaries that feature minimized electroosmosis and zone detection with conductivity and absorbance detectors.

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.

Some thoughts about enantioseparations in capillary electrophoresis

In this overview the goal of the authors was to analyze from the historical perspective the reasons of success and failure of chiral capillary electrophoresis. In addition, the current trends are analyzed, unique advantages of capillary electrophoresis are highlighted and some future directions are discussed.

Inverse cationic ITP for separation of methadone enantiomers with sulfated β-cyclodextrin as chiral selector

Chiral ITP of the weak base methadone using inverse cationic configurations with H⁺ as leading component and multiple isomer sulfated β-CD (S-β-CD) as leading electrolyte (LE) additive, has been studied utilizing dynamic computer simulation, a calculation model based on steady-state values of the ITP zones, and capillary ITP. By varying the amount of acidic S-β-CD in the LE composed of 3-morpholino-2-hydroxypropanesulfonic acid and the chiral selector, and employing glycylglycine as terminating electrolyte (TE), inverse cationic ITP provides systems in which either both enantiomers, only the enantiomer with weaker complexation, or none of the two enantiomers form cationic ITP zones. For the configuration studied, the data reveal that only S-methadone migrates isotachophoretically when the S-β-CD concentration in the LE is between about 0.484 and 1.113 mM. Under these conditions, R-methadone migrates zone electrophoretically in the TE. An S-β-CD concentration between about 0.070 and 0.484 mM results in both S- and R-methadone forming ITP zones. With >1.113 mM and < about 0.050 mM of S-β-CD in the LE both enantiomers are migrating within the TE and LE, respectively. Chiral inverse cationic ITP with acidic S-β-CD in the LE is demonstrated to permit selective ITP trapping and concentration of the less interacting enantiomer of a weak base.

Contemporary theory of enantioseparations in capillary electrophoresis

The first separation of enantiomers in capillary electrophoresis (CE) counts slightly longer than three decades. Fast development of the practice and theory of chiral CE occurred in the past 30 years and today one can consider this technology to have a solid and mature theoretical background. The goal of the present review is not only to summarize the history and contemporary theory of enantioseparations by using CE but also to present the authors personal view where shall we head to with this attractive technology not only from the viewpoint of separation of enantiomers but also for better understanding the mechanisms of non-covalent (enantioselective) interactions in chemistry, biology, medicine and related disciplines.

High-resolution dynamic computer simulation of electrophoresis using a multiphysics software platform

The modeling and simulation software COMSOL Multiphysics^® was recently extended with an electrophoretic transport interface. Its performance was investigated by comparison to results obtained using the 1D dynamic electrophoresis simulators GENTRANS and SIMUL5. Simulations of zone electrophoresis, isotachophoresis, isoelectric focusing and of an oscillating electrolyte system were performed. Smooth profiles were essentially identical indicating that the COMSOL electrophoretic transport interface is able to reproduce results of the 1D simulators. Differences in the way the respective numerical schemes handle steep concentration gradients and associated instabilities were observed. The COMSOL electrophoretic transport interface is expected to be useful as a general model for simulations in 1D, 2D or 3D geometries, as well as for simulations combining electrophoresis with other physical phenomena.

Computer simulation and enantioselective capillary electrophoresis to characterize isomer mixtures of sulfated β-cyclodextrins

The enantiomeric separation of methadone in the presence of multiple isomer mixtures of sulfated β-cyclodextrin (S-β-CD) was studied experimentally with CZE and theoretically using computer simulation. Experiments were performed over many years with several lots of S-β-CD from the same manufacturer with a specified degree of substitution of 7-11. Large differences in the migration patterns were observed between certain lots and it was concluded that the extent of labelling in lots released after a transition time was higher than originally specified. The migration pattern was observed to be associated with (i) the ionic strength increase resulting from using S-β-CDs with a higher charge state and (ii) differences in buffer composition. Apparent binding constants between methadone and the S-β-CD and complex mobilities were determined for different lots of S-β-CD at varying ionic strength using phosphate and 3-morpholino-2-hydroxypropanesulfonic acid buffers. The obtained values were used as input for simulations. For a given ionic strength, agreement between predicted and experimentally observed behavior was obtained for different buffers. R-methadone has a stronger interaction with S-β-CD than S-methadone. For any given configuration there is a distinct S-β-CD concentration range which results in the cationic migration of S-methadone while the migration direction of R-methadone is reversed. This configuration was demonstrated to be applicable for micropreparative CZE separations.

