Mean bending modulus, curved

Cq is the membrane intrinsic curvature, that is, the curvature of the membrane with zero deformation (e.g., a single layer of cylindrical molecules should have an intrinsic curvature of zero, but cone-shaped molecules will pack two dimensionally to have a curvature with no energy cost, k is the bending modulus, and is known as the saddle-splay modulus. As we can see in Figure 3.10, it is quite possible to have a curved membrane with a mean curvature of zero in the case of saddle-like deformations. Therefore, it becomes clear that to describe the energy cost of a saddle deformation the extra terms are necessary. 

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