Pattern formation in bacterial colonies with density-dependent diffusion
Pattern formation in bacterial colonies with density-dependent diffusion
复制标题
DOI：
10.1017/s0956792518000013
复制
发表时间：
2018-01
影响因子：
1.9
通讯作者：
Julien Smith-Roberge;D. Iron;T. Kolokolnikov
中科院分区：
文献类型：
--
作者：
Julien Smith-Roberge;D. Iron;T. Kolokolnikov
最近的实验表明，当种群密度（通过群体感应机制检测到）足够大时，经过遗传修饰的细菌菌落中会出现扩散下降的模式。我们研究了该系统的一个PDE模型，并构造了其非常数稳态解的形式的界面的细菌密度。我们推导出的接口运动的方程，并证明解析，这样的接口解决方案是稳定的，当细菌的扩散速率是大的，信号分子的扩散速率，DH，是小的。我们进一步证明，增加Dh诱导的Hopf分岔，导致稳定性的损失，这可能会导致复杂的时空动力学或灭绝的模式完全。数值模拟证实了这些结果。
Recent experiments have shown that patterns can emerge in bacterial colonies genetically modified to have a drop in diffusion when population densities (detected via a quorum sensing mechanism) are sufficiently large. We examine one PDE model of this system, and construct its non-constant stationary solutions in the form of an interface for the bacterial density. We derive the equations for the interface motion and demonstrate analytically that such interface solution is stable when the diffusion rate of bacteria is large and the diffusion rate of signalling molecules, Dh, is small. We further demonstrate that increasing Dh induces a Hopf bifurcation, resulting in a loss of stability, which can lead to either complex spatio-temporal dynamics or extinction of pattern altogether. These results are confirmed by numerical simulations.