Finite-size domains in membranes with active two-state inclusions

The distribution of inclusion-rich domains in membranes with active two-state inclusions is studied by simulations. Our study shows that typical size of inclusion-rich domains (L) can be controlled by inclusion activities in several ways. When there is effective attraction between state-1 inclusions, we find: (i) Small domains with only several inclusions are observed for inclusions with time scales (approximately 10(-3)s) and interaction energy [approximately Omicron(kBT)] comparable to motor proteins. (ii) L scales as 13 power of the lifetime of state-1 for a wide range of parameters. (iii) L shows a switch-like dependence on state-2 lifetime k12(-1). That is, L depends weakly on k12 when k12k12*, the crossover k12* occurs when the diffusion length of a typical state-2 inclusion within its lifetime is comparable to L. (iv) Inclusion-curvature coupling provides another length scale that competes with the effects of transition rates.