关键词:纳米药物;最小能量法;数值模拟 Abstract Receptor-mediated endocytosis is one of the means for cells to exchange materials with their environments. Vesicles coated with ligands on their surface are often adopted for the drug delivery in cancer therapy through receptor-mediated endocytosis as well. In the present work, we used a 3D mathematical model and energy minimization to study the endocytosis process of spherical drug nanoparticles. The total energy of the system including catch bonds was established. The minimization of the energy functional was carried out numerically. The shape of particle and cell membrane in each wrapping stage was obtained, and the influence of particle size on the minimum energy required for passive endocytosis was analysed. The results show that cell membrane and receptor-ligand bonds deformation energies are the major components of the total deformation energy, and each component changes as the wrapping area is increased. There exists an optimal size of nanoparticles for which the total energy consumption is minimum under given membrane stiffness and receptor-ligand bond strength. We also found that at the final stage of wrapping the endocytosis may not be completed because of the breaking of overstretched receptor-ligand bonds. This study provides a theoretical insight for the design of receptor mediated high efficiency drug delivery system.
本文针对受体介导下球型纳米颗粒被细胞膜包裹内吞的准静态过程建立轴对称模型,通过求解细胞膜和药物变形的能量方程的最小值,分析了细胞内吞药物所需最小能量与药物直径、细胞膜硬度、受体--配体绑定键强度之间的关系. 研究表明,内吞过程中细胞膜、药物颗粒和绑定键变形系统的总能量随着药物颗粒被包裹面积的增加而增大,其中,细胞膜变形能和绑定键变形能是总能量的主要构成部分,并且随着内吞药物被包裹面积的增大,细胞膜变形能占比增加,绑定键变形能占比减小;内吞过程中,细胞膜、药物颗粒和绑定键构成系统的总变形能并不随着药物颗粒半径的增加而增大,在本文给定的细胞膜和药物颗粒的硬度、绑定键强度等物理特性下存在最优药物尺寸,使得内吞过程中总能耗最小;在内吞进行的中前期绑定键变形能占比较大,因而不能忽略,在药物内吞进行的后期,包裹区域边缘的绑定键因伸长过大发生断裂,影响内吞的顺利完成. 本文研究对受体介导的药物设计、提高药物内吞效率有重要的参考价值. The authors have declared that no competing interests exist.
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