Coupling between membrane tilt-difference and dilation: a new ``ripple'' instability and multiple crystalline inclusions phases

A continuum Landau theory for the micro-elasticity of membranes is discussed, which incorporates a coupling between the bilayer thickness variation and the difference in the two monolayers' tilts. This coupling stabilizes a new phase with a rippled micro-structure. Interactions among membrane inclusions combine a dilation-induced attraction and a tilt-difference-induced repulsion that yield 2D crystal phases, with possible coexistence of different lattice spacings for large couplings. Inclusions favoring crystals are those with either a long-convex or a short-concave hydrophobic core.