论文标题
狭窄的捕获问题:基于遭遇的部分反应性目标的方法
The narrow capture problem: an encounter-based approach to partially reactive targets
论文作者
论文摘要
当前感兴趣的一般主题是分析具有较小的内部目标或陷阱(狭窄的捕获问题)的奇异扰动域中的扩散问题。一个主要应用是对细胞内扩散,其中靶标通常代表某种形式的反应性生化底物。大多数狭窄捕获问题的研究都将目标边界视为完全吸收。在本文中,我们在更现实的部分反应性目标边界的情况下分析了三维狭窄的捕获问题。我们首先要考虑经典的罗宾边界条件。匹配单粒子概率密度的内部和外部溶液,我们得出了拉普拉斯的渐近膨胀,以$ε$的功率转化为每个反应性表面,其中$ερ$是给定的目标大小。反过来,通量决定了目标吸收的分裂概率。然后,我们通过将匹配的渐近分析与基于相遇的扩散介导的表面反应的表述相结合,将分析扩展到更通用的反应性靶标。也就是说,我们得出了粒子位置和边界局部时间的关节概率密度的渐近扩展。然后,通过适当的停止条件在边界局部时间通过适当的停止条件合并表面反应的效果。最后,我们通过探索对拆分概率的领先贡献如何取决于表面反应的选择来说明理论。特别是,我们表明形式的$ρ\ rightarrowρ-\widetildeψ(1/ρ)$的目标半径有效地归一化,其中$ \widetildeψ$是停止局部时间分布的拉普拉斯变换。
A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the targets typically represent some form of reactive biochemical substrate. Most studies of the narrow capture problem treat the target boundaries as totally absorbing. In this paper, we analyze the three-dimensional narrow capture problem in the more realistic case of partially reactive target boundaries. We begin by considering classical Robin boundary conditions. Matching inner and outer solutions of the single-particle probability density, we derive an asymptotic expansion of the Laplace transformed flux into each reactive surface in powers of $ε$, where $ερ$ is a given target size. In turn, the fluxes determine the splitting probabilities for target absorption. We then extend our analysis to more general types of reactive targets by combining matched asymptotic analysis with an encounter-based formulation of diffusion-mediated surface reactions. That is, we derive an asymptotic expansion of the joint probability density for particle position and the boundary local time. The effects of surface reactions are then incorporated via an appropriate stopping condition for the boundary local time. Finally, we illustrate the theory by exploring how the leading-order contributions to the splitting probabilities depend on the choice of surface reactions. In particular, we show that there is an effective renormalization of the target radius of the form $ρ\rightarrow ρ-\widetildeΨ(1/ρ)$, where $\widetildeΨ$ is the Laplace transform of the stopping local time distribution.