Lipid bilayer mechanics
Local point deformations such as membrane protein interactions are typically modelled with the complex theory of biological liquid crystals but the mechanical properties of a homogeneous bilayer are often characterized in terms of only three mechanical elastic moduli: the area expansion modulus Ka, a bending modulus Kb and an edge energy
In particular, the values of Ka and Kb affect the ability of proteins and small molecules to insert into the bilayer.
[3] Since lipid bilayers are essentially a two dimensional structure, Ka 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.
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.
[4] Based on this understanding, a good first approximation of Ka for a monolayer is 2γ, where gamma is the surface tension of the water-lipid interface.
Based on this calculation, the estimate of Ka 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 Ka varies strongly with solution conditions[6] but only weakly with tail length and unsaturation.
[7] 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.
[8] More recently, atomic force microscopy (AFM) has been used to probe the mechanical properties of suspended bilayer membranes,[9] 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.
[4] 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.
Two factors primarily govern whether a lipid will form a bilayer or not: solubility and shape.
The primary factor governing which structure a given lipid forms is its shape (i.e.- its intrinsic curvature).
Other headgroups such as PS and PE are smaller and the resulting diacyl (two-tailed) lipids thus have a negative intrinsic curvature.
Lysolipids tend to have positive spontaneous curvature because they have one rather than two alkyl chains in the tail region.
is also an important parameter in biological phenomena as it regulates the self-healing properties of the bilayer following electroporation or mechanical perforation of the cell membrane.
The simplest model would be no change in bilayer orientation, such that the full length of the tail is exposed.
This is a high energy conformation and, to stabilize this edge, it is likely that some of the lipids rearrange their head groups to point out in a curved boundary.
[citation needed] The extent to which this occurs is currently unknown and there is some evidence that both hydrophobic (tails straight) and hydrophilic (heads curved around) pores can coexist.
[12] FE Modeling is a powerful tool for testing the mechanical deformation and equilibrium configuration of lipid membranes.
This consideration imply that Kirchhoff-Love plate theory can be applied to lipid bilayers to determine their stress-deformation behavior.
[16] FE methods can predict the equilibrium conformations of a lipid bilayer in response to external forces as shown in the following cases.
In such this case a finer mesh is applied near the pulling force area to have a more accurate prediction of the bilayer deformation.
[16] Tethering is an important mechanical event for cellular lipid bilayers, by this action membranes are able to mediate docking into substrates or components of the cytoskeleton.
Lipid bilayer budding is a commonplace phenomenon in living cells and relates to the transport of metabolites in the form of vesicles.
This eventually leads to a deformation of a typical spherical bilayer into different budding shapes.
