Robust dynamic optimization of enzyme-catalyzed carboligation: A point estimate-based back-off approach

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

Rigorous Model-Based Design and Experimental Verification of Enzyme-Catalyzed Carboligation under Enzyme Inactivation

Enzyme catalyzed reactions are complex reactions due to the interplay of the enzyme, the reactants, and the operating conditions. To handle this complexity systematically and make use of a design space without technical restrictions, we apply the model based approach of elementary process functions (EPF) for selecting the best process design for enzyme catalysis problems. As a representative case study, we consider the carboligation of propanal and benzaldehyde catalyzed by benzaldehyde lyase from Pseudomonas fluorescens (PfBAL) to produce (R)-2-hydroxy-1-phenylbutan-1-one, because of the substrate dependent reaction rates and the challenging substrate dependent PfBAL inactivation. The apparatus independent EPF concept optimizes the material fluxes influencing the enzyme catalyzed reaction for the given process intensification scenarios. The final product concentration is improved by 13% with the optimized feeding rates, and the optimization results are verified experimentally. In general, the rigorous model driven approach could lead to selecting the best existing reactor, designing novel reactors for enzyme catalysis, and combining protein engineering and process systems engineering concepts.

Advances in biological conversion technologies: new opportunities for reaction engineering

Reaction engineering needs to embrace biological conversion technologies, on the road to identify more sustainable routes for chemical manufacture.

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.