swell in response to osmotic stress. This method is, however, indirect and measurements can be perturbed by polydispersity in vesicle size. A more direct method of measuring Ka is the pipette aspiration method, in which a single giant unilamellar vesicle (GUV) is held and stretched with a micropipette. More recently, atomic force microscopy (AFM) has been used to probe the mechanical properties of suspended bilayer membranes, but this method is still under development. One concern with all of these methods is that, since the bilayer is such a flexible structure, there exist considerable thermal fluctuations in the membrane at many length scales down to sub-microscopic. Thus, forces initially applied to an unstressed membrane are not actually changing the lipid packing but are rather “smoothing out” these undulations, resulting in erroneous values for mechanical properties. This can be a significant source of error. Without the thermal correction typical values for Ka are 100-150 mN/m and with the thermal correction this would change to 220-270 mN/m. Bending modulus Bending modulus is defined as the energy required to deform a membrane from its natural 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 Ka in literature have actually been calculated from experimentally measured values of Kb 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. Curvature Only certain classes of lipids can form bilayers. Two factors primarily govern whether a lipid will form a bilayer or not: solubility and shape. For a self assembled structure such as a bilayer to form, the lipid should have a low solubility in water, which can also be described as a low critical micelle concentration (CMC). Above the CMC, molecules will aggregate and form larger structures such as bilayers, micelles or inverted micelles. The primary factor governing which structure a given lipid forms is its shape