Spontaneous and intrinsic curvature of lipid membranes: Back to the origins

We review the background behind the notions of spontaneous and intrinsic curvatures of lipid membranes with a goal to make clear a fundamental physical difference between them. We recall the underlying mechanical and thermodynamic models for intrinsically curved lipid monolayers, whose geometry is described by the intrinsic curvature, and for flat monolayers whose elastic stresses are captured by the spontaneous curvature. We describe the existing ideas concerning the spontaneous and intrinsic curvatures of mixed lipid membranes. We mention the conditions upon which the values of the spontaneous and intrinsic curvatures are expected to be similar and the specific systems for which each of the notions is relevant.