Cell penetration by high aspect-ratio vertical nanostructures such as nanowires and nanopillars provides a powerful method for accessing the cell interior for delivery and sensing. However, there is a lack of studies on the understanding of the mechanism of cell membrane penetration and how design nanostructures to optimize the efficiency of penetration remains unclear. Here, we propose an analytical model to elucidate the mechanism of cells penetration by analyzing the free-energy change of cells adhered to the nanostructures surface. Furthermore, we provide a simple method to evaluate the crossover radius or density for cell membrane penetration. By introducing a dimensionless parameter, i.e., adhesion area factor, we investigated the effects of the radius and distribution densities of nanostructures on cell membrane penetration which is determined by the competition between adhesion energy and deformation energy. Besides, a diagram of the distribution of cell penetration and no penetration is obtained. From the cell penetration diagram, one can determine easily and intuitively the relations of cell penetration state with the radius and distribution densities of nanostructures. Our theoretical results seem to show broad agreement with experimental observations, which implies that these studies would provide useful guidance to the design of nanopatterned surfaces for biomedical applications.

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垂直纳米结构穿透细胞的机理

高纵横比的垂直纳米结构（例如纳米线和纳米柱）对细胞的穿透提供了一种强大的方法，可进入细胞内部进行传递和传感。然而，关于细胞膜渗透机制的理解以及如何设计纳米结构以优化渗透效率的研究仍很缺乏。在这里，我们提出了一个分析模型，通过分析粘附在纳米结构表面的细胞的自由能变化来阐明细胞渗透的机制。此外，我们提供了一种简单的方法来评估细胞膜穿透的交叉半径或密度。通过引入无量纲参数，即粘附面积因子，我们研究了纳米结构的半径和分布密度对细胞膜渗透的影响，这由粘附能和变形能之间的竞争决定。此外，获得细胞渗透和无渗透的分布图。从细胞穿透图，可以轻松直观地确定细胞穿透状态与纳米结构的半径和分布密度之间的关系。我们的理论结果似乎表明与实验观察结果基本吻合，这意味着这些研究将为生物医学应用纳米图案表面的设计提供有用的指导。从细胞穿透图，可以轻松直观地确定细胞穿透状态与纳米结构的半径和分布密度之间的关系。我们的理论结果似乎表明与实验观察结果基本吻合，这意味着这些研究将为生物医学应用纳米图案表面的设计提供有用的指导。从细胞穿透图，可以轻松直观地确定细胞穿透状态与纳米结构的半径和分布密度之间的关系。我们的理论结果似乎表明与实验观察结果基本吻合，这意味着这些研究将为生物医学应用纳米图案表面的设计提供有用的指导。