Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ackermann J-U, Müller S, Lösche A, Bley T et al (1995) Methylobacterium rhodesianum cells tend to double the DNA content under growth limitations and accumulate PHB. J Biotechnol 39:9–20
Bailey JE, Ollis FD (1977) Biochemical engineering fundamentals. McGraw-Hill, New York
Bellgardt K-H (1994) Analysis of synchronous growth of baker’s yeast. Part i: development of a theoretical model for sustained oscillations. J Biotechnol 35:19–33
Ben-Jacob E, Schochet O, Tenenbaum A, Cohen I et al (1994) Generic modeling of cooperative growth patterns in bacterial colonies. Nature 368:46–49
Bley T, Schmidt A (1980) A two state microbial growth model for continuous fermentation. Stud Biophys 78:11–12
Bley T, Heinritz B, Schmidt A (1984) Some stationary properties of a two-state microbial growth model for continuous fermentation derived from the smith and martin hypothesis. Stud Biophys 98:119–124
Bley T (1987) State-structure models of microbial growth. Acta Biotechnol 7:173–177
Bley T, Wegner B (1988) Hopf bifurcation for a family of two-state microbial growth models. Acta Biotechnol 8:267–275
Bley T (1990) State structure models––a base for efficient control of fermentation processes. Biotechnol Adv 8:233–259
Bley T (1992) Delay-differential equations for modeling synchrony and periodic phenomena in microbial population dynamics. In: Karim MN, Stephanopoulos G (eds) Modeling and control of biotechnical processes. Pergamon Press, NY, pp 195–199
Bley T, Müller S (2002) How should microbial life be quantified to optimize bioprocesses. Acta Biotechnol 22:401–409
Boschke E, Bley T (1998) Growth patterns of yeast colonies depending on nutrient supply. Acta Biotechnol 18:17–27
Cazzador L, Mariani L, Martegani E, Alberghina L (1990) Structured segregated models and analysis of self-oscillating yeast continuous cultures. Bioprocess Eng 5:175–180
Cipollina C, Vai M, Porro D, Hatzis C (2007) Towards understanding of the complex structure of growing yeast populations. J Biotechnol 128:393–402
Cooper S (1979) A unifying model for the g1 period in prokaryotes and eukaryotes. Nature 280:17–19
Dawson PSS (1972) Continuously synchronized growth. J Appl Chem Biotechnol 22:79–103
Deutsch A, Dress A, Rensing L (1993) Formation of morphological differentiation patterns in the ascomycete Neurospora crassa. Mech Dev 44:17–31
Deutsch A, Dormann S (2005) Cellular automation modelling of biological pattern formation. Birkhauser, Boston
Eakman JM, Fredrickson AG, Tsuchiya HM (1966) Statistics and dynamics of microbial cell populations. Chem Eng Prog 62:37–49
Ferrer J, Prats C, López D (2008) Individual-based modelling: an essential tool for microbiology. J Biol Phys 34:19–37
Fredrickson AG, Ramkrishna D, Tsuchiya HM (1967) Statistics and dynamics of procaryotic cell populations. Math Biosci 1:327–374
Fredrickson AG, Mantzaris NV (2002) A new set of population balance equations for microbial and cell cultures. Chem Eng Sci 57:2265–2278
Fritsch M, Starruss J, Loesche A, Mueller S et al (2005) Cell cycle synchronization of Cupriavidus necator by continuous phasing measured via flow cytometry. Biotechnol Bioeng 92:635–642
Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University Press, Princeton
Große-Uhlmann R, Bley T (1999) A modular approach to situation identification of the dynamics of bacterial populations synthesizing poly-β-hydroxybutyrate. Bioprocess Eng 21:191–200
Gurney WS, Nisbet RM (1984) The systematic formulation of delay-differential models of age or size structured populations. Lect Notes Biomath 52:163–172
Hatzis C, Porro D (2006) Morphologically-structured models of growing budding yeast populations. J Biotechnol 124:420–438
Hellweger FL, Bucci V (2009) A bunch of tiny individuals––individual-based modeling for microbes. Ecol Model 220:8–22
Hjortso MA, Bailey JE (1982) Steady-state growth of budding yeast populations in well-mixed continuos-flow microbial reactors. Math Biosci 60:235–263
Hjortso MA, Nielsen J (1995) Population balance models of autonomous microbial oscillations. J Biotechnol 42:255–269
Kiefer J (1973) Zur Mathematischen Beschreibung der Zellproliferation. Biophysik 10:115–124
Kreft J-U, Booth G, Wimpenny JWT (1998) Bacsim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144:3275–3287
Kreft J-U, Picioreanu C, Wimpenny JWT, van Loosdrecht MCM (2001) Individual-based modeling of biofilms. Microbiology 147:2897–2912
Lapin A, Müller D, Reuss M (2004) Dynamic behavior of microbial populations in stirred bioreactors simulated with Euler–Lagrange methods: traveling along the lifelines of single cells. Ind Eng Chem Res 43:4647–4656
Lapin A, Schmidt J, Reuss M (2006) Modelling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor—a structured-segregated approach. Chem Eng Sci 61:4783–4797.
