Finite-size Domains in a Membrane with Two-state Active Inclusions

We propose a model that leads to the formation of non-equilibrium finite-size domains in a biological membrane. Our model considers the active conformational change of the inclusions and the coupling between inclusion density and membrane curvature. Two special cases with different interactions are studied by Monte Carlo simulations. In case (i) exited state inclusions prefer to aggregate. In case (ii) ground state inclusions prefer to aggregate. When the inclusion density is not coupled to the local membrane curvature, in case (i) the typical length scale ($\sqrt{M}$) of the inclusion clusters shows weak dependence on the excitation rate ($K_{on}$) of the inclusions for a wide range of $K_{on}$ but increases fast when $K_{on}$ becomes sufficiently large; in case (ii) $\sqrt{M}\sim {K_{on}}^{-{1/3}}$ for a wide range of $K_{on}$. When the inclusion density is coupled to the local membrane curvature, the curvature coupling provides the upper limit of the inclusion clusters. In case (i) (case (ii)), the formation of the inclusions is suppressed when $K_{off}$ ($K_{on}$) is sufficiently large such that the ground state (excited state) inclusions do not have sufficient time to aggregate. We also find that the mobility of an inclusion in the membrane depends on inclusion-curvature coupling. Our study suggests possible mechanisms that produce finite-size domains in biological membranes.