Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotDormancy of bacteria can be induced by starvation stress as prolonged lag time, and often contributes to the antibiotic tolerance of bacteria. We analyze the optimal lag time for wake-up from the starvation to survive the iterative and stochastic application of antibiotics. By using a population dynamics model, we show that the optimal lag time exhibits a discontinuous transition from zero lag time to a finite lag time when the severeness of the application of the antibiotic is increased. When the bacterial populations are able to split into subpopulations to have two phenotypes with different average lag time, the fraction of the finite lag time population shows continuous transition when changing the severeness of antibiotics application. The result suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application.ic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.

中文翻译：

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什么时候醒来？饥饿诱发的持久性的最佳唤醒策略

饥饿可导致细菌滞后时间延长，从而加剧了细菌对抗生素的耐受性。我们分析了生存和增长迭代和随机应用抗生素的最佳滞后时间。一个简单的模型表明，当增加抗生素使用的严格性（例如，暴露抗生素的概率，暴露下的死亡率和暴露时间）时，最佳滞后时间可能会出现不连续的过渡。这表明通过控制使用抗生素来减少耐受细菌的可能性。当细菌种群能够具有两种具有不同滞后时间的表型时，具有不同滞后时间的第二种表型的分数显示出连续的过渡。然后，我们提出了一个通用框架来研究给定分布的抗生物素的总种群适应度的最佳滞后时间分布。细菌的休眠可以通过饥饿应激延长滞后时间来诱导，并且常常有助于细菌的抗生素耐受性。我们分析了从饥饿中醒来的最佳滞后时间，以便在反复使用和随机使用抗生素的过程中生存。通过使用种群动力学模型，我们表明当增加抗生素的使用强度时，最佳滞后时间表现出从零滞后时间到有限滞后时间的不连续过渡。当细菌种群能够分裂成亚群而具有两种具有不同平均滞后时间的表型时，当改变抗生素应用的严重性时，有限滞后时间总体的分数显示出连续的过渡。结果表明，通过控制抗生素的施用时间来减少耐受细菌的可能性。对于广泛的抗生素施用持续时间分布，包括后者单调递减的情况，获得的最佳分布具有多个峰。该分析支持在细菌长期适应性的滞后时间内发展出多种可能离散表型的优势。对于广泛的抗生素施用持续时间分布，包括后者单调递减的情况，获得的最佳分布具有多个峰。该分析支持在细菌长期适应性的滞后时间内发展出多种可能离散表型的优势。对于广泛的抗生素施用持续时间分布，包括后者单调递减的情况，获得的最佳分布具有多个峰。该分析支持在细菌长期适应性的滞后时间内发展出多种可能离散表型的优势。