  The formation of dynamical clusters of proteins is ubiquitous in cellular
membranes and is in part regulated by the recycling of membrane components.
Mean-field models of out-of-equilibrium cluster formation with recycling
predict a broad cluster size distribution for infinite systems and must be
corrected for finite-size effects for small systems such as cellular
organelles. We show, using stochastic simulations and analytic modelling, that
tuning the system size is an efficient way to control the size of lateral
membrane heterogeneities. We apply these findings to a chain of enzymatic
reaction sensitive to membrane protein clustering. The reaction efficiency is
found to be a non-monotonic function of the system size, and can be optimal for
sizes comparable to those of cellular organelles.
