Interfacial Forces in Cryobiology and Anhydrobiology

Gary Bryant and Joe Wolfe,
School of Physics, The University of New South Wales, Sydney

This paper was published in Cryo-Letters 13, 23-36 (1992). For more recent reviews, see
  • Wolfe, J. and Bryant, G. "Cellular cryobiology: thermodynamic and mechanical effects" International Journal of Refrigeration, in press; and
  • Wolfe, J. and Bryant, G. (1999) "Freezing, drying and/or vitrification of membrane-solute-water systems" Cryobiology, 39, 103-129.


    The very large, repulsive forces that occur between amphiphilic surfaces in aqueous solutions at separations less than about 3 nanometers are important in cryobiology and anhydrobiology because: (i) they complicate the dehydration behaviour; (ii) they produce large anisotropic stresses in membranes and (iii) they can lead to component demixing.

    Key words: hydration forces, cryobiology, anhydrobiology, dehydration, membranes, phase behaviour.



    In 1938 Langmuir's experiments (1) on the repulsion and swelling of colloidal surfaces showed that, in addition to electric and van der Waals interactions between the surfaces, a strong repulsion at short range was required to explain the stability of bipolar colloids. "Hydration seems to be the most reasonable explanation", he concluded, and argued that a thin layer of water was held tightly to the surface by the strong local electric field. In 1976 LeNeveu, Rand and Parsegian (2) measured the dehydration properties of lipid lamellar phases and reported large forces between bilayers at separations of less than a few nanometres. In 1977 Israelachvili (3) measured directly the force-distance curves between mica surfaces in electrolyte solution and reported a large short-range repulsion. These forces are usually known as hydration forces (although see reference 4). Their magnitude may reach tens or hundreds of meganewtons per square metre and they are repulsive.

    These forces have not attracted the attention of most biologists for a good reason: under most conditions, the non-aqueous components of cells (such as membranes) are not usually this close together. Furthermore the pressures of tens of megapascals which are needed to overcome these very large forces are rarely expected in biological cells[footnote 1] .

    Important exceptions occur in cryobiology and anhydrobiology. In slowly frozen, intact cells and in substantially dried cells, the water content may be only several percent (by weight). With so little water present, all the non-aqueous components are brought very close together. If an organelle with a high membrane content (such as a chloroplast, mitochondrion, Golgi body or endoplasmic reticulum) is dehydrated to 20% water (by weight), and if the membranes are say 6 nm thick, then the average intermembrane separation is about 1.2 nm. This close approach, in spite of the existence of large repulsive hydration forces, may be brought about by the very large suctions which may be created by the freezing or evaporation of extra-cellular water, and the consequent exit of intracellular water.

    Large forces acting at such small separations create anisotropic stresses[footnote 2] in membranes or other non-aqueous components which are large in comparison with the stresses required to deform or to disrupt those components, and it has been suggested that such stresses are responsible for freezing or dehydration damage under some circumstances. The evidence is necessarily indirect: it is not yet possible to measure directly such forces in situ in dehydrated cells. Nevertheless a range of observations using different experimental techniques on different (usually model) systems have shown severe morphological changes in membranes, and this has encouraged investigation of the proposition that dehydration-induced stresses may be involved in cellular damage.

    This article gives a brief review of the nature of these short range forces, their effects on water relations, and the production of stresses in membranes and macromolecules. This will be followed by a brief discussion of the possible or likely implications for cryobiology and anhydrobiology.

    Short range interfacial forces

    When the surfaces of two objects in a fluid are brought into close approach, various forces are exerted between them: these include static electric[3] interactions (double-layer forces), dynamic electric interactions (van der Waals[4] or dispersion forces and ion correlation interactions) and extremely short range (electric) interactions called steric forces. In the case of water there is also the hydrophobic interaction. At very small separations - typically several diameters of the solvent molecule - another force is measured which cannot be directly included in the interactions listed above. This force not only has very short range, it also increases very rapidly with decreasing separation and at sufficiently close approach it usually becomes larger than the double-layer and van der Waals forces. It is repulsive.

    This force is usually[5] called the solvation force and it is usually attributed to perturbations of the liquid very near the surfaces. In the case of water it is called the hydration force.

    This extra force was first measured for lipid systems by LeNeveu et al. (2). They exposed samples of lipid-water lamellar phases to different degrees of hydration. The repeat spacing of the phase was in all cases measured by X-ray diffraction, and from this spacing and the composition, the interbilayer separation was calculated. The water was removed by one of three methods, depending on the pressure range. For small suctions (the kPa range), the samples were mixed with dextran of known osmotic pressure. For intermediate suctions, the lipids imbibed water across a dialysis membrane against a mechanical pressure imposed via a hydraulic pump. For the highest suctions[6] the samples were equilibrated with solutions of known humidity. Together these three methods are known as the osmotic stress technique.

