A SURFACE PHASE FIELD MODEL FOR TWO-PHASE BIOLOGICAL MEMBRANES
A SURFACE PHASE FIELD MODEL FOR TWO-PHASE BIOLOGICAL MEMBRANES
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DOI：
10.1137/090779917
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发表时间：
2010-01-01
影响因子：
1.9
通讯作者：
Stinner, Bjoern
中科院分区：
文献类型：
--
作者：
Elliott, Charles M.;Stinner, Bjoern
我们研究由脂质双分子层形成的囊泡，脂质双分子层由弹性弯曲能控制，脂质在其上横向分离形成两个不同的相。承载能量的相界面可以被建模为代表膜的超表面上的曲线（锐界面模型）。相场方法是另一个强大的工具来模拟这种相分离现象，其中薄层描述界面（扩散界面模型）。对于这两种方法，我们用受两相面积和体积约束的膜总能量的欧拉-拉格朗日方程来描述平衡形状。通过匹配适当的形式渐近展开式，我们进一步证明了当相界面的厚度趋于零时，由扩散界面模型得到尖锐界面模型。关键的挑战在于膜的几何形状是未知的，并且取决于表示界面厚度的一个小参数。
We study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases. The energy laden phase interfaces may be modeled as curves on the hypersurface representing the membrane (sharp interface model). The phase field methodology is another powerful tool to model such phase separation phenomena where thin layers describe the interfaces (diffuse interface model). For both approaches we characterize equilibrium shapes in terms of the Euler-Lagrange equations of the total membrane energy subject to constraints on the area of the two phases and the volume. We further show by matching appropriate formal asymptotic expansions that the sharp interface model is obtained from the diffuse interface model as the thickness of the phase interface tends to zero. The essential challenge lies in the fact that also the geometry of the membrane is unknown and depends on a small parameter representing the interface thickness.