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Modeling synchronous growth of bacterial populations in phased cultivation

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Abstract

The phasing technique is a method for synchronizing cell populations in a bioreactor. Periodic changes of substrate supply and depletion can provoke a cell cycle phasing of originally stochastic scattered proliferation patterns. Synchronized cell populations characterized by changes in DNA content distribution can be monitored by flow cytometry. Thus, studies of the dynamics of single cells in specific cell cycle phases are facilitated. Here we present an age structured model framework investigating synchronized populations using delay differential equations. Applying the framework not only cell populations synchronously increasing under balanced growth conditions, but also synchronized cultures growing in continuous phasing experiments can be described. A process model developed for describing phased cultures was fitted to growth data obtained from a synchronous cultivation of Cupriavidus necator. Its potential utility is demonstrated by a quantitative process description and by its ability to identify ways in which the grade of synchrony could be improved.

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Abbreviations

B(t),C(t),D(t):

concentration of cells in the respective cell cycle phases (cells/l)

k :

constant transition rate (h−1)

k ph (s):

phase transition rate of the process model (h−1)

k max :

maximal transition rate (h−1)

K s :

half-saturation constant of μ(s) (g/l)

K T :

half-saturation constant of k ph (s) (g/l)

n c :

number of executed phase cycles

N(t):

summed concentration of cells in all cell cycle phases (cells/l)

ps :

proportion of synchronization

R(t):

normalized cell division rate (h−1)

s(t):

substrate concentration (g/l)

T :

length of phase cycles (h)

t d :

doubling time (h)

t i :

time of volume exchange (h)

Y N/s :

yield coefficient (cells/g)

α:

volume exchange factor

δ(t):

Dirac delta function

φ(t):

history function of state variables (cells/l)

μ(s):

growth rate (h−1)

μmax :

maximal growth rate (h−1)

τ ph :

fixed phase duration (h)

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Authors and Affiliations

  1. Research Centre Jülich GmbH, Institute of Biotechnology 2, Leo-Brandt-Str., 52428, Jülich, Germany

    Stephan Noack

  2. Dresden University of Technology, Institute of Process Engineering and Environmental Engineering, Helmholtzstraße 14, 01069, Dresden, Germany

    Wolfgang Klöden

  3. Dresden University of Technology, Institute of Food Technology and Bioprocess Engineering, Bergstraße 120, 01069, Dresden, Germany

    Thomas Bley

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  1. Stephan Noack
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  2. Wolfgang Klöden
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  3. Thomas Bley
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Correspondence to Stephan Noack.

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Noack, S., Klöden, W. & Bley, T. Modeling synchronous growth of bacterial populations in phased cultivation. Bioprocess Biosyst Eng 31, 435–443 (2008). https://doi.org/10.1007/s00449-007-0180-6

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