Isotherm model discrimination for multimodal chromatography using mechanistic models derived from high-throughput batch isotherm data

Abstract

In this work, we have examined an array of isotherm formalisms and characterized them based on their relative complexities and predictive abilities with multimodal chromatography. The set of isotherm models studied were all based on the stoichiometric displacement framework, with considerations for electrostatic interactions, hydrophobic interactions, and thermodynamic activities. Isotherm parameters for each model were first determined through twenty repeated fits to a set of mAb – Capto MMC batch isotherm data spanning a range of loading, ionic strength, and pH as well as a set of mAb – Capto Adhere batch data at constant pH. The batch isotherm data were used in two ways—spanning the full range of loading or consisting of only the high concentration data points. Predictive ability was defined through the model's capacity to capture prominent changes in salt gradient elution behavior with respect to pH for Capto MMC or unique elution patterns and yield losses with respect to gradient slope for Capto Adhere. In both cases, model performance was quantified using a scoring metric based on agreement in peak characteristics for column predictions and accuracy of fit for the batch data. These scores were evaluated for all twenty isotherm fits and their corresponding column predictions, thereby producing a statistical distribution of model performances. Model complexity (number of isotherm parameters) was then considered through use of the Akaike information criterion (AIC) calculated from the score distributions. While model performance for Capto MMC benefitted substantially from removal of low protein concentration data, this was not the case for Capto Adhere; this difference was likely due to the qualitatively different shapes of the isotherms between the two resins. Surprisingly, the top-performing (high accuracy with minimal number of parameters) isotherm model was the same for both resins. The extended steric mass action (SMA) isotherm (containing both protein-salt and protein-protein activity terms) accurately captured both the pH-dependent elution behavior for Capto MMC as well as loss in protein recovery with increasing gradient slope for Capto Adhere. In addition, this isotherm model achieved the highest median score in both resin systems, despite it lacking any explicit hydrophobic stoichiometric terms. The more complex isotherm models, which explicitly accounted for both electrostatic and hydrophobic interaction stoichiometries, were ill-suited for Capto MMC and had lower AIC model likelihoods for Capto Adhere due to their increased complexity. Interestingly, the ability of the extended SMA isotherm to predict the Capto Adhere results was largely due to the protein-salt activity coefficient, as determined via isotherm parameter sensitivity analyses. Further, parametric studies on this parameter demonstrated that it had a major impact on both binding affinity and elution behavior, therein fully capturing the impact of hydrophobic interactions. In summary, we were able to determine the isotherm formalisms most capable of consistently predicting a wide range of column behavior for both a multimodal cation-exchange and multimodal anion-exchange resin with high accuracy, while containing a minimized set of model parameters.