  We present a simple two-state model to understand the size-dependent
endocytosis of nanoparticles. Using this model, we elucidate the relevant
energy terms required to understand the size-dependent uptake mechanism and
verify it by correctly predicting the behavior at large and small particle
sizes. In the absence of interactions between the nanoparticles we observe an
asymmetric distribution of sizes with maximum uptake at intermediate sizes and
a minimum size cut-off below which there can be no endocytosis. Including the
effect of interactions in our model has remarkable effects on the uptake
characteristics. Attractive interactions shift the minimum size cut-off and
increase the optimal uptake while repulsive interactions make the distribution
more symmetric lowering the optimal uptake.
