Model-based design and optimization of GSSR chromatography for peptide purification

Gradient with Steady State Recycle (GSSR) is a recently developed process for center-cut separation by solvent-gradient chromatography. The process comprises a multicolumn, open-loop system with cyclic steady-state operation that simulates a solvent gradient moving countercurrently with respect to the solid phase. However, the feed is always injected into the same column and the product always collected from the same column as in single-column batch chromatography. Here, three-column GSSR chromatography for peptide purification is optimized using state-of-the-art mathematical programming tools. The optimization problem is formulated using a full-discretization approach for steady periodic dynamics. The resulting nonlinear programming problem is solved by an efficient open-source interior-point solver coupled to a high-performance parallel linear solver for sparse symmetric indefinite matrices. The procedure is successfully employed to find optimal solutions for a series of process design problems with increasing number of decision variables. In addition to productivity and recovery, process performance is analyzed in terms of two key performance indicators: dilution ratio and solvent consumption ratio. Finally, the problem of robust process design under uncertainty in the solvent gradient manipulation is examined. The best solution is chosen only among candidate solutions that are robust feasible, i.e., remain feasible for all modifier gradient perturbations within the accuracy range of the gradient pump. This gives rise to a robust approach to optimal design in which the nominal problem is replaced by a worst case problem. Overall, our work illustrates the advantages of using advanced mathematical programming tools in designing and optimizing a GSSR process for which it is difficult to deduce sufficiently general heuristic design rules.