Mechanistic modeling and simulation of a complex low and high loading elution behavior of a polypeptide in cation exchange chromatography

Abstract

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.

Mechanistic modeling of cation exchange chromatography scale‐up considering packing inhomogeneities

“…The elution behavior could be successfully described using an extended version of the Self‐Association (SAS) isotherm. Model development using a small‐scale 1 ml calibration column and an intense parameter discussion are described in our previous publication [29]. The current study is a continuation of the earlier work and investigates the scalability of the developed mechanistic model from the small‐scale calibration column to larger benchtop columns up to 28.2 ml.…”

“…For the simulation of the ad-and desorption behavior of the polypeptide on the resin, an extended version of the SAS isotherm was used [30,31]. The applicability of the SAS isotherm to describe the anti-Langmuirian to Langmuirian elution behavior of a polypeptide [29] and a bispecific monoclonal antibody [32] was recently demonstrated. The sigmoid-shaped isotherm, which describes dimer formation on the resin induced through SAS, is given by:…”

“…where 𝑁 𝑎𝑐𝑖𝑑𝑖𝑐 and 𝑁 𝑏𝑎𝑠𝑖𝑐 denotes the number of the acidic and basic amino acid-like groups involved in binding with the corresponding pKa value 𝑝𝐾𝑎 𝑎𝑐𝑖𝑑𝑖𝑐 and 𝑝𝐾𝑎 𝑏𝑎𝑠𝑖𝑐 . Since the pH range in the modeling procedure at a small column scale was narrow, from pH 3.3 to pH 4.3, only one acidic and one basic amino acid-like group fit the data [29].…”

“…An empiric pH dependency in Mollerup's asymmetric activity coefficient model [36] of the protein in solution was described [29], which results in the following relationship:…”

“…For the simulation of the ad‐ and desorption behavior of the polypeptide on the resin, an extended version of the SAS isotherm was used [30, 31]. The applicability of the SAS isotherm to describe the anti‐Langmuirian to Langmuirian elution behavior of a polypeptide [29] and a bispecific monoclonal antibody [32] was recently demonstrated. The sigmoid‐shaped isotherm, which describes dimer formation on the resin induced through SAS, is given by: $$$$\begin{eqnarray} \frac{{{q}_i}}{{{c}_i}} = {K}_i\frac{{{{\tilde{\gamma }}}_i}}{{{{\tilde{\gamma }}}_s^{{v}_i}}}{\left( {\frac{{{\Lambda}}}{{{c}_s}}} \right)}^{{v}_i}{\left[ {1 - \left( {\frac{{{v}_i + {\xi }_i}}{\Lambda }} \right){q}_i} \right]}^{{v}_i}\left( {1 + 2\frac{{{K}_{D,i}}}{c}{c}_i{{\tilde{\gamma }}}_i} \right)\nonumber\hspace*{-10pt}\\ \end{eqnarray}$$$$where $${q}_i$$ denotes the adsorbed and $${c}_i$$ the mobile phase protein concentration of the species i , $${c}_s$$ the mobile phase salt ion concentration, Λ the ligand density, $${v}_i$$ the characteristic charge, $${\xi }_i$$ the shielding factor and c the molar density.…”