Effects of ligand distribution on receptor-diffusion-mediated cellular uptake of nanoparticles

Abstract

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.

Keywords: cellular uptake; controlled-release drug delivery; optimal ligand distribution; receptor diffusion.

Figure 1.

Schematic diagram of cellular uptake of NPs with different ligand distributions. (a) Remote mobile receptors diffusing to binding sites to drive cellular uptake. (b) Receptor density distribution along cell membrane. At the contact region, the receptor density is not constant.

Figure 2.

Different ligand distributions considered in the current work. (a) Harmonic distribution, (b) periodic linear distribution and (c) periodic piecewise distribution.

Figure 3.

Normalized wrapping degree as a function of time for different amplitudes of ligand density with λ = 1 and initial receptor density ξ₀ = 0.01ξ_L0 in harmonic ligand distribution.

Figure 4.

Wrapping time as a function of amplitude of ligand density for λ = 1, and initial receptor density at (a) ξ₀ = 0.01ξ_L0 and (b) ξ₀ = 0.1ξ_L0 in harmonic ligand distribution.

Figure 5.

Normalized wrapping degree as a function of time for different frequencies of ligand density with A = 0.45 and initial receptor density ξ₀ = 0.01ξ_L0 in harmonic ligand distribution.

Figure 6.

Wrapping time as a function of normalized slope of periodic linear-dependent ligand density for T_l = πR and initial receptor density ξ₀ = 0.01ξ_L0.

Figure 7.

Normalized wrapping degree as a function of time for different cycle numbers of ligand density with n = π/8 and initial receptor density ξ₀ = 0.01ξ_L0 in periodic linear ligand distribution.

Figure 8.

Wrapping time as a function of amplitude for cycle number N_p = 2 and initial receptor density ξ₀ = 0.01ξ_L0 in periodic piecewise distribution of ligand density.

Figure 9.

Normalized wrapping degree as a function of time for different cycle numbers for m = 0.25 and initial receptor density ξ₀ = 0.01ξ_L0 in periodic piecewise distribution of ligand density.

Figure 10.

Wrapping time as a function of normalized position of contact point under different (a) frequencies and (b) amplitudes of ligand density for ξ₀ = 0.01ξ_L0. (c) Variation in initial receptor boundary densities with normalized position of contact point for λ = 1. Harmonically distributed ligand density.

Figure 11.

Wrapping time as a function of normalized positions of contact points under different (a) frequencies and (b) normalized slope of ligand density for ξ₀ = 0.01ξ_L0. (c) Variation in initial receptor boundary density with normalized position of contact point for n = π/8, and T_l = πR. Ligands with periodic linear distribution.

Figure 12.

Wrapping time as a function of normalized positions of contact points under different (a) frequencies and (b) amplitude of ligand density for ξ₀ = 0.01ξ_L0. (c) Variation in initial receptor boundary density with normalized positions of contact points for m = 0.25, and T_p = πR. Ligands with periodic piecewise distribution.