Zhao Jia, Wang Qi
Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA.
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA.
Bull Math Biol. 2017 Apr;79(4):884-919. doi: 10.1007/s11538-017-0259-4. Epub 2017 Mar 13.
We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substance (EPS), quorum sensing (QS) molecules, solvent, and antibiotics. In the model, bacteria are classified into down-regulated QS, up-regulated QS, and non-QS cells based on their QS ability. The model is first benchmarked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development. It is then applied to study development of heterogeneous structures in biofilms due to interactions of QS regulation, hydrodynamics, and antimicrobial treatment. Our 3D numerical simulations have confirmed that (i). QS is beneficial for biofilm development in a long run by building a robust EPS population to protect the biofilm; (ii). biofilms located upstream can induce QS downstream when the colonies are close enough spatially; (iii). QS induction may not be fully operational and can even be compromised in strong laminar flows; (v). the hydrodynamic stress alters the biofilm morphology. Through further numerical investigations, our model suggests that (i). QS-regulated EPS production contributes to the structural formation of heterogeneous biofilms; (ii) QS down-regulated cells tend to grow at the surface of the biofilm while QS up-regulated ones tend to grow in the bulk; (iii) when nutrient supply is sufficient, QS induction might be more effective upstream than downstream; (iv) QS may be of little benefit in a short timescale in term of fighting against invading strain/species; (v) the material properties of biomass (bacteria and EPS) have strong impact on the dilution of QS molecules under strong shear flow. In addition, with this modeling framework, hydrodynamic details and rheological quantities associated with biofilm formation under QS regulation can be resolved.
我们开发了一种用于生物膜的多相流体动力学理论，该理论考虑了各种细菌表型、细胞外聚合物（EPS）、群体感应（QS）分子、溶剂和抗生素之间的相互作用。在该模型中，细菌根据其群体感应能力被分为群体感应下调、群体感应上调和非群体感应细胞。该模型首先通过与一个实验进行基准测试，该实验对生物膜形成过程中群体感应分子浓度和细胞密度的实验测量结果给出了极佳的拟合。然后将其应用于研究由于群体感应调节、流体动力学和抗菌处理的相互作用而导致的生物膜中异质结构的形成。我们的三维数值模拟证实了：（i）从长远来看，群体感应通过构建强大的EPS群体来保护生物膜，从而有利于生物膜的形成；（ii）当菌落空间距离足够近时，上游的生物膜可以诱导下游的群体感应；（iii）群体感应诱导可能无法完全发挥作用，甚至在强层流中会受到影响；（v）流体动力应力会改变生物膜的形态。通过进一步的数值研究，我们的模型表明：（i）群体感应调节的EPS产生有助于异质生物膜的结构形成；（ii）群体感应下调的细胞倾向于在生物膜表面生长，而群体感应上调的细胞倾向于在生物膜内部生长；（iii）当营养供应充足时，群体感应诱导在上游可能比下游更有效；（iv）在短期内，群体感应在对抗入侵菌株/物种方面可能益处不大；（v）生物质（细菌和EPS）的材料特性对强剪切流下群体感应分子的稀释有很大影响。此外，利用这个建模框架，可以解析与群体感应调节下生物膜形成相关的流体动力学细节和流变学量。
