Figure I.
Geometric definition of membrane curvature and examples of basic shapes. The two principle curvatures of a surface element, c1 and c2, are defined as inverse radii of the two arcs that represent the surface cross-sections in two perpendicular directions called the principle directions [74]. Lipid bilayers having properties of two-dimensional fluids are described by the two combinations of the principle curvatures: their sum J=c1+c2, called the total curvature, and their product K=c1c2, called the Gaussian curvature. The basic curved shapes are a spherical shape for which c1=c2; a cylindrical shape with c1=0 such that K=0; and a saddle-like shape characterized by c1=–c2 and, hence, J=0.