Steric mass action model

Figure 12.24 Displacement chromatogram of a protein mixture. (A) Experimental results. 10 X100 mm Protein-Pak SP-8HR cation exchange column eluent, 12.5 mM Na2P04 displacer, 15 mg/mL purified protamine. Feed, 10.78 mg a-chymotrypsinogen A, 7.86 mg cytochrome c, and 17.3 mg lysozyme in 1.7 mL. Fp 1 mL/min, 100 pL fractions. (B) Displacement chromatogram calculated with the ideal and the steric mass action models. Reproduced with permission from J. Gerstner and S. Cramer, Biotechnol. Progr., 8 (1992) 540 (Fig. 4). 1992, American Chemical Society.

Iyer H, Tapper S, Lester P et al. Use of the steric mass action model in ion-exchange chromatographic process development. J Chromatogr 1999 832 1-9. 

An iterative procedure using the solid film linear driving force model has been used with a steric mass action isotherm to model displacement chromatography on ion exchange materials and the procedure applied to the separation of horse and bovine cytochrome c using neomycin sulfate as the displacer.4 The solid film linear driving force model is a set of two differential equations imposing mass transfer limitations. 

The steric mass action (SMA) model has been shown to successfully predict nonlinear, multicomponent behavior in ion-exchange systems over a range of mobile phase salt concentrations.71-75 It has also been widely employed as a methods development tool for displacement separations.42,45,50 In this section, we will describe several graphical techniques derived this theory which can facilitate methods development in ion-exchange displacement systems. 

Brooks and Cramer [91] extended this work on the single-component mass action model to competitive isotherms. The steric factor (tr) that they introduced to accoimt for this effect depends on the nature of the resin e.g., density of ions), the ionic strength and composition of the solution (which control the molecular structure of the protein), and the nature of the protein and its concentration (most proteins will probably have a larger apparent footprint at high dilution than at high concentration). Thus, the steric factor appears as an additional but empirical... 

Wekenborg, Susanto, and Schmidt-Traub (2004,2005) and Wekenborg (2009) applied this method to estimate the operating plane for the nonisocratic SMB separation of P-lactoglobulin A and B proteins. The isotherm is described by the steric mass action (SMA) model developed for ion exchange chromatography by Brooks and Cramer (1992) (Section 2.5.2.4). 

The so-called Steric Mass Action (SMA) model, published in 1992 by Brooks and Cramer, constitutes one of the few mathematical tools currently available for the design of displacement separations. Since its first introduction, the model has been fine-tuned and the results have been published in a series of papers. To date most of the model s applications are for the simulation of separations of a number of smallish proteins using L- or O-type displacer substances (< 1000 g/mol). The model is based on the following assumptions ... 

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