Hence, the production of mAb is challenging and complex, with such complexities manifesting mathematically as an intricate nonhomogeneous differential algebraic system of equations (DAE) which is nontrivial to solve, including the estimation of unknown parameters. Therefore, there is a critical need to develop a modeling paradigm that can simultaneously (i) represent the complex dynamics of this process, (ii) be optimized, supplying generalizable predictions of process variables across multiple experiments simultaneously and (iii) is able to estimate the main process parameters present in the DAE model formulation.
To address these challenges, we develop a systematic optimization-based modeling framework for the mAb production process using state-of-the art techniques and tools such as the Pyomo.DAE [2] framework in Python and robust numerical methods, e.g., the simultaneous approach [3] for dynamic optimization problems. The nonhomogeneous DAE and the subsequent dynamic optimization problem are translated as a large-scale nonlinear program (NLP) that can be solved with well-known solvers such as Ipopt [4]. Our proposed framework allows the use of the same model structure to perform both parameter estimation using real industrial data available and simulation of new process conditions in an effortless manner, allowing the integrated modeling, simulation and parameter estimation of the process studied. The modeling paradigm embeds the kinetics, mass balances, complex control profiles of the fed-batch operation and parameter estimation into a single Pyomo model.
Experimental data, at different scales and multiple operating conditions available, were used to estimate the parameters that generalize the model adequately across all batches. Lastly, we perform parameter identifiability studies and employ uncertainty quantification techniques to assess the robustness of the model developed using the information obtained directly from the optimized model built in Pyomo through the Pyomo.Parmest package [5]. Our resulting mechanistic model structure and set of estimated parameters for the mAb production can predict key process variables with desired accuracy while minimizing the modeling, optimization and parameter estimation effort. This work is therefore a step forward towards robust optimization–based model and estimation techniques for the biopharmaceutical sector.
References
[1] K. Liang, H. Luo, and Q. Li, “Enhancing and stabilizing monoclonal antibody production by Chinese hamster ovary (CHO) cells with optimized perfusion culture strategies,” Front. Bioeng. Biotechnol., vol. 11, Jan. 2023, doi: 10.3389/fbioe.2023.1112349.
[2] B. Nicholson, J. D. Siirola, J.-P. Watson, V. M. Zavala, and L. T. Biegler, “pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations,” Math. Prog. Comp., vol. 10, no. 2, pp. 187–223, Jun. 2018, doi: 10.1007/s12532-017-0127-0.
[3] L. T. Biegler, “An overview of simultaneous strategies for dynamic optimization,” Chemical Engineering and Processing: Process Intensification, vol. 46, no. 11, pp. 1043–1053, Nov. 2007, doi: 10.1016/j.cep.2006.06.021.
[4] A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., vol. 106, no. 1, pp. 25–57, Mar. 2006, doi: 10.1007/s10107-004-0559-y.