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Abstract

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect.

When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth.

The concept of energy conductance, defined as the ratio of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coll is close to the mean value for a wide variety of animals.

Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.

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References

  • Aksnes DL & Egge JK (1991) A theoretical model for nutrient uptake in phytoplankton. Mar. Ecol. Prog. Series 70: 65–72

    Article  Google Scholar 

  • Bremer H & Dennis PP (1987) Modulation of chemical composition and other parameters of the cell by growth rate. In: Neidhardt FC (Ed) Escherichia coli and Salmonella typhimuriwn (pp 1527–1542). Am. Soc. Microbiol., Washington

    Google Scholar 

  • Button DK (1991) Biochemical basis for whole-cell uptake kinetics: specific affinity, oligotrophic capacity, and the meaning of Michaelis constant. Appl. Envir. Microbiol. 57: 2033–2038

    CAS  Google Scholar 

  • Collins JF & Richmond MH (1962) Rate of growth of Bacillus cereus between divisions. J. Gen. Microbiol. 28: 15–33

    Article  PubMed  CAS  Google Scholar 

  • Cooper S (1989) The constrained hoop: an explanation of the overshoot in cell length during a shift-up of Escherichia coil. J. Bact. 171: 5239–5243

    PubMed  CAS  Google Scholar 

  • Cooper S (1991) Bacterial Growth and Division. Academic Press, London

    Google Scholar 

  • Dawes EA (1976) Endogenous metabolism and the survival of starved prokaryotes. In: Gray TR & Postgate JR (Eds) The Survival of Vegetative Microbes (pp 19–53). Cambridge Univ. Press, Cambridge

    Google Scholar 

  • Dawes EA (1986) Microbial Energetics. Blackie, Glasgow

    Google Scholar 

  • DeLaca TE, Karl DM & Lipps JH (1981) Direct use of dissolved organic carbon by agglutinated benthic foraminifera. Nature 289: 287–289

    Article  CAS  Google Scholar 

  • Donachie WD (1968) Relationship between cell size and time of initiation of DNA replication. Nature 219: 1077–1079

    Article  PubMed  CAS  Google Scholar 

  • Donachie WD, Begg KG & Vicente M. (1976) Cell length, cell growth and cell division. Nature 264: 328–333

    Article  PubMed  CAS  Google Scholar 

  • Droop MR (1983) 25 years of algal growth kinetics. Botanica Marina 26: 99–112

    Article  Google Scholar 

  • Esener AA, Veerman T, Rods JA & Kossen NWF (1982) Modeling of bacterial growth: formulation and evaluation of a structured model Biotechnol. Bioeng. 24: 1749–1764

    Article  CAS  Google Scholar 

  • Esener AA, Roels JA & Kossen NWF (1983) Theory and applications of unstructured growth models: kinetic and energetic aspects. Biotechnol. Bioeng. 25: 2803–2841

    Article  PubMed  CAS  Google Scholar 

  • Evers EG & Kooijman SALM (1989) Feeding and oxygen consumption in daphnia magna: a study in energy budgets. Neth. J. Zool. 39: 56–78

    Article  Google Scholar 

  • Fredrickson AG, Ramkrishna D & Tsuchiya MM (1967) Statistics and dynamics of procaryotic cell populations. Math. Biosci. 1: 327–374

    Article  Google Scholar 

  • Grover NB, Zaritsky A, Woldringh CL & Rosenberger RF (1980) Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up. I. Theory. J. Theor. Biol. 86: 421–439

    Article  CAS  Google Scholar 

  • Harder A & Roels JA (1982) Application of simple structured models in bioengineering. Adv. Biochem. Eng. 21: 55–107

    CAS  Google Scholar 

  • Harvey RJ, Marr AG & Painter PR (1967) Kinetics of growth of individual cells of Escherichia coil and Azotobacter agilis. J. Bacteriol. 93: 605–617

    PubMed  CAS  Google Scholar 

  • Knaysi G (1941) A morphological study of Streptococcus faecalis. J. Bacteriol. 42: 575–586

