1887

Abstract

Summary: The generic, quantitative, spatially explicit, individual-based model BacSim was developed to simulate growth and behaviour of bacteria. The potential of this approach is in relating the properties of microscopic entities – cells – to the properties of macroscopic, complex systems such as biofilms. Here, the growth of a single cell into a colony was studied. The object-oriented program BacSim is an extension of Gecko, an ecosystem dynamics model which uses the Swarm toolkit for multi-agent simulations. The model describes bacterial properties including substrate uptake, metabolism, maintenance, cell division and death at the individual cell level. With the aim of making the model easily applicable to various bacteria under different conditions, the model uses as few as eight readily obtainable parameters which can be randomly varied. For substrate diffusion, a two-dimensional diffusion lattice is used. For growth-rate-dependent cell size variation, a conceptual model of cell division proposed by Donachie was examined. A mechanistic version of the Donachie model led to unbalanced growth at higher growth rates, whereas including a minimum period between subsequent replication initiations ensured balanced growth only if this period was unphysiologically long. Only a descriptive version of the Donachie model predicted cell sizes correctly. For maintenance, the Herbert model (constant specific rate of biomass consumption) and for substrate uptake, the Michaelis-Menten or the Best equations were implemented. The simulator output faithfully reproduced all input parameters. Growth characteristics when maintenance and uptake rates were proportional to either cell mass or surface area are compared. The authors propose a new generic measure of growth synchrony to quantify the loss of synchrony due to random variation of cell parameters or spatial heterogeneity. Variation of the maximal uptake rate completely desynchronizes the simulated culture but variation of the volume-at-division does not. A new measure for spatial heterogeneity is introduced: the standard deviation of substrate concentrations as experienced by the cells. Spatial heterogeneity desynchronizes population growth by subdividing the population into parts synchronously growing at different rates. At a high enough spatial heterogeneity, the population appears to grow completely asynchronously.

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1998-12-01
2024-10-10
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References

