AI 中文总结
研究利用偏微分方程框架，纳入运动能量权衡，通过最大化种群产量的优化问题，评估不同环境下细菌运动策略，揭示最佳运动反应对资源分布敏感，为实验微生物学现象提供理论解释，是预测细菌行为的有力工具。
AI 中文摘要
细菌运动是领土扩张和资源获取的基本特征。现有依赖营养的运动模型通常未明确考虑与运动相关的代谢成本，而这些成本在营养有限或封闭系统中至关重要。本研究利用偏微分方程开发了一个数学框架，明确纳入运动的能量权衡。通过制定以最大化种群产量（由总细胞数定义）为重点的优化问题，我们评估了不同环境背景下的各种运动策略。结果表明，最佳运动反应对资源分布高度敏感。特别是在不可预测的环境中，非单调运动反应成为最佳策略，为实验微生物学中观察到的剂量反应曲线提供了有力的理论解释。该框架是预测资源受限生态系统中细菌行为的强大且可解释的工具，并为环境压力如何塑造此类适应性策略提供了新见解。
英文摘要
Bacterial motility is a fundamental trait for territorial expansion and resource acquisition. While existing models of nutrient-dependent motility often do not explicitly account for the metabolic costs associated with motility, these costs become critical in nutrient-limited or closed systems. In this study, we developed a mathematical framework using partial differential equations (PDEs) that explicitly incorporates the energetic trade-offs of motility. By formulating an optimization problem focused on maximizing population yield---defined by the total cell count---we evaluated various motility strategies across different environmental contexts. Our results demonstrate that the optimal motility response is highly sensitive to resource distribution. Specifically, we show that in unpredictable environments, a non-monotonic motility response emerges as the optimal strategy, providing a robust theoretical explanation for dose-response curves observed in experimental microbiology. This framework serves as a powerful, interpretable tool for predicting bacterial behavior in resource-constrained ecosystems and offers new insights into how such adaptive strategies are shaped by environmental pressures.
