A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory

The relationship between the two-dimensional theory of tilted lipid membranes and three-dimensional liquid crystal theory is discussed in detail. The latter framework furnishes an appropriate foundation for membrane theory and facilitates a straightforward reduction to a well-posed two-dimensional model. This emerges as a special case of the Cosserat theory of elastic shells and incorporates a model of generalized capillarity in which the membrane energy responds to surface curvature and also to surface dilation and its gradient.

► A 2D model for lipid membranes with tilt and distension is derived from 3D liquid crystal theory.
► The derived model is shown to be energetically optimal.
► A theory for gradient capillarity emerges as a special case.