  The proper sorting of membrane components by regulated exchange between
cellular organelles is crucial to intra-cellular organisation. This process
relies on the budding and fusion of transport vesicles, and should be strongly
influenced by stochastic fluctuations considering the relatively small size of
many organelles. We identify the perfect sorting of two membrane components
initially mixed in a single compartment as a first passage process, and we show
that the mean sorting time exhibits two distinct regimes as a function of the
ratio of vesicle fusion to budding rates. Low ratio values lead to fast
sorting, but results in a broad size distribution of sorted compartments
dominated by small entities. High ratio values result in two well defined
sorted compartments but is exponentially slow. Our results suggest an optimal
balance between vesicle budding and fusion for the rapid and efficient sorting
of membrane components, and highlight the importance of stochastic effects for
the steady-state organisation of intra-cellular compartments.
