Callan-Jones Andrew, Durand Marc, Fournier Jean-Baptiste
Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France.
Soft Matter. 2016 Feb 14;12(6):1791-800. doi: 10.1039/c5sm02507a. Epub 2016 Jan 4.
We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions (σ > 10(-8) N m(-1)) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.
我们考虑含有任意形状跨膜蛋白的脂质双层的流体动力学。这个受生物学启发的问题与细胞膜相关，细胞膜的波动动力学在细胞迁移、细胞间运输和细胞通讯等现象中起着关键作用。利用昂萨格变分原理，我们推导了控制膜形状、双层小叶质量密度以及扩散蛋白浓度弛豫动力学的方程。通过我们的通用形式体系，我们得到了关于膜动力学的几个结果。我们发现跨越双层的蛋白会增加层间摩擦系数。这种重整化可能很显著，且与蛋白的迁移率成反比。其次，我们发现不对称蛋白与膜曲率以及单层密度差异相互耦合。对于几乎所有可及的膜张力（σ > 10^(-8) N m^(-1)），我们表明蛋白密度是弛豫最慢的变量。此外，由于与曲率的耦合，其弛豫速率在小波长处会降低。我们将我们的形式体系应用于浓缩蛋白斑块的大规模扩散。我们发现由于有效扩散系数的波矢依赖性，扩散分布不是自相似的。