  1. Adam G., Läuger P., Stark G. 1977 Pbysikalische Chemie und Biopbysik. Berlin: Springer;
    [Google Scholar]
  2. Ben-Jacob E., Schochet O., Tenenbaum A., Cohen I., Czirok A., Vicsek T. 1994; Generic modeling of cooperative growth-patterns in bacterial colonies.. Nature 368:46–49
    [Google Scholar]
  3. Blumenthal L.K., Zahler S.A. 1962; Index for measurement of synchronization of cell populations.. Science 135:724
    [Google Scholar]
  4. Booth G. 1997; Gecko: a continuous 2-D world for ecological modeling.. Artif Life 3:147–163
    [Google Scholar]
  5. Button D.K. 1993; Nutrient-limited microbial growth kinetics: overview and recent advances.. Antonie Leeuwenhoek 63:225–235
    [Google Scholar]
  6. Cooper S. 1991 Bacterial Growth and Division. San Diego: Academic Press;
    [Google Scholar]
  7. Davey H.M., Kell D.B. 1996; Flow cytometry and cell sorting of heterogeneous microbial populations: the importance of singlecell analyses.. Microbiol Rev 60:641–696
    [Google Scholar]
  8. DeAngelis D.L., Gross L.J. 1992 Individual-based Models and Approaches in Ecology: Populations, Communities, and Ecosystems. New York: Chapman & Hall;
    [Google Scholar]
  9. Domach M. M., Leung S. K., Cahn R. E., Cocks G. G., Shuler M. L. 1984; Computer model for glucose-limited growth of a single cell of Escherichia coli B/r-A.. Biotechnol Bioeng 26203–216
    [Google Scholar]
  10. Donachie W.D. 1968; Relationship between cell size and time of initiation of DNA replication.. Nature 219:1077–1079
    [Google Scholar]
  11. Donachie W.D., Robinson A.C. 1996; Cell division: parameter values and the process.. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd edn. pp. 1578–1593 Edited by Neidhardt F.C. others Washington, DC: American Society for Microbiology;
    [Google Scholar]
  12. Grimson M.J., Barker G.C. 1994; Continuum model for the spatiotemporal growth of bacterial colonies.. Phys Rev E 49:1680–1684
    [Google Scholar]
  13. Helmstetter C.E. 1996; Timing of synthetic activities in the cell cycle.. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd edn. pp. 1627–1639 Edited by Neidhardt F.C. others Washington, DC: American Society for Microbiology;
    [Google Scholar]
  14. Herbert D. 1958; Some principles of continuous culture.. In Resumes de Travaux Presentées à Sessions de Rapports: 7th Congrès International de Microbiologie, Stockholm pp. 381–396 Edited by Tunevall G. Uppsala: Almqvist & Wiksells;
    [Google Scholar]
  15. Hughes W.H. 1955; The inheritance of differences in growth rate in Escherichia coli.. J Gen Microbiol 12:265–268
    [Google Scholar]
  16. Ingraham J.L., MaalØe O., Neidhardt F.C. 1983 Growth of the Bacterial Cell. Sunderland, MA: Sinauer Associates;
    [Google Scholar]
  17. Jaworska J.S., Hallam T.G., Schultz T.W. 1996; A community model of ciliate Tetrahymena and bacteria E. coli. Part 1. Individual-based models of Tetrahymena and E. coli populations.. Bull Math Biol 58:247–264
    [Google Scholar]
  18. Jeong J.W., Snay J., Ataai M.M. 1990; A mathematical model for examining growth and sporulation processes of Bacillus subtilis.. Biotechnol Bioeng 35:160–184
    [Google Scholar]
  19. Joshi A., Palsson B.O. 1988; Escherichia coli growth dynamics: a three-pool biochemically based description.. Biotechnol Bioeng 31:102–116
    [Google Scholar]
  20. Koch A.L. 1985; The macroeconomics of bacterial growth.. In Bacteria in Their Natural Environments pp. 1–42 Edited by Fletcher M., Floodgate G.D. London: Academic Press;
    [Google Scholar]
  21. Koch A.L. 1993; Biomass growth rate during the prokaryote cell cycle.. Crit Rev Microbiol 19:17–42
    [Google Scholar]
  22. Koch A.L. 1996a; What size should a bacterium be ? A question of scale.. Annu Rev Microbiol 50:317–348
    [Google Scholar]
  23. Koch A.L. 1996b; Similarities and differences of individual bacteria within a clone.. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd edn. pp. 1640–1651 Edited by Neidhardt F.C. others Washington, DC: American Society for Microbiology;
    [Google Scholar]
  24. Koch A.L. 1997; Microbial physiology and ecology of slow growth.. Microbiol Mol Biol Rev 61:305–318
    [Google Scholar]
  25. Koch A.L., Schaechter M. 1962; A model for statistics of the cell division process.. J Gen Microbiol 29:435–454
    [Google Scholar]
  26. Koch A.L., Wang C.H. 1982; How close to the theoretical diffusion limit do bacterial uptake systems function ?. Arch Microbiol 131:36–42
    [Google Scholar]
  27. Kooijman S.A.L.M., Muller E.B., Stouthamer A.H. 1991; Microbial growth dynamics on the basis of individual budgets.. Antonie Leeuwenhoek 60:159–174
    [Google Scholar]
  28. Koppes L.J.H., Meyer M., Oonk H.B., de Jong M.A., Nanninga N. 1980; Correlation between size and age at different events in the cell division cycle of Escherichia coli.. J Bacteriol 143:1241–1252
    [Google Scholar]
  29. Korber D.R., Lawrence J.R., Hendry M.J., Caldwell D.E. 1993; Analysis of spatial variability within mot + and mot Pseudomonas fluorescens biofilms using representative elements.. Biofouling 7:339–358
    [Google Scholar]
  30. Matsushita M. 1997; Formation of colony patterns by a bacterial population.. In Bacteria as Multicellular Organisms pp. 366–393 Edited by Shapiro J.A., Dworkin M. New York: Oxford University Press;
    [Google Scholar]
  31. Minar N., Burkhart R., Langton C., Askenazi M. 1996; The Swarm simulation system: a toolkit for building multi-agent simulations.. SFl Working Paper 96-06-042 http:// www.santafe.edu/sfi/publications
    [Google Scholar]
  32. Neidhardt F.C., Umbarger H.E. 1996; Chemical composition of Escherichia coli.. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd edn. pp. 13–16 Edited by Neidhardt F.C. others Washington, DC: American Society for Microbiology;
    [Google Scholar]
  33. Neijssel O.M., de Mattos M.J.T., Tempest D.W. 1996; Growth yield and energy distribution.. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd edn. pp. 1683–1692 Edited by Neidhardt F.C. others Washington, DC: American Society for Microbiology;
    [Google Scholar]
  34. Picioreanu C., van Loosdrecht M. C. M., Heijnen J. J. 1998a; A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads.. Biotechnol Bioeng 57718–731
    [Google Scholar]
  35. Picioreanu C., van Loosdrecht M.C.M., Heijnen J.J. 1998b; Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach.. Biotechnol Bioeng 58101–116
    [Google Scholar]
  36. Pirt S.J. 1965; The maintenance energy of bacteria in growing cultures.. Proc R Soc London B 163224–231
    [Google Scholar]
  37. Pirt S.J. 1967; A kinetic study of the mode of growth of surface colonies of bacteria and fungi.. J Gen Microbiol 47:181–197
    [Google Scholar]
  38. Schaechter M., Williamson J.P., Hood J.R. Jr Koch A.L. 1962; Growth, cell and nuclear divisions in some bacteria.. J Gen Microbiol 29:421–434
    [Google Scholar]
  39. Schmitz O.J., Booth G. 1997; Modeling food web complexity: the consequence of individual-based spatially explicit behavioral ecology on trophic interactions.. Evol Ecol 11:379–398
    [Google Scholar]
  40. Shapiro J.A., Dworkin M. 1997 Bacteria as Multicellular Organisms. New York: Oxford University Press;
    [Google Scholar]
  41. Shuler M.L., Leung S.K., Dick C.C. 1979; A mathematical model for the growth of a single bacterial cell.. Ann N Y Acad Sci 326:35–55
    [Google Scholar]
  42. Tempest D.W., Neijssel O.M. 1984; The status of YATP and maintenance energy as biologically interpretable phenomena.. Annu Rev Microbiol 38:459–486
    [Google Scholar]
  43. Wimpenny J.W.T. 1992; Microbial systems: patterns in time and space.. Adv Microb Ecol 12:469–522
    [Google Scholar]
  44. Wimpenny J.W.T., Colasanti R. 1997; A unifying hypothesis for the structure of microbial biofilms based on cellular automation models.. FEMS Microbiol Ecol 22:1–16
    [Google Scholar]
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