(504c) A Bi-Level Metabolic and Regulatory Network Optimization Model for Microbial Strain Design

Modeling of cellular metabolism provides a powerful tool for suggesting genetic manipulations for desired properties. A number of computational algorithms based on metabolic networks have been developed for optimization of strains with gene knock-outs, up-regulations and down-regulations. On the other hand, regulatory networks are also important factors in determining cellular metabolism and have started being incorporated, to some extent, in the modeling of metabolism. However, integrating metabolic and regulatory networks for strain design remains a promising while under-explored research topic. Here we present a strain optimization model that considers both metabolic network modifications and regulatory network rewiring for over-productions of biochemicals. To take into account the interaction between cellular metabolic networks and regulatory networks, we built on the regulatory flux balance analysis (rFBA) framework. By incorporating regulatory boolean logic equations within the standard flux balance analysis (FBA) model, rFBA considers transcriptional regulations that alter the solution space of flux distributions of the metabolic network. Two states, active or inhibited, exist for each metabolic reaction under transcriptional regulation and the inhibited reactions can not carry any fluxes. Thus, two types of effects can be introduced by modifying regulatory networks: inactivate active reactions and re-activate inhibited reactions. A bi-level mixed-integer linear programming (MILP) model has been developed, which allows these changes simultaneously with gene knockouts to optimize strains for desired products. Due to the linear structure, this bi-level optimization problem can be solved as a single level MILP by utilizing duality properties of the inner level linear programming problem. We have applied this method to Escherichia coli K12 for a number of biochemicals and potential biofuel molecules, including ethanol, succinate, and fatty acids. The metabolic network we utilized contained the central carbon metabolism and fatty acid synthesis pathways together with certain related regulations. Various carbon sources were considered, including glucose, glycerol, ribose and mixed carbon sources. Both anaerobic and aerobic conditions were investigated. We have found that in most of the cases we can improve the production substantially by re-activating specific inhibited metabolic reactions, compared to allowing gene knockouts only. This effect was the most significant under the mixed carbon source conditions, in which, for example, over 200% improvement for fatty acid production can be achieved theoretically. We are currently experimentally testing some of the genetic manipulations suggested by this model.