A mathematical model of electrophoretic separation processes has been developed and adapted for computer simulations. The model is used to predict the characteristic behavior of a variety of electrophoretic techniques from a knowledge of chemical equilibria and physical transport phenomena. The model provides a unifying basis for a rational classification of all electrophoretic processes.

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.

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...

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Of all electrophoretic methods, isoelectric focusing offers the highest resolution and is best suited for preparative applications. Over the years, several instruments were developed for this purpose, all operating in free fluids, in the absence of gels or other supporting matrices. In such systems, the avoidance of gravity or electrically driven convections is essential. Successful stratagems for fluid control included rapid recycling or rotation, in combination with either fine porosity screens or narrow gaps between parallel plates. The most successful apparatus so far is the Rotofor, in which fluid is stabilized by combining horizontal rotation with fine porosity screen partitioning. Recycling isotachophoresis offers the potential of separating proteins at high concentration. A new concept of tangential electrophoresis is described. To optimize the use of these devices for protein separation, low molecular weight, biologically acceptable buffers of known composition are essential. The buffering system developed for this purpose comprises a series of binary buffers that cover the pH range in steps of 1 pH unit or less. The pH gradient can be custom-designed and is of remarkable stability in operation.