Kinetics of receptor-mediated endocytosis of elastic nanoparticles

Abstract

It is now widely recognized that mechanical properties play critical roles in the cell uptake of nanomaterials. Here we conduct a theoretical study on the kinetics of receptor-mediated endocytosis of elastic nanoparticles that is limited by receptor diffusion, specifically focusing on how the uptake rate depends on the nanoparticle stiffness and size, membrane tension and binding strength between membrane receptors and ligands grafted on the nanoparticle surface. It is shown that, while soft nanoparticles are energetically less prone to full wrapping than stiff ones, the wrapping of the former is kinetically faster than that of the latter. Spherical and cylindrical elastic nanoparticles show dramatic differences in the effect of stiffness on the uptake rate. Additional theoretical analysis is performed to investigate the role of the stochastic receptor-ligand binding in the endocytosis of elastic nanoparticles. The relation between the uptake efficiency and uptake proneness is discussed. This study provides new insight into the elasticity effects on cell uptake and may serve as a design guideline for the controlled endocytosis and diagnostics delivery.

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

“…Cylindrical NPs and membrane surface tension are not considered. Kinetic reaction between receptor and ligand molecules [32,46,52–54], and viscoelastic deformation of cytoskeleton [23,55] are neglected.…”

Theory, simulations and the design of functionalized nanoparticles for biomedical applications: A Soft Matter Perspective

“…Instead, for softer particles, the Design of nanoparticles: A Soft Matter Perspective S Angioletti-Uberti process was frustrated, either due to ligands depletion from the part of the nanoparticle initially not in contact with the cell membrane or because the nanoparticle deformation leads to a metastable wrapped state. All the aforementioned features of soft nanoparticles observed in simulations were either earlier predicted 22 or later rationalised 11,23 by theoretical models. In practice, this was done by starting with the model developed by Gao et al 19 for hard nanoparticles and simply adding an energy term to account for nanoparticles' elastic deformation, further proving the generality of the theoretical model to describe a wide range of nanoparticles' design.…”

“…Different aspects of receptor-mediated endocytosis have been intensively studied using both theory, 11,[19][20][21][22][23][24][25] and different types of simulations 10,[26][27][28][29][30][31][32][33][34][35][36][37] with coarse-grained models, often combining the two. 10,27 A pioneering work on this problem is that of Gao et al, 19 who proposed a theoretical model to address the size dependence of this process, drawing from previous work on the growth of membrane adhesion patches.…”

“…The timescale for its adsorption and endocytosis ranges from seconds to hours depending on details of the system. 11 A truly atomistic description is thus a computationally intractable problem. Moreover, one such simulation would provide a single point in the multidimensional parameter space (e.g., ligand length and strength, nanoparticle size, etc.…”

The Effects of Physicochemical Properties of Nanomaterials on Their Cellular Uptake In Vitro and In Vivo

“…It has been suggested that the wrapping of harder NMs is kinetically faster than that of soft ones. Moreover, by investigating the correlation between cellular uptake and rigidity of spherical and cylindrical elastic nanoparticles, researchers find that receptor–ligand binding amount (the average binding energy per receptor–ligand bond ranges from 10 k B T to 25 k B T) during the process of endocytosis of elastic nanoparticles is also an important factor to determine the rigidity‐mediated NMs cellular uptake …”