Determination of parameters for the steric mass action model--a comparison between two approaches

The application of mechanistic modeling for the optimization of chromatographic steps increased recently due to time efficiency of algorithms and rising calculation power. In the modeling of ion exchange chromatography steps, the sorption processes occurring on adsorbent particle surfaces can be simulated with the steric mass action (SMA) model introduced by Brooks and Cramer (1992) [14]. In this paper, two approaches for the determination of SMA parameters will be carried out and discussed concerning their specific experimental effort, quality of results, method differences, reasons for uncertainties and consequences for SMA parameter determination: Approach I: estimation of SMA parameters based on gradient and frontal experiments according to instructions in Brooks and Cramer (1992) [14] and Shukla et al. (1998) [16]. Approach II: application of an inverse method for parameter estimation, resulting in SMA parameters that induce a best fit of chromatographic data to a mechanistic model for column chromatography. These approaches for SMA parameter determination were carried out for three proteins (ribonuclease A, cytochrome c and lysozyme) at pH 5 and pH 7. The results were comparable and the order of parameter values and their relations to the chromatographic data similar. Nevertheless, differences in the complexity and effort of methods as well as the parameter values themselves were observed. The comparison of methods demonstrated that discrepancies depend mainly on model sensitivities and additional parameters influencing the calculations. However, the discrepancies do not affect predictivity; predictivity is high in both approaches. The approach based on an inverse method and the mechanistic model has the advantage that not only retention times but also complete elution profiles can be predicted. Thus, the inverse method based on a mechanistic model for column chromatography is the most comfortable way to establish highly predictive SMA parameters lending themselves for the optimization of chromatography steps and process control.