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On the growth of non-motile bacteria colonies: an agent-based model for pattern formation

The European Physical Journal B volume 92, Article number: 216 (2019) Cite this article

Abstract

In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characterise the screening effect observed in the structures by analysing the multifractal properties of the growth probability.

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References

  1. G. De Magistris, D. Marenduzzo, Physica A 418, 65 (2015)

    Article  ADS  Google Scholar 

  2. J. Henrichsen, Bacteriol. Rev. 36, 478 (1972)

    Google Scholar 

  3. M.J. McBride, Annu. Rev. Microbiol. 55, 49 (2001)

    Article  Google Scholar 

  4. M.G. Mazza, J. Phys. D: Appl. Phys. 49, 203001 (2016)

    Article  ADS  Google Scholar 

  5. J.W. Costerton, Z. Lewandowski, D.E. Caldwell, D.R. Korber, H.M. Lappin-Scott, Annu. Rev. Microbiol. 49, 711 (1995)

    Article  Google Scholar 

  6. L. Hall-Stoodley, J.W. Costerton, P. Stoodley, Nat. Rev. Microbiol. 2, 95 (2004)

    Article  Google Scholar 

  7. G. O’Toole, H.B. Kaplan, R. Kolter, Annu. Rev. Microbiol. 54, 49 (2000)

    Article  Google Scholar 

  8. H.C. Flemming, J. Wingender, Nat. Rev. Microbiol. 8, 623 (2010)

    Article  Google Scholar 

  9. T. Matsuyama, M. Sogawa, Y. Nakagawa, FEMS Microbiol. Lett. 52, 243 (1989)

    Article  Google Scholar 

  10. M. Matsushita, H. Fujikawa, Physica A 168, 498 (1990)

    Article  ADS  Google Scholar 

  11. M. Matsushita, J. Wakita, H. Itoh, I. Ràfols, T. Matsuyama, H. Sakaguchi, M. Mimura, Physica A 249, 517 (1998)

    Article  ADS  Google Scholar 

  12. M. Ohgiwari, M. Matsushita, T. Matsuyama, J. Phys. Soc. Jpn. 61, 816 (1992)

    Article  ADS  Google Scholar 

  13. H. Fujikawa, Physica A 189, 15 (1992)

    Article  ADS  Google Scholar 

  14. K. Kawasaki, A. Mochizuki, M. Matsushita, T. Umeda, N. Shigesada, J. Theor. Biol. 188, 177 (1997)

    Article  Google Scholar 

  15. M. Mimura, H. Sakaguchi, M. Matsushita, Physica A 282, 283 (2000)

    Article  ADS  Google Scholar 

  16. C. Giverso, M. Verani, P. Ciarletta, J. R. Soc. Interface 12, 20141290 (2015)

    Article  Google Scholar 

  17. I. Golding, Y. Kozlovsky, I. Cohen, E. Ben-Jacob, Physica A 260, 510 (1998)

    Article  ADS  Google Scholar 

  18. M. Matsushita, J. Wakita, H. Itoh, K. Watanabe, T. Arai, Physica A 274, 190 (1999)

    Article  ADS  Google Scholar 

  19. Y. Kozlovsky, I. Cohen, I. Golding, E. Ben-Jacob, Phys. Rev. E 59, 7025 (1999)

    Article  ADS  Google Scholar 

  20. M. Matsushita, F. Hiramatsu, N. Kobayashi, T. Ozawa, Y. Yamazaki, T. Matsuyama, Biofilms 1, 305 (2004)

    Article  Google Scholar 

  21. A.M. Lacasta, I.R. Cantalapiedra, C.E. Auguet, A. Peñaranda, L. Ramírez-Piscina, Phys. Rev. E 59, 7036 (1999)

    Article  ADS  Google Scholar 

  22. H. Tronnolone, A. Tam, Z. Szenczi, J.E. Green, S. Balasuriya, E.L. Tek, J.M. Gardner, J.F. Sundstrom, V. Jiranek, S.G. Oliver et al., Sci. Reports 8, 1 (2018)

