Advertisement

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
Originals

Abstract

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.

Keywords

Waste Water Fermentation Water Management Water Pollution Tryptophan 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

D l/h

dilution rate

Km g/l

Monod constant

p

probability of plasmid loss per generation

s g/l

substrate concentration

t h

time

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

Subscripts

1

cells without plasmids

2

cells with plasmids

s

steady state

Superscript

o

inlet stream

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baylor, D. A.;Hodgkin, A. L.;Lamb, T. D.: The electrical response of turtle cones to flashes and steps of light. J. Physiol. 242 (1974) 685–727CrossRefGoogle Scholar
  2. 2.
    MacDonald, N.: Cyclical neutropenia: models with two cell types and two time lags. In: Valleron, A. J.; MacDonald, P. D. M. (Eds.) Biomathematics and Cell Kinetics, pp. 287–295. Amsterdam: North Holland 1978Google Scholar
  3. 3.
    Plant, R. E.: A Fitzhugh differential-difference equation modeling recurrent neural feedback. SIAM J. Appl. Math. 40 (1981) 150–162CrossRefGoogle Scholar
  4. 4.
    MacDonald, N.: Time delays in chemostat models. In: Brazin, M. J. (Ed.) Microbial Population Dynamics, pp. 33–53. Boca Raton, Florida: C. R. C. Press 1982Google Scholar
  5. 5.
    Lyberatos, G.: The effect of delay on the feedback identification of chemical reaction systems. Chem. Eng. Sci. 40 (1985) 2160–2162CrossRefGoogle Scholar
  6. 6.
    Powell, E. O.: Hypertrophic growth. J. Appl. Chem. Biotechnol. 22 (1972) 71–78CrossRefGoogle Scholar
  7. 7.
    O'Neill, D. G.;Lyberatos, G.: Feedback identification of continuous microbial growth systems. Biotechnol. Bioeng. 28 (1986) 1323–1333CrossRefGoogle Scholar
  8. 8.
    Stephens, M. L.;Christensen, C.;Lyberatos, G.: Plasmid stabilization of an Escherichia coli culture through cycling. Biotechnol. Prog. 8 (1992) 1–4CrossRefGoogle Scholar
  9. 9.
    Summers, D. K.: The kinetics of plasmid loss. Trends Biotechnol. 9 (1991) 273–278CrossRefGoogle Scholar
  10. 10.
    Stephens, M. L.;Lyberatos, G.: Effect of cycling on final mixed culture fate. Biotechnol. Bioeng. 29 (1987) 672–678CrossRefGoogle Scholar
  11. 11.
    Stephens, M. L.;Lyberatos, G.: Effect of cycling on the stability of plasmid-bearing microorganisms in continuous culture. Biotechnol. Bioeng. 31 (1988) 464–469CrossRefGoogle Scholar
  12. 12.
    Weber, A. E.;San, K.-Y.: Enhanced plasmid maintenance in a CSTR upon square-wave oscillations in the dilution rate. Biotechnol. Lett. 10 (1988) 531–536CrossRefGoogle Scholar
  13. 13.
    Ollis, D. F.;Chang, H. T.: Batch fermentation kinetics with unstable recombinant cultures. Biotechnol. Bioeng. 24 (1982) 2583–2586CrossRefGoogle Scholar
  14. 14.
    Lee, S. B.;Ryu, D. D. Y.;Seigel, R.;Park, S. H.: Performance of recombinant fermentation and evaluation of gene expression efficiency for gene product in two-stage continuous culture system. Biotechnol. Bioeng. 31 (1988) 805–820CrossRefGoogle Scholar
  15. 15.
    Lee, S. B.;Seressiotsis, A.;Bailey, J. E.: A kinetic model for product formation in unstable recombinant populations. Biotechnol. Bioeng. 27 (1985) 1699–1709CrossRefGoogle Scholar
  16. 16.
    Ioos, G.;Joseph, D. D.: Elementary Stability and Bifurcation Theory, Heidelberg: Springer Verlag 1980CrossRefGoogle Scholar
  17. 17.
    Lyberatos, G.;Kuszta, B.;Bailey, J. E.: Normal forms for chemical reaction systems via the affine transformation. Chem. Eng. Sci. 40 (1985) 1177–1189CrossRefGoogle Scholar
  18. 18.
    MacDonald, N.: Biological Delay Systems: Linear Stability Theory, Ch. 6. Cambridge: Cambridge University Press 1989Google Scholar
  19. 19.
    Patnaik, P. R.: Dependence of process variables on fermentation parameters during start-up of a continuous flow reactor with recombinant microorganisms. Biotechnol. Lett. 7 (1993) 137–142Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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

Personalised recommendations