  Cell membranes are out of thermodynamic equilibrium notably because of
membrane recycling, i.e. active exchange of material with the cytosol. We
propose an analytically tractable model of biomembrane predicting the effects
of recycling on the size of protein nanodomains. It includes a short-range
attraction between proteins and a weaker long-range repulsion which ensures the
existence of so-called cluster phases at equilibrium, where monomeric proteins
coexist with finite-size domains. Our main finding is that when taking
recycling into account, the typical cluster size increases logarithmically with
the recycling rate. Using physically realistic model parameters, the predicted
two-fold increase due to recycling in living cells is very likely
experimentally measurable with the help of super-resolution microscopy.
