Bioprocess and Biosystems Engineering

, Volume 41, Issue 5, pp 641–655 | Cite as

A systematic approach for finding the objective function and active constraints for dynamic flux balance analysis

  • Ali Nikdel
  • Richard D. Braatz
  • Hector M. Budman
Research Paper


Dynamic flux balance analysis (DFBA) has become an instrumental modeling tool for describing the dynamic behavior of bioprocesses. DFBA involves the maximization of a biologically meaningful objective subject to kinetic constraints on the rate of consumption/production of metabolites. In this paper, we propose a systematic data-based approach for finding both the biological objective function and a minimum set of active constraints necessary for matching the model predictions to the experimental data. The proposed algorithm accounts for the errors in the experiments and eliminates the need for ad hoc choices of objective function and constraints as done in previous studies. The method is illustrated for two cases: (1) for in silico (simulated) data generated by a mathematical model for Escherichia coli and (2) for actual experimental data collected from the batch fermentation of Bordetella Pertussis (whooping cough).


Dynamic flux balance analysis Flux balance analysis Metabolic networks Metabolic engineering Bioprocess modeling 



Stoichiometric matrix


Vector of fluxes


Number of reactions


Time instance




Fluxes that satisfy tight constraints


Fluxes that satisfy relaxed constraints


Weight of sum of squared errors


Identity matrix


Time-varying values of the weights for all the metabolites


Weight of upper bound


Maximum allowable value for \(w_{i}^{{{\text{sc}}}}\)


Weight of lower bound


Number of the objective functions’ candidates


Estimated noise in the growth rate


Total number of metabolites


Number of measured metabolites


Maximum rate


Half saturation concentration


Measurement error


The biomass value at time \(~k\)


The weight coefficients of the objective function candidates



The authors would like to thank Natural Science and Engineering Research Council (NSERC).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ali Nikdel
    • 1
  • Richard D. Braatz
    • 2
  • Hector M. Budman
    • 1
  1. 1.Department of Chemical EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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