Invasion speeds in microbial systems with toxin production and quorum sensing
Invasion speeds in microbial systems with toxin production and quorum sensing
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DOI：
10.1016/j.jtbi.2017.01.034
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发表时间：
2017-05-07
影响因子：
2
通讯作者：
Fagan, William F.
中科院分区：
文献类型：
--
作者：
Bewick, Sharon;Staniczenko, Phillip P. A.;Fagan, William F.
入侵和入侵速度的理论传统上是在宏观系统中研究的。令人惊讶的是，微生物入侵受到的关注较少。虽然微生物与大型生物体之间的竞争有许多共同的特征，但它们也表现出独特的行为，需要新的数学处理来充分理解微生物系统中的入侵。最值得注意的是长距离相互作用的可能性，包括通过扩散毒素介导的种群之间的竞争和使用群体感应的单个种群中的个体之间的合作。在本文中，我们使用耦合偏微分方程系统的基础上费舍尔方程的细菌入侵模型。我们的模型认为，在某些情况下，表达在响应群体感应的扩散毒素的竞争系统。首先，我们推导出快速和缓慢的毒素扩散的限制的入侵速度的分析近似。然后，我们测试我们的分析近似的有效性，并探讨中间速率的毒素扩散，使用数值模拟。有趣的是，我们发现毒素在进攻性使用时应该迅速扩散，但当毒素被用作防御机制时，有两种最佳策略。具体地说，当毒素的杀伤效力高时，毒素应迅速扩散，但当毒素的杀伤效力低时，毒素应缓慢扩散。我们的方法允许明确的调查的性质和特点的扩散化合物用于非本地的竞争，是相关的微生物系统和选择宏观类群，如植物和珊瑚，可以通过生物化学物质相互作用。
The theory of invasions and invasion speeds has traditionally been studied in macroscopic systems. Surprisingly, microbial invasions have received less attention. Although microbes share many of the features associated with competition between larger-bodied organisms, they also exhibit distinctive behaviors that require new mathematical treatments to fully understand invasions in microbial systems. Most notable is the possibility for long-distance interactions, including competition between populations mediated by diffusible toxins and cooperation among individuals of a single population using quorum sensing. In this paper, we model bacterial invasion using a system of coupled partial differential equations based on Fisher's equation. Our model considers a competitive system with diffusible toxins that, in some cases, are expressed in response to quorum sensing. First, we derive analytical approximations for invasion speeds in the limits of fast and slow toxin diffusion. We then test the validity of our analytical approximations and explore intermediate rates of toxin diffusion using numerical simulations. Interestingly, we find that toxins should diffuse quickly when used offensively, but that there are two optimal strategies when toxins are used as a defense mechanism. Specifically, toxins should diffuse quickly when their killing efficacy is high, but should diffuse slowly when their killing efficacy is low. Our approach permits an explicit investigation of the properties and characteristics of diffusible compounds used in non-local competition, and is relevant for microbial systems and select macroscopic taxa, such as plants and corals, that can interact through biochemicals.