Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling.

We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system described by the reaction-diffusion (RD) equation of Turing, focusing on anisotropic diffusion using the Finsler geometry (FG) modeling technique. In FG modeling, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor. Because of this dynamical diffusion coefficient, FG modeling of the RD equation sharply contrasts with the standard numerical technique in which direction-dependent coefficients are manually assumed. To find the solution of the RD equations in FG modeling, we use a hybrid numerical technique combining the Metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of the activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are a possible origin of spontaneously emergent anisotropic patterns of living organisms, such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with the direction of cell diffusion accompanied by thermal fluctuations.

Morphologies of Bacillus subtilis communities responding to environmental variation.

Bacterial communities exhibit a variety of growth morphologies in constructing robust systems under different environmental conditions. We review the diverse morphologies of Bacillus subtilis communities and their mechanisms of self-organization. B. subtilis uses different cell types to suit environmental conditions and cell density. The subpopulation of each cell type exhibits various environment-sensitive properties. Furthermore, division of labor among the subpopulations results in flexible development for the community as a whole. We review how B. subtilis community morphologies and growth strategies respond to environmental perturbations.

Self-organization of bacterial communities against environmental pH variation: Controlled chemotactic motility arranges cell population structures in biofilms.

As with many living organisms, bacteria often live on the surface of solids, such as foods, organisms, buildings and soil. Compared with dispersive behavior in liquid, bacteria on surface environment exhibit significantly restricted mobility. They have access to only limited resources and cannot be liberated from the changing environment. Accordingly, appropriate collective strategies are necessarily required for long-term growth and survival. However, in spite of our deepening knowledge of the structure and characteristics of individual cells, strategic self-organizing dynamics of their community is poorly understood and therefore not yet predictable. Here, we report a morphological change in Bacillus subtilis biofilms due to environmental pH variations, and present a mathematical model for the macroscopic spatio-temporal dynamics. We show that an environmental pH shift transforms colony morphology on hard agar media from notched 'volcano-like' to round and front-elevated 'crater-like'. We discover that a pH-dependent dose-response relationship between nutritional resource level and quantitative bacterial motility at the population level plays a central role in the mechanism of the spatio-temporal cell population structure design in biofilms.