Biophysical-factor-dependent cellular uptake of nanoparticles (NPs) through receptor-diffusion-mediated endocytosis bears significance in pathology, cellular immunity and drug-delivery systems. Advanced nanotechnology of NP synthesis provides methods for modifying NP surface with different ligand distributions. However, no report discusses effects of ligand distribution on NP surface on receptor-diffusion-mediated cellular uptake. In this article, we used a statistical dynamics model of receptor-diffusion-mediated endocytosis to examine ligand-distribution-dependent cellular uptake dynamics by considering that ligand–receptor complexes drive engulfing to overcome resistance to membrane deformation and changes in configuration entropy of receptors. Results showed that cellular internalization of NPs strongly depended on ligand distribution and that cellular-uptake efficiency of NPs was high when ligand distribution was within a range around uniform distribution. This feature of endocytosis ensures robust infection ability of viruses to enter host cells. Interestingly, results also indicated that optimal ligand distribution associated with highest cellular-uptake efficiency slightly depends on distribution pattern of ligands and density of receptors, and the optimal distribution becomes uniform when receptor density is sufficiently large. Position of initial contact point is also a factor affecting dynamic wrapping. This study explains why most enveloped viruses present almost homogeneous ligand distribution and is useful in designing controlled-release drug-delivery systems.

Precise measurement of mechanical properties of living cells is important in understanding their mechanics-biology relations. In this study, we adopted the atomic force microscope to measure the creep deformation and stress relaxation of six different human cell lines. We examined whether the measured creep and relaxation trajectories satisfy a verification relation derived based on the linear viscoelastic theory. We compared the traditional spring-dashpot and the newly developed power-law-type constitutive relations in fitting the experimental measurements. We found that the human normal liver (L02), hepatic cancer (HepG2), hepatic stellate (LX2) and gastric cancer (NCI-N87) cell lines are linear viscoelastic materials, and human normal gastric (GES-1) and gastric cancer (SGC7901) cell lines are nonlinear due to failing in satisfying the verification relation for linear viscoelastic theory. The three-parameter power-law-type constitutive relation can fit the experimental measurements better than that of the five-parameter classical spring-dashpot.

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand–receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

Molecular dynamic simulations and experiments have recently demonstrated how cylindrical nanoparticles (CNPs) with large aspect ratios penetrate animal cells and inevitably deform cytoskeletons. Thus, a coupled elasticity–diffusion model was adopted to elucidate this interesting biological phenomenon by considering the effects of elastic deformations of cytoskeleton and membrane, ligand–receptor binding and receptor diffusion. The mechanism by which the binding energy drives the CNPs with different orientations to enter host cells was explored. This mechanism involved overcoming the resistance caused by cytoskeleton and membrane deformations and the change in configurational entropy of the ligand–receptor bonds and free receptors. Results showed that deformation of the cytoskeleton significantly influenced the engulfing process by effectively slowing down and even hindering the entry of the CNPs. Additionally, the engulfing depth was determined quantitatively. CNPs preferred or tended to vertically attack target cells until they were stuck in the cytoskeleton as implied by the speed of vertically oriented CNPs that showed much faster initial engulfing speeds than horizontally oriented CNPs. These results elucidated the most recent molecular dynamics simulations and experimental observations on the cellular uptake of carbon nanotubes and phagocytosis of filamentous Escherichia coli bacteria. The most efficient engulfment showed the stiffness-dependent optimal radius of the CNPs. Cytoskeleton stiffness exhibited more significant influence on the optimal sizes of the vertical uptake than the horizontal uptake.