Theoretical Studies in Isoelectric Focusing
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THEORETICAL STUDIES IN ISOELECTRIC FOCUSING
R. A. MOSHER, 0. A. PALUSINSKI AND M. BIER Biophysics Technology Laboratory, University of Arizona,
Tucson, Arizona,
USA
ABSTRACT Our overall objective is the development of a process for large scale purification of biologicals by isoelectric focusing (IEF). Thus, it was important to gain a better understanding of the underlying physical phenomena through mathematical modeling and computer simulation of the process. A mathematical model of the steady state in IEF was developed for an L-component system of ampholytes or monovalent buffers. It is based on the fundamental equations describing the components' dissociation equilibria, mass transport due to diffusion and electromigration, electroneutrality, and the conservation of charge. The model consists of ordinary differential equations coupled to a system of algebraic equations. The validity and usefulness of these simulations has been confirmed in the formulation of actual buffer mixtures for experimental IEF. This model was recently extended to include the transient evolution to a steady state. Furthermore the new formulation applies to other electrophoretic processes, notably isotachophoresis and zone electrophoresis. As a result, we now have the first general model which predicts the behavior of a given chemical system in a variety of electrophoretic processes.
INTRODUCTION Isoelectric focusing (IEF) is widely used for the analysis of proteins because of its exquisite resolution. IEF is based on the electrophoretic transport of amphoteric sample components to their respective isoelectric points (pI) in a stable pH gradient. Svensson (1, 2) was the first to show the usefulness of IEF, by generating stable pH gradients through the focusing of a complex buffering mixture of polyamino-polycarboxylic acids. This buffer was synthesized for this specific purpose by random polymerization (3) and introduced commercially by LKB Produkter of Bromma, Sweden, under the trade name Ampholine. Svensson (1) also developed the theory of IEF of a protein sample assuming the pre-existence of a stable linear pH profile and uniform conductivity. Ampholine-generated pH profiles approximate these assumptions fairly well. However, the effectiveness of Ampholine has, in some sense, stymied the development of theories dealing with the establishment of the pH gradient, since the composition of Ampholine is unknown. Ampholine and other similar commercial buffers are excellent for analytical purposes, but are unacceptable for many preparative tasks as they result in contamination of the purified protein by a chemically and biologically illdefined mixture. Thus, there have been numerous empirical attempts to develop stable pH gradients using mixtures of chemically well-defined amphoteric or nonamphoteric buffers (4-9). These efforts were largely unsuccessful, due in part to the absence of a readily applicable theory dealing with the establishment of
256 the pH profile. The only theoretical treatment of the problem is that of Almgren (10
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