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.

A mathematical model of the electrophoretic behavior of proteins is presented. The Debye-Hückel-Henry theory is used for the description of protein mobility, which has the important result of making net mobility a function of ionic strength. A net charge vs pH relationship and a diffusion coefficient are required to describe a specific protein. The model is employed for the computer simulation of three distinct electrophoretic modes: isoelectric focusing, isotachophoresis, and zone electrophoresis. The validity of the model is tested by comparing simulation with experimental data. Excellent qualitative agreement was found.

A dynamic electrophoresis simulator that accepts 150 components and voltage gradients employed in the laboratory was used to provide a detailed description of the focusing process of proteins under conditions that were hitherto inaccessible. High-resolution focusing data of four hemoglobin variants in a convection-free medium are presented for pH 3-10 and pH 5-8 gradients formed with 20 and 40 carrier ampholytes/pH unit, respectively. With 300 V/cm, focusing is shown to occur within 5-10 min, whereas at 600 V/cm separation is predicted to be complete between 2.5 and 5 min. The time interval required for focusing of proteins is demonstrated to be dependent on the input protein charge data and, however less, on the properties of the carrier ampholytes. The simulation data reveal that the number of transient protein boundaries migrating from the two ends of the column towards the focusing positions is equal to the number of sample components. Each protein is being focused via the well-known double-peak approach to equilibrium, a process that is also characteristic for focusing of the carrier ampholytes. The predicted focusing dynamics for the hemoglobin variants in pH 3-10 and pH 5-8 gradients are shown to qualitatively agree well with experimental data obtained by whole-column optical imaging.

The production of anodic, cathodic and symmetrical drifts of a pH 3.5-10 gradient formed by isoelectric focusing in polyacrylamide gels is demonstrated experimentally by manipulation of the electrolyte concentrations. Experimental behavior is reproduced by computer simulation of a model mixture of 15 hypothetical carrier ampholytes whose pIs span the pH range 3-10. The mechanism which produces the drifts is elucidated and approaches to minimize such drifts are discussed. The data suggest why most experimentally observed drifts are cathodic.

Focusing of four hemoglobins with concurrent electrophoretic mobilization was studied by computer simulation. A dynamic electrophoresis simulator was first used to provide a detailed description of focusing in a 100-carrier component, pH 6-8 gradient using phosphoric acid as anolyte and NaOH as catholyte. These results are compared to an identical simulation except that the catholyte contained both NaOH and NaCl. A stationary, steady-state distribution of carrier components and hemoglobins is produced in the first configuration. In the second, the chloride ion migrates into and through the separation space. It is shown that even under these conditions of chloride ion flux a pH gradient forms. All amphoteric species acquire a slight positive charge upon focusing and the whole pattern is mobilized towards the cathode. The cathodic gradient end is stable whereas the anodic end is gradually degrading due to the continuous accumulation of chloride. The data illustrate that the mobilization is a cationic isotachophoretic process with the sodium ion being the leading cation. The peak height of the hemoglobin zones decreases somewhat upon mobilization, but the zones retain a relatively sharp profile, thus facilitating detection. The electropherograms that would be produced by whole column imaging and by a single detector placed at different locations along the focusing column are presented and show that focusing can be commenced with NaCl present in the catholyte at the beginning of the experiment. However, this may require detector placement on the cathodic side of the catholyte/sample mixture interface.

The mathematical model outlined in Part I is recast in a form suitable for numerical computation. The spatial derivatives are replaced by finite-difference expressions, which leads to a set of ordinary differential equations coupled to a set of nonlinear algebraic relations. This system is solved using existing integration techniques. The resulting algorithm simulates the characteristic behavior of the classical modes of electrophoresis, which is shown by examples involving moving boundary electrophoresis and isoelectric focusing. In the first example two different integration schemes are used and their accuracy and stability investigated. The second example illustrates the versatility of the methodology. 0. SCOPEIn the model presented in Part I (Saville and Palusinski), the electrophoresis of amphoteric compounds is described by a set of partial differential equations coupled to a system of algebraic equations. Separation of sample components arises from interactions between the chemical equilibria and the transport processes. These interactions alter the effective mobilities of the various species and induce them to separate under the action of the electric field in nonequilibrium processes such as isotachophoresis. In equilibrium processes such as isoelectric focusing, the action of the field produces a pH gradient and the amphoteric constituents move to positions where they are isoelectric. In either case, the evolution of the process is best followed by numerical methods. The purpose of this paper is twofold: 1. To show how the mathematical model derived in Part I can be expressed in a form suitable for numerical computation. 2.To demonstrate the model depicts the detailed characteristics of electrophoretic processes.The numerical algorithm selected employs a five-point finite-difference expression to approximate the spatial derivatives at a set of mesh points. This converts the set of partial differential equations into a set of ordinary differential equations describing the temporal evolution of the concentration fields at each mesh point. These equations can be integrated using any one of a variety of schemes for solving sets of firstorder ordinary differential equations. Boundary conditions at either end of a separation column are incorporated by adjusting the form of the finite-difference expressions at the boundary points. In a similar fashion, the algorithm can easily be adapted for simulation of novel separation methods such as the use of immobilized ampholytes, molecular sieving, or ion-selective membranes at the boundaries. CONCLUSIONS AND SIGNIFICANCEThe implementation of the algorithm describing electrophoretic transport processes is illustrated by simulating moving boundary electrophoresis and isoelectric focusing with immobilized species. Both examples are intended to illustrate particular electrophoretic processes using rather simple systems. Attention concentrates on the essential characteristics of a particular mode, For the isoelectric focusing example, the central feature is the migration...

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.

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