    LeNeveu et al. found a large discrepancy between the force-distance relationship they measured and that predicted using electric double layer and van der Waals forces. The difference could be accounted for by an exponentially decaying repulsive force whose range was of the order of 1 nm. In subsequent papers (5-9), a large number of lipids were studied using this technique, and the repulsive forces and van der Waals interactions of the species were measured. They found that the extra force could be characterised by an empirical exponential law, i.e. most of the data could be well fit by the equation:

    F = Po exp (-y/l) (Eqn 1)

    where F is the repulsive force per unit area[7], Po is the extrapolated force per unit area at bilayer contact, l is the characteristic decay length of the force, and y is the interbilayer separation. For pure lipids, these investigators found that the decay length l was usually in the range 0.1 to 0.3 nm, and that the pre-exponential factor Po was about 100 MPa to 10 GPa (7). They attributed this force to a force of hydration between the bilayers.

    Independently of these studies, Israelachvili (3) measured large, short-range forces between mica surfaces. The apparatus consists of two sheets of mica separated by the medium under study (e.g. water), which are brought into close proximity. The mica sheets are curved as sections of cylinders, and the axes of the cylinders are crossed at right angles. One sheet and its glass support are mounted on a calibrated spring whose deflection is measured to give the force. On each mica sheet the side which does not face the medium is partially silvered. The separation between these silvered surfaces is measured by optical interference (using white light and fringes of equal chromatic order). The thickness of the mica is measured by allowing the surfaces to contact, and this thickness is effectively subtracted[8] from measurements to give the interfacial separation. This technique is called the surface forces technique.

    Apart from the van der Waals, double layer and adhesion forces that had been expected, Israelachvili found repulsive forces with a range of about 1 nm which decreased approximately exponentially with separation.

    The surface forces technique was used to study the forces between mica surfaces coated with phosphatidylcholine bilayers during close approach and fusion (10), and to study the force-distance curves of a range of phospholipids in aqueous solutions (11-14).

    There are several important differences between the osmotic stress and surface forces techniques, and so the observed behaviour of bilayers is different in the two cases. In the surface forces apparatus the force is applied locally, whereas in the osmotic stress technique a suction is applied throughout the water volume. This sometimes leads to qualitatively different behaviour of bilayer-water systems subjected to the different experimental constraints. In the surface forces apparatus, the regions of two membranes which are locally in close approach can relax their potential energy by fusing together and expelling the excess lipid material from the compressed region. In the osmotic stress technique, all membranes are subject to the same stress, so fusion would not change the energy, and it is presumed not to happen.

    Further differences are due to the motion of lipid molecules both independently and collectively. Individual lipid molecules can diffuse laterally in bilayers. In the surface forces apparatus, lateral diffusion away from the compressed region lowers the potential energy. Thus at sufficiently large force the supported bilayers would be expected to thin, giving a larger area per molecule. (An increase in area of one percent requires an applied stress of about 30 MPa; 14). In contrast, the dehydration and large forces imposed in the osmotic stress technique cause a reduction in area per molecule in the plane of the bilayer and an increase in length in the normal direction (7). Collective motions of the bilayers also distinguish the methods. In the mica experiments the supported bilayers are relatively immobile in the normal direction, whereas fluctuations in the normal direction may occur in the osmotic stress technique. This is important because such fluctuations are believed to extend the range of the hydration forces considerably in unsupported bilayers (15-17).

    As well as the differences between the physical conditions that obtain in the two cases, there is a further difficulty in giving a direct comparison of data from the two methods. This arises from different working definitions of the bilayer surface. In the osmotic stress technique, the bilayer interface is the density weighted mean surface between bilayer and water. By this definition, there would be considerable bilayer overlap at zero separation. In the surface forces apparatus, separation is defined with respect to bilayer "contact". This can be calculated after two bilayers fuse to become one, whose thickness is taken as the separation of the mica surfaces after fusion. Horn resolved many of the apparent disagreements initially presented by protagonists of the two techniques, and demonstrated that the results of the two methods were in reasonable agreement, given the different conditions listed above (18).

    A final important difference between the two techniques is that the osmotic stress technique can be applied to arrays of macromolecules, whereas the surfaces forces apparatus is (as yet) only applied to the forces between two large surfaces. Parsegian and co-workers (19, 20) have used the former technique to provide pressure-spacing and pressure-volume curves for DNA and hemoglobin S. DNA exhibits an exponential repulsion with a characteristic length of 0.3 nm which those authors interpret as due to the work of removing water molecules.

    A related experimental technique uses pipette aspiration (21, 22). Two cells or vesicles are partially sucked into glass micropipettes. Enough suction is applied to remove wrinkles in the membrane. The cell or vesicle thus adopts a regular geometry: the section in the pipette is a cylinder with a hemispherical cap, and the external portion is spherical. The areas can therefore be calculated. The cells or vesicles are then brought close together, the suction in one pipette is reduced. This relaxes the tension in the membrane of that cell or vesicle, which allows it to spread over the surface of the other. Measures of the suctions, the curvatures and the contact angle between the two membranes allow the calculation of the surface free energy of adhesion. This method yields the energy per unit area at a single separation, rather than force-distance curves. The results can however be compared to the integral of the force curves obtained from the other two methods.


