  Molecular sorting is a fundamental process that allows eukaryotic cells to
distill and concentrate specific chemical factors in appropriate cell membrane
subregions, thus endowing them with different chemical identities and
functional properties. A phenomenological theory of this molecular distillation
process has recently been proposed [arXiv:1811.06760], based on the idea that
molecular sorting emerges from the combination of: a) phase-separation-driven
formation of sorting domains, and b) domain-induced membrane bending, leading
to the production of submicrometric lipid vesicles enriched in the sorted
molecules. In this framework, a natural parameter controlling the efficiency of
molecular distillation is the critical size of phase-separated domains. In the
experiments, sorting domains appear to fall into two classes: unproductive
domains, characterized by short lifetimes and low probability of extraction,
and productive domains, that evolve into vesicles that ultimately detach from
the membrane system. It is tempting to link these two classes to the different
fates predicted by classical phase separation theory for subcritical and
supercritical phase-separated domains. Here, we discuss the implication of this
picture in the framework of the previously introduced phenomenological theory
of molecular sorting. Several predictions of the theory are verified by
numerical simulations of a lattice-gas model. Sorting is observed to be most
efficient when the number of sorting domains is close to a minimum. To help in
the analysis of experimental data, an operational definition of the critical
size of sorting domains is proposed. Comparison with experimental results shows
that the statistical properties of productive/unproductive domains inferred
from experimental data are in agreement with those predicted from numerical
simulations of the model.