    PubMed  CAS  Google Scholar 

  • Koch AL (1970) Overall controls on the biosynthesis of ribo-somes in growing bacteria. J. Theor. Bio1. 28: 203–231

    Article  CAS  Google Scholar 

  • Koch AL (1985) The macroeconomics of bacterial growth. In: Fletcher M & Floodgate GD (Eds) Bacteria in Their Natural Environment. Special Publ. Soc. Gen. Microbiol. 16: 1–42

    Google Scholar 

  • Koch AL & Schaechter M (1962) A model for the statistics of the division process. J. Gen. Microbiol. 29: 435–454

    Article  PubMed  CAS  Google Scholar 

  • Kooi BW & Kooijman SALM (1991) Existence and stability of microbial prey-predator systems. (submitted)

    Google Scholar 

  • Kooijman SALM (1986a) Population dynamics on the basis of budgets. In: Metz JAJ & Diekmann O (Eds) The Dynamics of Physiologically Structured Populations (pp 266–297). Springer Lecture Notes in Biomathematics. Springer-Verlag, Berlin

    Google Scholar 

  • Koppes LJH, Woldringh CL & Nanninga N (1978) Size variations and correlation of different cell cycle events in slow-growing Escherichia coli. J. Bacteriol. 134: 423–433

    PubMed  CAS  Google Scholar 

  • Kubitschek HE (1990a) Cell volume increase in Escherichia cols after shifts to richer media. J. Bact. 172: 94–101

    CAS  Google Scholar 

  • Kubitschek HE (1990b) Cell growth and abrupt doubling of membrane proteins in Escherichia coil during the division cycle. J. Gen. Microbiol. 136: 599–606

    Article  CAS  Google Scholar 

  • Marr AG (1991) Growth rate of Escherichia coli. Bacterial Reviews 55: 316–333

    CAS  Google Scholar 

  • Marr AG, Painter PR & Nilson EH (1969) Growth and division of individual bacteria. Symp. Soc. Gen. Microbiol. 19: 237–261

    Google Scholar 

  • Metz JAJ & Diekmann O (Eds) (1986). The Dynamics of Physiologically Structured Populations. Springer Lecture Notes in Biomathematics. Springer-Verlag, Berlin

    Google Scholar 

  • Mitchison JM (1961) The growth of single cells. III. Streptococcus faecalis. Exp. Cell. Res. 22: 208–225

    Article  PubMed  CAS  Google Scholar 

  • Moreno S, Nurse P & Russell P (1990) Regulation of mitosis by cyclic accumulation of p80cdc25 mitotic inducer in fission yeast. Nature 344: 549–552

    Article  PubMed  CAS  Google Scholar 

  • Morita RJ (1982) Starvation-survival of heterotrophs in the marine environment. Adv. Microb. Ecol. 6: 171–198

    Article  Google Scholar 

  • Owens JD & Legan JD (1987) Determination of the monod substrate saturation constant for microbial growth. FEMS Microbiol. Rev.46: 419–432

    Article  CAS  Google Scholar 

  • Painter PR & Marr AG (1968) Mathematics of microbial populations. Annu. Rev. Microbiol. 22: 519–548

    Article  PubMed  CAS  Google Scholar 

  • Pedersen S (1984) Escherichia coil ribosomes translate in vivo with variable rate. EMBO J. 3: 2895–2898

    PubMed  CAS  Google Scholar 

  • Pirt SJ (1965) The maintenance energy of bacteria in growing cultures. Proc. Roy. Soc. B 163: 224–231

    Article  CAS  Google Scholar 

  • Pirt SJ & Callow DS (1960) Studies of the growth of Penicillium chrysogenum in continuous flow culture with reference to penicillin production. J. Appl. Bact. 23: 87–98

    Article  Google Scholar 

  • Prescott DM (1957) Relations between cell growth and cell division. In: Rudnick D (Ed) Rhythmic and Synthetic Processes in Growth (pp 59–74). University Press, Princeton

