Mathematical Modeling, Analysis and Simulation of Biofilm Processes

生物膜过程的数学建模、分析和模拟

• 批准号: RGPIN-2014-04375
• 负责人: Eberl, Hermann
• 金额: $ 2.48万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=649908
• 关键词: Mathematical; Modeling; Analysis; Simulation; Biofilm

Bacterial biofilms are microbial depositions on submerged surfaces (a.k.a substratum). In the initial reversible step of biofilm formation bacteria attach to the surface. Cells that stay adhered start producing an extracellular polymeric substance in which they are themselves embedded and that protects them against mechanical washout and antimicrobials. In this protective layer, vivid microbial communities develop. Biofilms are important, e.g for the development of technologies for wastewater treatment or soil remediation. On the other hand biofilms are detrimental in a medical context, where they can lead to difficult to eradicate bacterial infections or hygienic problems. Despite their name, biofilms are often not homogeneous films but can develop in highly irregular architectures. Life in biofilm communities is substantially different from life in suspended or planktonic populations, on which experimental and mathematical microbiology have traditionally focused. This is largely due to the spatial organisation of biofilms, which leads to substrate gradients, and, hence, to spatially heterogeneous growth conditions. Therefore, many of the traditional models of microbial ecology, typically formulated as ODEs for batch or continuous cultures, cannot be applied, but an entirely different class of models must be developed. The microbial and physical complexity of biofilms is often reflected in the mathematical complexity of these models.*Several mathematical models of biofilms have been proposed in the literature, drawing on very different mathematical concepts and approaches. Our focus will be on density-dependent diffusion-reaction systems, which we have shown can be interpreted both as a spatially structured microbial populations and as a description of biofilms as complex fluids. In its simplest prototype form this model comprises a porous medium degeneracy when the dependent variable vanishes and simultaneously a super-diffusion singularity when the dependent variable reaches maximum cell density. We have developed a solution theory for this protoype system previously, as well as numerical methods for their simulation. Over the duration of this grant new aspects of biofilms will be incorporated in this model framework which lead to additional mathematical challenges and require a substantial extension and re-thinking of these techniques.*One focus will be on spatial mixing in multi-species systems. We revise our previous model to show how the problem leads to additional cross-diffusion terms which we have so far neglected. Another emphasis will be on what we vaguely call chemically induced detachment (to distinguish it from shear induced detachment), including detachment controlled by cell-to-cell signaling, or breakdown of the EPS by enzymes. This will require us to consider concurrently motile and sessile bacterial phases and the exchange between these two modes of growth. A third aspect we want to include is the situation where bacteria degrade the substratum on which they grow, which requires us to consider reactive boundary conditions. This is a phenomenon observed for certain biofuel producing biofilms.*Some of the biofilm aspects that we will study are of fundamental nature, others are closely tied to specific systems. In all cases they will be motivated by particular biofilm applications. Applications that we consider will include biofuel production by cellulolytic biofilms; wastewater treatment processes; signal based biofilm control strategies; groundwater protection and soil remediation; (bio)control of detrimental biofilms in food safety and industry.

细菌生物膜是淹没表面上的微生物沉积（也是底层）。在最初可逆的生物膜形成步骤中，细菌附着在表面上。保持粘附的细胞开始产生细胞外聚合物物质，它们本身是嵌入的，并保护它们免受机械冲洗和抗菌剂的侵害。在这个保护层中，生动的微生物群落发展。生物膜很重要，例如用于开发废水处理或土壤修复技术。另一方面，生物膜在医学环境中有害，在这种情况下，它们可能导致难以消除细菌感染或卫生问题。尽管有它们的名字，但生物膜通常不是同质的电影，而是可以在高度不规则的建筑中发展。生物膜群落中的生活与悬浮或浮游生物种群中的生活大不相同，传统上是实验性和数学微生物学的重点。这在很大程度上是由于生物膜的空间组织，从而导致底物梯度，因此在空间上存在异质生长条件。因此，无法应用许多传统的微生物生态学模型，通常以批处理或连续培养为单位的ODE，但是必须开发完全不同的模型。生物膜的微生物和物理复杂性通常反映在这些模型的数学复杂性中。我们的重点将放在密度依赖性扩散反应系统上，我们已经显示的可以将其解释为空间结构的微生物种群，也可以将生物膜描述为复杂的流体。在其最简单的原型形式中，当因变量消失并同时在因变量达到最大细胞密度时同时消失并同时具有超扩散奇异性时，该模型包含多孔介质退化。 我们以前已经为该原型系统开发了解决方案理论，以及用于模拟的数值方法。在这笔赠款期间，将在此模型框架中纳入生物膜的新方面，从而导致其他数学挑战，并需要对这些技术进行大量扩展和重新思考。*一个重点将放在多种物种系统中的空间混合上。我们修改了以前的模型，以显示问题如何导致到目前为止忽略的其他交叉扩散术语。 另一个重点将是我们隐约称为化学诱导的脱离（将其与剪切诱导的脱离区分开），包括由细胞到细胞信号控制的脱离，或酶对EPS的分解。这将要求我们考虑同时运动和无梗细菌阶段以及这两种生长模式之间的交换。我们要包括的第三个方面是细菌降解它们生长的底层的情况，这要求我们考虑反应性边界条件。这是对某些生物燃料产生生物膜的一种现象。在所有情况下，它们都会受到特定生物膜应用的动机。 我们考虑的应用将包括纤维素分解生物膜生产的生产；废水处理过程；基于信号的生物膜控制策略；地下水保护和土壤修复； （生物）控制食品安全和工业中有害生物膜。