Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules.
Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules.
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DOI：
10.1016/j.jcp.2015.12.055
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发表时间：
2016-03-15
影响因子：
4.1
通讯作者：
Aland S
中科院分区：
文献类型：
--
作者：
Lowengrub J;Allard J;Aland S
在胞吞作用和其他细胞过程中发生的从较大膜形成膜囊泡通常由附着于膜的曲率诱导分子协调。最近的报道表明，囊泡可以在几毫秒内重新形成。在这些尺度上的膜动力学强烈地受到流体动力学相互作用的影响。为了研究这个问题，我们开发了新的扩散界面模型的动态不可扩展的囊泡在粘性流体与刚性，曲率诱导分子。该模型将Navier-Stokes方程与膜诱导弯曲力（包含浓度相关的弯曲刚度系数和自发曲率）、分子输运方程和拉格朗日乘数方程耦合起来，以增强局部不可扩展性。两种形式的表面输运方程被认为是：Fickian表面扩散和Cahn-Hilliard表面动力学，前者更适合于小分子和后者更适合于大分子。该系统使用自适应有限元方法在三维轴对称几何形状。结果表明，流体动力学确实可以使一个小囊泡连接到膜上的一个狭窄的颈部快速形成。当使用Fickian模型时，这是一个瞬态，稳态是一个由于扩散而具有均匀分布的分子浓度的平膜。当使用Cahn-Hilliard模型时，分子浓度梯度被维持，颈部稳定，并且系统发展到具有附着于膜的小而紧凑的囊泡的稳态。通过改变Cahn-Hilliard模型中分子的膜覆盖率，我们发现存在一个临界（最小）颈部半径和一个临界（最快）出芽时间。这些临界点与囊泡形态从球形到蘑菇状的变化有关，因为膜上的分子覆盖率增加。
The formation of membrane vesicles from a larger membrane that occurs during endocytosis and other cell processes are typically orchestrated by curvature-inducing molecules attached to the membrane. Recent reports demonstrate that vesicles can form de novo in a few milliseconds. Membrane dynamics at these scales are strongly influenced by hydrodynamic interactions. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. The model couples the Navier-Stokes equations with membrane-induced bending forces that incorporate concentration-dependent bending stiffness coefficients and spontaneous curvatures, with equations for molecule transport and for a Lagrange multiplier to enforce local inextensibility. Two forms of surface transport equations are considered: Fickian surface diffusion and Cahn-Hilliard surface dynamics, with the former being more appropriate for small molecules and the latter being better for large molecules. The system is solved using adaptive finite element methods in 3D axisymmetric geometries. The results demonstrate that hydrodynamics can indeed enable the rapid formation of a small vesicle attached to the membrane by a narrow neck. When the Fickian model is used, this is a transient state with the steady state being a flat membrane with a uniformly distributed molecule concentration due to diffusion. When the Cahn-Hilliard model is used, molecule concentration gradients are sustained, the neck stabilizes and the system evolves to a steady-state with a small, compact vesicle attached to the membrane. By varying the membrane coverage of molecules in the Cahn-Hilliard model, we find that there is a critical (smallest) neck radius and a critical (fastest) budding time. These critical points are associated with changes in the vesicle morphology from spherical to mushroom-like as the molecule coverage on the membrane is increased.