Abstract
Multi-modal chromatography emerged as a powerful tool for the separation of proteins in the production of biopharmaceuticals. In order to maximally benefit from this technology it is necessary to set up an optimal process control strategy. To this end, we present a mechanistic model with a recent kinetic adsorption isotherm that takes process controls such as pH and buffer salt concentration into account. Maximizing the yield of a target component subject to purity requirements leads to a mixed-integer nonlinear optimal control problem constrained by a partial differential equation. Computational experiments indicate that a good separation in a two-component system can be achieved.
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References
Rathore, A.S., Kumar, D., Kateja, N.: Recent developments in chromatographic purification of biopharmaceuticals. Biotechnol. Lett. 40(6), 895–905 (2018)
Geißler, B., Kolb, O., Lang, J., Leugering, G., Martin, A., Morsi, A.: Mixed integer linear models for the optimization of dynamical transport networks. Math. Methods Oper. Res. 73(3), 339–362 (2011)
Hante, F.M., Sager, S.: Relaxation methods for mixed-integer optimal control of partial differential equations. Comput. Optim. Appl. 55(1), 197–225 (2013)
Buchheim, C., Kuhlmann, R., Meyer, C.: Combinatorial optimal control of semilinear elliptic PDEs. Comput. Optim. Appl. 70(3), 641–675 (2018)
Schmidt-Traub, H., Schulte, M., Seidel-Morgenstern, A. (eds.): Preparative Chromatography, 2nd edn. Wiley-VCH, Weinheim (2012)
Mollerup, J.M.: A review of the thermodynamics of protein association to ligands, protein adsorption, and adsorption isotherms. Chem. Eng. Technol. 31(6), 864–874 (2008)
Nfor, B.K., Noverraz, M., Chilamkurthi, S., Verhaert, P.D.E.M., van der Wielen, L.A., Ottens, M.: High-throughput isotherm determination and thermodynamic modeling of protein adsorption on mixed mode adsorbents. J. Chromatogr. A 1217(44), 6829–6850 (2010)
Deitcher, R.W., Rome, J.E., Gildea, P.A., O’Connell, J.P., Fernandez, E.J.: A new thermodynamic model describes the effects of ligand density and type, salt concentration and protein species in hydrophobic interaction chromatography. J. Chromatogr. A 1217(2), 199–208 (2010)
Danckwerts, P.V.: Continuous flow systems. Distribution of residence times. Chem. Eng. Sci 2(1), 1–13 (1953)
Sager, S., Bock, H.G., Diehl, M.: The integer approximation error in mixed-integer optimal control. Math. Program. 133(1), 1–23 (2012)
von Lieres, E., Andersson, J.: A fast and accurate solver for the general rate model of column liquid chromatography. Comput. Chem. Eng. 34(8), 1180–1191 (2010)
Andersson, J.A.E., Gillis, J., Horn, G., Rawlings, J.B., Diehl, M.: CasADi: a software framework for nonlinear optimization and optimal control. Math. Progam. Comput. 11(1), 1–36 (2019)
Hindmarsh, A.C., Brown, P.N., Grant, K.E., Lee, S.L., Serban, R., Shumaker, D.E., Woodward, C.S.: SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 31(3), 363–396 (2005)
Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)
Manns, P., Kirches, C.: Improved regularity assumptions for partial outer convexification of mixed-integer PDE-constrained optimization problems. ESAIM: Control Optim. Calculus Var. 26, 32 (2020)
Acknowledgements
The authors gratefully acknowledge support by the German Federal Ministry for Education and Research, grant no. 05M17MBA-MOPhaPro.
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Cebulla, D.H., Kirches, C., Potschka, A. (2020). Mixed-Integer Nonlinear PDE-Constrained Optimization for Multi-Modal Chromatography. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_10
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DOI: https://doi.org/10.1007/978-3-030-48439-2_10
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