**Bending Modulus**

Bending modulus is defined as the energy required to deform a membrane from its intrinsic curvature to some other curvature. For an ideal bilayer the intrinsic curvature is zero, so this expression is somewhat simplified. The bending modulus, compression modulus and bilayer thickness are related by such that if two of these parameters are known the other can be calculated. This relationship derives from the fact that to bend the inner face must be compressed and the outer face must be stretched. The thicker the membrane, the more each face must deform to accommodate a given curvature (see bending moment). Many of the values for K_{a} in literature have actually been calculated from experimentally measured values of K_{b} and t. This relation holds only for small deformations, but this is generally a good approximation as most lipid bilayers can support only a few percent strain before rupturing.

Read more about this topic: Lipid Bilayer Mechanics

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“No ray is dimmed, no atom worn,

My oldest force is good as new,

And the fresh rose on yonder thorn

Gives back the *bending* heavens in dew.”

—Ralph Waldo Emerson (1803–1882)