Journal of Statistical Physics

, Volume 144, Issue 2, pp 303–315 | Cite as

Universality in Bacterial Colonies

  • Juan A. Bonachela
  • Carey D. Nadell
  • João B. Xavier
  • Simon A. Levin


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.


Computational biology Interfaces in random media (Theory) Self-affine roughness (Theory) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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) ADSCrossRefGoogle Scholar
  2. 2.
    Guimerà, R., Amaral, L.A.N.: Functional cartography of complex-metabolic networks. Nature 433, 895–900 (2005) ADSCrossRefGoogle Scholar
  3. 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) ADSCrossRefGoogle Scholar
  4. 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) ADSCrossRefGoogle Scholar
  5. 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) CrossRefGoogle Scholar
  6. 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) CrossRefGoogle Scholar
  7. 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) CrossRefGoogle Scholar
  8. 8.
    Fujikawa, H., Matsushita, M.: Fractal growth of Bacillus Subtilis on agar plates. J. Phys. Soc. Jpn. 58, 3875–3878 (1989) ADSCrossRefGoogle Scholar
  9. 9.
    Barabási, A.-L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995) zbMATHCrossRefGoogle Scholar
  10. 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) CrossRefGoogle Scholar
  11. 11.
    Fujikawa, H.: Diversity of the growth patterns of Bacillus Subtilis colonies on agar plates. FEMS Microbiol. Ecol. 13, 159–168 (1994) CrossRefGoogle Scholar
  12. 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) ADSCrossRefGoogle Scholar
  13. 13.
    Ben-Jacob, E., Garik, P.: The formation of patterns in non-equilibrium growth. Nature 434, 523–530 (1990) ADSCrossRefGoogle Scholar
  14. 14.
    Fujikawa, H.: Periodic growth of Bacillus Subtilis colonies on agar plates. Physica A 189, 15–21 (1992) ADSCrossRefGoogle Scholar
  15. 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) ADSCrossRefGoogle Scholar
  16. 16.
    Witten, T.A., Jr., Snader, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981) ADSCrossRefGoogle Scholar
  17. 17.
    Cserzö, M., Horváth, V.K., Vicsek, T.: Self-affine growth of bacterial colonies. Physica A 167, 315–321 (1990) ADSCrossRefGoogle Scholar
  18. 18.
    Kessler, D.A., Levine, H.: Fluctuation-induced diffusive instabilities. Nature 394, 556–558 (1998) ADSCrossRefGoogle Scholar
  19. 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) CrossRefGoogle Scholar
  20. 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) ADSCrossRefGoogle Scholar
  21. 21.
    López, J.M.: Scaling approach to calculate critical exponents in anomalous surface roughening. Phys. Rev. Lett. 83, 4594–4597 (1999) ADSCrossRefGoogle Scholar
  22. 22.
    López, J.M., Rofríguez, M.A., Cuerno, R.: Superroughening versus intrinsic anomalous scaling of surfaces. Phys. Rev. E 56, 3993–3998 (1997) ADSCrossRefGoogle Scholar
  23. 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) ADSCrossRefGoogle Scholar
  24. 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) ADSCrossRefGoogle Scholar
  25. 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) ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    Kardar, M., Parisi, G., Zhang, Y.-C.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986) ADSzbMATHCrossRefGoogle Scholar
  27. 27.
    Csahók, Z., Honda, K., Vicsek, T.: Dynamics of surface roughening in disordered media. J. Phys. A, Math. Gen. 26, L171–L178 (1993) ADSCrossRefGoogle Scholar
  28. 28.
    Bonachela, J.A., Nadell, C.D., Xavier, J.B., Levin, S.A.: in preparation (2011) Google Scholar
  29. 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) CrossRefGoogle Scholar
  30. 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. 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) CrossRefGoogle Scholar
  32. 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. 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) ADSCrossRefGoogle Scholar
  34. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Meakin, P.: Fractals, Scaling and Growth far from Equilibrium. Cambridge University Press, Cambridge (1998) zbMATHGoogle Scholar
  36. 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) ADSCrossRefGoogle Scholar
  37. 37.
    Klapper, I., Dockery, J.: Finger formation in biofilm layers. SIAM J. Appl. Math. 62, 853–869 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    López, J.M., Jensen, H.J.: Generic model of morphological changes in growing colonies of fungi. Phys. Rev. E 65, 021903 (2002) ADSCrossRefGoogle Scholar
  39. 39.
    Monod, J.: Technique de culture continue. Theory et applications. Ann. Inst. Pasteur 79, 390–410 (1950) Google Scholar
  40. 40.
    Mimura, M., Sakaguchi, H., Matsushita, M.: Reaction-diffusion modelling of bacterial colony patterns. Physica A 282, 283–303 (2000) ADSCrossRefGoogle Scholar
  41. 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) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Juan A. Bonachela
    • 1
  • Carey D. Nadell
    • 1
    • 2
  • João B. Xavier
    • 3
  • Simon A. Levin
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA
  2. 2.Department of Molecular BiologyPrinceton UniversityPrincetonUSA
  3. 3.Program in Computational BiologyMemorial Sloan-Kettering Cancer CenterNew YorkUSA

Personalised recommendations