A Mixed Integer Linear Programming Model for the Optimal Synthesis of Protein Purification Processes with Product Loss

E. Vasquez-Alvarez and J. M. Pinto

Abstract
The objective of this work is to develop a mixed integer linear programming (MILP) model for the synthesis of protein purification processes that incorporates product losses. Mathematical models for each chromatographic technique rely on physicochemical data on the protein mixture, which contains the desired product and provide information on its potential purification. In previous works, MILP models assumed the complete recovery of the desired protein. The present model incorporates losses in the target protein along the purification process, in order to evaluate the trade-off between product by purity and quantity. A formulation that is based on a convex hull representation is proposed to calculate the minimum number of steps from a set of chromatographic techniques that must achieve a specified purity level as well as the amount of product recovered. Model linearity is achieved by assuming that the product is recovered in discrete percentage levels. The methodology is validated in examples with experimental data and results are shown to provide an important guideline for synthesizing purification processes.

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Keywords
Purification processes, chromatographic steps, convex hull representation, MILP