Line Tension and Interaction Energies of Membrane Rafts Calculated from Lipid Splay and Tilt

Abstract

Membrane domains known as rafts are rich in cholesterol and sphingolipids, and are thought to be thicker than the surrounding membrane. If so, monolayers should elastically deform so as to avoid exposure of hydrophobic surfaces to water at the raft boundary. We calculated the energy of splay and tilt deformations necessary to avoid such hydrophobic exposure. The derived value of energy per unit length, the line tension gamma, depends on the elastic moduli of the raft and the surrounding membrane; it increases quadratically with the initial difference in thickness between the raft and surround; and it is reduced by differences, either positive or negative, in spontaneous curvature between the two. For zero spontaneous curvature, gamma is approximately 1 pN for a monolayer height mismatch of approximately 0.3 nm, in agreement with experimental measurement. Our model reveals conditions that could prevent rafts from forming, and a mechanism that can cause rafts to remain small. Prevention of raft formation is based on our finding that the calculated line tension is negative if the difference in spontaneous curvature for a raft and the surround is sufficiently large: rafts cannot form if gamma < 0 unless molecular interactions (ignored in the model) are strong enough to make the total line tension positive. Control of size is based on our finding that the height profile from raft to surround does not decrease monotonically, but rather exhibits a damped, oscillatory behavior. As an important consequence, the calculated energy of interaction between rafts also oscillates as it decreases with distance of separation, creating energy barriers between closely apposed rafts. The height of the primary barrier is a complex function of the spontaneous curvatures of the raft and the surround. This barrier can kinetically stabilize the rafts against merger. Our physical theory thus quantifies conditions that allow rafts to form, and further, defines the parameters that control raft merger.

Progressive ordering with decreasing temperature of the phospholipids of influenza virus

“…Thus proteins may play only a limited role in the phase behavior of lipids in the intact viral envelope. However, they may affect line tension at boundaries between coexisting phases 39 .…”

Organization, dynamics, and segregation of Ras nanoclusters in membrane domains

“…Clearly, tH clustering has a thermodynamic consequence on the bilayer structure. The link between line tension and membrane curvature (34,(36)(37)(38) implies that the tH-induced reduction of F l may affect the curvature behavior of our model bilayer. To explore this issue, we analyzed the average orientation of the bilayer lipids at each monolayer by computing their tilt angle, ϕ lipid , defined as the angle between a vector along the principal axis of lipids and the bilayer normal (Fig.…”

Clustering and Lateral Concentration of Raft Lipids by the MAL Protein

“…Approximated calculations based on previously published values for line-tension energies of exposed hydrophobic amino acids of TMDs (Kuzmin et al, 2005) indicate that alleviation of positive mismatch (between MAL TMDs and lipid tails) by cluster formation easily compensates for the loss of entropy (Kozlov, personal communication). Thus, we propose that our findings on MAL illustrate a potential mechanism by which sphingolipid rafts may form a functional protein and lipid sorting domain.…”

“…This perturbation occurs mainly because exposure of hydrophobic moieties to the aqueous environment is energetically unfavorable. Hence, membrane lipids may yield by bending as well as by selective accumulation of lipids with matching tail lengths (Kuzmin et al, 2005). Alternatively, positively mismatched membrane proteins have been shown to respond to mismatch with the surrounding lipids by aggregating, to minimize the mismatched contact zones (Gil et al, 1997;Fernandes et al, 2003), although substantial aggregation requires additional binding inducement in the form of protein-protein interactions (Sperotto and Mouritsen, 1991).…”