Toward an Integrated Physiological Theory of Microbial Growth: From Subcellular Variables to Population Dynamics
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1.
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005
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2.
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105
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Received:
01 September 2004
Accepted:
29 June 2018
Published:
01 November 2004
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MSC :
92D25, 92D37, 92D45.
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The dynamics of microbial growth is a problem of fundamental interest in microbiology,
microbial ecology, and biotechnology. The pioneering work of Jacob
Monod, served as a starting point for developing a wealth of mathematical
models that address different aspects of microbial growth in
batch and continuous cultures. A number of phenomenological models
have appeared in the literature over the last half century. These
models can capture the steady-state behavior of pure and mixed cultures,
but fall short of explaining most of the complex dynamic phenomena.
This is because the onset of these complex dynamics is invariably
driven by one or more intracellular variables not accounted
for by phenomenological models.
 
In this paper, we provide an overview of the experimental data, and
introduce a different class of mathematical models that can be used
to understand microbial growth dynamics. In addition to the standard
variables such as the cell and substrate concentrations, these models
explicitly include the dynamics of the physiological variables responsible
for adaptation of the cells to environmental variations. We present
these physiological models in the order of increasing complexity.
Thus, we begin with models of single-species growth in environments
containing a single growth-limiting substrate, then advance to models
of single-species growth in mixed-substrate media, and conclude with
models of multiple-species growth in mixed-substrate environments.
Throughout the paper, we discuss both the analytical and simulation
techniques to illustrate how these models capture and explain various
experimental phenomena. Finally, we also present open questions and
possible directions for future research that would integrate these
models into a global physiological theory of microbial growth.
Citation: Atul Narang, Sergei S. Pilyugin. Toward an Integrated Physiological Theory of Microbial Growth: From Subcellular Variables to Population Dynamics[J]. Mathematical Biosciences and Engineering, 2005, 2(1): 169-206. doi: 10.3934/mbe.2005.2.169
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Abstract
The dynamics of microbial growth is a problem of fundamental interest in microbiology,
microbial ecology, and biotechnology. The pioneering work of Jacob
Monod, served as a starting point for developing a wealth of mathematical
models that address different aspects of microbial growth in
batch and continuous cultures. A number of phenomenological models
have appeared in the literature over the last half century. These
models can capture the steady-state behavior of pure and mixed cultures,
but fall short of explaining most of the complex dynamic phenomena.
This is because the onset of these complex dynamics is invariably
driven by one or more intracellular variables not accounted
for by phenomenological models.
 
In this paper, we provide an overview of the experimental data, and
introduce a different class of mathematical models that can be used
to understand microbial growth dynamics. In addition to the standard
variables such as the cell and substrate concentrations, these models
explicitly include the dynamics of the physiological variables responsible
for adaptation of the cells to environmental variations. We present
these physiological models in the order of increasing complexity.
Thus, we begin with models of single-species growth in environments
containing a single growth-limiting substrate, then advance to models
of single-species growth in mixed-substrate media, and conclude with
models of multiple-species growth in mixed-substrate environments.
Throughout the paper, we discuss both the analytical and simulation
techniques to illustrate how these models capture and explain various
experimental phenomena. Finally, we also present open questions and
possible directions for future research that would integrate these
models into a global physiological theory of microbial growth.
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