Funkhouser Chloe M, Solis Francisco J, Thornton K
Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011912. doi: 10.1103/PhysRevE.76.011912. Epub 2007 Jul 17.
We present a method for modeling phase transitions and morphological evolution of binary lipid membranes with approximately planar geometries. The local composition and the shape of the membrane are coupled through composition-dependent spontaneous curvature in a Helfrich free energy. The evolution of the composition field is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics. Our method explicitly treats the full nonlinear form of the geometrical scalars, tensors, and differential operators associated with the curved shape of the membrane. The model is applied to examine morphological evolution and stability of lipid membranes initialized in a variety of compositional and geometric configurations. Specifically, we investigate the dynamics of systems which have a lamellar structure as their lowest energy state. We find that evolution is very sensitive to initial conditions; only membranes with sufficiently large lamellar-type compositional perturbations or ripple-type shape perturbations in their initial configuration can deterministically evolve into a lamellar equilibrium morphology. We also observe that rigid topographical surface patterns have a strong effect on the phase separation and compositional evolution in these systems.
我们提出了一种对具有近似平面几何形状的二元脂质膜的相变和形态演化进行建模的方法。膜的局部组成和形状通过Helfrich自由能中依赖于组成的自发曲率相互耦合。组成场的演化由Cahn-Hilliard型方程描述，而形状变化则由松弛动力学描述。我们的方法明确处理了与膜的弯曲形状相关的几何标量、张量和微分算子的完全非线性形式。该模型用于研究在各种组成和几何构型下初始化的脂质膜的形态演化和稳定性。具体而言，我们研究了以层状结构作为其最低能量状态的系统的动力学。我们发现演化对初始条件非常敏感；只有在初始构型中具有足够大的层状型组成扰动或波纹型形状扰动的膜才能确定性地演化为层状平衡形态。我们还观察到刚性地形表面图案对这些系统中的相分离和组成演化有很强的影响。
