Bacterial metabolic heterogeneity: from stochastic to deterministic models

Carl Graham; Jérôme Harmand; Sylvie Méléard; Josué Tchouanti; Carl Graham; Jérôme Harmand; Sylvie Méléard; Josué Tchouanti

doi:10.3934/mbe.2020276

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5120-5133. doi: 10.3934/mbe.2020276

Previous Article Next Article

Research article Special Issues

Bacterial metabolic heterogeneity: from stochastic to deterministic models

1.
CMAP, CNRS, École Polytechnique, IP Paris, 91128 Palaiseau, France
2.
LBE, INRAE, Universite de Montpellier, LBE, 11100, Narbonne, France
3.
Inria Saclay Île-de-France, France
4.
Institut Universitaire de France, France

Received: 21 May 2020 Accepted: 10 July 2020 Published: 29 July 2020

We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem behave homogeneously with respect to both sugars, all consuming the first one and then switching to the second when the first is exhausted. We propose here a stochastic model which describes what is called "metabolic heterogeneity". It allows to consider small populations as in microfluidics as well as large populations where billions of individuals coexist in the medium in a batch or chemostat. We highlight the link between the stochastic model and the deterministic behavior in real large cultures using a large population approximation. Then the influence of model parameter values on model dynamics is studied, notably with respect to the lag-phase observed in real systems depending on the sugars on which the microorganism grows. It is shown that both metabolic parameters as well as initial conditions play a crucial role on system dynamics.
- diauxic growth,
- metabolic heterogeneity,
- stochastic model,
- deterministic model
Citation: Carl Graham, Jérôme Harmand, Sylvie Méléard, Josué Tchouanti. Bacterial metabolic heterogeneity: from stochastic to deterministic models[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5120-5133. doi: 10.3934/mbe.2020276

Related Papers:

Abstract

We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem behave homogeneously with respect to both sugars, all consuming the first one and then switching to the second when the first is exhausted. We propose here a stochastic model which describes what is called "metabolic heterogeneity". It allows to consider small populations as in microfluidics as well as large populations where billions of individuals coexist in the medium in a batch or chemostat. We highlight the link between the stochastic model and the deterministic behavior in real large cultures using a large population approximation. Then the influence of model parameter values on model dynamics is studied, notably with respect to the lag-phase observed in real systems depending on the sugars on which the microorganism grows. It is shown that both metabolic parameters as well as initial conditions play a crucial role on system dynamics.

References

[1]	J. Monod, Recherches Sur La Croissance Des Cultures Bactériennes, Hermann & Cie, Paris, 1942.
[2]	A. M. Liquori, A. Monroy, E. Parisi, A. Tripiciano, A theoretical equation for diauxic growth and its application to the kinetics of the early development of the sea urchin embryo, Differentiation, 20 (1981), 174-175.
[3]	V. Turon, Coupling Dark Fermentation with Microalgal Heterotrophy: Influence of Fermentation Metabolites Mixtures, Light, Temperature and Fermentation Bacteria on Microalgae Growth, Ph.D thesis, Université de Montpellier, 2015.
[4]	G. Van Dedem, M. Moo-Young, A model of diauxic growth, Biotechnol. Bioeng., 17 (1975), 1301-1312.
[5]	R. L. Bertrand, Lag phase is a dynamic, organized, adaptative, and evolvable period that prepares bacteria for cell division, J. Bacteriol., 201 (2019), e00697-18.
[6]	V. Takhaveev, M. Heinemann, Metabolic heterogeneity in clonal microbial populations, Curr. Opin. Microbiol., 45 (2018), 30-38.
[7]	B. Enjalbert, P. Millard, M. Dinciaux, J. C. Portais, F. Létisse, Acetate fluxes in Escherichia coli are determined by the thermodynamic contol of the Pta-AckA pathway, Sci. Rep., 7 (2017), 42135.
[8]	M. Barthe, J. Tchouanti, P. H. Gomes, C. Bideaux, D. Lestrade, C. Graham, et al., Duration of the glucose-xylose lag is controlled stochastically by the molecular switch XylR in Escherichia coli., Submitted, 2020.
[9]	S. N. Ethier, T. G. Kurtz, Markov Processes: Characterization and Convergence, John Wiley & Sons, 1986.
[10]	D. F. Anderson, T. G. Kurtz, Stochastic Analysis of Biochemical Systems, Springer, 2015.
[11]	V. Bansaye, S. Méléard, Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior, Springer, 2015.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)