Theory & Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany.
Soft Matter. 2017 Mar 15;13(11):2155-2173. doi: 10.1039/c6sm02796b.
Biological membranes and lipid vesicles often display complex shapes with non-uniform membrane curvature. When adhesive nanoparticles with chemically uniform surfaces come into contact with such membranes, they exhibit four different engulfment regimes as recently shown by a systematic stability analysis. Depending on the local curvature of the membrane, the particles either remain free, become partially or completely engulfed by the membrane, or display bistability between free and completely engulfed states. Here, we go beyond stability analysis and develop an analytical theory to leading order in the ratio of particle-to-vesicle size. This theory allows us to determine the local and global energy landscapes of uniform nanoparticles that are attracted towards membranes and vesicles. While the local energy landscape depends only on the local curvature of the vesicle membrane and not on the overall membrane shape, the global energy landscape describes the variation of the equilibrium state of the particle as it probes different points along the membrane surface. In particular, we find that the binding energy of a partially engulfed particle depends on the 'unperturbed' local curvature of the membrane in the absence of the particle. This curvature dependence leads to local forces that pull the partially engulfed particles towards membrane segments with lower and higher mean curvature if the particles originate from the exterior and interior solution, respectively, corresponding to endo- and exocytosis. Thus, for partial engulfment, endocytic particles undergo biased diffusion towards the membrane segments with the lowest membrane curvature, whereas exocytic particles move towards segments with the highest curvature. The curvature-induced forces are also effective for Janus particles with one adhesive and one non-adhesive surface domain. In fact, Janus particles with a strongly adhesive surface domain are always partially engulfed which implies that they provide convenient probes for experimental studies of the curvature-induced forces that arise for complex-shaped membranes.
生物膜和脂质体通常呈现出具有非均匀膜曲率的复杂形状。当具有化学均匀表面的粘性纳米颗粒与这些膜接触时，如最近的系统稳定性分析所示，它们表现出四种不同的吞噬状态。根据膜的局部曲率，颗粒要么保持自由，要么部分或完全被膜吞噬，要么在自由和完全吞噬状态之间表现出双稳定性。在这里，我们超越了稳定性分析，发展了一种在颗粒与囊泡尺寸比的领先阶次下的分析理论。该理论允许我们确定朝向膜和囊泡的均匀纳米颗粒的局部和全局能量景观。虽然局部能量景观仅取决于囊泡膜的局部曲率，而不取决于整体膜形状，但全局能量景观描述了在颗粒沿着膜表面探测不同点时其平衡状态的变化。特别是，我们发现部分吞噬颗粒的结合能取决于在没有颗粒存在时膜的“未受扰”局部曲率。这种曲率依赖性导致局部力，当颗粒分别来自外部和内部溶液时，将部分吞噬的颗粒拉向具有较低和较高平均曲率的膜段，这对应于内吞作用和胞吐作用。因此，对于部分吞噬，内吞颗粒会朝着曲率最低的膜段进行有偏差的扩散，而外排颗粒则会朝着曲率最高的膜段移动。曲率诱导的力对于具有一个粘性和一个非粘性表面域的 Janus 颗粒也有效。事实上，具有强粘性表面域的 Janus 颗粒总是部分被吞噬，这意味着它们为复杂形状的膜产生的曲率诱导力的实验研究提供了方便的探针。
