Skip to main content
SpringerLink
Log in

Universality in Bacterial Colonies

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative picture of the different structures that such colonies can exhibit, depending on the medium on which they are growing. However, there are relatively few quantitative descriptions of these patterns. In this paper, we use a mechanistically detailed simulation framework to measure the scaling exponents associated with the advancing fronts of bacterial colonies on hard agar substrata, aiming to discern the universality class to which the system belongs. We show that the universal behavior exhibited by the colonies can be much richer than previously reported, and we propose the possibility of up to four different sub-phases within the medium-to-high nutrient concentration regime. We hypothesize that the quenched disorder that characterizes one of these sub-phases is an emergent property of the growth and division of bacteria competing for limited space and nutrients.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bastolla, U., Fortuna, M.A., Pascual-García, A., Ferrera, A., Luque, B., Bascompte, J.: The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009)

    Article  ADS  Google Scholar 

  2. Guimerà, R., Amaral, L.A.N.: Functional cartography of complex-metabolic networks. Nature 433, 895–900 (2005)

    Article  ADS  Google Scholar 

  3. Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., Viale, M.: Scale-free correlations in starling flocks. Proc. Natl. Acad. Sci. USA 107, 11865–11870 (2010)

    Article  ADS  Google Scholar 

  4. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)

    Article  ADS  Google Scholar 

  5. Nadell, C.D., Foster, K.R., Xavier, J.B.: Emergence of spatial structure in cell groups and the evolution of cooperation. PLoS Comput. Biol. 6, e1000716 (2010)

    Article  Google Scholar 

  6. Nadell, C.D., Xavier, J.B., Levin, S.A., Foster, K.R.: The evolution of quorum sensing in bacterial biofilms. PLoS Biol. 6, e14 (2008)

    Article  Google Scholar 

  7. Matsuyama, T., Sogawa, M., Nakagawa, Y.: Fractal spreading growth of Serratia Marcescens which produces surface active exolipids. FEMS Microbiol. Lett. 61, 243–246 (1989)

    Article  Google Scholar 

  8. Fujikawa, H., Matsushita, M.: Fractal growth of Bacillus Subtilis on agar plates. J. Phys. Soc. Jpn. 58, 3875–3878 (1989)

    Article  ADS  Google Scholar 

  9. Barabási, A.-L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  10. Xavier, J.B., Kim, W., Foster, K.R.: A molecular mechanism that stabilizes cooperative secretions in pseudomonas aeruginosa. Mol. Microbiol. 79, 166–179 (2011)

    Article  Google Scholar 

  11. Fujikawa, H.: Diversity of the growth patterns of Bacillus Subtilis colonies on agar plates. FEMS Microbiol. Ecol. 13, 159–168 (1994)

    Article  Google Scholar 

  12. Wakita, J., Itoh, H., Matsuyama, T., Matsushita, M.: Self-affinity for the growing interface of bacterial colonies. J. Phys. Soc. Jpn. 66, 67–72 (1997)

    Article  ADS  Google Scholar 

  13. Ben-Jacob, E., Garik, P.: The formation of patterns in non-equilibrium growth. Nature 434, 523–530 (1990)

    Article  ADS  Google Scholar 

  14. Fujikawa, H.: Periodic growth of Bacillus Subtilis colonies on agar plates. Physica A 189, 15–21 (1992)

    Article  ADS  Google Scholar 

  15. Shimada, H., Ikeda, T., Wakita, J.-I., Itoh, H., Kurosu, S., Hiramatsu, F., Nakatsuchi, M., Yamazaki, Y., Matsuyama, T., Matsushita, M.: Dependence of local cell density on concentric ring colony formation by bacterial species Bacillus Subtilis. J. Phys. Soc. Jpn. 189, 1082–1089 (2004)

    Article  ADS  Google Scholar 

  16. Witten, T.A., Jr., Snader, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981)

    Article  ADS  Google Scholar 

  17. Cserzö, M., Horváth, V.K., Vicsek, T.: Self-affine growth of bacterial colonies. Physica A 167, 315–321 (1990)

    Article  ADS  Google Scholar 

  18. Kessler, D.A., Levine, H.: Fluctuation-induced diffusive instabilities. Nature 394, 556–558 (1998)

    Article  ADS  Google Scholar 

  19. Matsushita, M., Wakita, J., Itoh, H., Ràfols, I., Matsuyama, T., Sakaguchi, H., Mimura, M.: Interface growth and pattern formation in bacterial colonies. Physica A 249, 517–524 (1998)

    Article  Google Scholar 

  20. Family, F., Vicsek, T.: Scaling of the active zone in the eden process on percolation networks and the ballistic deposition model. J. Phys. A 18, L75 (1985)

    Article  ADS  Google Scholar 

  21. López, J.M.: Scaling approach to calculate critical exponents in anomalous surface roughening. Phys. Rev. Lett. 83, 4594–4597 (1999)

