Journal of Mathematical Biology

, Volume 75, Issue 6–7, pp 1487–1515 | Cite as

Dynamic flux balance analysis with nonlinear objective function

  • Xiao Zhao
  • Stephan Noack
  • Wolfgang Wiechert
  • Eric von Lieres


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.


Dynamic flux balance analysis Ordinary differential equations with embedded optimization Extreme pathway analysis Karush–Kuhn–Tucker conditions 

Mathematics Subject Classification

92B05 34A38 90C30 90C46 



The authors gratefully acknowledge financial support from Bioeconomy Science Center (BioSC, Grant No. 005-1304-0001) in Germany and the German Federal Ministry of Education and Research (BMBF, Grant. No. 031L0015). Xiao Zhao would like to thank his colleagues Jannick Kappelmann for fruitful discussions on flux balance analysis and Ralf Hannemann-Tamas from RWTH Aachen University for the discussion of ODEO and the KKT-based solution method.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.IBG-1, Biotechnology, Forschungszentrum Juelich GmbHJuelichGermany

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