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.

细菌生物膜是水下表面（又称基质）上的微生物沉积物。在生物膜形成的初始可逆步骤中，细菌附着在表面。保持粘附的细胞开始产生细胞外聚合物质，细胞自身嵌入其中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，活跃的微生物群落发展起来。生物膜很重要，例如对于废水处理或土壤修复技术的开发。另一方面，生物膜在医疗环境中是有害的，它们可能导致难以根除的细菌感染或卫生问题。尽管有其名称，生物膜通常不是均匀的膜，而是可以形成高度不规则的结构。生物膜群落中的生命与实验和数学微生物学传统上关注的悬浮或浮游种群中的生命有很大不同。这主要是由于生物膜的空间组织导致了基质梯度，从而导致了空间异质的生长条件。因此，许多传统的微生物生态学模型（通常被表述为用于批量或连续培养的 ODE）无法应用，但必须开发一类完全不同的模型。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。*文献中已经提出了几种生物膜数学模型，借鉴了截然不同的数学概念和方法。我们的重点将是密度依赖性扩散反应系统，我们已经证明该系统既可以解释为空间结构的微生物种群，也可以解释为复杂流体的生物膜的描述。在其最简单的原型形式中，该模型包括当因变量消失时的多孔介质简并性以及当因变量达到最大细胞密度时的超扩散奇点。 我们之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。在这笔资助期间，生物膜的新方面将被纳入该模型框架中，这会带来额外的数学挑战，并需要对这些技术进行实质性扩展和重新思考。*一个重点将是多物种系统中的空间混合。我们修改了之前的模型，以显示该问题如何导致我们迄今为止忽略的额外交叉扩散项。 另一个重点是我们模糊地称为化学诱导分离（以区别于剪切诱导分离），包括由细胞间信号传导控制的分离，或酶对 EPS 的分解。这将要求我们同时考虑运动和固着细菌阶段以及这两种生长模式之间的交换。我们想要包括的第三个方面是细菌降解它们生长的基质的情况，这需要我们考虑反应边界条件。这是在某些产生生物燃料的生物膜中观察到的现象。*我们将研究的一些生物膜方面具有基本性质，其他方面则与特定系统密切相关。在所有情况下，他们都会受到特定生物膜应用的推动。 我们考虑的应用包括通过纤维素分解生物膜生产生物燃料；废水处理工艺；基于信号的生物膜控制策略；地下水保护和土壤修复；食品安全和工业中有害生物膜的（生物）控制。