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Modeling of Reaction Kinetics

  • Chapter
Bioreaction Engineering Principles

Abstract

In Chapter 3, measurements of rates of biomass and metabolite production and of substrate consumption were used to put life into the mathematical formalism of the first part of Chapter 2. It was shown that volumetric rate measurements can be used to obtain key parameters for the design of fermentation processes. Likewise it was demonstrated how carefully planned fermentation experiments, after digestion of the results by means of a powerful mathematical procedure, can provide important information relevant to fundamental biochemical research. Not only are rates of missing overall reactions calculable, but the rates r of cellular pathway reactions can also be calculated and interactions between different parts of the cell machinery studied.

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Reference

  • Alexander, M. A. and Jeffries, T. W. (1990). “Respiratory efficiency and metabolite partitioning as regulatory phenomena in yeast,” Enzyme Microb. Technol. 12, 2–19.

    Article  CAS  Google Scholar 

  • Bailey, J. E. and 011is, D. F. (1986). Biochemical Engineering Fundamentals, 2d. ed., McGraw-Hill, New York.

    Google Scholar 

  • Bajpai, R. K. and Ghose, T. K. (1978). “An induction-repression model for growth of yeasts on glucosecellobiose mixtures,” Biotechnol. Bioeng. 20, 927–935.

    Article  CAS  Google Scholar 

  • Baltzis, B. C. and Fredrickson, A. G. (1988). “Limitation of growth by two complementary nutrients: Some elementary, but neglected considerations,” Biotechnol. Bioeng. 31, 75–86.

    Article  PubMed  CAS  Google Scholar 

  • Barford, J. P. and Hall, R. J. (1979). “An examination of the Crabtree effect in Saccharomyces cerevisiae: The role of respiratory adaption,” J. Gen. Microbiol. 114, 267–275.

    CAS  Google Scholar 

  • Barford, J. P., Jeffrey, P. M., and Hall, R. J. (1981). “The Crabtree effect in Saccharomyces cerevisiaeprimary control mechanism or transient,” in Advances in Biotechnology 1, M. Moo-Young, ed., Pergamon Press, Englewood Cliffs, New Jersey 255–260.

    Google Scholar 

  • Benthin, S (1992). Growth and Product Formation of Lactococcus Cremoris, Ph.D. thesis, Technical University of Denmark, Lyngby.

    Google Scholar 

  • Benthin, S., Nielsen, J., and Villadsen, J. (1991). “A simple and reliable method for the determination of cellular RNA content,” Biotechnol. Techniques. 5, 39–42.

    Article  CAS  Google Scholar 

  • Bibal, B., Goma, G., Vayssier, Y.. and Pareilleux, A. (1988). “Influence of pH, lactose and lactic acid on the growth of Streptococcus cremoris: a kinetic study,” Appl. Microbiol. Biotechnol. 28, 340–344.

    Article  CAS  Google Scholar 

  • Bibal, B., Kapp, C., Goma, G., and Pareilleux, A. (1989). “Continuous culture of Streptococcus cremoris on lactose using various medium conditions,” Appl. Microbiol. Biotechnol. 32, 155–159.

    Article  Google Scholar 

  • Dedem, G. van and Moo-Young, M. (1975). “A model for diauxic growth,” Biotechnol. Bioeng. 17, 1301–1312.

    Article  PubMed  Google Scholar 

  • Dhurjati, P., Ramkrishna, D., Flickinger, M. C., Tsao, G. T. (1985). “A cybernetic view of microbial growth: Modeling of cells as optimal strategists,” Biotechnol. Bioeng. 27, 1–9.

    Article  PubMed  CAS  Google Scholar 

  • Domach, M. M., Leung, S. K., Cahn, R. E., Cocks, G. G., and Shuler, M. L. (1984). “Computer model for glucose-limited growth of a single cell of Escherichia coli B/r-A,” Biotechnol. Bioeng. 26, 203216.

    Google Scholar 

  • Egli, T. (1991). “On multiple nutrient limited growth of microorganisms with special reference to dual limitation by carbon and nitrogen substrates,” Antonie van Leeuwenhoek 60, 225–234.

    Article  PubMed  CAS  Google Scholar 

  • Esener, A. A., Roels, J. A., and Kossen, N. W. F. (1981a). “The influence of temperature on the maximum specific growth rate of Klebsiella pneumoniae,” Biotechnol. Bioeng. 23, 1401–1405.

    Article  Google Scholar 

  • Esener, A. A., Roels, J. A., and Kossen, N. W. F. (1981b). “Fed-batch culture: Modeling and applications in the study of microbial energies,” Biotechnol. Bioeng. 27, 1851–1871.