Insights into head-column field-amplified sample stacking: Part II. Study of the behavior of the electrophoretic system after electrokinetic injection of cationic compounds across a short water plug

Part I on head-column field-amplified sample stacking comprised a detailed study of the electrokinetic injection of a weak base across a short water plug into a phosphate buffer at low pH. The water plug is converted into a low conductive acidic zone and cationic analytes become stacked at the interface between this and a newly formed phosphoric acid zone. The fundamentals of electrokinetic processes occurring thereafter were studied experimentally and with computer simulation and are presented as part II. The configuration analyzed represents a discontinuous buffer system. Computer simulation revealed that the phosphoric acid zone at the plug-buffer interface becomes converted into a migrating phosphate buffer plug which corresponds to the cationically migrating system zone of the phosphate buffer system. Its mobility is higher than that of the analytes such that they migrate behind the system zone in a phosphate buffer comparable to the applied background electrolyte. The temporal behaviour of the current and the conductivity across the water plug were monitored and found to reflect the changes in the low conductivity plug. Determination of the buffer flow in the capillary revealed increased pumping caused by the mismatch of electroosmosis within the low conductivity plug and the buffer. This effect becomes elevated with increasing water plug length. For plug lengths up to 1% of the total column length the flow quickly drops to the electroosmotic flow of the buffer and simulations with experimentally determined current and flow values predict negligible band dispersion and no loss of resolution for both low and large molecular mass components.

Insights into head-column field-amplified sample stacking: Part I. Detailed study of electrokinetic injection of a weak base across a short water plug

The fundamentals of electrokinetic injection of the weak base methadone across a short water plug into a phosphate buffer at low pH were studied experimentally and with computer simulation. The current during electrokinetic injection, the formation of the analyte zone, changes occurring within and around the water plug and mass transport of all compounds in the electric field were investigated. The impact of water plug length, plug injection velocity, and composition of sample, plug and background electrolyte are discussed. Experimental data revealed that properties of sample, water plug and stacking boundary are significantly and rapidly altered during electrokinetic injection. Simulation provided insight into these changes, including the nature of the migrating boundaries and the stacking of methadone at the interface to a newly formed phosphoric acid zone. The data confirm the role of the water plug to prevent contamination of the sample by components of the background electrolyte and suggest that mixing caused by electrohydrodynamic instabilities increases the water plug conductivity. The sample conductivity must be controlled by addition of an acid to prevent generation of reversed flow which removes the water plug and to create a buffering environment. Results revealed that a large increase in background electrolyte concentration is not accompanied with a significant increase in stacking.

Validation of CE modeling with a contactless conductivity array detector

Dynamic computer simulation data are compared for the first time with CE data obtained with a laboratory made system comprising an array of 8 contactless conductivity detectors (C(4) Ds). The experimental setup featured a 50 μm id linear polyacrylamide (LPA) coated fused-silica capillary of 70 cm length and a purpose built sequential injection analysis manifold for fluid handling of continuous or discontinuous buffer configurations and sample injection. The LPA coated capillary exhibits a low EOF and the manifold allows the placement of the first detector at about 2.7 cm from the sample inlet. Agreement of simulated electropherograms with experimental data was obtained for the migration and separation of cationic and anionic analyte and system zones in CZE configurations in which EOF and other column properties are constant. For configurations with discontinuous buffer systems, including ITP, experimental data obtained with the array detector revealed that the EOF is not constant. Comparison of simulation and experimental data of ITP systems provided the insight that the EOF can be estimated with an ionic strength dependent model similar to that previously used to describe EOF in fused-silica capillaries dynamically double coated with Polybrene and poly(vinylsulfonate). For the LPA coated capillaries, the electroosmotic mobility was determined to be 17-fold smaller compared to the case with the charged double coating. Simulation and array detection provide means for quickly investigating electrophoretic transport and separation properties. Without realistic input parameters, modeling alone is not providing data that match CE results.

