Nanoparticles have recently attracted increased interest due to a variety of potential applications. However, not much is known about their interaction with biological cells. Cellular uptake of particles, viruses, and parasites is a complex biological process: particles with sizes comparable to the thickness of the lipid bilayer enter by penetration, while particles with sizes of 20nm or larger get wrapped by the membrane. We calculate the energies for wrapping and characterize particle uptake analogously to thermodynamic phase transitions. We present wrapping phase diagrams for various curvature-elastic properties of the membrane, membrane-particle interaction strengths, and particle sizes and shapes. The transitions between unbound, partially-wrapped, and completely-wrapped states can be continuous or discontinuous and may involve reorientation of the particle. By systematic studies for the particle shape, we find that in particular elongated particles show reduced complete wrapping, but enhanced binding to the cell membrane.

*Zajednički seminar Hrvatskog biofizičkog društva i Instituta za fiziku