Front instability and stripe formation in expanding bacterial colonies

Recently, a team of researchers from HKU, UCSD, Marburg and HKBU conducted experiments of pattern formation in open geometry by controlling the motility of bacteria via a synthetic circuit [C. Liu et al., Science 334, 238 (2011)]. The work opens up a novel route to pattern formation in autonomous systems without invoking external guidance. It has been shown that the Fisher-Kolmogorov type equations that implement the density-dependent diffusivity of an active species correctly reproduce the stripe patterns seen in the experiments. However, a number of important theoretical issues have been left unanswered so far. In this project, we construct and analyze a three- species continuum model that takes into account the delayed response of bacterium to its environment. The multi-species model is expected to give a more accurate description of the microscopic process that gives rise to the front instability and stripe formation. Traveling wave solutions to the continuum equations will be worked out and their stability against small perturbations analyzed. The cyclic generation of new stripes during the colony expansion will be investigated numerically. Build on this model, we will examine the robustness of the pattern formation process against variations in cell motility, either transient (due to protein copy number fluctuations) or genetic (due to mutations). We will also investigate whether presence of a residual chemotactic component in bacterial movement significantly alters certain key aspects of the pattern formation process. The study will yield a better understanding of the robustness of the proposed pattern formation scheme and the conditions that need to be fulfilled for it to work. It will not only enable a closer comparison between the modeling and experimental results, but also open up new directions of research for the active matter community