Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 572-588, January 2020.
Single-particle tracking experiments have recently found that C. elegans zygotes rely on space-dependent switching diffusivities to form intracellular gradients during cell polarization. The relevant proteins switch between fast-diffusing and slow-diffusing states on timescales that are much shorter than the timescale of diffusion or gradient formation. This manifests in models as a small parameter, allowing an asymptotic analysis of the gradient formation. In this paper we consider how this mechanism of rapidly switching diffusive states interacts with a locally varying periodic microstructure in the cell, incorporated through a second small parameter. We show that an asymptotic analysis based on both small parameters yields different results based on the order of limits taken and suggest an explicit relation between the two parameters for when each type of analysis is appropriate. We further investigate a mean first passage time problem for a diffusing protein to gain insight into the effects of the microstructure on the global environment.

中文翻译：

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转换扩散率和细胞微结构之间的相互作用

2020年1月，《多尺度建模与仿真》，第18卷，第2期，第572-588页。
最近，单粒子跟踪实验发现秀丽隐杆线虫合子依赖于空间依赖的开关扩散性在细胞极化过程中形成细胞内梯度。相关蛋白质在比扩散或梯度形成的时间尺度短得多的时间尺度上在快扩散状态和慢扩散状态之间切换。这在模型中表现为一个小参数，可以渐进分析梯度的形成。在本文中，我们考虑了这种快速转换扩散状态的机制如何与细胞中局部变化的周期性微结构（通过第二个小参数合并）相互作用。我们表明，基于这两个小参数的渐近分析根据采取的极限顺序产生不同的结果，并建议在每种类型的分析都适当时，这两个参数之间的显式关系。我们进一步研究扩散蛋白的平均首次通过时间问题，以了解微观结构对全球环境的影响。