A new type of migrating zone boundary in electrophoresis: 2. Transient sample zone shapes

A new type of migrating zone boundary in electrophoresis is presented theoretically and evidenced experimentally. This type of the boundary (called hybrid boundary) shows simultaneously a steady-state part with self-sharpening properties and an unsteady-state part with time-dependent electromigration dispersion. It is shown that a sample zone may possess a hybrid boundary both as its front and rear one simultaneously. In such a case, the evolution of a sample zone injected originally as a rectangular pulse exhibits very complex transient shapes before it reaches the well-known fronting or tailing triangular shape. Depending on the stage at which detection of such a sample zone occurs, variable and peculiar-shape peaks may appear in the electropherogram. Based on theoretical predictions, experimental examples of the above-mentioned phenomena are presented in this contribution for direct and indirect UV absorbance detection of sample zones. Excellent agreement of theoretical predictions with the experiments has been found. The knowledge of hybrid boundaries is of key significance for correct interpretation of records of CE analyses in practice.     

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/ .     

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.     

基于电迁移的蛋白质制备技术和方法新进展

基于电迁移的蛋白质制备技术是对一类分离和制备技术的统称,其特征是在电场的作用下对目标物质进行分离和纯化制备,这种技术在生物大分子和蛋白质组的研究中应用广泛。基于电迁移的制备技术主要包括制备型电泳、制备型电色谱、制备型等电聚焦和自由流电泳等。本文对每种制备型电迁移装置的设计、特点和基于该种装置的各种应用方法的优缺点进行了详细阐述,并列举了一些实例。另外,微量级制备型电泳因分离度高、回收率高以及高效快速的优点,在微量级生物样本分析中发挥着日益重要的作用,近年来备受关注,本文也着重关注了这方面的进展,并对基于电迁移的制备技术做了展望。     

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.     

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.     

Protein and peptide mobility in capillary zone electrophoresis : A comparison of existing models and further analysis

Capillary zone electrophoresis of peptide fragments from the tryptic digest of human recombinant insulin-like growth factor I (rhIGF-I) has been carried out and the observed mobilities used to compare the relative applicability of existing mobility models. In addition, the physical forces affecting electromigration have been systematically analyzed in order to more accurately describe the physical chemistry involved. Such an approach should further improve the ability to predict electrophoretic mobility in capillary zone electrophoresis.     

Computer simulation of affinity capillary electrophoresis

A computer-simulated model of affinity capillary electrophoresis is developed. Unlike existing models, it is able to describe the situation where the concentrations of sample molecules and ligand molecules are commensurable, or even the situation where the zones occupied by these molecules are not mixed initially. The model permits to study the dependence of the spatial and temporal distributions of sample molecules on various parameters such as reaction rate constants, concentrations of sample and reagent, electromigration velocities of sample and reagent and sample injection volume. A collection of peak shapes for different values of parameters is presented. The dependence of peak variance on the ratio of the time of analysis to the characteristic time of reaction is studied.     

Comprehensive model of electromigrative transport in microfluidic paper based analytical devices

A complete mathematical model for electromigration in paper-based analytical devices is derived, based on differential equations describing the motion of fluids by pressure sources and EOF, the transport of charged chemical species, and the electric potential distribution. The porous medium created by the cellulose fibers is considered like a network of tortuous capillaries and represented by macroscopic parameters following an effective medium approach. The equations are obtained starting from their open-channel counterparts, applying scaling laws and, where necessary, including additional terms. With this approach, effective parameters are derived, describing diffusion, mobility, and conductivity for porous media. While the foundations of these phenomena can be found in previous reports, here, all the contributions are analyzed systematically and provided in a comprehensive way. Moreover, a novel electrophoretically driven dispersive transport mechanism in porous materials is proposed. Results of the numerical implementation of the mathematical model are compared with experimental data, showing good agreement and supporting the validity of the proposed model. Finally, the model succeeds in simulating a challenging case of free-flow electrophoresis in paper, involving capillary flow and electrophoretic transport developed in a 2D geometry.     

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.     

Peak shape modeling by Haarhoff-Van der Linde function for the determination of correct migration times: a new insight into affinity capillary electrophoresis

Among the different experimental strategies available in capillary electrophoresis (CE) to determine binding parameters, affinity capillary electrophoresis (ACE) has been the most widely embraced due to its easiness of implementation and of data handling. Ligand-substrate binding constants are thus directly derived from the substrate migration time shifts resulting from the variation of ligand concentration introduced in a background electrolyte. Classically, the substrate migration time is measured on top of the electrophoretic peak, assuming symmetrical peak shape. Depending on both substrate and ligand concentrations that may be required to meet detection sensitivity or complexation conditions, zonal migrations in ACE may, however, produce triangular peak shape, most often due to pronounced electromigration dispersion (EMD), and this may result in positively or negatively erroneous migration time assessments. In this work, EMD distorted triangular peak shapes obtained in the course of host-guest complexation studies were fitted with the Haarhoff-Van der Linde function, allowing better estimation of migration time. The model systems studied were those of beta-cyclodextrin and naproxen, 2-naphthalenesulfonate, or 1-adamantanecarboxylate. The impact of this correction on binding isotherms and binding constant evaluation was exemplified. Furthermore, in situations where the substrate concentration injected by far overtakes that of the ligand in the electrolyte, the interest in this peak shape correction was discussed in connection with the question of whether the free ligand concentration can be still considered equal to the ligand concentration introduced, a question that still remains under debate nowadays.     