    Article  Google Scholar 

  • Esener, A. A., Roels, J. A., Kossen, N. W. F., and Roozenburg, J. W. H. (1981c). “Description of microbial growth behaviour during the wash-out phase; determination of the maximum specific growth rate,” Eur. J. Appl. Microbiol. Biotechnol. 13, 141–144.

    Article  Google Scholar 

  • Esener, A. A., Veerman, T., Roels, J. A., and Kossen, N. W. F. (1982). “Modeling of bacterial growth; Formulation and evaluation of a structured model, Biotechnol. Bioeng. 29, 1749–1764.

    Google Scholar 

  • Fredrickson, A. G. (1976). “Formulation of structured growth models,” Biotechnol. Bioeng. 18, 1481–1486.

    Article  Google Scholar 

  • Goodenough, U. (1984). Genetics, Saunders College Publishing, New York.

    Google Scholar 

  • Han, K. and Levenspiel, O. (1988). “Extended Monod kinetics for substrate, product, and cell inhibition,” Biotechnol. Bioeng. 32, 430–437.

    Article  PubMed  CAS  Google Scholar 

  • Harder, A. and Roels, J. A. (1982). “Application of simple structured models in bioengineering,” Adv. Biochem. Eng. 21, 55–107.

    CAS  Google Scholar 

  • Heijnen, J. J. and Roels, J. A. (1981). “A macroscopic model describing yield and maintenance in aerobic fermentation processes,” Biotechnol. Bioeng. 23, 739–763.

    Article  CAS  Google Scholar 

  • Heijnen, J. J., Rods, J. A., and Stouthamer, A. H. (1979). “Application of balancing methods in modeling the penicillin fermentation,” Biotechnol. Bioeng. 21, 2175–2201.

    Article  PubMed  CAS  Google Scholar 

  • Heinmets, F. (1969). “Analysis of cellular growth process,” Biomathematics 1, 157–184.

    Google Scholar 

  • Herbert, D. (1959). “Some principles of continuous culture,” Recent Prog. Microbiol. 7, 381–396.

    Google Scholar 

  • Herendeen, S. L., van Bogelen, R. A., and Neidhardt, F. C. (1979). “Levels of major proteins of Escherichia coli during growth at different temperatures,” J. Bacteriol. 139, 185–194.

    Google Scholar 

  • Ingraham, J. L., Maaloe, 0., and Neidhardt, F. C. (1983). Growth of the Bacterial Cell, Sinauer Associates, Inc., Sunderland.

    Google Scholar 

  • Jeong, J. W., Snay, J., and Ataai, M. M. (1990). “A mathematical model for examining growth and sporulation processes of Bacillus subtilis,” Biotechnol. Bioneg. 34, 160–184.

    Article  Google Scholar 

  • Jöbses, I. M. L., Egberts, G. T. C., van Baalen, A., and Roels, J. A. (1985). “Mathematical modeling of growth and substrate conversion of Zymomonas mobilis at 30 and 35 °C,” Biotechnol. Bioeng. 27, 984–995.

    Article  PubMed  Google Scholar 

  • Joshi, A. and Palsson, B. O. (1988). “Escherichia coli growth dynamics: A three-pool biochemically based description,” Biotechnol. Bioeng. 31, 102–116.

    Article  PubMed  CAS  Google Scholar 

  • Kompala, D. S., Ramkrishna, D., and Tsao, G. T. (1984). “Cybernetic modeling of microbial growth on multiple substrates,” Biotechnol. Bioeng. 26, 1272–1281.

    Article  PubMed  CAS  Google Scholar 

  • Kompala, D. S., Ramkrishna, D., Jansen, N. B., and Tsao, G. T. (1986). “Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models,” Biotechnol. Bioeng. 28, 1044–1055.

    Article  PubMed  CAS  Google Scholar 

  • Larsen, J. E. L., Gerdes, K., Light, J., and Molin, S. (1984). “Low-copy-number plasmid-cloning vectors amplifiable by depression of an inserted foreign promoter,” Gene 28, 45–54.

    Article  PubMed  CAS  Google Scholar 

  • Lee, S. B. and Bailey, J. E. (1984a). “A mathematical model for Ado plasmid replication: Analysis of wild-type plasmid,” Plasmid 11, 151–165.

    Google Scholar 

  • Lee, S. B. and Bailey, J. E. (1984b). “A mathematical model for Ado plasmid replication: Analysis of copy number mutants,” Plasmid 11, 166–177.

