Figure: A cartoon of the lipid water phases of model membranes exhibiting dehydration strains

Mechanical equilibrium in the normal direction requires that the suction in the inter-membrane phase have the same magnitude as the repulsive force. In the lateral direction it requires that the membranes support a compressive stress equal in magnitude to the inter-membrane suction times the inter- membrane separation. Severe dehydration of membrane rich regions thus causes stacks of membranes which resemble a lamellar phase, while compressing them laterally to make them thicker in the normal direction. In regions of the cell rich in macromolecules, the macromolecules will also be pushed into close separation and will suffer anisotropic internal stresses which compress them along their longer axes, although in this case the geometry is less simple (Wolfe and Bryant, 1999). We will concentrate only on membranes here. Colligative properties of membranes and solutes are compared in the figure below.

Figure: Comparing the freezing point depression due to solutes and to membranes. (a) and (c) show the behaviour of an ideal solution. In (a) it is shown as equilibrium freezing point depression as a function of concentration (for sugars, the experimental curve is lower than the line at high concentration). In (c) the same relation is represented as the molecular ratio water:solute, as a function of temperature. The horizontal lines show the simple fact that, for a sample with a given composition, the composition is constant above the equilibrium freezing temperature. The colligative effects of membranes are usually described in terms of the inter- membrane repulsion and the inter-membrane separation. For a large range of lipid membranes, this relation is well approximated by a repulsion that decreases exponentially with separation, as shown in (b). Converting this to a plot of water:lipid ratio as a function of temperature gives (d). Note the qualitative similarity to (c). In the membrane case, the water:lipid ratio has an upper limit: at about 30:1 the inter-membrane energy is a minimum (the force is zero) and so adding further water to such a sample simply creates an excess water phase (at temperatures above freezing), or more ice (at freezing temperatures). For experimental data, see Yoon et al. (1998) or Wolfe and Bryant (1999).

How large are these effects? Consider a single component lipid membrane. The gel-liquid crystal phase transition involves a reduction in area per molecule and an increase in its thickness. When these quasi two dimensional objects are compressed in the plane by a lateral stress p , the gel phase, which has a lower area per molecule, is favoured and the temperature of the transition is therefore elevated due to the Clausius-Clapeyron effect. (This is the effect which, in three dimensions, causes the boiling point of water to depend upon atmospheric pressure.) Using typical values this yields an elevation of order 0.5 °C for each extra mN/m in lateral stress. At a separation of 0.5 nm and with a repulsion of 20 MPa, the lateral stress is about 10 mN/m (more detail in Wolfe and Bryant, 1992; 1999).

One spectacular way in which membranes can respond to this lateral stress is by forming non-planar geometries, including the inverted hexagonal (H II ) phase, as shown in a previous figure. For weakly hydrating species, this geometry allows a large ratio of lipid volume to water volume, however this transition cannot be analysed with such a simple model because it involves energies associated with the curvature of the interface.

In a membrane composed of mixtures of lipids having different phase transition temperatures, a number of the phases described above can coexist (e.g. gel-fluid coexistence) over a range of temperature. This is analogous to solid-liquid phase coexistence between the melting points of the components of mixtures of three dimensional materials.

In membranes at low hydration, a different mechanism can give rise to separation into two coexisting liquid crystal phases. Consider the case where two or more components have very different hydration properties (e.g. different P o ) - ie you have a mixture of a highly hydrating species and a weakly hydrating species. In this case an homogeneous mix of the components has an internal energy that is rather higher than that of the separated phases. In many cases, this difference in internal energy is large enough to overcome the entropy of demixing, and the mixture will phase separate. previous figure. Here one phase has a higher concentration of the highly hydrating species and a higher inter-membrane separation than the other.

This effect was first predicted theoretically (Bryant and Wolfe, 89), and then observed experimentally using small angle X-ray diffraction and solid state NMR (Bryant et al., 1992) for mixtures of POPC and POPE (two mixed chain unsaturated phospholipids typical of those found in plant membranes). In excess water, the two species are completely miscible, forming a single lamellar phase. At 10% water content and 315 K however, the mixture separates into two separate lamellar phases with different water separations. Dehydration induced fluid-fluid phase separations have since been observed for other systems (Webb et al. 1993).

The existence of fluid-fluid phase separations is not, in itself, necessarily a danger to biological materials. However, it could be a necessary intermediate stage in the formation of damaging inverted phases (such as H II ). Cell membranes are composed mostly of strongly hydrating lipids that tend to form lamellar phases at all hydrations. Weakly hydrating species (that tend to form inverted phases at low hydrations) are normally in the minority: if they were not, then the bilayer membranes would not be stable. Even under severe dehydrations, inverted phases are unlikely to occur in these membranes if they remain homogeneous. However, if fluid-fluid phase separation occurs, the weakly hydrating lipids are concentrated into low hydration fluid phases, and are then free to undergo the transition to an inverted phase if the hydration is low enough. Thus fluid-fluid phase separations may be a precursor to the formation of the inverted phases which have been correlated with membrane damage during dehydration and freezing.