Lavric V, Graham DW (2010) Birth, growth and death as structuring operators in bacterial population dynamics. J Theor Biol 264:45–54
Lee MW, Vassiliadis VS, Park JM (2009) Individual-based and stochastic modelling of cell population dynamics considering substrate dependency. Biotechnol Bioeng 103:891–899
Mantzaris NV (2007) From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture. Biophys J 92:4271–4288
Mhaskar P, Hjortso MA, Henson MA (2002) Cell population modelling and parameter estimation for continuous cultures of Saccharomyces cerevisiae. Biotechnol Prog 18:1010–1026
Möckel B, Bley T, Böhme B (1989) Cyclic control of continuous biotechnological processes on the basis of a hierarchical control system. Syst Anal Model Simul 6:181–196
Möckel B, Bley T, Böhme B (1990) Model simulation of an efficient periodic control strategy for continuous fermentation processes. Acta Biotechnol 10:395–400
Müller S, Bley T, Babel W (1999) Adaptive responses of Ralstonia eutropha to feast and famine conditions analyzed by flow cytometry. J Biotechnol 75:81–97
Müller S (2007) Modes of cytometric bacterial DNA pattern: a tool for pursuing growth. Cell Prolif 40:621–639
Müller S, Harms H, Bley T (2010) Origin and analysis of microbial population heterogeneity in bioprocesses. Curr Opin Biotechnol 21:100–113
Nishimura Y, Bailey JE (1980) On the dynamics of Cooper-Helmstetter-Donachie populations. Math Biosci 51:305–328
Noack S, Klöden W, Bley T (2008) Modelling synchronous growth of bacterial populations in phased cultivation. Bioprocess Biosyst Eng 31:435–443
Porro D, Vai M, Vanoni M, Alberghina L et al (2009) Analysis and modeling of growing budding yeast populations at the single cell level. Cytometry 75A:114–120
Prats C, López D, Giró A, Ferrer J et al (2006) Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase. J Theor Biol 241:939–953
Priori L, Ubezio P (1996) Mathematical modelling and computer simulation of cell synchrony. Methods Cell Sci 18:83–91
Sherer E, Tocce E, Hannemann RE, Rundell AF et al (2008) Identification of age-structured models: cell cycle phase transition. Biotechnol Bioeng 99:960–974
Slater ML, Sharrow SO, Gart JJ (1977) Cell cycle of Saccharomyces cerevisiae in populations growing at different rates. Proc Natl Acad Sci USA 74:3850–3854
Smith JA, Martin L (1973) Do cells cycle? Proc Natl Acad Sci USA 70:1263–1267
Srienc F (1999) Cytometric data as the basis for rigorous models of cell population dynamics. J Biotechnol 71:233–238
Starruß J, Bley T, Sogaard-Andersen L, Deutsch A (2007) A new mechanism for collective migration in Myxococcus xanthus. J Stat Phys 128:269–286.
Trucco E (1965) Mathematical models for cellular systems: the von Foerster equation. Part i and ii. Bull Math Biophys 27:285–304 (see also pp 449–471).
von Foerster H (1959) Some remarks on changing populations. In: Stohlman F (ed) The kinetics of cellular proliferation. Grune & Stratton, New York
Walther T, Reinsch H, Große A, Ostermann K et al (2004) Mathematical modeling of regulatory mechanisms in yeast colony development. J Theor Biol 229:327–338
Walther T, Reinsch H, Ostermann K, Deutsch A et al (2005) Coordinated development of yeast colonies: B) quantitative modeling of diffusion-limited growth. Eng Life Sci 5:125–133.
Walther Th, Reinsch H, Ostermann K, Deutsch A, Bley Th (2010) Applying dimorphic yeasts as model organisms to study mycelial growth: Part 2: application of mathematical models to identify different construction principles in yeast colonies. Bioprocess Biosyst Eng. doi:10.1007/s00449-010-0443-5. Accessed 15 June 2010
Winfree AT (1990) The geometry of biological time. Springer, Berlin
Xavier JB, Foster KR (2007) Cooperation and conflict in microbial biofilms. Proc Natl Acad Sci USA 104:876–881
Zamamiri AM, Zhang Y, Henson MA, Hjortso MA (2002) Dynamics analysis of an age distribution model of oscillating yeast cultures. Chem Eng Sci 57:2169–2181
Zhu G-Y, Zamamiri A, Henson MA, Hjortso MA (2000) Model predictive control of continuous yeast bioreactors using cell population balance models. Chem Eng Sci 55:6155–6167
Acknowledgments
The author would like to thank Florian Centler, Andreas Deutsch, and Felix Lenk for their critical reading of the manuscript and their helpful notes.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bley, T. (2010). From Single Cells to Microbial Population Dynamics: Modelling in Biotechnology Based on Measurements of Individual Cells. In: Müller, S., Bley, T. (eds) High Resolution Microbial Single Cell Analytics. Advances in Biochemical Engineering / Biotechnology, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10_2010_79
Download citation
DOI: https://doi.org/10.1007/10_2010_79
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16886-4
Online ISBN: 978-3-642-16887-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)