Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 1, 2010
Cell migration
Page(s) 148 - 162
DOI https://doi.org/10.1051/mmnp/20105107
Published online 03 February 2010
  1. M. Banaha, A. DaerrL. Limat. Spreading of liquid drops on agar gels. Eur. Phys. J. Special Topics, 166 (2009), 185–188 [CrossRef] [EDP Sciences]
  2. M. Bees, P. Andresén, E. MosekildeM. Givskov. The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens. J. Math. Biol., 40 (2000), 27–63 [CrossRef] [MathSciNet] [PubMed]
  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(44) (2006), 1–32.
  4. S. E. Esipov, J. A. Shapiro. Kinetic model of Proteus mirabilis swarm colony development. J. Math. Biology, 36 (1998), No 1 Cell migration, 249–268. [CrossRef]
  5. E. Frénod. Existence result of a model of Proteus mirabilis swarm. Diff. and Integr. eq., 19 (2006), No 1 Cell migration, 697–720.
  6. I. Golding, Y. Kozlovsky, I. CohenE. Ben-Jacob. Studies of bacterial branching growth using reaction-diffusion models for colonial development. Phys. A, 260 (1998), 510–554 [CrossRef]
  7. P. Gray, S. K. Scott. Autocatalytic reactions in the isothermal continuous stirred tank reactor: isolas and other forms of multistability. Chem. Eng. Sci., 38 (1983), No 1 Cell migration, 29–43. [CrossRef]
  8. K. Hamze, D. Julkowska, S. Autret, K. Hinc, K. Nagorska, A. Sekowska, I. B. HollS. J. Séror. Identification of genes required for different stages of dendritic swarming in Bacillus subtilis, with a novel role for phrC. Microbiology, 155 (2009), 398–412 [CrossRef] [PubMed]
  9. D. Julkowska, M. Obuchowski, I. B. HollS. J. Séror. Branched swarming patterns on a synthetic medium formed by wild type Bacillus subtilis strain 3610. Microbiology, 150 (2004), 1839–1849 [CrossRef] [PubMed]
  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. 187 (2005), 65–74. [CrossRef] [PubMed]
  11. K. Kawasaki, A. Mochizuki, M. Matsushita, T. Umeda, N. Shigesada. Modeling spatio-temporal patterns created by Bacillus-subtilis. J. Theor. Biol. 188 (1997), 177–185. [CrossRef] [PubMed]
  12. E. F. KellerL. A. Segel. Model for chemotaxis. J. Theor. Biol., 30 (1971), 225–234 [CrossRef] [PubMed]
  13. D. A. KesslerH. Levine. Fluctuation induced diffusive instabilities. Nature, 394 (1998), 556–558 [CrossRef]
  14. T. Kolokolnikov, M. J. WardJ. Wei. The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Physica D, 202 (2005), 258–293 [CrossRef] [MathSciNet]
  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, 50 (1999), 7025–7035.
  16. A. Marrocco. 2D simulation of chemotactic bacteria aggregation. ESAIM: Math. Modelling and Numerical Analysis, 37 (2003), 617–630 [CrossRef]
  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 453 (2008), 745–750. [CrossRef] [PubMed]
  19. M. Mimura, H. SakaguchiM. Matsushita. Reaction diffusion modelling of bacterial colony patterns. Physica A, 282 (2000), 283–303 [CrossRef]
  20. J. Müller, W. van Saarloos. Morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion. Phys. Rev. E, 65 (2002), 061111. [CrossRef]
  21. C. B. Muratov, V. V. Osipov. Traveling spike autosolitons in the Gray-Scott model. Physica D, 155 (2001), 112–131. [CrossRef] [MathSciNet]
  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. 178 (1996), 6525–6538. [PubMed]
  25. S. M. Troian, X. L. WuS. A. Safran. Fingering instabilities in thin wetting films. Phys. Rev. Lett., 62 (1989), 1496–1499 [CrossRef] [PubMed]
  26. J. Y. Wakano, A. Komoto, Y. Yamaguchi. Phase transition of traveling waves in bacterial colony pattern. Phys. Rev. E 69 (2004), 051904, 1–9.

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