    Article  PubMed  CAS  Google Scholar 

  • Lee, S. B. and Bailey, J. E. (1984c). “Analysis of growth rate effects on productivity of recombinantEscherichia coli populations using molecular mechanism models,” Biotechnol. Bioeng. 26, 66–73.

    Article  PubMed  CAS  Google Scholar 

  • Lee, S. B. and Bailey, J. E. (1984d). “Genetically structured models for lac promoter-operator function in the Escherichia coli chromosome and in multicopy plasmids: lac operator function,” Biotechnol. Bioeng. 26, 1372–1382.

    Article  Google Scholar 

  • Lee, S. B. and Bailey, J. E. (1984e). “Genetically structured models for lac promoter-operator function in the Escherichia coli chromosome and in multicopy plasmids: lac promoter function,” Biotechnol. Bioeng. 26. 1381–1389.

    Google Scholar 

  • Lehninger, A. L. (1965). Bioenergetics, 2nd. ed., W. A. Benjamin, Palo Alto, CA.

    Google Scholar 

  • Luedeking, R. and Piret, E. L. (1959a). “A kinetic study of the lactic acid fermentation batch process at controlled pH,” J. Biochem. Microbiol. Technol. Eng. 1, 393–412.

    Article  CAS  Google Scholar 

  • Luedeking. R. and Piret, E. L. (1959b). “Transient and steady states in continuous fermentation. Theory and experiment,” J. Biochem. Microbiol. Technol. Eng. 1, 431–459.

    Article  Google Scholar 

  • Meyenburg, K. von (1969). Katabolit-Repression and der Sprossungszyklus von Saccharomyces cerevisiae, Diss. ETH, Zürich.

    Google Scholar 

  • Monod, J. (1942). Recherches sur la croissance des cultures bacteriennes, Hermann et C1e, Paris. Nielsen, J. and Villadsen, J. (1992). “Modeling of microbial kinetics,” Chem. Eng. Sci. 47, 4225–4270.

    Google Scholar 

  • Nielsen, J., Nikolajsen, K., and Villadsen, J. (1991a). “Structured modeling of a microbial system 1. A theoretical study of the lactic acid fermentation,” Biotechnol. Bioeng. 38, 1–10.

    Article  PubMed  CAS  Google Scholar 

  • Nielsen, J., Nikolajsen, K., and Villadsen, J. (1991b). “Structured modeling of a microbial system 2. Verification of a structured lactic acid fermentation model,” Biotechnol. Bioeng. 38, 11–23.

    Article  PubMed  CAS  Google Scholar 

  • Nielsen, J., Pedersen, A. G., Strudsholm, K., and Villadsen, J. (1991c). “Modeling fermentations with recombinant microorganisms: Formulation of a structured model,” Biotechnol. Bioeng. 37, 802–808.

    Article  PubMed  CAS  Google Scholar 

  • Palsson, B. O. and Joshi, A. (1987). “On the dynamic order of structured Escherichia coli growth models,” Biotechnol. Bioeng. 29, 789–792.

    Article  PubMed  CAS  Google Scholar 

  • Peretti, S. W. and Bailey, J. E. (1986). “Mechanistically detailed model of cellular metabolism for glucose-limited growth of Escherichia coli B/r-A,” Biotechnol. Bioeng. 28, 1672–1689.

    Article  PubMed  CAS  Google Scholar 

  • Peretti, S. W. and Bailey, J. E. (1987). “Simulations of host-plasmid interactions in Escherichia coli: Copy number, promoter strength, and ribosome binding site strength effects on metabolic activity and plasmid gene expression,” Biotechnol. Bioeng. 29, 316–328.

    Article  PubMed  CAS  Google Scholar 

  • Pirt, S. J. (1965). “The maintenance energy of bacteria in growing cultures,” Proc. Royal Soc. London Ser. B. 163, 224–231.

    Article  CAS  Google Scholar 

  • Powell, E. O. (1967). “The growth rate of microorganisms as a function of substrate concentration,” in 3 Int. Symposium on Microbial Physiology and Continuous Culture, E. O. Powell, ed., 23–33.

    Google Scholar 

  • Ramkrishna, D. (1979). “Statistical models of cell populations,” Adv. Biochem. Eng. 11, 1–47.

    Google Scholar 

  • Ramkrishna, D. (1982). “A cybernetic perspective of microbial growth,” in Foundations of Biochemical Engineering: Kinetics and Thermodynamics in Biological Systems, American Chemical Society, 161178.

    Google Scholar 

  • Ramkrishna, D., Fredrickson, A. G., and Tsuchiya, H. M. (1967). “Dynamics of microbial propagation: Models considering inhibitors and variable cell composition, Biotechnol. Bioeng. 9, 129–170.

