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.
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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)
Guimerà, R., Amaral, L.A.N.: Functional cartography of complex-metabolic networks. Nature 433, 895–900 (2005)
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)
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)
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)
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)
Matsuyama, T., Sogawa, M., Nakagawa, Y.: Fractal spreading growth of Serratia Marcescens which produces surface active exolipids. FEMS Microbiol. Lett. 61, 243–246 (1989)
Fujikawa, H., Matsushita, M.: Fractal growth of Bacillus Subtilis on agar plates. J. Phys. Soc. Jpn. 58, 3875–3878 (1989)
Barabási, A.-L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)
Xavier, J.B., Kim, W., Foster, K.R.: A molecular mechanism that stabilizes cooperative secretions in pseudomonas aeruginosa. Mol. Microbiol. 79, 166–179 (2011)
Fujikawa, H.: Diversity of the growth patterns of Bacillus Subtilis colonies on agar plates. FEMS Microbiol. Ecol. 13, 159–168 (1994)
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)
Ben-Jacob, E., Garik, P.: The formation of patterns in non-equilibrium growth. Nature 434, 523–530 (1990)
Fujikawa, H.: Periodic growth of Bacillus Subtilis colonies on agar plates. Physica A 189, 15–21 (1992)
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)
Witten, T.A., Jr., Snader, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981)
Cserzö, M., Horváth, V.K., Vicsek, T.: Self-affine growth of bacterial colonies. Physica A 167, 315–321 (1990)
Kessler, D.A., Levine, H.: Fluctuation-induced diffusive instabilities. Nature 394, 556–558 (1998)
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)
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)
López, J.M.: Scaling approach to calculate critical exponents in anomalous surface roughening. Phys. Rev. Lett. 83, 4594–4597 (1999)
López, J.M., Rofríguez, M.A., Cuerno, R.: Superroughening versus intrinsic anomalous scaling of surfaces. Phys. Rev. E 56, 3993–3998 (1997)
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)
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)
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)
Kardar, M., Parisi, G., Zhang, Y.-C.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986)
Csahók, Z., Honda, K., Vicsek, T.: Dynamics of surface roughening in disordered media. J. Phys. A, Math. Gen. 26, L171–L178 (1993)
Bonachela, J.A., Nadell, C.D., Xavier, J.B., Levin, S.A.: in preparation (2011)
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)
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)
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)
Eden, M.: In: Neyman, J. (ed.) Proc. 4th Berkeley Symp. Mathematical Statistics and Probability, p. 223. University of California Press, Berkeley (1961)
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)
Paiva, L.R., Ferreira, S.C., Jr.: Universality class of isotropic on-lattice eden clusters. J. Phys. A, Math. Theor. 40, F43–F49 (2007)
Meakin, P.: Fractals, Scaling and Growth far from Equilibrium. Cambridge University Press, Cambridge (1998)
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)
Klapper, I., Dockery, J.: Finger formation in biofilm layers. SIAM J. Appl. Math. 62, 853–869 (2001)
López, J.M., Jensen, H.J.: Generic model of morphological changes in growing colonies of fungi. Phys. Rev. E 65, 021903 (2002)
Monod, J.: Technique de culture continue. Theory et applications. Ann. Inst. Pasteur 79, 390–410 (1950)
Mimura, M., Sakaguchi, H., Matsushita, M.: Reaction-diffusion modelling of bacterial colony patterns. Physica A 282, 283–303 (2000)
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)
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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
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DOI: https://doi.org/10.1007/s10955-011-0179-x