The mechanistic modeling of preparative liquid chromatography is still a challenging task. Nonideal thermodynamic conditions may require activity coefficients for the mechanistic description of preparative chromatography. In this work, a chromatographic cation exchange step with a polypeptide having a complex elution behavior in low and high loading situations is modeled.Model calibration in the linear range of the isotherm is done by applying counterion-induced linear gradient elution experiments between pH 3.3 and 4.3.Inverse fitting with column loads up to 25 mg/mL CV is performed for parameter estimation in the nonlinear range. The polypeptide elution peak shows an anti-Langmuirian behavior with fronting under low loading conditions and a switch to a Langmuirian behavior with increasing load. This unusual elution behavior could be described with an extended version of the sigmoidal Self-Association isotherm including two activity coefficients for the polypeptide and counterion in solution. The activity coefficient of the solute polypeptide shows a strong influence on the model parameters and is crucial in the linear and nonlinear range of the isotherm. The modeling procedure results in a unique and robust model parameter set that is sufficient to describe the complex elution behavior and allows modeling over the full isotherm range.

In process development and characterization, the scale-up of chromatographic steps is a crucial part and brings a number of challenges. Usually, scale-down models are used to represent the process step, and constant column properties are assumed. The scaling is then typically based on the concept of linear scale-up. In this work, a mechanistic model describing an anti-Langmuirian to Langmuirian elution behavior of a polypeptide, calibrated with a pre-packed 1 ml column, is applied to demonstrate the scalability to larger column volumes up to 28.2 ml. Using individual column parameters for each column size, scaling to similar eluting salt concentrations, peak heights, and shapes is experimentally demonstrated by considering the model's relationship between the normalized gradient slope and the eluting salt concentration. Further scale-up simulations show improved model predictions when radial inhomogeneities in packing quality are considered.

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