A method is developed to predict protein chromatographic behavior from batch isotherm using a a systematic empirical interpolation (EI) scheme and without relying on a mechanistic description of the dependence of protein binding on protein and salt concentration. Coupled with a lumped kinetic model with rate parameters determined from HETP measurements for non-binding conditions, the EI scheme is used to numerically predict the column behavior. For two experimental cation exchange systems considered in this work, lysozyme on SP-Sepharose-FF and a monoclonal antibody on POROS XS, predictions based on the EI scheme are in excellent agreement with experimental elution profiles under highly overloaded conditions without using any adjustable parameters. A qualitative study of the sensitivity of predicting protein elution profiles to the precision, granularity, and extent of the batch adsorption data is conducted. Based on the results for a hypothetical system, whose properties are comparable to those found in practice for protein cation exchange chromatography the results of this show that the interpolation scheme is relatively insensitive, requiring only that the ranges of protein and salt concentrations in the experimental dataset overlap those under which the protein actually elutes from the column and along with a 10% measurement precision.

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high-throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high-throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.

A previously developed empirical interpolation (EI) method is extended to predict highly overloaded multicomponent elution behavior on a cation exchange (CEX) column based on batch isotherm data. Instead of a fully mechanistic model, the EI method employs an empirically modified multicomponent Langmuir equation to correlate two-component adsorption isotherm data at different salt concentrations. Piecewise cubic interpolating polynomials are then used to predict competitive binding at intermediate salt concentrations. The approach is tested for the separation of monoclonal antibody monomer and dimer mixtures by gradient elution on the cation exchange resin Nuvia HR-S. Adsorption isotherms are obtained over a range of salt concentrations with varying monomer and dimer concentrations. Coupled with a lumped kinetic model, the interpolated isotherms predict the column behavior for highly overloaded conditions. Predictions based on the EI method shows good agreement with experimental elution curves for protein loads up to 40 mg mL column or about 50% of the column binding capacity. The approach can be extended to other chromatographic modalities and to more than two components.

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