Energy of the interaction between membrane lipid domains calculated from splay and tilt deformations

Specific domains, called rafts, are formed in cell membranes. Similar lipid domains can be formed in model membranes as a result of phase separation with raft size may remaining small ($10$–$100$ nm) for a long time. The characteristic lifetime of a nanoraft ensemble strongly depends on the nature of mutual raft interactions. The interaction energy between the boundaries of two rafts has been calculated under the assumption that the thickness of the raft bilayer is greater than that of the surrounding membrane, and elastic deformations appear in order to smooth the thickness mismatch at the boundary. When rafts approach each other, deformations from their boundaries overlap, making interaction energy profile sophisticated. It has been shown that raft merger occurs in two stages: rafts first merge in one monolayer of the lipid bilayer and then in another monolayer. Each merger stage requires overcoming of an energy barrier of about ($0.08$–$0.12$)$k_{\text{BT}}$ per $1$ nm of boundary length. These results allow us to explain the stability of the ensemble of finite sized rafts.