Traveling Pulses for a Two-Species Chemotaxis Model.
Traveling Pulses for a Two-Species Chemotaxis Model.
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DOI：
10.1371/journal.pcbi.1004843
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发表时间：
2016-04
影响因子：
4.3
通讯作者：
Vauchelet N
中科院分区：
文献类型：
--
作者：
Emako C;Gayrard C;Buguin A;Neves de Almeida L;Vauchelet N
数学模型已被广泛用于描述细菌的趋化性集体运动。特别是，已经通过实验观察到在狭窄通道中行进的细菌浓度波，并且由于宏观尺度的数学模型，可以精确地描述细菌浓度波。这种模型是在使用基于精确描述的介观运行和翻滚过程的动力学模型中推导出来的。我们将这种方法扩展到研究两个群体之间的相互作用的行为。杆菌单独地，每个种群在通道中以自己的速度行进。当放在一起时，可以观察到行进脉冲的速度的同步。我们表明，这种同步取决于快速种群的比例。我们的方法是基于偏微分方程的宏观模型的数学分析。数值模拟与实验观测结果相比，定性的协议。使用数学工具来描述细菌群落的自组织已经引起了很多兴趣，因为它允许实验观察到的现象的精确描述。在过去的40年里，已经提出了一个层次的数学模型的动态的一个单一的细菌种群。这些模型已经逐渐考虑到单个细菌行为的更精确方面（如奔跑和翻滚行为）。如今，一个自然而具有挑战性的问题是使用这样的模型来描述不同细菌种群之间的相互作用。在这项工作中，我们考虑一个宏观系统的方程来自介观尺度来描述两个种群的细菌之间的相互作用。由于这个模型得到的预测相比，实验观察到的行为的细菌在通道中的旅行脉冲。
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in using a kinetic model based on an accurate description of the mesoscopic run-and-tumble process. We extend this approach to study the behavior of the interaction between two populations of E. Coli. Separately, each population travels with its own speed in the channel. When put together, a synchronization of the speed of the traveling pulses can be observed. We show that this synchronization depends on the fraction of the fast population. Our approach is based on mathematical analysis of a macroscopic model of partial differential equations. Numerical simulations in comparison with experimental observations show qualitative agreement. The use of mathematical tools to describe self-organization of bacterial communities has raised a lot of interest since it permits a precise description of experimentally observed phenomena. In the last 40 years a hierarchy of mathematical models for the dynamics of a single bacterial population has been proposed. These models have progressively taken into account more precise aspects of individual bacterial behavior (like the run and tumble behavior). Nowadays, a natural and challenging issue is to use such models to describe the interaction between different populations of bacteria. In this work, we consider a macroscopic system of equations derived from the mesoscopic scales to describe the interaction between two populations of bacteria. The prediction obtained thanks to this model is compared to experimental observations concerning the behavior of traveling pulses of bacteria in a channel.