Interaction of lipid domains originating from differential domain-monolayer contact energy

We consider a flat membrane containing pure lipid domains located in the membrane monolayers and separated in the membrane plane. We assume the energy of contact along the membrane mid-surface between a domain and the underlying monolayer to be different from that between the two monolayers. We theoretically analyse the effect of the differential contact energy on the elastic deformations of tilt and splay in the membrane monolayers and the resulting interaction between two domains situated in the apposed monolayers. We demonstrate that the character of this interaction depends on the ratio, η, between the domain rigidity and that of a regular membrane monolayer. For the rigidity ratio smaller than a critical value, η < η* ≈ 3, the domain interaction is predicted to be attractive for all inter-monolayer distances. For the super-critical values of the rigidity ratio, η > η*, the interaction is repulsive for small distances and attractive for large distances with a certain equilibrium inter-domain separation corresponding to a vanishing interaction force. The predicted attractive interaction is proposed to favor the registration in the membrane plane of apposed domains as observed in most domain-containing membranes.