Cellular uptake of nanoparticle (NP) is an important biological process involving mechanically and structurally heterogeneous environments, such as biophysical heterogeneity of single extracellular vesicles and biomechanical heterogeneity of small viral capsids. Despite of these heterogeneous environments, poor understanding of membrane interacting with vesicle NP of non-uniform mechanical properties still exists. To address this issue, combining the continuum Canham–Helfrich theory of membrane and the stochastic Markov method on state transition, we establish a theoretical model of the wrapping of a NP with any variable bending stiffness. As NPs are hypothesized with two typical types of non-uniform bending stiffness distributions (Gaussian-like and piecewise), through both minimum energy and stochastic dynamic approaches, it is identified that the membrane tends to encapsulate the NP with a sealing near soft region of NP. Because complete wrapping of NP with a sealing near its stiff region requires large elastic deformation of membrane. In addition, during cellular uptake, rotation phenomenon of the NP with variable bending stiffness is found, which is reminiscent of previous observations on homogeneous NP as reported in literature. These predictions are verified by relevant Monte Carlo simulations. Our findings are of interest to not only the fundamental understanding of cellular uptake but also the applications in the design of nanocarriers for drug delivery.

纳米颗粒（NP）的细胞摄取是一个重要的生物过程，涉及机械和结构异质环境，例如单个细胞外囊泡的生物物理异质性和小病毒衣壳的生物力学异质性。尽管存在这些异质环境，但对膜与具有不均匀机械性能的囊泡 NP 相互作用的理解仍然不足。为了解决这个问题，结合连续的 Canham-Helfrich 膜理论和状态转换的随机马尔可夫方法，我们建立了具有任意可变弯曲刚度的 NP 包裹的理论模型。由于通过最小能量和随机动态方法假设 NPs 具有两种典型类型的非均匀弯曲刚度分布（类高斯分布和分段），可以确定，膜倾向于用 NP 软区域附近的密封来封装 NP。因为在其刚性区域附近用密封完全包裹 NP 需要膜的大弹性变形。此外，在细胞摄取过程中，发现了具有可变弯曲刚度的 NP 的旋转现象，这让人想起文献中报道的先前对均质 NP 的观察。这些预测通过相关的蒙特卡罗模拟得到验证。我们的研究结果不仅对细胞摄取的基本理解感兴趣，而且对设计用于药物递送的纳米载体的应用也很有意义。在细胞摄取过程中，发现了具有可变弯曲刚度的 NP 的旋转现象，这让人想起文献中报道的先前对均质 NP 的观察。这些预测通过相关的蒙特卡罗模拟得到验证。我们的研究结果不仅对细胞摄取的基本理解感兴趣，而且对设计用于药物递送的纳米载体的应用也很有意义。在细胞摄取过程中，发现了具有可变弯曲刚度的 NP 的旋转现象，这让人想起文献中报道的先前对均质 NP 的观察。这些预测通过相关的蒙特卡罗模拟得到验证。我们的研究结果不仅对细胞摄取的基本理解感兴趣，而且对设计用于药物递送的纳米载体的应用也很有意义。