  We consider two volume-surface reaction-diffusion systems arising from cell
biology. The first system describes the localisation of the protein Lgl in the
asymmetric division of Drosophila SOP stem cells, while the second system
models the JAK2/STAT5 signalling pathway. Both model systems have in common
that i) different species are located in different spatial compartments, ii)
the involved chemical reaction kinetics between the species satisfies a complex
balance condition and iii) that the associated complex balance equilibrium is
spatially inhomogeneous. By using recent advances on the entropy method for
complex balanced reaction-diffusion systems, we show for both systems
exponential convergence to the equilibrium with constants and rates, which can
be explicitly estimated.
