We present the electron density map of the asymmetric ripple phase of dilauroylphosphatidylcholine. We find that the primary feature characterizing the "asymmetry" of the rippled bilayers is the difference in the bilayer thickness in the two arms, and not the asymmetry of the bilayer height profile as is generally assumed. This difference in the bilayer thickness can be attributed to a mean tilt of the hydrocarbon chains of the lipid molecules along the direction of the ripple wave vector. We propose a Landau theory for this phase which takes into account the anisotropic elastic properties of a bilayer with tilt order.
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