Lipid Bilayer Mechanics - Area Expansion Modulus

Area Expansion Modulus

Further information: Elasticity of cell membranes See also: Elastic Modulus

Since lipid bilayers are essentially a two dimensional structure, K_a is typically defined only within the plane. Intuitively, one might expect that this modulus would vary linearly with bilayer thickness as it would for a thin plate of isotropic material. In fact this is not the case and K_a is only weakly dependent on bilayer thickness. The reason for this is that the lipids in a fluid bilayer rearrange easily so, unlike a bulk material where the resistance to expansion comes from intermolecular bonds, the resistance to expansion in a bilayer is a result of the extra hydrophobic area exposed to water upon pulling the lipids apart. Based on this understanding, a good first approximation of K_a for a monolayer is 2γ, where gamma is the surface tension of the water-lipid interface. Typically gamma is in the range of 20-50mJ/m2. To calculate K_a for a bilayer it is necessary to multiply the monolayer value by two, since a bilayer is composed of two monolayer leaflets. Based on this calculation, the estimate of K_a for a lipid bilayer should be 80-200 mN/m (note: N/m is equivalent to J/m2). It is not surprising given this understanding of the forces involved that studies have shown that K_a varies strongly with solution conditions but only weakly with tail length and unsaturation.

The compression modulus is difficult to measure experimentally because of the thin, fragile nature of bilayers and the consequently low forces involved. One method utilized has been to study how vesicles 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 K_a 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.