Dipolar ordering in the ripple phases of molecular-scale models of lipid membranes

Symmetric and asymmetric ripple phases have been observed to form in molecular dynamics simulations of a simple molecular-scale lipid model. The lipid model consists of an dipolar head group and an ellipsoidal tail. Within the limits of this model, an explanation for generalized membrane curvature is a simple mismatch in the size of the heads with the width of the molecular bodies. The persistence of a bilayer structure requires strong attractive forces between the head groups. One feature of this model is that an energetically favorable orientational ordering of the dipoles can be achieved by out-of-plane membrane corrugation. The corrugation of the surface stabilizes the long range orientational ordering for the dipoles in the head groups which then adopt a bulk anti-ferroelectric state. We observe a common feature of the corrugated dipolar membranes: the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis.