Prediction of protein breakthrough behavior using simplified analytical solutions

The predictability of the breakthrough behavior of lysozyme on the strong cation exchanger SP Sepharose FF was evaluated using two different but related analytical solutions. The first solution, known as the Thomas equation, assumes that adsorption can be represented by a pseudo second-order reaction rate law which translates into a Langmuir isotherm at equilibrium. The second solution, known as the Bohart–Adams equation, assumes that adsorption can be described by a quasi-chemical rate law which reduces to a rectangular isotherm at equilibrium. The Bohart–Adams solution can be regarded as a limiting form of the Thomas solution. The equilibrium and rate parameters embedded in the two solutions were extracted from batch experiments. Predictions using the two simplified solutions agreed with experimental breakthrough data. When the isotherm is highly favorable the simpler Bohart–Adams solution can be used as a practically useful modeling tool in lieu of the mathematically complicated Thomas solution.