Biofilms are complex communities of bacteria that exhibit a variety of collective behaviors. These behaviors improve their ability to survive in many different environments. One of these collective behaviors seen in Bacillus subtilis is the ability for starving cells to stop the growth of other cells using potassium signaling and voltage changes. This signaling produces an oscillatory growth pattern so that during periods of low growth the nutrients diffuse deeper into the biofilm and reach the nutrient-starved, interior regions of the biomass. In this paper, we develop a mathematical model to describe this oscillatory behavior, and we use this model to develop a two-dimensional simulation that reproduces many of the important features seen in the experimental data. This simulation allows us to examine the spatial patterning of the oscillatory behavior to better understand the relationships between the various regions of the biofilm. Studying the spatial components of the metabolic and voltage oscillations could allow for the development of new control techniques for biofilms with complex shapes.

生物膜是表现出多种集体行为的复杂细菌群落。这些行为提高了他们在许多不同环境中生存的能力。在枯草芽孢杆菌中看到的这些集体行为之一是饥饿细胞利用钾信号和电压变化来阻止其他细胞生长的能力。这种信号会产生一种振荡生长模式，因此在低生长期间，营养物质会更深地扩散到生物膜中，并到达营养物质匮乏的生物质内部区域。在本文中，我们开发了一个数学模型来描述这种振荡行为，并使用该模型开发了一个二维模拟，该模拟再现了实验数据中看到的许多重要特征。这种模拟使我们能够检查振荡行为的空间模式，以更好地了解生物膜各个区域之间的关系。