Richard A. Mosher

Modeling of the Impact of Ionic Strength on the Electroosmotic Flow in Capillary Electrophoresis with Uniform and Discontinuous Buffer Systems

A new dynamic computer model permitting the combined simulation of the temporal behavior of electroosmosis and electrophoresis under constant voltage or current conditions and in a capillary which exhibits a pH-dependent surface charge has been constructed and applied to the description of capillary zone electrophoresis, isotachophoresis, and isoelectric focusing with electroosmotic zone displacement. Electroosmosis is calculated via use of a normalized wall titration curve (mobility vs pH). Two approaches employed for normalization of the experimentally determined wall titration data are discussed, one that considers the electroosmotic mobility to be inversely proportional to the square root of the ionic strength (method based on the Gouy-Chapman theory with the counterion layer thickness being equal to the Debye-Hückel length) and one that assumes the double-layer thickness to be the sum of a compact layer of fixed charges and the Debye-Hückel thickness and the existence of a wall adsorption equilibrium of the buffer cation other than the proton (method described by Salomon, K.; et al. J. Chromatogr. 1991, 559, 69). The first approach is shown to overestimate the magnitude of electroosmosis, whereas, with the more complex dependence between the electroosmotic mobility and ionic strength, qualitative agreement between experimental and simulation data is obtained. Using one set of electroosmosis input data, the new model is shown to provide detailed insight into the dynamics of electroosmosis in typical discontinuous buffer systems employed in capillary zone electrophoresis (in which the sample matrix provides the discontinuity), in capillary isotachophoresis, and in capillary isoelectric focusing.

Options in electrolyte systems for on-line combined capillary isotachophoresis and capillary zone electrophoresis

Abstract A theoretical description of the electrolyte systems that can be used in the on-line combination of isotachophoresis and zone electrophoresis is given. A classification of these systems is presented, based on the type of electrolyte used for the zone electrophoretic separation step. It is shown that transient sample stacking effects always persist from the isotachophoretic step to the beginning of the zone electrophoretic step and that they may negatively influence the zone electrophoretic separation and detection of the sample components. A mathematical description of these effects is given that allows the calculation of their magnitude and consequently the selection of operating conditions such that the stacking is decreased to an acceptable extent. In order to verify the reliability of the theoretical model, a modified PC simulation pack was prepared and used for investigating the behaviour of some model systems.

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

Abstract An abbreviated version of a mathematical model of the steady state in isoelectric focusing is presente. Details of the mathematical trasformations leading to a model suitable for computer implementation and numerical solution are given in the Appendix. The model describes the structure of concentration, pH, conductivity and potential gradients arising from the focusing of electrochemically defined ampholytes. Some of the results of computer simulations of two and three component systems are of particular interest to the experimentalist and are presented together with experimental validation of this model.

Experimental and theoretical dynamics of isoelectric focusing - Elucidation of a general separation mechanism

Abstract The transient states is isoelectric focusing were monitored using a potential gradient array detector. Electric field profiles are presented which show the formation of transient moving boundaries, as well as the approach of the steady state distribution, during the focusing of two and three component systems. The experimental results are completely consistent with corresponding computer simulation data. The focusing process is comprised of two sequential phases, a relatively rapid separation phase and a much slower stabilizing phase. A phenomenological separation mechanism is presented for the two and three component systems, based on distinct, transient moving boundaries, which describes the first phase. This mechanism is discussed with respect to n component diealized systems. The second phase provides insight into a primary cause of pH gradient instability. It was found that the time necessary for the adjustment to the steady state, the second phase, can be as much as twenty times longer than the time needed for the separation of the constituents.

High-resolution computer simulation of the dynamics of isoelectric focusing using carrier ampholytes: The post-separation stabilizing phase revisited

A dynamic electrophoresis simulator that accepts 150 components and voltage gradients employed in the laboratory was used to provide a detailed description of the stabilizing phase in isoelectric focusing under conditions that were hitherto inaccessible. High‐resolution focusing data are presented for pH gradients spanning 7 units (pH 3–10 and pH 4–11 with 20 carrier ampholytes/pH unit) and 3.5 units (pH 7–10.5 and pH 5–8.5 with 40 carrier ampholytes/pH unit). Stabilizing phase behavior for configurations (i) with the focusing column ends only permeable to OH– and H+ at cathode and anode, respectively, and (ii) with the focusing column being sandwiched between NaOH (catholyte) and phosphoric acid (anolyte) are described. Simulation data reveal the stabilizing phase to be diffusion‐controlled and characterized by changes that progress from the column ends towards neutrality (i.e., towards the center in case of pH gradients bracketing neutrality). Transient states are characterized by moving concentration valleys of carrier ampholytes that significantly alter the distributions of pH and conductivity. Nonlinear pH gradients are produced. The magnitude of the changes occuring is dependent on the span of the pH gradient. Gradients that encompass greater extremes of pH show more pronounced stabilizing phases. For all systems subjected to a constant 300 V/cm, the initial separation and subsequent stabilization require less than 10 min and more than 7000 min, respectively. The presence of electrolytes at the column ends disrupts the stabilizing phase, with the degree of disruption dependent on the concentrations of the acid and base employed as electrode solutions. The data not only indicate that a true steady state is never attained in the average laboratory experiment, they also suggest that a true steady state in absence of immobilized pH gradients cannot be achieved experimentally at all.

