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Numerical study of clathrin-mediated endocytosis of nanoparticles by cells under tension

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Abstract

In this study, a three-dimensional mathematical model was used to study the contribution of clathrins during the process of cellular uptake of spherical nanoparticles under different membrane tensions. The clathrin-coated pit (CCP) that forms around the inward budding of the cell membrane was modeled as a vesicle with bending rigidity. An optimization algorithm was proposed for minimizing the total energy of the system, which comprises the deforming nanoparticle, receptor–ligand bonds, cell membrane, and CCP, in which way, the profile of the system is acquired. The results showed that the CCP enable full wrapping of the nanoparticles at various membrane tensions. When the cell membrane tension increases, the total deformation energy also increases, but the ratio of CCP bending to the minimum value of the total energy of the system decreases. The results also showed that the diameter of the endocytic vesicles determined by the competition between the stretching of the cell membrane and confinement of the coated pits are much larger than the nanoparticles, which is quit different as the results in passive endocytosis that is not facilitated by the CCPs. The present results indicate that variations of tension on cell membranes constitutes a biophysical marker for understanding the size distribution of CCPs observed in experiments. The present results also suggest that the early abortion of endocytosis is related to that the receptor–ligand bonds cannot generate adequate force to wrap the nanoparticles into the cell membrane before the clathrins respond to support the endocytic vesicles. Correspondingly, late abortion may relate to the inability of CCPs to confine the nanoparticles until the occurrence of the necking stage of endocytosis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant 11872040) and the Natural Science and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Key Laboratory of Hydrodynamics (Ministry of Education), Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Xinyue Liu, Yunqiao Liu & Xiaobo Gong

  2. Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China

    Hongwei Yang

  3. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Huaxiong Huang

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  1. Xinyue Liu
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  2. Hongwei Yang
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  3. Yunqiao Liu
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  4. Xiaobo Gong
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  5. Huaxiong Huang
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Correspondence to Xiaobo Gong.

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Liu, X., Yang, H., Liu, Y. et al. Numerical study of clathrin-mediated endocytosis of nanoparticles by cells under tension. Acta Mech. Sin. 35, 691–701 (2019). https://doi.org/10.1007/s10409-019-00839-0

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  • DOI: https://doi.org/10.1007/s10409-019-00839-0

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