关于膜表面蛋白质的曲率驱动旋转扩散
On Curvature Driven Rotational Diffusion of Protein on Membrane Surface
AI总结：
本文研究膜表面蛋白质在无相互作用和相关情况下的取向定位，通过引入熵能和曲率能构建能量泛函，并利用Onsager变分原理推导出广义Smoluchowski方程，证明了稳态解的存在性和唯一性。
摘要：
双层膜的形态动力学本质上与膜蛋白的平移和取向定位紧密相关。本文关注膜蛋白在无蛋白质相互作用和相关性情况下的取向定位。引入依赖于角分布函数的熵能和依赖于主曲率向量的曲率能，以构建耦合系统的能量泛函。应用Onsager变分原理得到一个广义Smoluchowski方程，该方程描述了蛋白质取向的时变和角变。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固定点存在，并在生物相关条件下获得解的唯一性。为了在傅里叶空间中近似稳态解，我们构造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。在生物相关条件下证明了数值解的存在性和唯一性。
英文摘要：
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.
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