毛细管电泳样品电堆积富集过程的数值研究

毛细管电泳样品电堆积富集过程可以浓缩样品组分,从而提高检测灵敏度,是一种有效的样品富集技术。本文通过合理的简化和假设,把毛细管中电堆积富集过程中所涉及的主要变量根据电势分布方程、缓冲溶液的浓度方程和样品粒子的质量传输方程进行耦合求解,建立了一个一维的数学模型,并应用有限元的方法对该模型进行了求解。计算结果给出了毛细管中缓冲溶液浓度及电场强度的分布随时间变化的过程,以及富集过程中毛细管中的电势分布曲线;得到了样品粒子浓度在电堆积富集过程和富集之后的再次扩散过程中的分布曲线以及正、负样品粒子的分离过程;最后分析了不同缓冲溶液浓度比对样品富集效果的影响。该研究为样品电堆积富集技术的进一步完善提供了一种简单可行的理论研究方法。     

Dispersive phenomena in electromigration separation methods

A review on dispersive effects and on peak broadening in electromigration separation methods (capillary electrophoresis and electrochromatography) is presented, mainly covering papers published between the beginning of 1997 and the beginning of 2000. Most attention is drawn to work dealing with nonlinear effects that cause anomalous electromigration dispersion in electrolyte systems with two or multiple coions. Further, topics cover the comparison of electroosmotic and pressure-driven modes in electrochromatography, dispersive effects due to nonhomogeneous velocity fields in packed electrochromatography columns, to nonuniform electroosmotic flow, to sorption of analytes (mainly proteins) at the column wall or the stationary phase, and due to the influence of the nonideal column geometry like coiling or irregularities in shape.     

Determination of impurities and counterions of pharmaceuticals by capillary electromigration methods

The review presents a survey of recent applications of high‐performance capillary electromigration methods—capillary zone electrophoresis, nonaqueous capillary electrophoresis, capillary isotachophoresis, micellar electrokinetic chromatography, microemulsion electrokinetic chromatography and capillary electrochromatography—for the determination of impurities of pharmaceuticals, including chiral impurities, for the period 2007–2013. In addition, due to the missing evaluation of the determination of counterions of pharmaceuticals by capillary electromigration methods in the last 20 years, the publications dealing with this topic since 1995 are included in this review. General aspects of both these types of applications of capillary electromigration methods in pharmaceutical analysis are discussed, and detailed experimental conditions used for determination of various chemical impurities and counterions of many particular drugs are described.     

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.     

Prediction and understanding system peaks in capillary zone electrophoresis

Introduction of a sample into the separation column (microchip channel) in capillary zone electrophoresis (microchip electrophoresis) will cause a disturbance in the originally uniform composition of the background electrolyte. The disturbance, a system zone, can move in some electrolyte systems along the separation channel and, on reaching the position of the detector, cause a system peak. As shown by the linear theory of electromigration based on linearized continuity equations formulated in matrix form, the mobility of the system zone--the system eigenmobility--can be obtained as the eigenvalue of the matrix. Progress in the theory of electromigration allows us to predict the existence and mobilities of the system zones, even in very complex electrolyte systems consisting of several multivalent weak electrolytes, or in micellar systems (systems with SDS micelles) used for protein sizing in microchips. The theory is implemented in PeakMaster software, which is available as freeware (www.natur.cuni.cz/gas). The linearized theory also predicts background electrolytes having no stationary injection zone (water zone, water gap, water dip, EO zone) or unstable electrolyte systems exhibiting oscillations and creating periodic structures. The oscillating systems have complex system eigenmobilities (eigenvalues of the matrix are complex). This paper reviews the theoretical background of the system peaks (system eigenpeaks) and gives practical hints for their prediction and for preparing background electrolytes not perturbed by the occurrence of system peaks and by excessive peak broadening.     

Optimization of protein separation by continuous-flow electrophoresis: influence of the operating conditions and the chamber thickness.

The separation of protein by continuous-flow electrophoresis is disturbed by a number of effects which cause spreading of the protein streams with a loss of resolution. Two numerical models have been used to describe the coupling between the various spreading phenomena. A simple model takes into account molecular diffusion, electroosmosis and residence time gradients; the main model differs from the simple one by taking account of electrohydrodynamics. The influence of the separation chamber thickness, the radius of the sample filament, the field strength, and the residence time is explored. The simulations show that each dispersive effect has its own range of predominance, so that an optimum is found for the thickness of the separation chamber.