Adkins Melissa R, Zhou Y C
Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874.
J Comput Phys. 2017 Sep 15;345:260-274. doi: 10.1016/j.jcp.2017.05.029. Epub 2017 May 18.
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
脂质双分子层膜并非均匀一致，在膜的普遍无序脂质环境中存在着处于更有序状态的脂质簇。这些有序脂质微区的簇现在被称为脂筏。最近的报告将这些微区的形成归因于边界上不同种类脂质的几何和分子力学不匹配。在这里，我们引入测地曲率来表征域边界的几何形状，并开发了一个测地曲率能量模型来描述这些微区由于能量最小化而形成的过程。我们的模型接受任何二元脂质混合物的固有测地曲率作为输入，并将通过三组数值模拟证明产生给定测地曲率的微区。我们的结果与经典表面Cahn-Hilliard方程预测的表面相分离形成对比，后者由于线张力最小化往往会产生大的区域。我们的模型提供了对脂质双分子层膜结构不均匀性的直接和定量描述，并且可以与对膜上生物过程的研究相结合，而这种不均匀性在这些生物过程中起着至关重要的作用。
