Fig. 6. Mathematical model of nanoparticle uptake provides calculated adhesion energy.

a In the model the particle (blue) with radius R, immobilized by a force sensor (spring) is homogenously covered with ligands (black dots) that can adhere to the cell surface receptors (gray). We assume that initially the particle is already halfway wrapped. b Normalized energy values of contributions from adhesion energy, E_W (blue), curvature energy, E_κ (green), and stress energy, E_σ (red), calculated according to Eq. 6. c Calculated adhesion energy density W as a function of uptake force (solid line). The orange and green region shows the uncertainty of the adhesion energy caused by the uncertainty of the rupture length z and surface tension σ, respectively. The blue points show the predicted adhesion energy for the uptake forces of AuNPs with three different coatings.