Mathematical Modeling of Protein Chromatograms

The most used mathematical models with a phenomenological basis for simulating chromatographic curves of proteins in size exclusion chromatography, ion exchange chromatography, affinity chromatography, and hydrophobic interaction chromatography are reviewed. The plate model (PM) and the general rate model (GRM) are briefly described, followed by various applications of these models to the different chromatographic strategies. Based on these examples it is concluded that the GRM is the most complete and informative model, despite it needs several parameters that have to be estimated from theoretical correlations nonspecific for proteins. Additionally, values for the effective pore diffusion coefficient are not generally available. Appropriate calibration leads in most cases to predictions that compare favorably with experimental data. The possibility to predict chromatographic curves under different operational conditions similar to those used at industrial scale by applying mathematical models is still a challenge because it could contribute to the reduction of costs involved in suitable purification processes. In addition, new proteins are continually designed and for each case different conditions are needed. The use of the theoretical plate concept and the general rate model (GRM) for simulating protein chromatograms in size exclusion, ion exchange, affinity, and hydrophobic interaction is reviewed. Adsorption kinetics and parameters used in the modeling were presented. Based on different examples, the GRM turned out to be the most complete and informative model.