An elastic theory for line tension at a boundary separating two lipid monolayer regions of different thickness

To study theoretically the physics of the interface between liquid ordered (“raft”) and liquid disordered domains in biological cells and bilayer lipid membranes, we approximated this complex system by considering the energetics of one planar lipid monolayer leaflet at the interface between two regions of different thickness. Because it is energetically unfavorable to expose the hydrophobic lipid tails of the thicker region to water, lipid molecules deform near the interface in order to diminish the area of the acyl chain-water contact. This deformation is used to calculate the interfacial line tension. Leaflets are treated as a continuous elastic medium and the spatial distribution of deformations and the line tension are obtained by minimizing the total (elastic and hydrophobic) energy of the monolayer. Using reasonable values of elastic and spatial parameters, we found that lipid deformation completely eliminates any hydrophobic contact with water due to thickness differences. The energy of the system is therefore determined exclusively by the elastic deformation of the monolayer. Lipid deformations occur over a narrow region of ∼2–4 nm near the interface boundary. The value of the monolayer line tension is calculated to be ∼0.5kT/nm for a ∼0.5 nm difference in monolayer thickness. This value of the line tension is sufficient to maintain the circular shape of cholesterol–sphingolipid domains observed in lipid bilayer membranes. The energy of interaction of two thick domains separated by a thinner domain is obtained: thick domains attract from a distance of 1–2 nm.