Defining operating regimes for partition coefficient measurements in protein chromatography

Partition coefficient (K_p) measurements are widely used in early- and late-stage downstream process development for biologics to screen binding, elution, and selectivity behaviors of chromatographic resins and conditions. Although the procedure for performing these experiments is straightforward, obtaining accurate K_p and selectivity measurements can be challenging with equilibrium concentrations often being below the limit of detection (LOD) of the analyzing device, and with no guarantee that the partition coefficient measurement will sample from the linear portion of the isotherm. This work develops a theoretical framework and corresponding software tool to inform the selection of phase ratio and protein loading such that partition coefficient experiments satisfy the following three criteria: i.) equilibrium concentrations are above the LOD, ii.) measurements are sampled from the linear portion of the isotherm, and iii.) partition coefficient values fall within a practically relevant range for utility in downstream process development. First, the concept of feasibility maps is developed which calculates equilibrium concentrations, separation factors, and K_p values on the K_L vs. q_m plane to define a feasibility regime based on a determined LOD, minimum-required separation factor, and maximum relevant K_p. These data are then superimposed onto a large database of historical isotherm data from the literature comprised of 6,310 Langmuir isotherm points over a broad range of chromatography resins and protein modalities, which are used to binarily determine whether these three criteria are met for a given phase ratio and resin loading. Feasibility maps are calculated as a function of phase ratio and resin loading to define an operating regime bounded by a top operating curve and bottom operating line on the resin loading vs. phase ratio plane. Further, closed-form expressions for these operating curves are derived, and the sensitivity of these curves to experimental parameters such as hold-up volume, intraparticle porosity, isotherm linearity criteria, and LOD is then evaluated and discussed in the context of relative error due to isotherm curvature. The impact of measuring K_p values inside vs. outside these operating regimes is assessed by experimentally measuring K_p vs. salt sampled from these two regions and predicting elution salt by mechanistic column modeling from these equilibrium data. These results indicate that K_p measurements sampled from outside the operating regime result in substantial error in model prediction compared to column experiments. Together, this work provides a theoretical foundation for obtaining accurate partition coefficient and selectivity measurements for informing robust experimental design. Further, it develops a software tool for calculating operating regimes, which can leverage in-house historical isotherm data to calculate custom operating regimes.