标题： 关于膜表面上蛋白质的曲率驱动旋转扩散 显示英文标题

标题： On Curvature Driven Rotational Diffusion of Protein on Membrane Surface

摘要： 双层膜的形态动力学与膜蛋白的平移和取向定位内在耦合。 在本文中，我们关注在没有蛋白质相互作用和关联的情况下膜蛋白的取向定位。 引入了依赖于角分布函数的熵能和依赖于主曲率矢量的曲率能，以构建耦合系统的能量泛函。 应用Onsager变分原理得出一个广义的Smoluchowskii方程，该方程描述蛋白质取向的时间和角度变化。 我们证明了该方程的稳态解作为连续非线性非局部映射的不动点存在，并在生物相关条件下获得了解的唯一性。 为了在傅里叶空间中近似稳态解，我们构建了一种高效的数值方法，该方法减少了展开并使系数与第一类修正贝塞尔函数相关联。 在生物相关条件下，验证了数值解的存在性和唯一性。 显示英文摘要

摘要： Morphological dynamics of bilayer membrane is intrinsically coupled to the translational and orientational localization of membrane proteins. In this paper we are concerned with the orientational localization of membrane proteins in the absence of protein interaction and correlation. Entropic energy depending on the angular distribution function and the curvature energy depending on the principal curvature vectors are introduced to assemble an energy functional for the coupled system. Application of the Onsager's variational principle gives rise to a generalized Smoluchowskii equation governing the temporal and angular variations of the protein orientation. We prove the existence of the stationary solution of the equation as fixed points of a continuous nonlinear nonlocal map, and for biologically relevant conditions we obtain the uniqueness of the solution. To approximate the stationary solution in the Fourier space we construct an efficient numerical method that reduces the expansion and relates the coefficients to the modified Bessel functions of the first kind. Existence and uniqueness of the numerical solution are justified for biologically relevant conditions.