Computer simulation and experimental validation of the electrophoretic behavior of proteins. III: Use of titration data predicted by the protein's amino acid composition

Abstract To simulate the electrophoretic behavior of a protein, a diffusion coefficient and a tabular representation of net charge vs . pH (titration curve) are required. So far data taken from the literature have been employed, the tables being extracted from experimentally determined titration curves. The construction of data tables from the amino acid composition of proteins is reported and compared with those from the literature. The predicted data serve as a rough approximation only, because p K values are dependent on the local environment. Shifting the curve along the pH axis to match the experimentally determined p I is shown to yield simulation data which is in better agreement with experimental data. However, the predicted protein charge numbers are typically too large. Reduction by a pH-independent factor is shown to provide meaningful data for computer simulation. The utility of the titration data employed is documented with good agreement between simulation and experimental data obtained by capillary isotachophoresis.

Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

Software is available, which simulates all basic electrophoretic systems, including moving boundary electrophoresis, zone electrophoresis, ITP, IEF and EKC, and their combinations under almost exactly the same conditions used in the laboratory. These dynamic models are based upon equations derived from the transport concepts such as electromigration, diffusion, electroosmosis and imposed hydrodynamic buffer flow that are applied to user‐specified initial distributions of analytes and electrolytes. They are able to predict the evolution of electrolyte systems together with associated properties such as pH and conductivity profiles and are as such the most versatile tool to explore the fundamentals of electrokinetic separations and analyses. In addition to revealing the detailed mechanisms of fundamental phenomena that occur in electrophoretic separations, dynamic simulations are useful for educational purposes. This review includes a list of current high‐resolution simulators, information on how a simulation is performed, simulation examples for zone electrophoresis, ITP, IEF and EKC and a comprehensive discussion of the applications and achievements.

Capillary isoelectric focusing: effects of capillary geometry, voltage gradient and addition of linear polymer

Abstract Free-fluid focusing of both simple buffer and Ampholine systems in various capillaries of rectangular cross-sections was investigated by following the temporal behavior of the current under constant voltage and the transient double peak approach to equilibrium of colored test proteins. For systems comprising two and three buffer constituents the ratio of initial to final focusing current compares well with data obtained by computer simulation. Experiments have also been performed in the presence of linear, non-crosslinked polyacrylamide to assess its fluid stabilizing potential in capillaries. Good focusing and resolution are commensurate with a high initial to final current ratio, no substantial drifts after separation (attainment of steady state) and proper boundary conditions at both column ends. The production of turbulent protein foci at high-voltage gradients is discussed with the aid of electric field profiles monitored along the focusing column.

Dynamic computer simulations of electrophoresis: three decades of active research.

Dynamic models for electrophoresis are based upon model equations derived from the transport concepts in solution together with user‐inputted conditions. They are able to predict theoretically the movement of ions and are as such the most versatile tool to explore the fundamentals of electrokinetic separations. Since its inception three decades ago, the state of dynamic computer simulation software and its use has progressed significantly and Electrophoresis played a pivotal role in that endeavor as a large proportion of the fundamental and application papers were published in this periodical. Software is available that simulates all basic electrophoretic systems, including moving boundary electrophoresis, zone electrophoresis, ITP, IEF and EKC, and their combinations under almost exactly the same conditions used in the laboratory. This has been employed to show the detailed mechanisms of many of the fundamental phenomena that occur in electrophoretic separations. Dynamic electrophoretic simulations are relevant for separations on any scale and instrumental format, including free‐fluid preparative, gel, capillary and chip electrophoresis. This review includes a historical overview, a survey of current simulators, simulation examples and a discussion of the applications and achievements of dynamic simulation.

Experimental and theoretical dynamics of isoelectric focusing. II: Elucidation of the impact of the electrode assembly

Abstract The effects of several different electrode assemblies on the establishment of pH gradients in isoelectric focusing (IEF) in free fluids were investigated. The term “assembly” refers to the nature and relative volume of the electrolytes and the types of membranes used to isolate those electrolytes from the separation space. Experiments were performed in capillary systems. Dialysis membranes, ion-exchange membranes and thin palladium foils were employed with electrolytes consisting of strong acids and bases, or ampholytes, in varying concentrations and volumes. The progress of focusing was monitored by recording the temporal behavior of the current, at constant voltage, or the voltage gradient profile across the capillary at constant current. Mixtures of simple ampholytes, as well as commercial carrier ampholytes were investigated. Computer simulation data were used to aid the interpretation of some of the experimental results. It was found that the different assemblies do not have an impact on the separation mechanism, but do affect separation speed, resolution, and the stability of the pH gradient. Specifically, palladium electrodes and ion-exchange membranes provide the greatest gradient stability and eliminate any impact of electrode solution concentration and volume. If dialysis membranes are used, small electrode volumes and high buffer concentrations constitute the best focusing conditions. In contrast, large electrolyte volumes of low concentration destabilize the separative pattern continuously and rapidly by an isotachophoretic mechanism. This destabilization can take the form of a cathodic, anodic or symmetrical drift. The arrangements discussed illustrate the similarities and differences of IEF and isotachophoresis and are relevant to free fluid and gel IEF.