SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 1-24, January 2021.
The first time a searcher finds a target is called a first passage time (FPT). In many physical, chemical, and biological processes, the searcher is “mortal,” which means that the searcher might become inactivated (degrade, die, etc.) before finding the target. In the context of intracellular signaling, an important recent work discovered that fast inactivation can drastically alter the conditional FPT distribution of a mortal diffusive searcher, if the searcher is conditioned to find the target before inactivation. In this paper, we prove a general theorem that yields an explicit formula for all the moments of such conditional FPTs in the fast inactivation limit. This formula is quite universal, as it holds under very general conditions on the diffusive searcher dynamics, the target, and the spatial domain. These results prove in significant generality that if inactivation is fast, then the conditional FPT compared to the FPT without inactivation is (i) much faster, (ii) much less affected by spatial heterogeneity, and (iii) much less variable. Our results agree with recent computational and theoretical analysis of a certain discrete intracellular diffusion model and confirm a conjecture related to the effect of spatial heterogeneity on intracellular signaling.

中文翻译：

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快速灭活对道德扩散搜索者有条件的首次通过时间的影响

SIAM应用数学杂志，第81卷，第1期，第1-24页，2021年1月。
搜索者第一次找到目标的时间称为第一通过时间（FPT）。在许多物理，化学和生物过程中，搜索者是“致命的”，这意味着搜索者可能会在找到目标之前失活（退化，死亡等）。在细胞内信号传导的背景下，一项重要的近期研究发现，如果使搜索者具备在灭活之前找到目标的条件，那么快速灭活可以极大地改变致命扩散搜索者的条件性FPT分布。在本文中，我们证明了一个通用定理，该定理可为这种条件FPT在快速灭活极限内的所有时刻产生一个明确的公式。这个公式非常通用，因为它在非常普遍的条件下适用于扩散搜索器动力学，目标和空间域。这些结果在很大程度上具有普遍性，即如果灭活很快，那么与没有灭活的FPT相比，条件FPT的速度要快得多，受空间异质性的影响要小得多，可变性的影响要小得多。我们的研究结果与某些离散的细胞内扩散模型的最新计算和理论分析相吻合，并证实了一个与空间异质性对细胞内信号传导影响有关的猜想。