Geodesic
Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
A. Marrocco1 ; H. Henry2 ; I. B. Holland3 ; M. Plapp2 ; S. J. Séror3 ; B. Perthame1, 4
1 INRIA Paris-Rocquencourt, BANG, BP105, F78153 LeChesnay cedex
2 Physique de la Matière Condensée, École Polytechnique, CNRS, F-91128 Palaiseau
3 Institut de Génétique et Microbiologie, CNRS UMR 8621, Univ. Paris-Sud, F-91405 Orsay
4 Univ. Pierre et Marie Curie, Laboratoire J.-L. Lions, CNRS UMR 7598
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 1, pp. 148-162.

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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.
DOI : 10.1051/mmnp/20105107

A. Marrocco 1 ; H. Henry 2 ; I. B. Holland 3 ; M. Plapp 2 ; S. J. Séror 3 ; B. Perthame 1, 4

1 INRIA Paris-Rocquencourt, BANG, BP105, F78153 LeChesnay cedex
2 Physique de la Matière Condensée, École Polytechnique, CNRS, F-91128 Palaiseau
3 Institut de Génétique et Microbiologie, CNRS UMR 8621, Univ. Paris-Sud, F-91405 Orsay
4 Univ. Pierre et Marie Curie, Laboratoire J.-L. Lions, CNRS UMR 7598 
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A. Marrocco; H. Henry; I. B. Holland; M. Plapp; S. J. Séror; B. Perthame. Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 1, pp. 148-162. doi : 10.1051/mmnp/20105107. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105107/

[1] M. Banaha, A. Daerr, L. Limat Spreading of liquid drops on agar gels Eur. Phys. J. Special Topics 2009 185 188

[2] M. Bees, P. Andresén, E. Mosekilde, M. Givskov The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens J. Math. Biol. 2000 27 63

[3] A. Blanchet, J. Dolbeault, B. Perthame Two dimensional Keller-Segel model in ℝ2: optimal critical mass and qualitative properties of the solution Electron. J. Diff. Eqns. 2006 1 32

[4] S. E. Esipov, J. A. Shapiro Kinetic model of Proteus mirabilis swarm colony development J. Math. Biology 1998 249 268

[5] E. Frénod Existence result of a model of Proteus mirabilis swarm Diff. and Integr. eq. 2006 697 720

[6] I. Golding, Y. Kozlovsky, I. Cohen, E. Ben-Jacob Studies of bacterial branching growth using reaction-diffusion models for colonial development Phys. A 1998 510 554

[7] P. Gray, S. K. Scott Autocatalytic reactions in the isothermal continuous stirred tank reactor: isolas and other forms of multistability Chem. Eng. Sci. 1983 29 43

[8] K. Hamze, D. Julkowska, S. Autret, K. Hinc, K. Nagorska, A. Sekowska, I. B. Holl, S. J. Séror Identification of genes required for different stages of dendritic swarming in Bacillus subtilis, with a novel role for phrC Microbiology 2009 398 412

[9] D. Julkowska, M. Obuchowski, I. B. Holl, S. J. Séror Branched swarming patterns on a synthetic medium formed by wild type Bacillus subtilis strain 3610 Microbiology 2004 1839 1849

[10] D. Julkowska, M. Obuchowski, I. B. Holland, S. J. Séror 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. 2005 65 74

[11] K. Kawasaki, A. Mochizuki, M. Matsushita, T. Umeda, N. Shigesada Modeling spatio-temporal patterns created by Bacillus-subtilis J. Theor. Biol. 1997 177 185

[12] E. F. Keller, L. A. Segel Model for chemotaxis J. Theor. Biol. 1971 225 234

[13] D. A. Kessler, H. Levine Fluctuation induced diffusive instabilities Nature 1998 556 558

[14] T. Kolokolnikov, M. J. Ward, J. Wei The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime Physica D 2005 258 293

[15] Y. Kozlovsky, I. Cohen, I. Golding, E. Ben-Jacob Lubricating bacteria model for branching growth of bacterial colony Phys. Rev. E, Phys. plasmas fluids Relat. Interdisciplinary Topics 1999 7025 7035

[16] A. Marrocco 2D simulation of chemotactic bacteria aggregation ESAIM: Math. Modelling and Numerical Analysis 2003 617 630

[17] 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

[18] R. J. Metzger, O. D. Klein, G. R. Martin, M. A. Krasnow The branching programme of mouse lung development Nature 2008 745 750

[19] M. Mimura, H. Sakaguchi, M. Matsushita Reaction diffusion modelling of bacterial colony patterns Physica A 2000 283 303

[20] J. Müller, W. Van Saarloos Morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion Phys. Rev. E 2002

[21] C. B. Muratov, V. V. Osipov Traveling spike autosolitons in the Gray-Scott model Physica D 2001 112 131

[22] J. D. Murray. Mathematical biology, Vol. 1 and 2, Second edition. Springer (2002).

[23] B. Perthame. Transport Equations in Biology (LN Series Frontiers in Mathematics), Birkhauser, (2007).

[24] O. Rauprich, M. Matshushita, C. J. Weijer, F. Siegert, S. E. Esipov, J. A. Shapiro Periodic phenomena in Proteus mirabilis swarm colony development J. Bacteriol. 1996 6525 6538

[25] S. M. Troian, X. L. Wu, S. A. Safran Fingering instabilities in thin wetting films Phys. Rev. Lett. 1989 1496 1499

[26] J. Y. Wakano, A. Komoto, Y. Yamaguchi Phase transition of traveling waves in bacterial colony pattern Phys. Rev. E 2004 1 9

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