球形膜中的旋转迁移率：Saffman-Delbrück长度与内含物尺寸之间的相互作用
Rotational mobility in spherical membranes: The interplay between Saffman-Delbrück length and inclusion size
AI总结：
本文将Saffman-Delbrück理论推广到球形膜，半解析计算有限尺寸刚性球冠内含物的旋转迁移率，揭示其与SD长度和内含物尺寸的关系。
摘要：
流体膜中颗粒的迁移率是许多生物过程的一个基本方面。在1975年的一篇论文[1]中，Saffman和Delbrück证明了外部Stokes溶剂的存在，对于正则化无限平坦膜内看似奇异的流动至关重要。在本文中，我们扩展了这一经典工作，计算了位于嵌入Stokes溶剂中的球形膜内、具有有限尺寸的刚性颗粒的旋转迁移率。我们将该颗粒视为球冠，以半解析方式求解流动，将其表示为Saffman-Delbrück（SD）长度（膜与溶剂黏度之比）以及该颗粒所形成立体角的函数。我们研究了迁移率和流动对内含物尺寸及SD长度的依赖关系，并将平坦空间迁移率作为一个特例恢复。我们的结果将适用于一系列生物问题，包括旋转Brown运动、脂筏动力学，以及水通道蛋白通道响应水流的运动。我们的方法将提供一种新途径，通过大型内含物的旋转扩散来测量膜的黏度；对于这类内含物，常用的平面Saffman-Delbrück理论并不适用。
英文摘要：
The mobility of particles in fluid membranes is a fundamental aspect of many biological processes. In a 1975 paper [1], Saffman and Delbrück demonstrated how the presence of external Stokesian solvents is crucial in regularising the apparently singular flow within an infinite flat membrane. In the present paper, we extend this classical work and compute the rotational mobility of a rigid finite-sized particle located inside a spherical membrane embedded in Stokesian solvents. Treating the particle as a spherical cap, we solve for the flow semi-analytically as a function of the Saffman-Delbrück (SD) length (ratio of membrane to solvent viscosity) and the solid angle formed by the particle. We study the dependence of the mobility and flow on inclusion size and SD length, recovering the flat-space mobility as a special case. Our results will be applicable to a range of biological problems including rotational Brownian motion, the dynamics of lipid rafts, and the motion of aquaporin channels in response to water flow. Our method will provide a novel way of measuring a membrane's viscosity from the rotational diffusion of large inclusions, for which the commonly used planar Saffman-Delbrück theory does not apply.
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