Dynamic flux balance analysis with nonlinear objective function
- 405 Downloads
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.
KeywordsDynamic flux balance analysis Ordinary differential equations with embedded optimization Extreme pathway analysis Karush–Kuhn–Tucker conditions
Mathematics Subject Classification92B05 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.
- Holmström K (1997) TOMLAB—an environment for solving optimization problems in matlab. Proc Nordic Matlab Conf 97:27–28Google Scholar
- Joy J, Kremling A (2010) Study of the growth of Escherichia coli on mixed substrates using dynamic flux balance analysis. In: 11th IFAC symposium on computer applications in biotechnology, pp 401–406Google Scholar
- Nocedal J, Wright S (2006) Numerical optimization, 2nd edn. Springer Series in Operations Research and Financial Engineering, SpringerGoogle Scholar
- Ramakrishna R, Edwards J, McCulloch A, Palsson B (2001) Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. Am J Physiol Regul Integr Comp Physiol 280(3):695–704Google Scholar
- Schuetz R, Kuepfer L, Sauer U (2007) Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol Syst Biol 3(1):119Google Scholar
- Stephanopoulos G, Aristidou A, Nielsen J (1998) Metabolic engineering: principles and methodologies. Academic Press, WalthamGoogle Scholar
- Zelle E, Nöh K, Wiechert W (2015) Corynebacterium glutamicum: from systems biology to biotechnological applications. In: Burkowski A (ed) Growth and production capabilities of corynebacterium glutamicum: Interrogating a genome-scale metabolic network model. Horizon Press, Far Hills, pp 39–54Google Scholar