Bioprocess Engineering

, Volume 12, Issue 4, pp 199–203 | Cite as

Analysis of bifurcations in continuous fermentation using recombinant microorganisms with delayed responses

  • P. R. Patnaik


When the feed rate to a fermenter is varied periodically in order to favor the growth of plasmid-containing cells, a transition may occur from the starting stationary state to another state. The resulting state may be constant or oscillatory. A generalised model based on the adaption times of plasmid-free and plasmid-harboring cells has been used. Analytical conditions have been derived for bifurcation from one nonoscillatory state to another or to an oscillatory state (Hopf bifurcation). The frequency of oscillation is shown to have an upper bound, which can be controlled by manipulating certain process parameters. The production of tryptophan synthetase by the plasmid pPLc23trpAl in E. coli is used as an example to determine the nature of the Hopf bifurcations.


Waste Water Fermentation Water Management Water Pollution Tryptophan 
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List of Symbols

D l/h

dilution rate

Km g/l

Monod constant


probability of plasmid loss per generation

s g/l

substrate concentration

t h


Ti h

delay time of cells ofi-th kind

Xi g/l

concentration of cells ofi-th kind

Yi g/g

yield coefficient of cells ofi-th kind

Greek Symbols

μi l/h

specific growth rate of i-th species

μim l/h

maximum possible value ofμ i

τ h

generalised delay time



cells without plasmids


cells with plasmids


steady state



inlet stream


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • P. R. Patnaik
    • 1
  1. 1.Institute of Microbial TechnologyChandigarhIndia

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