Modeling of dual gradient elution in ion exchange and mixed-mode chromatography

Abstract Protein retention using dual gradient elution in ion exchange- and mixed-mode chromatography can be modeled using the combination of a modified Yamamoto's LGE model and a conversion term to correlate the elution salt concentration and pH at any given gradient slope. Incorporation of the pH dependence of the binding charges into the model also provides some insights on the dual effects of salt and pH in protein–ligand interaction. The fitted thermodynamic parameters ( Δ G P 0 / R T , Δ G S 0 / R T , number of charged amino acids involved in binding) of the dual gradient elution data using lysozyme and mAbs on SP Sepharose ® FF, Eshmuno ® HCX, and Capto ® MMC ImpRes were consistent to the results of mono gradient data. This gives rise to an approach to perform thermodynamic modeling of protein retention in ion exchange- and mixed-mode chromatography by combining both salt and pH gradient into a single run of dual gradient elution which will increase time and cost efficiency. The dual gradients used in this study encompassed a wide range of pH (4–8) and NaCl concentrations (0–1 M). Curve fits showed that Δ G P 0 / R T is protein type and ligand dependent. Δ G S 0 / R T is strongly dependent on the stationary phase but not the protein. For mAb04 on mixed-mode resin Capto ® MMC, Δ G S 0 / R T is 5–6 times higher than the result reported for the same protein on cation exchanger Fractogel ® EMD SO 3 − (S).