Isabelle L. Arnaud Jacques Josserand Joël S. Rossier Hubert H. Girault Laboratoire d’Electrochimie, Département de Chimie, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Finite element simulation of Off-Gel  buffering The protonation of an aqueous solution of two ampholytes AH and BH next to a gel buffered by immobilized acid moieties IH has been studied by finite element simulation in an iterative scheme. A ten species model has been formulated, taking into account transient diffusion and equilibrium kinetics of the two amphoteric species AH and BH, of water and of the immobilized species IH. This model has been developed to illus- trate the pH evolution between an ampholyte solution and an Immobiline gel, and to study the influence of the Immobiline concentration on protons and ampholyte distri- butions. It has been demonstrated that a minimum initial Immobiline concentration of 10 22 M is necessary to maintain the pH in the gel in contact with a closed chamber, when the difference between the isoelectric points of AH and BH is 4 and when the initial concentration of the ampholytes in solution is in the micromolar range. This approach provides a first theoretical framework for the recently developed Off-Gel  electrophoresis. Keywords: Ampholyte / Diffusion / Equilibria / Finite element simulation / Immobilized pH gradient / Isoelectric focusing / Isoelectric purification EL 5033 1 Introduction Numerical simulations of electromigration and diffusion have been used since the 1980s to enhance the under- standing of the four principal modes of electrophoresis (capillary zone electrophoresis (CZE), moving boundary electrophoresis (MBE), isotachophoresis (ITP), isoelectric focusing (IEF)) [1–10]. IEF is a technique used to concen- trate peptides or proteins at their isoelectric point (pI) in a pH gradient, under the application of an electric field [11, 12]. Mathematical models of the electrophoretic mobility of the proteins have also been presented [13– 16], and modeling of IEF has been studied either in the presence of carrier ampholytes [17, 18] or in recycling free-flow IEF [19]. The original IEF method using carrier ampholytes to gener- ate a pH gradient was first derived in 1961 by Svensson [20, 21] and then applied experimentally in 1969 by Vester- berg [22]. When an electric field is applied, the carrier ampholytes migrate towards the anode or the cathode according to their pI and thereby determine the pH of their environment. Since carrier ampholytes have a high rate of diffusion in the gel, they constantly diffuse away from their pI and migrate back electrophoretically. Bjellqvist et al. [23] developed in 1982 an alternative method, the so-called immobilized pH gradient or IPG. The gradient is composed of buffering groups called Immobilines, which are copoly- merized with the acrylamide monomers in a polyacryl- amide gel. Immobilines are weak acids or bases and offer a stable pH gradient. Similarly, glass fiber membranes can be buffered by Immobiline and used in segmented IEF. In this method, the proteins are captured in an isoelectric trap formed by two membranes of pI encompassing the pI of the proteins [24–26]. IPG gels have been extensively stu- died [27–29], and in particular Mosher et al. [30] made numerical simulations on extended acidic and alkaline pH gradient. Such IPG gels are used nowadays, either for the first dimension of 2-D electrophoresis or in other devices such as Off-Gel  electrophoresis [31]. Off-Gel  technology is a fractionation method which enables the purification of one or several proteins in a complex mixture. Biological samples (e.g., A, B, C in so- lution) are introduced in a chamber, where one wall is in contact with an IPG gel. The pH of the gel next to the chamber is chosen to be the pI of the ampholyte AH to purify. When an electric field is applied along the gel, charged species (e.g., BH 2 1 , C) migrate into the gel and only the neutral form AH (i.e.,pI = pH) remains in the chamber. The gist of the system (Fig. 1) is that the ampho- teric species to purify reach their pI in the solution and do not have to penetrate the gel. For that, pH buffering is required in the thin layer of solution close to the gel. This buffering of the solution by the Immobilines in the gel is not established if the ampholyte concentrations in the so- lution are too high or if the buffering capacity of the gel is too low. As a consequence, it is important to study the pH evolution of the thin layer of solution close to the gel under different analytical conditions. Correspondence: Prof. Hubert H. Girault, Laboratoire d’Electro- chimie, Département de Chimie, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland E-mail: hubert.girault@epfl.ch Fax: 141-216933667 Electrophoresis 2002, 23, 3253–3261 3253  2002 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 0173-0835/02/1910–3253 $17.501.50/0 General