2005, 2(1): 169-206. doi: 10.3934/mbe.2005.2.169

Toward an Integrated Physiological Theory of Microbial Growth: From Subcellular Variables to Population Dynamics

1. 

Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005, United States

2. 

Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States

Received  September 2004 Revised  October 2004 Published  November 2004

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. Mathematical Biosciences & Engineering, 2005, 2 (1) : 169-206. doi: 10.3934/mbe.2005.2.169
[1]

Yi Wang, Chengmin Zheng. Normal and slow growth states of microbial populations in essential resource-based chemostat. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 227-250. doi: 10.3934/dcdsb.2009.12.227

[2]

Tewfik Sari, Miled El Hajji, Jérôme Harmand. The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Mathematical Biosciences & Engineering, 2012, 9 (3) : 627-645. doi: 10.3934/mbe.2012.9.627

[3]

Wenzhang Huang. Co-existence of traveling waves for a model of microbial growth and competition in a flow reactor. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 883-896. doi: 10.3934/dcds.2009.24.883

[4]

Joydeb Bhattacharyya, Samares Pal. Microbial disease in coral reefs: An ecosystem in transition. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 373-398. doi: 10.3934/dcdsb.2016.21.373

[5]

T. Caraballo, M. J. Garrido-Atienza, J. López-de-la-Cruz. Dynamics of some stochastic chemostat models with multiplicative noise. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1893-1914. doi: 10.3934/cpaa.2017092

[6]

Yan Wang, Lei Wang, Yanxiang Zhao, Aimin Song, Yanping Ma. A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 381-392. doi: 10.3934/naco.2015.5.381

[7]

Jingang Zhai, Guangmao Jiang, Jianxiong Ye. Optimal dilution strategy for a microbial continuous culture based on the biological robustness. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 59-69. doi: 10.3934/naco.2015.5.59

[8]

Jinggui Gao, Xiaoyan Zhao, Jinggang Zhai. Optimal control of microbial fed-batch culture involving multiple feeds. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 339-349. doi: 10.3934/naco.2015.5.339

[9]

Yanan Mao, Caixia Gao, Ruidong Yan, Aruna Bai. Modeling and identification of hybrid dynamic system in microbial continuous fermentation. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 359-368. doi: 10.3934/naco.2015.5.359

[10]

Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141

[11]

Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin. Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture. Journal of Industrial & Management Optimization, 2009, 5 (4) : 835-850. doi: 10.3934/jimo.2009.5.835

[12]

Lei Wang, Jinlong Yuan, Yingfang Li, Enmin Feng, Zhilong Xiu. Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 103-113. doi: 10.3934/naco.2014.4.103

[13]

J. Leonel Rocha, Sandra M. Aleixo. An extension of Gompertzian growth dynamics: Weibull and Fréchet models. Mathematical Biosciences & Engineering, 2013, 10 (2) : 379-398. doi: 10.3934/mbe.2013.10.379

[14]

Shikun Wang. Dynamics of a chemostat system with two patches. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-18. doi: 10.3934/dcdsb.2019138

[15]

Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou. Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3011-3035. doi: 10.3934/dcdsb.2018297

[16]

Lambertus A. Peletier, Willem de Winter, An Vermeulen. Dynamics of a two-receptor binding model: How affinities and capacities translate into long and short time behaviour and physiological corollaries. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2171-2184. doi: 10.3934/dcdsb.2012.17.2171

[17]

Frederic Mazenc, Gonzalo Robledo, Michael Malisoff. Stability and robustness analysis for a multispecies chemostat model with delays in the growth rates and uncertainties. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1851-1872. doi: 10.3934/dcdsb.2018098

[18]

Tewfik Sari, Frederic Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences & Engineering, 2011, 8 (3) : 827-840. doi: 10.3934/mbe.2011.8.827

[19]

D. V. Osin. Peripheral fillings of relatively hyperbolic groups. Electronic Research Announcements, 2006, 12: 44-52.

[20]

J. K. Krottje. On the dynamics of a mixed parabolic-gradient system. Communications on Pure & Applied Analysis, 2003, 2 (4) : 521-537. doi: 10.3934/cpaa.2003.2.521

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]