  The asymmetric stem-cell division of Drosophila SOP precursor cells is driven
by the asymmetric localisation of the key protein Lgl (Lethal giant larvae)
during mitosis, when Lgl is phosphorylated by the kinase aPKC on a subpart of
the cortex and subsequently released into the cytoplasm.
  In this paper, we present a volume-surface reaction-diffusion system, which
models the localisation of Lgl within the cell cytoplasm and on the cell
cortex. We prove well-posedness of global solutions as well as regularity of
the solutions. Moreover, we rigorously perform the fast reaction limit to a
reduced quasi-steady-state approximation system, when phosphorylated Lgl is
instantaneously expelled from the cortex. Finally, we apply a suitable first
order finite element scheme to simulate and discuss interesting numerical
examples, which illustrate i) the influence of the presence/absence of
surface-diffusion to the behaviour of the system and the complex balance steady
state and ii) the dependency on the release rate of phosphorylated cortical
Lgl.
