From single cells to microbial population dynamics: modelling in biotechnology based on measurements of individual cells.

The development of dynamic modelling of microbial populations in bioprocesses is reviewed. In the 1960s Arnold Fredrickson established the theoretical basis of such models, and other researchers have subsequently advanced them. This review explores the relationships that describe cell proliferation and evaluates the importance of the application of flow cytometry to the fundamental parameterisation of the models for their use in bioprocess engineering. The section "Individual-Based Modelling" discusses recent theoretical developments. Delay-differential equations are demonstrated to describe accurately temporal variation of the cell proliferation cycle and specialised approaches and related iconography are applied to stochastic and deterministic modelling of stages of cellular development. Synchronised cultures of the bacterium Cupriavidus necator were prepared and monitored using a flow cytometer. The data obtained demonstrate that cell proliferation could be simulated quantitatively using the developed model.

[1]  Michael A. Henson,et al.  Model predictive control of continuous yeast bioreactors using cell population balance models , 2000 .

[2]  T. Bley,et al.  Hopf bifurcation for a family of two‐state microbial growth models , 1988 .

[3]  A. G. Fredrickson,et al.  A new set of population balance equations for microbial and cell cultures , 2002 .

[4]  Lilia Alberghina,et al.  Analysis and modeling of growing budding yeast populations at the single cell level , 2009, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[5]  Nikos V Mantzaris,et al.  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. , 2007, Biophysical journal.

[6]  A. Deutsch,et al.  Mathematical modeling of regulatory mechanisms in yeast colony development. , 2004, Journal of theoretical biology.

[7]  William Gurney,et al.  The systematic formulation of delay-differential models of age or size structured populations , 1983 .

[8]  R. Große-Uhlmann,et al.  A modular approach to situation identification of the dynamics of bacterial populations synthesizing poly-β-hydroxybutyrate , 1999 .

[9]  B. Möckel,et al.  Model simulation of an efficient periodic control strategy for continuous fermentation processses , 1990 .

[10]  D. Porro,et al.  Morphologically-structured models of growing budding yeast populations. , 2006, Journal of biotechnology.

[11]  Thomas Bley,et al.  Methylobacterium rhodesianum cells tend to double the DNA content under growth limitations and accumulate PHB , 1995 .

[12]  C. Capatana.  Cellular Automaton Modelling of Biological Pattern Formation , 2008 .

[13]  E. Sherer,et al.  Identification of age‐structured models: Cell cycle phase transitions , 2008, Biotechnology and bioengineering.

[14]  M. Slater,et al.  Cell-cycle of Saccharomyces cerevisiae in populations growing at different rates ( flow microfluorometry / yeast / mithramycin / DNA replication , 2022 .

[15]  David F. Ollis,et al.  Biochemical Engineering Fundamentals , 1976 .

[16]  K. Bellgardt.  Analysis of synchronous growth of baker's yeast. Part I: Development of a theoretical model for sustained oscillations , 1994 .

[17]  Matthias Reuss,et al.  Modeling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor- : A structured-segregated approach , 2006 .

[18]  J. Smith,et al.  Do cells cycle? , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[19]  A. Deutsch,et al.  A New Mechanism for Collective Migration in Myxococcus xanthus , 2007 .

[20]  Steven F. Railsback,et al.  Individual-based modeling and ecology , 2005 .

[21]  A. Deutsch,et al.  Applying dimorphic yeasts as model organisms to study mycelial growth: part 2. Use of mathematical simulations to identify different construction principles in yeast colonies , 2011, Bioprocess and biosystems engineering.

[22]  Matthias Reuss,et al.  Dynamic Behavior of Microbial Populations in Stirred Bioreactors Simulated with Euler−Lagrange Methods: Traveling along the Lifelines of Single Cells† , 2004 .

[23]  F. Hellweger,et al.  A bunch of tiny individuals—Individual-based modeling for microbes , 2009 .

[24]  Growth patterns of yeast colonies depending on nutrient supply , 1998 .

[25]  Formation of morphological differentiation patterns in the ascomycete Neurospora crassa , 1993, Mechanisms of Development.