    Google Scholar 

  • Ramkrishna D (1979) Statistical models of cell populations. Adv. Biochem. Eng. 11: 1–45

    Google Scholar 

  • Rutgers M, Teixeira de Mattos MI, Postma PW & Dam K van (1987) Establishment of the steady state in glucose-limited chemostat cultures of Kleibsiella pneumoniae. J. Gen. Microbiol. 133: 445–453

    PubMed  CAS  Google Scholar 

  • Schmalhausen II & Syngajewskaja E (1925) Studien über Wachstum und Differenzierung. I. Die individuelle Wachtumskurve von Paramaecium caudatum. Roux Arch. 105: 711–717

    Article  Google Scholar 

  • Schulze KL & Lipe RS (1964) Relationship between substrate concentration, growth rate, and respiration rate of Escherichia coli in continuous culture. Arch. Mikrobiol. 48: 1–20

    Article  PubMed  CAS  Google Scholar 

  • Senn HP (1989) Kinetik und Regulation des Zuckerabbaus von Escherichia coli ML 30 bei tiefen Zuckerkonzentrationen. Ph-D thesis, Techn. Hochschule Zurich

    Google Scholar 

  • Stouthamer AH, Bulthuis BA & Verseveld HW van (1990) Energetics of growth at low growth rates and its relevance for the maintenance concept. In: Poole RK, Bazin MJ & Keevil CW (Eds) Microbial Growth Dynamics (pp 85–102). Irl Press, Oxford

    Google Scholar 

  • Syngajewskaja E (1935) The individual growth of protozoa: Blepharisma lateritia and Actinophrys sp. Tray. de l’Inst. Zool. Biol. Acad. Sci. Ukr. 8: 151–157

    Google Scholar 

  • Taylor WD (1978) Growth responses of ciliate protozoa to the abundance of their bacterial prey. Microb. Ecol. 4: 207–214

    Article  Google Scholar 

  • Trinci API, Robson GD, Wiebe MG, Cunliffe B & Naylor TW (1990) Growth and morphology of Fusarium graminearum and other fungi in batch and continuous culture. In: Poole RK, Bazin MJ & Keevil CW (Eds) Microbial Growth Dynamics (pp 17–38). Irl Press, Oxford

    Google Scholar 

  • Trueba FI (1981) A morphometric analysis of Escherichia coli and other rod-shaped bacteria. Ph-D Thesis, University of Amsterdam

    Google Scholar 

  • Tsai SP & Lee YH (1990) A model for energy-sufficient culture growth. Biotechnol. Bioeng. 35: 138–145

    Article  PubMed  CAS  Google Scholar 

  • Voom WJ & Koch AL (1986) Characterization of the stable size distribution of cultured cells by moments. In: Metz JAJ & Diekmann O (Eds) The Dynamics of Physiologically Structured Populations (pp 430–473). Springer Lecture Notes in Biomathematics. Springer-Verlag, Berlin

    Google Scholar 

  • Westerhoff HV, Dam K van (1987) Thermodynamics and control of biological free-energy transduction. Elsevier, Amsterdam

    Google Scholar 

  • Zaritsky A, Woldringh CL, Grover NB, Naaman J & Rosenberger RF (1982) Growth and form in bacteria. Comments Mol. Cell. Biophys. 4: 237–260

    Google Scholar 

  • Zonneveld C & Kooijman SALM (1989) The application of a dynamic energy budget model to Lymnaea stagnalis. Func. Ecol. 3: 269–278

    Article  Google Scholar 

  • Zonneveld C & Kooijman SALM (1991) The comparative kinetics of embryo development. (submitted)

    Google Scholar 

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Kooijman, S.A.L.M., Muller, E.B., Stouthamer, A.H. (1992). Microbial growth dynamics on the basis of individual budgets. In: Stouthamer, A.H. (eds) Quantitative Aspects of Growth and Metabolism of Microorganisms. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2446-1_4

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  • DOI: https://doi.org/10.1007/978-94-011-2446-1_4

  • Publisher Name: Springer, Dordrecht

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