Efficient MILP formulations for the optimal synthesis of chromatographic protein purification processes

The use of recombinant proteins has increased greatly in recent years, as well as the techniques used for their purification. The selection of an efficient process to purify proteins is a major bottleneck found when trying to scale up results obtained in the laboratory to a large-scale industrial process. One of the main challenges in the synthesis of downstream purification stages in biotechnological processes is the appropriate selection and sequencing of chromatographic steps. The objective of this work is to develop mixed integer linear programming models for the synthesis of protein purification processes. Models for each chromatographic technique rely on physicochemical data of a protein mixture, which contains the desired product and provide information on its potential purification. Formulations that are based on convex hull representations are proposed to calculate the minimum number of steps from a set of chromatographic techniques that must achieve a specified purity level and alternatively to maximize purity for a given number of steps. The proposed models are tested in several examples with experimental data and present time reductions of up to three orders of magnitude when compared to big-M formulations.