[26]  James E. Bailey,et al.  On the dynamics of Cooper-Helmstetter-Donachie procaryote populations , 1980 .

[27]  K. Foster,et al.  Cooperation and conflict in microbial biofilms , 2007, Proceedings of the National Academy of Sciences.

[28]  J W Wimpenny,et al.  Individual-based modelling of biofilms. , 2001, Microbiology.

[29]  T. Bley.  State‐structure models of microbial growth , 1987 .

[30]  D. Porro,et al.  Towards understanding of the complex structure of growing yeast populations. , 2007, Journal of biotechnology.

[31]  T. Bley.  State-structure models--a base for efficient control of fermentation processes. , 1990, Biotechnology advances.

[32]  Lilia Alberghina,et al.  Structured segregated models and analysis of self-oscillating yeast continuous cultures , 1990 .

[33]  Thomas Bley,et al.  Origin and analysis of microbial population heterogeneity in bioprocesses. , 2010, Current opinion in biotechnology.

[34]  A. Winfree.  The geometry of biological time , 1991 .

[35]  Stephan Noack,et al.  Modeling synchronous growth of bacterial populations in phased cultivation , 2008, Bioprocess and biosystems engineering.

[36]  T. Vicsek,et al.  Generic modelling of cooperative growth patterns in bacterial colonies , 1994, Nature.

[37]  P. Dawson.  Continuously synchronised growth , 2007 .

[38]  Prashant Mhaskar,et al.  Cell Population Modeling and Parameter Estimation for Continuous Cultures of Saccharomyces cerevisiae , 2002, Biotechnology progress.

[39]  Friedrich Srienc,et al.  Cytometric data as the basis for rigorous models of cell population dynamics , 1999 .

[40]  Michael A. Henson,et al.  Dynamics analysis of an age distribution model of oscillating yeast cultures , 2002 .

[41]  T. Walther,et al.  Coordinated Development of Yeast Colonies: Quantitative Modeling of Diffusion‐Limited Growth – Part 2 , 2005 .

[42]  Clara Prats,et al.  Individual-based Modelling: An Essential Tool for Microbiology , 2008, Journal of biological physics.

[43]  S. Müller.  Modes of cytometric bacterial DNA pattern: a tool for pursuing growth , 2007, Cell proliferation.

[44]  G. Booth,et al.  BacSim, a simulator for individual-based modelling of bacterial colony growth. , 1998, Microbiology.

[45]  Doraiswami Ramkrishna,et al.  Statistics and dynamics of procaryotic cell populations , 1967 .

[46]  H. M. Tsuchiya,et al.  Statistics and dynamics of microbial cell populations. , 1966 .

[47]  E Trucco,et al.  Mathematical models for cellular systems the Von Foerster equation. I. , 1965, The Bulletin of mathematical biophysics.

[48]  E. Trucco,et al.  Mathematical models for cellular systems. The von foerster equation. Part II , 1965 .

[49]  Vasile Lavric,et al.  Birth, growth and death as structuring operators in bacterial population dynamics. , 2010, Journal of theoretical biology.

[50]  J. Starruß,et al.  Cell cycle synchronization of Cupriavidus necator by continuous phasing measured via flow cytometry. , 2005, Biotechnology and bioengineering.

[51]  S. Müller,et al.  Adaptive responses of Ralstonia eutropha to feast and famine conditions analysed by flow cytometry. , 1999, Journal of biotechnology.

[52]  Vassilios S. Vassiliadis,et al.  Individual‐based and stochastic modeling of cell population dynamics considering substrate dependency , 2009, Biotechnology and bioengineering.

[53]  J. Nielsen,et al.  Population balance models of autonomous microbial oscillations. , 1995, Journal of biotechnology.

[54]  P. Ubezio,et al.  Mathematical modelling and computer simulation of cell synchrony , 1996 .

[55]  James E. Bailey,et al.  Steady-State growth of budding yeast populations in well-mixed continous-flow microbial reactors , 1982 .

[56]  Stephen Cooper,et al.  A unifying model for the G1 period in prokaryotes and eukaryotes , 1979, Nature.

[57]  Clara Prats,et al.  Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase. , 2006, Journal of theoretical biology.