论文标题
最慢的第一次通行时间，冗余和更年期的时机
Slowest first passage times, redundancy, and menopause timing
论文作者
论文摘要
当一个随机的“搜索者”找到“目标”时，通常会启动生物事件，这被称为第一个通道时间（FPT）。在一些涉及多个搜索者的生物系统中，一个重要的时间表是它需要最慢的搜索器找到目标的时间。例如，在女性卵巢储备中成千上万的原始卵泡中，这是触发更年期开始的最慢的卵泡。这样最慢的FPT也可能有助于细胞信号通路的可靠性，并影响细胞定位外部刺激的能力。在本文中，我们使用极值理论和渐近分析来获得与最慢的FPT的完整概率分布和矩的严格近似值。尽管结果在许多搜索者的限制中得到了证明，但数值模拟表明，在典型的感兴趣的情况下，对于任何数量的搜索者，近似值都是准确的。我们将这些一般数学结果应用于卵巢衰老和更年期时机的模型，这揭示了最慢的FPT在理解生物系统中冗余的作用。我们还将理论应用于几种流行的随机搜索模型，包括通过扩散，延伸和致命搜索者进行搜索。
Biological events are often initiated when a random "searcher" finds a "target," which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest searcher(s) to find a target. For example, of the hundreds of thousands of primordial follicles in a woman's ovarian reserve, it is the slowest to leave that trigger the onset of menopause. Such slowest FPTs may also contribute to the reliability of cell signaling pathways and influence the ability of a cell to locate an external stimulus. In this paper, we use extreme value theory and asymptotic analysis to obtain rigorous approximations to the full probability distribution and moments of slowest FPTs. Though the results are proven in the limit of many searchers, numerical simulations reveal that the approximations are accurate for any number of searchers in typical scenarios of interest. We apply these general mathematical results to models of ovarian aging and menopause timing, which reveals the role of slowest FPTs for understanding redundancy in biological systems. We also apply the theory to several popular models of stochastic search, including search by diffusive, subdiffusive, and mortal searchers.
