Yield optimization of regulated metabolic systems using deterministic branch-and-reduce methods

This paper addresses product yield optimization in microorganisms grown in continuous culture. Traditional optimization strategies of random mutagenesis and selection will eventually have limited efficacy, thus requiring more focused strategies. The best candidates for such strategies appear to be mathematical models that capture the essence of metabolic systems and permit optimization with computational methods. In the past, models used for this purpose have been stoichiometric, kinetic in the form of S-systems, or ad hoc. This work presents a deterministic approach based on generalized mass action (GMA) systems. These systems are interesting in that they allow direct merging of stoichiometric and S-system models. Two illustrations are considered. In the first case, the fermentation pathway in Saccharomyces cerevisiae is optimized for ethanol production under steady-state conditions. The model of this pathway is relatively small, with five states and eight rate constants. The second example addresses the maximization of citric acid in the mold Aspergillus niger. For the optimization of this larger pathway system with 30 states and 60 reactions, a Mixed Integer Nonlinear Programming (MINLP) is proposed. It is shown that efficient MINLP algorithms, based on convexification, branch-and-reduce methods, and binary variable selection, are essential for solving these difficult optimization problems.