Self-Organized Pattern Formation of a Bacteria Colony Modeled by a Reaction Diffusion System and Nucleation Theory

Self-organized pattern formation is observed in bacterial colony growth. The recently reported knotted-branching pattern of the Bacillus circulans colony consists of the trajectories of aggregates which grow, move, and reproduce simultaneously. We modeled these processes by combining a reaction diffusion system of nutrient dynamics, nucleation theory for aggregate generation, and individual based dynamics of motion and growth of aggregates. The branching pattern produced by computer simulation shows great similarity with experiments. Response to the initial nutrient concentration is also consistent with the experiments.

Figure 1

Colony patterns of B. circulance. (a) A typical knotted-branching pattern (KBP). (b) When nutrient concentration is denser. The pattern is more isotropic with more branches and less gaps. (c) When agar medium is harder. This branching pattern is called an Eden-like pattern in which knots are not clearly distinguished. (d) When agar medium is softer. No spatial structure is formed.

Figure 2

Schematic illustration of the model. (a) An aggregate (nucleus) swims in the surrounding lubricant, which stands still due to friction. The lubricant secreted by an aggregate also plays the role of a solvent of dispersed bacteria. (b) Bacteria reproduce in both the envelope and the active layer of a nucleus. As the envelope is supersaturated and adsorption (nucleus growth) is dominant, net adsorption rate is considered in the model.

Figure 3

Simulation results. The final patterns when all nuclei become inactive are shown. The shaded area represents the size of the nucleus when it passes the corresponding point of the branch. For appropriate parameters, KBP is reproduced (a). When the initial nutrient concentration is increased, the number of branches increases and the pattern becomes more isotropic (b). When a friction coefficient is large, which corresponds to a hard agar condition, a nucleus can hardly move and thus nutrient concentration is expected to be almost the same among nuclei. However, simulation reproduced a branching pattern (c). All these results are consistent with corresponding experimental results (Fig. 1).

Figure 4

Enlarged pictures of simulation (left) and experimental (right) results. The great similarity is observed.