A Bilevel Programming Approach for the Dynamic Optimization of Cyanobacterial C-phycocyanin Production under Uncertainty

C-phycocyanin is a high-value bioproduct synthesized by cyanobacterium Arthrospira platensis with a significant global market demand given its applications in the pharmaceutical, food and colorant industries. Unfortunately, its biosynthesis is currently characterized by low productivity and large uncertainty during the production process. High variability and unreliable expectations on product yields substantially hinder the industrialization of microorganism derived biochemicals as they present a risk to the profitability and safety of the underlying systems. Therefore, in this work, we propose a robust optimization approach to determine the lower and upper product yield expectations for the sustainable production of C-phycocyanin. Kinetic modeling is adopted in this study as a tool for fast prototyping, prediction and optimization of chemical and biochemical processes. On the upside, parameters in bioprocess kinetic models are used as a simplification of the complex metabolic networks to enable the simulation, design and control of the process. On the downside, this conglomeration of parameters may result in significant model uncertainty. To address this challenge, we formulate a bilevel max-min optimization problem to obtain the worst-case scenario of our system given the uncertainty on the model parameters. By constructing parameter confidence ellipsoids, we determined the feasible region along which the parameters can minimize the system's performance, while nutrient and light controls are used to maximize the biorenewable production. The inner minimization problem is embedded by means of the optimality conditions into the upper maximization problem and hence both are solved simultaneously. Through this approach, we determined pessimistic and optimistic scenarios for the bioproduction of C-phycocyanin and hence compute reliable expectations on the yield and profit of the process.