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Receptor-Mediated Endocytosis of a Cylindrical Nanoparticle in the Presence of Cytoskeleton Substrate

Internalization of particles by cells plays a crucial role for adsorbing nutrients and fighting infection. Endocytosis is one of the most important mechanisms of the particles uptake which encompass multiple pathways. Although endocytosis is a complex mechanism involving biochemical signaling and active force generation, the energetic cost associated to the large deformations of the cell membrane wrapping around the foreign particle is an important factor controlling this process, which can be studied using quantitative physical models. Of particular interest is the competition between membrane - cytoskeleton and membrane - target adhesion. Here, we explore the wrapping of a lipid membrane around a long cylindrical object in the presence of a substrate mimicking the cytoskeleton. Using discretization of the Helfrich elastic energy that accounts for the membrane bending rigidity and surface tension, we obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy that includes unwrapped, partially wrapped and fully wrapped states. We provide an analytical expression for the boundary between the different regimes. While the transition to partial wrapping is independent of membrane tension, the transition to full wrapping is very much influenced by membrane tension. We also show that target wrapping may proceed in an asymmetric fashion in the full wrapping regime.