    Article  Google Scholar 

  23. A. Marrocco, H. Henry, I.B. Holland, M. Plapp, S.J. Séror, B. Perthame, Math. Model. Nat. Phenom. 5, 148 (2010)

    Article  MathSciNet  Google Scholar 

  24. E. Ben-Jacob, O. Schochet, A. Tenenbaum, I. Cohen, A. Czirók, T. Vicsek, Nature 368, 46 (1994)

    Article  ADS  Google Scholar 

  25. F.D.C. Farrell, O. Hallatschek, D. Marenduzzo, B. Waclaw, Phys. Rev. Lett. 111, 1 (2013)

    Article  Google Scholar 

  26. B. Li, J. Wang, B. Wang, W. Liu, Z. Wu, Europhys. Lett. 30, 239 (1995)

    Article  ADS  Google Scholar 

  27. P. Melke, P. Sahlin, A. Levchenko, H. Jönsson, PLoS Comput. Biol. 6, e1000819 (2010)

    Article  ADS  Google Scholar 

  28. S.N. Santalla, S.C. Ferreira, Phys. Rev. E 98, 022405 (2018)

    Article  ADS  Google Scholar 

  29. Y. Hayakawa, S. Sato, M. Matsushita, Phys. Rev. A 36, 1963 (1987)

    Article  ADS  Google Scholar 

  30. W. Kinsner, JITR 1, 62 (2008)

    Google Scholar 

  31. A.L. Barabasi, H.E. Stanley,Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)

  32. H. Hentschel, I. Procaccia, Physica D 8, 435 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  33. T. Halsey, M. Jensen, L. Kadanoff, I. Procaccia, B. Shraiman, Phys. Rev. A 33, 1141 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  34. A.B. Chhabra, C. Meneveau, R.V. Jensen, K.R. Sreenivasan, Phys. Rev. A 40, 5284 (1989)

    Article  ADS  Google Scholar 

  35. P.C. Ivanov, Q.D. Ma, R.P. Bartsch, J.M. Hausdorff, L.A. Nunes Amaral, V. Schulte-Frohlinde, H.E. Stanley, M. Yoneyama, Phys. Rev. E 79, 1 (2009)

    Google Scholar 

  36. H. Risken, inSpringer Series in Synergetics (Springer, Berlin, Heidelberg, 1989), Vol. 18

  37. E. Catto, inGame developer conference (2005), Vol. 2, p. 5

  38. A. Bashan, R. Bartsch, J.W. Kantelhardt, S. Havlin, Physica A 387, 5080 (2008)

    Article  ADS  Google Scholar 

  39. J.M. Li, L. Lü, M.O. Lai, B. Ralph, inImage-based fractal description of microstructures (Springer US, Boston, MA, 2003), Chap. 6, p. 129

  40. M. Matsushita, Y. Hayakawa, S. Sato, K. Honda, Phys. Rev. Lett. 59, 86 (1987)

    Article  ADS  Google Scholar 

  41. S. Ohta, H. Honjo, Phys. Rev. Lett. 60, 611 (1988)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600, Mar del Plata, Argentina

    Lautaro Vassallo, David Hansmann & Lidia A. Braunstein

  2. Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600, Mar del Plata, Argentina

    Lautaro Vassallo, David Hansmann & Lidia A. Braunstein

  3. Physics Department and Center for Polymer Studies, Boston University, Boston, Massachusetts, 02215, USA

    Lidia A. Braunstein

Authors
  1. Lautaro Vassallo
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  2. David Hansmann
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  3. Lidia A. Braunstein
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Correspondence to Lautaro Vassallo.

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Vassallo, L., Hansmann, D. & Braunstein, L.A. On the growth of non-motile bacteria colonies: an agent-based model for pattern formation. Eur. Phys. J. B 92, 216 (2019). https://doi.org/10.1140/epjb/e2019-100265-0

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  • DOI: https://doi.org/10.1140/epjb/e2019-100265-0

Keywords

  • Statistical and Nonlinear Physics