(55e) SMA and ACT: A Tale of Two Isotherms

It has been >30 years since Brooks and Cramer unleashed their Steric Mass-Action (SMA) isotherm for ion exchange chromatography unto the separations community (Brooks and Cramer, AIChE Journal [1992]; doi:10.1002/aic.690381212). This physically motivated isotherm expression solved a key problem in quantitatively explaining observed retention behaviors for both adsorbing macromolecules (especially proteins) and counter-ions by explicitly accounting for the impact of both exchangeable (displaced) and non-exchangeable (sterically hindered) salt counter-ions. It is a simple, intuitive – in hindsight! – and accurate model that became the new standard isotherm for ion exchange chromatography as evidenced by its widespread adoption in the literature as well as its incorporation within popular chromatography modeling software packages such as CADET and ChromX. Ion exchange chromatography is pervasive in downstream biomanufacturing and the SMA isotherm is the go-to constitutive equation for the design and simulation of ion exchange separations.

In a similar spirit, we have aimed to address a gap in the modeling of affinity chromatography for protein separations such Protein A (ProA) based capture of monoclonal antibodies (mAbs): the need to either manually manipulate Langmuir isotherm parameters or to empirically modify isotherm expressions to be able to describe both adsorption and elution operations. We derived a pH-dependent isotherm that accounts for an averaged number of contributing, titratable amino acid residues within the primary mAb and ProA binding sites as well as for the mAb-ProA binding stoichiometry. We have termed this model the affinity complex titration (ACT) isotherm. We’ve demonstrated the utility of the ACT isotherm by estimating model parameters with a limited number of gradient elution experiments (typically two) and then making accurate, extrapolative predictions of mAb breakthrough during loading and elution during step, linear and non-linear pH gradients. Further, the estimated ACT parameters yield biophysically satisfying interpretations, including the use of differences in elution pH during linear gradient elution to estimate differences in binding free energies for different mAbs and to predict competitive mAb adsorption phenomena in polyclonal antibody separations. We expect the ACT isotherm to be generalizable to a broad range of titrable, competitive affinity chromatography media.