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 [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  5. E. Frénod. Existence result of a model of Proteus mirabilis swarm. Diff. and Integr. eq., 19 (2006), No 1 Cell migration, 697–720. [Google Scholar]
  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 [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  12. E. F. KellerL. A. Segel. Model for chemotaxis. J. Theor. Biol., 30 (1971), 225–234 [CrossRef] [PubMed] [Google Scholar]
  13. D. A. KesslerH. Levine. Fluctuation induced diffusive instabilities. Nature, 394 (1998), 556–558 [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  16. A. Marrocco. 2D simulation of chemotactic bacteria aggregation. ESAIM: Math. Modelling and Numerical Analysis, 37 (2003), 617–630 [CrossRef] [Google Scholar]
  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 [Google Scholar]
  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] [Google Scholar]
  19. M. Mimura, H. SakaguchiM. Matsushita. Reaction diffusion modelling of bacterial colony patterns. Physica A, 282 (2000), 283–303 [Google Scholar]
  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] [Google Scholar]
  21. C. B. Muratov, V. V. Osipov. Traveling spike autosolitons in the Gray-Scott model. Physica D, 155 (2001), 112–131. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. D. Murray. Mathematical biology, Vol. 1 and 2, Second edition. Springer (2002). [Google Scholar]
  23. B. Perthame. Transport Equations in Biology (LN Series Frontiers in Mathematics), Birkhauser, (2007). [Google Scholar]
  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] [Google Scholar]
  25. S. M. Troian, X. L. WuS. A. Safran. Fingering instabilities in thin wetting films. Phys. Rev. Lett., 62 (1989), 1496–1499 [CrossRef] [PubMed] [Google Scholar]
  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. [Google Scholar]

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