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Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Published online by Cambridge University Press:  03 February 2010

A. Marrocco ,
H. Henry ,
I. B. Holland ,
M. Plapp ,
S. J. Séror  and
B. Perthame
A. Marrocco
Affiliation:
INRIA Paris-Rocquencourt, BANG, BP105, F78153 LeChesnay cedex
H. Henry
Affiliation:
Physique de la Matière Condensée, École Polytechnique, CNRS, F-91128 Palaiseau
I. B. Holland
Affiliation:
Institut de Génétique et Microbiologie, CNRS UMR 8621, Univ. Paris-Sud, F-91405 Orsay
M. Plapp
Affiliation:
Physique de la Matière Condensée, École Polytechnique, CNRS, F-91128 Palaiseau
S. J. Séror
Affiliation:
Institut de Génétique et Microbiologie, CNRS UMR 8621, Univ. Paris-Sud, F-91405 Orsay
B. Perthame*
Affiliation:
INRIA Paris-Rocquencourt, BANG, BP105, F78153 LeChesnay cedex Univ. Pierre et Marie Curie, Laboratoire J.-L. Lions, CNRS UMR 7598
*
*Corresponding author. E-mail: benoit.perthame@upmc.fr
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Abstract

Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare them to relevant experimental data together with a critical analysis of the validity of the models based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are likely present.

Keywords

Dendritic patternsBacillus subtilis swarmingReaction-diffusion equationsCell community growth.
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 1: Cell migration , 2010 , pp. 148 - 162
Copyright
© EDP Sciences, 2010

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References

Banaha, M., Daerr, A. Limat, L.. Spreading of liquid drops on agar gels . Eur. Phys. J. Special Topics, 166 (2009), 185–188 CrossRefGoogle Scholar
Bees, M., Andresén, P., Mosekilde, E. Givskov, M.. The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens . J. Math. Biol., 40 (2000), 27–63 CrossRefGoogle ScholarPubMed
Blanchet, A., Dolbeault, J., Perthame, B.. Two dimensional Keller-Segel model in ℝ2 : optimal critical mass and qualitative properties of the solution . Electron. J. Diff. Eqns., 2006(44) (2006), 1–32. Google Scholar
Esipov, S. E., Shapiro, J. A.. Kinetic model of Proteus mirabilis swarm colony development . J. Math. Biology, 36 (1998), No 1 , 249–268. CrossRefGoogle Scholar
Frénod, E.. Existence result of a model of Proteus mirabilis swarm . Diff. and Integr. eq., 19 (2006), No 1 , 697–720. Google Scholar
Golding, I., Kozlovsky, Y., Cohen, I. Ben-Jacob, E.. Studies of bacterial branching growth using reaction-diffusion models for colonial development . Phys. A, 260 (1998), 510–554 CrossRefGoogle Scholar
Gray, P., Scott, S. K.. Autocatalytic reactions in the isothermal continuous stirred tank reactor: isolas and other forms of multistability . Chem. Eng. Sci., 38 (1983), No 1 , 29–43. CrossRefGoogle Scholar
Hamze, K., Julkowska, D., Autret, S., Hinc, K., Nagorska, K., Sekowska, A., Holl, I. B. Séror, S. J.. Identification of genes required for different stages of dendritic swarming in Bacillus subtilis, with a novel role for phrC . Microbiology, 155 (2009), 398–412 CrossRefGoogle ScholarPubMed
Julkowska, D., Obuchowski, M., Holl, I. B. Séror, S. J.. Branched swarming patterns on a synthetic medium formed by wild type Bacillus subtilis strain 3610 . Microbiology, 150 (2004), 1839–1849 CrossRefGoogle ScholarPubMed
Julkowska, D., Obuchowski, M., Holland, I. B., Séror, S. J.. Comparative analysis of the development of swarming communities Bacillus subtilis 168 and a natural wild type: critical effects of surfactin and the composition of the medium . J. Bacteriol. 187 (2005), 65–74. CrossRefGoogle Scholar
Kawasaki, K., Mochizuki, A., Matsushita, M., Umeda, T., Shigesada, N.. Modeling spatio-temporal patterns created by Bacillus-subtilis . J. Theor. Biol. 188 (1997), 177–185. CrossRefGoogle Scholar
Keller, E. F. Segel, L. A.. Model for chemotaxis . J. Theor. Biol., 30 (1971), 225–234 CrossRefGoogle ScholarPubMed
Kessler, D. A. Levine, H.. Fluctuation induced diffusive instabilities . Nature, 394 (1998), 556–558 CrossRefGoogle Scholar
Kolokolnikov, T., Ward, M. J. Wei, J.. The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime . Physica D, 202 (2005), 258–293 CrossRefGoogle Scholar
Kozlovsky, Y., Cohen, I., Golding, I., Ben-Jacob, E.. Lubricating bacteria model for branching growth of bacterial colony . Phys. Rev. E, Phys. plasmas fluids Relat. Interdisciplinary Topics, 50 (1999), 7025–7035. Google Scholar
Marrocco, A.. 2D simulation of chemotactic bacteria aggregation . ESAIM: Math. Modelling and Numerical Analysis, 37 (2003), 617–630 CrossRefGoogle Scholar
A. Marrocco. Aggrégation de bactéries. Simulations numériques de modèles de réaction-diffusion à l’aide d’éléments finis mixtes. INRIA report (2007) : http://hal.inria.fr/docs/00/12/38/91/PDF/RR-6092.pdf
Metzger, R. J., Klein, O. D., Martin, G. R., Krasnow, M. A.. The branching programme of mouse lung development. Nature 453 (2008), 745–750. CrossRefGoogle ScholarPubMed
Mimura, M., Sakaguchi, H. Matsushita, M.. Reaction diffusion modelling of bacterial colony patterns . Physica A, 282 (2000), 283–303 CrossRefGoogle Scholar
Müller, J., van Saarloos, W.. Morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion . Phys. Rev. E, 65 (2002), 061111. CrossRefGoogle ScholarPubMed
Muratov, C. B., Osipov, V. V.. Traveling spike autosolitons in the Gray-Scott model. Physica D, 155 (2001), 112–131. CrossRefGoogle Scholar
J. D. Murray. Mathematical biology, Vol. 1 and 2, Second edition. Springer (2002).
B. Perthame. Transport Equations in Biology (LN Series Frontiers in Mathematics), Birkhauser, (2007).
Rauprich, O., Matshushita, M., Weijer, C. J., Siegert, F., Esipov, S. E., Shapiro, J. A.. Periodic phenomena in Proteus mirabilis swarm colony development . J. Bacteriol. 178 (1996), 6525–6538. CrossRefGoogle ScholarPubMed
Troian, S. M., Wu, X. L. Safran, S. A.. Fingering instabilities in thin wetting films . Phys. Rev. Lett., 62 (1989), 1496–1499 CrossRefGoogle Scholar
Wakano, J. Y., Komoto, A., Yamaguchi, Y.. Phase transition of traveling waves in bacterial colony pattern . Phys. Rev. E 69 (2004), 051904, 1–9. CrossRefGoogle ScholarPubMed