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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635695
• 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.

细菌生物膜是沉水表面(也称为底物)上的微生物沉积。在生物膜形成的最初可逆步骤中，细菌附着在表面。贴壁的细胞开始产生一种细胞外聚合物，它们自己被嵌入其中，保护它们免受机械清洗和抗菌剂的破坏。在这个保护层中，生长出生动的微生物群落。生物膜对于废水处理或土壤修复技术的发展是很重要的。另一方面，生物膜在医学方面是有害的，因为它们可能导致难以根除细菌感染或卫生问题。尽管名为生物膜，但生物膜往往不是均匀的膜，而是可以在高度不规则的建筑中发展。生物膜群落中的生命与悬浮或浮游种群中的生命有很大不同，实验微生物学和数学微生物学传统上一直专注于这一领域。这在很大程度上是由于生物膜的空间组织，这导致了底物梯度，从而导致了空间上不同的生长条件。因此，许多传统的微生物生态模型，通常作为批量或连续培养的颂歌，不能应用，但必须开发出完全不同类别的模型。生物膜的微生物和物理复杂性往往反映在这些模型的数学复杂性上。文献中提出了几个生物膜的数学模型，它们采用了非常不同的数学概念和方法。我们的重点将是密度相关的扩散-反应系统，我们已经证明，它既可以被解释为空间结构的微生物种群，也可以被解释为将生物膜描述为复杂的流体。在其最简单的原型形式中，该模型包含因变量消失时的多孔介质简并性和因变量达到最大细胞密度时的超扩散奇异性。我们已经发展了这个原型系统的解理论，以及它们的模拟的数值方法。在这笔赠款期间，生物膜的新方面将被纳入这一模型框架中，这将导致额外的数学挑战，并需要对这些技术进行实质性的扩展和重新思考。其中一个重点将是多物种系统中的空间混合。我们修改了以前的模型，以显示问题如何导致额外的交叉扩散项，我们到目前为止一直忽略了这一点。另一个重点将是我们模糊地称之为化学诱导的脱离(以区别于剪切诱导的脱离)，包括由细胞间信号控制的脱离，或通过酶对EPS的分解。这将要求我们同时考虑细菌的运动和静止阶段，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底物的情况，这要求我们考虑反应边界条件。这是在某些产生生物膜的生物燃料中观察到的现象。我们将研究的生物膜的一些方面是基本性质的，其他方面与特定的系统密切相关。在所有情况下，它们都将受到特定生物膜应用的推动。我们考虑的应用将包括利用纤维素分解生物膜生产生物燃料；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)食品安全和工业中有害生物膜的控制。