    Google Scholar 

  • Ramkrishna, D., Kompala, D. S., and Tsao, G. T. (1984). “Cybernetic modeling of microbial populations. Growth on mixed substrates,” in Frontiers in Chemical Reaction Engineering, Vol. 1, Wiley Eastern Ltd., New Delhi, 241–261.

    Google Scholar 

  • Ramkrishna, D., Kompala, D. S., and Tsao, G. T. (1987). “Are microbes optimal strategists?” Biotechnol. Prog. 3, 121–126.

    Article  Google Scholar 

  • Rieger, M., Käppeli, O., and Fiechter, A. (1983). “The role of limited respiration in the incomplete oxidation of glucose by Saccharomyces cerevisiae.”./. Gen. Microbiol. 129, 653–661.

    Google Scholar 

  • Roels, J. A. (1983). Energetics and Kinetics in Biotechnology. Elsevier Biomedical Press, Amsterdam. Roels, J. A. and Kossen, N. W. F. (1978). “On the modeling of microbial metabolism,” Prog. Ind. Microbiol. 14, 95–204.

    Google Scholar 

  • Seo, J.-H. and Bailey, J. E. (1985). Effects of recombinant plasmid content on growth properties and cloned gene product formation in Escherichia coli. Bane, huol. Bioeng. 27, 1668–1674.

    Article  CAS  Google Scholar 

  • Shuler, M. L. and Domach, M. M. (1982). “Mathematical models of the growth of individual cells,” in Foundations of Biochemical Engineering: /inch(s and lhcrnuuhnamics in Biological Systems, American Chemical Society Publications. 93 133.

    Google Scholar 

  • Shuler, M. L., Leung, S. K., and Dick, C. C. 1979). ’\mathematical model for the growth of a single bacterial cell,“ Ann. N.Y. Acad. Sei. 326. 35 55.

    Google Scholar 

  • Sonnleitner, B. and Käppeli, O. (1986). “Grouch of S,,cchmonnces cerevisiae is controlled by its limited respiratory capacity: Formulation and veri)ic,iuon oi,, livp„thrsis. Biotechnol. Bioeng. 28, 927–937.

    Google Scholar 

  • Strudsholm, K., Nielsen, J., and Emborg, C. 1199’ Pnatu.t formation during batch fermentation with recombinant E. coli containing a runa a plasmid.“ 1t5.1., Inc. 8. 173–181.

    Google Scholar 

  • Sweere, A. P. J., Giesselbach, J., Barendse. R.. de Knrgei. R. I;outlet-d, G.. and Luyben, K. Ch. A. M. (1988). “Modeling the dynamic behaviour of Saccliai o m.c. eere%isiae and its application in control experiments,” Appl. Microbial. Biotechnol. 28. I It, i t

    Google Scholar 

  • Tsao, G. T. and Hanson, T. P. (1975). “Extended Monod equation for batch cultures with multiple exponential phases,” Biotechnol. Bioeng. 17, 1591–1598.

    Article  Google Scholar 

  • Turner, B. G. and Ramkrishna, D. (1988). “Revised enzyme synthesis rate expression in cybernetic models of bacterial growth,” Biotechnol. Bioeng. 31, 41–43.

    Article  PubMed  CAS  Google Scholar 

  • Uhlin, B. E., Molin, S., Gustafsson, P., and Nordström, K. (1979). “Plasmids with temperature-dependent copy number for amplification of cloned genes and their products,” Gene 6, 91–106.

    Article  PubMed  CAS  Google Scholar 

  • Urk, H. van, Mak, P. R., Scheffers, W. A., and van Dijken, J. P. (1988). “Metabolic responses of Saccharomyces cerevisiae CBS8066 and Candida utilis CBS621 upon transition from glucose limitation to glucose excess,” Yeast 4, 283–291.

    Google Scholar 

  • Williams, F. M. (1967). “A model of cell growth dynamics,” J. Theoret. Biol. 15, 190–207.

    Google Scholar 

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  1. Technical University of Denmark, Lyngby, Denmark

    Jens Nielsen & John Villadsen

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  1. Jens Nielsen
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  2. John Villadsen
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© 1994 Springer Science+Business Media New York

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Nielsen, J., Villadsen, J. (1994). Modeling of Reaction Kinetics. In: Bioreaction Engineering Principles. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4645-7_4

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  • DOI: https://doi.org/10.1007/978-1-4757-4645-7_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-4647-1

  • Online ISBN: 978-1-4757-4645-7

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