膜表面曲率驱动的分子流
Curvature-driven molecular flows on membrane surfaces
摘要：
生物体内双层膜的形态变化不是自发的，而是受到多种蛋白质的调控。大多数这些调节与相关蛋白在双层膜中拥挤的脂质环境中的定位有关。本文提出了一种适用于多种扩散分子在膜表面定位的数学模型。我们从弯曲膜表面上分子分布的能量描述开始，通过组装双层膜的弯曲能和扩散分子的熵能。引入了膜中分子的自发曲率，定义了双层膜的自发曲率是膜表面分子浓度的函数。这种联系产生了漂移扩散方程来控制表面分子浓度的梯度流动。我们重铸的充满活力的制定和相关的控制方程在欧拉框架，通过使用相场函数，定义的膜形态。计算模拟与建议的数学模型和相关的数值技术预测的分子定位在膜表面上的位置与首选的平均曲率。
英文摘要：
Morphological change of bilayer membrane in vivo is not a spontaneous procedure but modulated by various types of proteins in general. Most of these modulations are associated with the localization of related proteins in the crowded lipid environment in bilayer membrane. This work presents an mathematical model for the localization of multiple species of diffusion molecules on membrane surfaces. We start with the energetic description of the distributions of molecules on curved membrane surface, by assembling the bending energy of bilayer membrane and the entropic energy of diffusive molecules. We introduce the spontaneous curvature of molecules in membrane, and define the spontaneous curvature of bilayer membrane as a function of the molecule concentrations on membrane surfaces. This connection gives rise to a drift-diffusion equation to govern the gradient flows of the surface molecule concentrations. We recast the energetic formulation and the related governing equations in the Eulerian framework by using a phase field function that defines the membrane morphology. Computational simulations with the proposed mathematical model and related numerical techniques predict the molecular localization on membrane surfaces at locations with preferred mean curvature.
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