Impact of Taylor-Aris diffusivity on analyte and system zone dispersion in CZE assessed by computer simulation and experimental validation

Application of pressure-driven laminar flow has an impact on zone and boundary dispersion in open tubular CE. The GENTRANS dynamic simulator for electrophoresis was extended with Taylor-Aris diffusivity which accounts for dispersion due to the parabolic flow profile associated with pressure-driven flow. Effective diffusivity of analyte and system zones as functions of the capillary diameter and the amount of flow in comparison to molecular diffusion alone were studied for configurations with concomitant action of imposed hydrodynamic flow and electroosmosis. For selected examples under realistic experimental conditions, simulation data are compared with those monitored experimentally using modular CE setups featuring both capacitively coupled contactless conductivity and UV absorbance detection along a 50 μm id fused-silica capillary of 90 cm total length. The data presented indicate that inclusion of flow profile based Taylor-Aris diffusivity provides realistic simulation data for analyte and system peaks, particularly those monitored in CE with conductivity detection.

Computer simulation of electrophoretic aspects of enantiomer migration and separation in capillary electrochromatography with a neutral selector

A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.

Complexation of buffer constituents with neutral complexation agents: part II. Practical impact in capillary zone electrophoresis

This article elucidates the practical impact of the complexation of buffer constituents with complexation agents on electrophoretic results, namely, complexation constant determination, system peak development, and proper separation of analytes. Several common buffers, which were selected based on the pH study in Part I of this paper series (Riesová, M.; Svobodová, J.; Tošner, Z.; Beneš, M.; Tesařová, E.; Gaš, B. Anal. Chem., 2013, DOI: 10.1021/ac4013804); e.g., CHES, MES, MOPS, Tricine were used to demonstrate behavior of such complex separation systems. We show that the value of a complexation constant determined in the interacting buffers environment depends not only on the analyte and complexation agent but it is also substantially affected by the type and concentration of buffer constituents. As a result, the complexation parameters determined in the interacting buffers cannot be regarded as thermodynamic ones and may provide misleading information about the strength of complexation of the compound of interest. We also demonstrate that the development of system peaks in interacting buffer systems significantly differs from the behavior known for noncomplexing systems, as the mobility of system peaks depends on the concentration and type of neutral complexation agent. Finally, we show that the use of interacting buffers can totally ruin the results of electrophoretic separation because the buffer properties change as the consequence of the buffer constituents' complexation. As a general conclusion, the interaction of buffer constituents with the complexation agent should always be considered in any method development procedures.

Simulation of the effects of complex- formation equilibria in electrophoresis: II. experimental verification

The complete mathematical model of electromigration in systems with complexation agents introduced in the Part I of this article (V. Hruška et al., Eletrophoresis, 2012, 33, this issue), which was implemented into our simulation program Simul 5, was verified experimentally. Three different chiral selector (CS) systems differing in the type of the CS, the magnitude of the complexation constants as well as in the experimental conditions were selected for verification. The experiments and simulations were performed at various concentrations of the CSs in order to discuss the influence of the concentration of the CS on the separation. The simulated and experimental electropherograms show very good agreement in the position, shape and amplitude of the analyte peaks. The new Simul 5 Complex offers a deep insight into electrophoretical separations that take place in systems containing complexing agents, for example into enantiomer separations. Using Simul 5 Complex we were able to predict and explain the significant electromigration dispersion of analyte peaks. It was clarified that the electromigration dispersion in these systems results directly from complexation. The new Simul 5 Complex was also shown to be a useful and powerful tool for the prediction of the results of enantioseparations.