Along with other forms of internalisation, phagocytosis and receptormediated
endocytosis are vitally important for many cell types, ranging
from single-cell organisms to immune cells. It is known experimentally
that engulfment in both cases depends critically on particle
shape and orientation. However, most previous theoretical work
has focused only on spherical particles and hence disregards the wideranging
particle shapes occurring in nature, such as those of bacteria.
Here, by implementing a simple model in one- and two-dimensions, we
compare and contrast receptor-mediated endocytosis and phagocytosis
for a range of biologically-relevant shapes, including spheres, ellipsoids,
capped-cylinders and hourglasses. We find a whole range of different engulfment
behaviours with some ellipsoids engulfing quicker than spheres,
and that phagocytosis is able to engulf a greater range of target shapes
than other types of endocytosis. Further, the two-dimensional model
can explain why some non-spherical particles engulf quickest (not at all)
when presented to the membrane tip-first (lying flat). Our work reveals
how some bacteria may avoid being internalised simply by their shape,
and suggests shapes for optimal drug delivery.