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Phenotypic-dependent variability and the emergence of tolerance in bacterial populations

机译：表型依赖性变异性和细菌群体耐受性的出现

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Ecological and evolutionary dynamics have been historically regarded as unfolding atbroadly separated timescales. However, these two types of processes are nowadays well documented to intersperse much more tightly than traditionally assumed, especially in communities of microorganisms. Advancing the development of mathematical and computational approaches to shed novel light onto eco-evolutionary problems is a challenge ofutmost relevance. With this motivation in mind, here we scrutinize recent experimentalresults showing evidence of rapid evolution of tolerance by lag in bacterial populations thatare periodically exposed to antibiotic stress in laboratory conditions. In particular, the distribution of single-cell lag times—i.e., the times that individual bacteria from the communityremain in a dormant state to cope with stress—evolves its average value to approximatelyfit the antibiotic-exposure time. Moreover, the distribution develops right-skewed heavytails, revealing the presence of individuals with anomalously large lag times. Here, wedevelop a parsimonious individual-based model mimicking the actual demographic processes of the experimental setup. Individuals are characterized by a single phenotypic trait:their intrinsic lag time, which is transmitted with variation to the progeny. The model—in aversion in which the amplitude of phenotypic variations grows with the parent’s lag time—isable to reproduce quite well the key empirical observations. Furthermore, we develop a general mathematical framework allowing us to describe with good accuracy the properties ofthe stochastic model by means of a macroscopic equation, which generalizes the CrowKimura equation in population genetics. Even if the model does not account for all the biological mechanisms (e.g., genetic changes) in a detailed way—i.e., it is a phenomenologicalone—it sheds light onto the eco-evolutionary dynamics of the problem and can be helpful todesign strategies to hinder the emergence of tolerance in bacterial communities. From abroader perspective, this work represents a benchmark for the mathematical frameworkdesigned to tackle much more general eco-evolutionary problems, thus paving the road tofurther research avenues.
机译：生态和进化动态在历史上被认为是展开与砖川分离的时间尺度。然而，这两种类型的过程如今被众所周置的流程，而不是传统上假设的，特别是在微生物的社区中。推进在生态进化问题上揭示新颖的新光的数学和计算方法的发展是一种挑战。通过这种动机，我们在这里，我们仔细审查了最近的实验事项，显示了在实验室条件下定期暴露于抗生素应激的细菌群体中滞后的耐受性快速演变的证据。特别地，单细胞滞后时间-1的分布。，单个细菌的休眠状态中的单个细菌的次数应对应力 - 演变其平均值，以促进抗生素暴露时间。此外，分布发展右偏斜的重型，揭示了具有异常大的滞后时间的个体存在。在这里，Wedevelop2模仿实际​​的基于个人的模型模仿实验设置的实际人口过程。个体的特征在于单一表型特征：它们的内在滞后时间，其具有与后代变化的变化。在其级别变化的幅度的模型厌恶与父母的滞后时间增长，以相当良好地再现关键的经验观察。此外，我们开发一般的数学框架，允许我们通过宏观方程良好地描述随机模型的性能，这概括了人口遗传学中的Crowkimura方程。即使该模型不能以详细的方式考虑所有生物机制（例如，遗传变化），即，即，它是一种现象，它 - 它揭示了问题的生态进化动态，并且有助于阻碍策略细菌社区耐受的出现。从Abroader的角度来看，这项工作代表了数学框架的基准，以解决更多普遍的生态进化问题，从而铺设了Tofurther研究途径的道路。

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