title: Dynamic flux balance analysis with nonlinear objective function.
abstract: Dynamic flux balance analysis (DFBA) extends flux balance analysis and enables the combined simulation of both intracellular and extracellular environments of microbial cultivation processes. A DFBA model contains two coupled parts, a dynamic part at the upper level (extracellular environment) and an optimization part at the lower level (intracellular environment). Both parts are coupled through substrate uptake and product secretion rates. This work proposes a Karush-Kuhn-Tucker condition based solution approach for DFBA models, which have a nonlinear objective function in the lower-level part. To solve this class of DFBA models an extreme-ray-based reformulation is proposed to ensure certain regularity of the lower-level optimization problem. The method is introduced by utilizing two simple example networks and then applied to a realistic model of central carbon metabolism of wild-type Corynebacterium glutamicum.
authors.affiliation: IBG-1, Biotechnology, Forschungszentrum Juelich GmbH, 52425, Juelich, Germany.
authors.forename: Xiao
authors.initials: X
authors.lastname: Zhao
authors.affiliation: IBG-1, Biotechnology, Forschungszentrum Juelich GmbH, 52425, Juelich, Germany.
authors.forename: Stephan
authors.initials: S
authors.lastname: Noack
authors.affiliation: IBG-1, Biotechnology, Forschungszentrum Juelich GmbH, 52425, Juelich, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Wiechert
authors.affiliation: IBG-1, Biotechnology, Forschungszentrum Juelich GmbH, 52425, Juelich, Germany. e.von.lieres@fz-juelich.de.
authors.forename: Eric von
authors.identifier: 0000-0002-0309-8408
authors.initials: EV
authors.lastname: Lieres
mesh_terms: D002244:Carbon / Q000378:metabolism; D003198:Computer Simulation; D048230:Corynebacterium glutamicum / Q000378:metabolism; D007700:Kinetics; D055641:Mathematical Concepts; D064688:Metabolic Flux Analysis / Q000706:statistics & numerical data*; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D017711:Nonlinear Dynamics
chemical_list: D002244:Carbon
keywords: Dynamic flux balance analysis; Extreme pathway analysis; Karush–Kuhn–Tucker conditions; Ordinary differential equations with embedded optimization