Genome-Scale Metabolic Model Embedding for Fed-Batch Optimal Feed Policy Determination

A new method for genome-scale metabolic model into culture kinetics, resulting in a dynamic flux balance analysis model is described and used to calculate optimal feed policies for fed-batch cultures where the dynamics of the fermentation process is captured by a set of differential equations and the metabolism is described by a genome scale flux balance analysis.

The methodology transforms the bounds of the embedded linear programming problems of flux balance analysis via a logarithmic barrier (interior point) approach. Further algebraic manipulations produce an implicit ordinary differential equations system.

The system of differential equations obtained, is embedded in an optimal control solver (using gPROMS), to optimize the feed flow rate profiles, substrate concentration in the feed and dissolved oxygen profiles in the culture. For genome-scale models, the optimal control problem has thousands of ordinary differential equations. Despite its size, a simulation can be performed in less than one second, and the full optimal control task can be completed in a fraction of a minute. This represents a significant improvement from previous works presented in literature, where problem reformulation based in collocation results in a large non-linear programming problem, and where only a network describing the central metabolism was addressed using this methodology.

Case studies include genome-scale metabolic models for Escherichia coli where total biomass accumulation at the end of the fermentation was maximized and a case study for ethanol accumulation from xylose and glucose using the yeast Scheffersomyces stipitis.