    Article  ADS  Google Scholar 

  22. López, J.M., Rofríguez, M.A., Cuerno, R.: Superroughening versus intrinsic anomalous scaling of surfaces. Phys. Rev. E 56, 3993–3998 (1997)

    Article  ADS  Google Scholar 

  23. Bonachela, J.A., Dornic, I., Chaté, H., Muñoz, M.A.: Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality. Phys. Rev. Lett. 98, 155702 (2007)

    Article  ADS  Google Scholar 

  24. Lacasta, A.M., Cantalapiedra, C.E., Auguet, C.E., Peñaranda, A., Ramírez-Piscina, L.: Modelling of spatio-temporal patterns in bacterial colonies. Phys. Rev. E 59, 7036–7041 (1999)

    Article  ADS  Google Scholar 

  25. Kobayashi, N., Moriyama, O., Kitsunezaki, S., Yamazaki, M., Matsushita, Y.: Dynamic scaling of the growing rough surfaces. J. Phys. Soc. Jpn. 73, 2112–2116 (2004)

    Article  ADS  MATH  Google Scholar 

  26. Kardar, M., Parisi, G., Zhang, Y.-C.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986)

    Article  ADS  MATH  Google Scholar 

  27. Csahók, Z., Honda, K., Vicsek, T.: Dynamics of surface roughening in disordered media. J. Phys. A, Math. Gen. 26, L171–L178 (1993)

    Article  ADS  Google Scholar 

  28. Bonachela, J.A., Nadell, C.D., Xavier, J.B., Levin, S.A.: in preparation (2011)

  29. Xavier, J.B., Picioreanu, C., van Loosdrecht, M.C.M.: A framework for multidimensional modelling of activity and structure of multispecies biofilms. Environ. Microbiol. 7, 1085–1103 (2005)

    Article  Google Scholar 

  30. Xavier, J.B., Picioreanu, C., Van Loosdrecht, M.C.M.: Assesment of three-dimensional biofilm models through direct comparison with confocal microscopy imaging. Water Sci. Technol. 49, 177–185 (2004)

    Google Scholar 

  31. Xavier, J.B., De Kreuk, M.K., Picioreanu, C., Van Loosdrecht, M.C.M.: Multi-scale individual-based model of microbial and bioconversion dynamics in aerobic granular sludge. Environ. Sci. Technol. 41, 6410 (2007)

    Article  Google Scholar 

  32. Eden, M.: In: Neyman, J. (ed.) Proc. 4th Berkeley Symp. Mathematical Statistics and Probability, p. 223. University of California Press, Berkeley (1961)

    Google Scholar 

  33. Jullien, R., Botet, R.: Scaling properties of the surface of the eden model in d=2,3,4. J. Phys. A, Math. Gen. 18, 2279–2287 (1985)

    Article  ADS  Google Scholar 

  34. Paiva, L.R., Ferreira, S.C., Jr.: Universality class of isotropic on-lattice eden clusters. J. Phys. A, Math. Theor. 40, F43–F49 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Meakin, P.: Fractals, Scaling and Growth far from Equilibrium. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  36. Amaral, L.A.N., Barabási, A.-L., Makse, H.A., Stanley, E.H.: Scaling properties of driven interfaces in disordered media. Phys. Rev. E 52, 4087–4104 (1995)

    Article  ADS  Google Scholar 

  37. Klapper, I., Dockery, J.: Finger formation in biofilm layers. SIAM J. Appl. Math. 62, 853–869 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  38. López, J.M., Jensen, H.J.: Generic model of morphological changes in growing colonies of fungi. Phys. Rev. E 65, 021903 (2002)

    Article  ADS  Google Scholar 

  39. Monod, J.: Technique de culture continue. Theory et applications. Ann. Inst. Pasteur 79, 390–410 (1950)

    Google Scholar 

  40. Mimura, M., Sakaguchi, H., Matsushita, M.: Reaction-diffusion modelling of bacterial colony patterns. Physica A 282, 283–303 (2000)

    Article  ADS  Google Scholar 

  41. Kobayashi, N., Sato, T., Yamazaki, Y., Matsushita, M.: Modelling and numerical analysis of the colony formation of bacteria. J. Phys. Soc. Jpn. 72, 970–971 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, 08544-1003, USA

    Juan A. Bonachela, Carey D. Nadell & Simon A. Levin

  2. Department of Molecular Biology, Princeton University, Princeton, NJ, 08544-1033, USA

    Carey D. Nadell

  3. Program in Computational Biology, Memorial Sloan-Kettering Cancer Center, 1275 York Avenue, Box 460, New York, NY, 10065, USA

    João B. Xavier

Authors
  1. Juan A. Bonachela
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carey D. Nadell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. João B. Xavier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Simon A. Levin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan A. Bonachela.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bonachela, J.A., Nadell, C.D., Xavier, J.B. et al. Universality in Bacterial Colonies. J Stat Phys 144, 303–315 (2011). https://doi.org/10.1007/s10955-011-0179-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-011-0179-x

Keywords

Search

Navigation