Modelling and Numerical Analysis of the Colony Formation of Bacteria

In this Note we report the attempt of generalization of Mimura et al. (MSM) model for colony formation of bacteria. We also show the numerical results, which are then compared with experiments. Bacterial species Bacillus subtilis exhibits various colony patterns in response to two environmental parameters, i.e., concentrations of nutrient Cn and agar Ca in a thin agar plate as incubation medium. They are observed in the regions of morphological diagram labeled as A–E in Fig. 1. If Cn is low and Ca is high (region A), colony patterns exhibit tipsplitting growth with diffusion-limitted aggregation (DLA)like ramified structures. In fact colony growth in this region can be explained by the DLA model. Increasing Cn with Ca fixed high (region B), they exhibit round shape with Edenlike rough interface. If Cn is high and Ca is low (region D), they look macroscopically disk-like. The colony growth in this region was found to be consistent with the solution of two-dimentional Fisher’s equation. Decreasing Cn with Ca fixed in-between (region E), they show highly branched structures reminiscent of dense-branching morphology (DBM). Finally, in the region C, colonies exhibit concentric-ring patterns which are produced through alternate migration and consolidation by bacterial cells. In order to explain these observations various reaction– diffusion models have already been proposed. They are, however, not very successful in that they can reproduce only some of the observed patterns such as DLA-like and DBMlike. MSM tried to make a unified model to reproduce all of the observed patterns. They assumed that bacterial cells consist of two types, active and inactive cells, based on experimental observations of colony growth. They proposed the following MSM model: