Cellular uptake through membranes plays an important role in adsorbing nutrients and fighting infection and can be used for nanomedicine developments. Endocytosis is one of the pathways of cellular uptake which associate with elastic deformation of the membrane wrapping around the foreign particle. The deformability of the membrane is strongly regulated by the presence of a cortical cytoskeleton placed underneath the membrane. It is shown that shape and orientation of the particles influence on their internalization. Here, we study the role of particle local curvature in cellular uptake by investigating the wrapping of an elastic membrane around a long cylindrical object with an elliptical cross-section. The membrane itself is adhered to a substrate mimicking the cytoskeleton. Membrane wrapping proceeds differently whether the initial contact occurs at the target's highly curved part (vertical) or along its long side (horizontal). We obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy, which includes three distinct regimes (unwrapped, partially wrapped and fully wrapped), separated by two phase transitions. We also provide analytical expressions for the boundaries between the different regimes which confirm that the transitions strongly depend on the orientation and aspect ratio of the nanowire.
Keywords: cellular wrapping; cytoskeleton; elasticity; membrane deformation; phagocytosis.