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A two-dimensional multi-species model for different Listeria monocytogenes biofilm structures and its numerical simulation
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.amc.2020.125383
Eva Balsa-Canto , Alejandro López-Núñez , Carlos Vázquez

Abstract In this work we propose a two-dimensional multi-species model to describe the dynamics of biofilms formed by the pathogenic bacteria Listeria monocytogenes. Different Listeria monocytogenes strains produce biofilms with different structures, namely flat, honeycomb and clustered. Previous works showed that glucose impaired uptake and the appearance of damaged or dead cells are critical mechanisms underlying Listeria monocytogenes biofilm dynamics. Here we explicitly propose an extension of the two-dimensional multi-species model proposed by Alpkist and Klapper to account for those mechanisms. The result is a continuous two-dimensional multi-species model with non-linear detachment and mass action nutrient consumption. Moreover, we also propose a set of efficient numerical methods to solve the coupled model and we have developed their computer implementation from scratch in C/C++. Mainly based on finite differences schemes, these numerical techniques include Crank-Nicolson schemes for time discretization, Gibou’s ghost node techniques and level set methods to cope with the free boundary associated to the determination of the time-dependent biofilm domain. To finish with, we compare our simulation results with the dynamics of real biofilms as observed in the laboratory. More precisely, by using model parameters calibrated to experiments, the numerical results clearly illustrate the performance of the proposed model and the numerical methods to reproduce the real dynamics of flat, clustered and honeycomb structures shown by different Listeria monocytogenes strains.

中文翻译:

不同单核细胞增生李斯特菌生物膜结构的二维多物种模型及其数值模拟

摘要 在这项工作中,我们提出了一个二维多物种模型来描述由病原菌单核细胞增生李斯特菌形成的生物膜的动态。不同的单核细胞增生李斯特菌菌株产生不同结构的生物膜,即扁平、蜂窝状和簇状。以前的工作表明,葡萄糖摄取受损和受损或死细胞的出现是单核细胞增生李斯特菌生物膜动力学的关键机制。在这里,我们明确提出了对 Alpkist 和 Klapper 提出的二维多物种模型的扩展,以解释这些机制。结果是具有非线性分离和质量作用养分消耗的连续二维多物种模型。而且,我们还提出了一套有效的数值方法来解决耦合模型,并且我们已经在 C/C++ 中从头开发了它们的计算机实现。这些数值技术主要基于有限差分方案,包括用于时间离散化的 Crank-Nicolson 方案、Gibou 的鬼节点技术和水平集方法,以处理与确定时间相关的生物膜域相关的自由边界。最后,我们将模拟结果与实验室中观察到的真实生物膜的动力学进行比较。更准确地说,通过使用根据实验校准的模型参数,数值结果清楚地说明了所提出的模型的性能以及重现不同单核细胞增生李斯特菌菌株显示的扁平、簇状和蜂窝状结构的真实动态的数值方法。
更新日期:2020-11-01
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