Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several novel models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per-capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest at new opportunities for experimental investigation and design. Overall, we provide a new way of conceptualising and modelling cellular decision-making in volatile environments by explicitly unifying theory from mathematical biology and finance.

中文翻译：

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持久性作为最佳对冲策略

细菌投资于一个生长缓慢的亚群，称为持久性，以确保在面对不确定性时生存。这种对冲策略与金融对冲非常相似，在金融对冲中，投资组合的多样化可以防止经济不确定性。我们通过优化控制理论将生物种群动力学研究与金融风险管理数学相结合，为理解细胞对冲提供了新的理论基础。受波动性在持久性出现中的广泛接受作用的推动，我们考虑了几种由连续时间随机过程描述的环境波动新模型。这使我们能够研究一种新兴的细胞对冲策略，以最大限度地提高人口的预期人均增长率。分析和模拟结果探索了最佳的持久化策略，揭示了与实验观察一致的结果，并为实验研究和设计提供了新的机会。总体而言，我们通过明确统一数学生物学和金融学的理论，提供了一种在多变环境中概念化和建模细胞决策的新方法。