    Two different effects have been accused of giving rise to the large short-range forces: perturbation of solvent structure near the interface (i.e. solvation forces), and steric interaction due to thermally excited motion of the interfaces on both molecular and larger scales[9]. The relative contributions of these components are boisterously debated[10]. Rand and Parsegian (9) argue that solvation forces dominate at close approach. Israelachvili and Wennerstrom (4, 23) argue that the available data can in most cases be fitted by the sum of the osmotic, electrical and thermal motion forces, without introducing a further interaction. We shall briefly review the theories of both.

    Before introducing explicit theories of solvation forces, we shall give a simple general explanation and obtain an estimate of their magnitude. The fluid near an interface is perturbed by the interface, and the work required to create this perturbation equals the free energy of the liquid surface. (The interfacial free energy per unit area equals the surface tension for an interface between two pure liquids.) When two interfaces approach closely, the intervening liquid is also perturbed by the interfaces. The change from two non-overlapping to overlapping perturbed layers involves a change in free energy. If this change is positive (as is usually the case), work must be done to bring them together, and the solvation force is repulsive. Attractive solvation forces of course arise from a negative change in free energy on approach (see 24). One can easily obtain a rough estimate of the characteristic force per unit area associated with introducing or removing the perturbation. The surface tension (and thus the free energy per unit area) of a single interface is typically of order tens of mN/m. The perturbed region is several molecules thick (say a couple of hundred pm). Division and neglect of dimensionless factors gives a force per unit area of order 100 MPa.

    One could consider the free energy of an aqueous interface as a sort of "free energy of hydration"[11] for several "layers" of water near the surface. The free energy of the first hydration layer would be largest, with successive layers having successively lower enthalpies. The free energy would be given by the integral of P (eqn 1) across the layer[12]. This picture is useful for giving a chemical intuition, but it is potentially misleading. The "layers" are imaginary boundaries in a fluid whose molecules have properties only slightly different from those of normal bulk water. The free energies per molecule are quite small compared to those of normal chemical reactions. Parsegian et al. (20) are careful to point out that hydration effects which act over a range of several water molecules do not imply that there are several layers of "bound water" because nearly all of the water involved is in a state very closely resembling that of bulk water. A small change in the energy of a water molecule divided by the very small volume of a water molecule gives a substantial pressure.

    The exponential form for the repulsive force (eqn 1) was initially introduced as an empirical equation which fitted the data. Since then there have been several theoretical analyses of the hydration force. Marcelja and co-workers (25-28) assumed that the force arises from the perturbation of the layer of water adjacent to the lipid surface[13] (i.e. that it is indeed a hydration force). The water molecules adjacent to the surface have a non-zero mean orientation, or other specific dipolar orientations, due to several effects. First, the surface may be charged or dipolar (as is usually the case for lipids). Water molecules are strongly dipolar and so the first layer will be oriented to some extent. Further, the surface will disrupt the hydrogen bonding network close to the surface. The surface in most cases will be unable to form hydrogen bonds. Those surfaces that do form hydrogen bonds will not do so with the same spacing and orientation as does an arbitrary surface in bulk water. The first layer is therefore specifically orientated (usually polarized), which causes the second layer to become oriented, although less so than the original surface because of entropy and because of the lower energy of hydrogen bonded water molecules. So the perturbation is propagated through the medium, decaying away from the surface.

    The earliest and simplest theoretical treatment gives a useful qualitative insight. Gruen and Marcelja (25) treated the water as "ice with defects": i.e. a regular hydrogen bonded array with a spatially varying local concentration of bond defects. The concentration of defects in the hydrogen bonded structure of the water is large at the polarizing surface, but decays to a bulk value in the water remote from the surface. (A crude analogy may be made with the standard electric double layer, where hydrogen bond defects are analogous to excess charges. There are some similarities in the equations, and each has a characteristic length which depends on the medium.)

    The next level of complexity in solvation theories is to include the electrical inhomogeneity of the interfaces by setting a lattice of charges and/or dipoles on the interface, but to treat the fluid as a continuum. Continuum theories of fluids must, however, fail at sufficiently small separations.

    To include the molecular structure of water in theoretical treatments is rather more difficult. Simple intermolecular potentials (e.g. that of hard spheres) may be treated analytically, but such potentials neglect the strong asymmetry of the water molecule. A more realistic model of water has four charges at the vertices of a tetrahedron (the ST2 potential, 29). Such a potential can be used in Monte Carlo or molecular dynamics calculations to produce data on the physical state of a small finite container of fluid subject to given boundary conditions. These calculations have the limitation that the interactions among water molecules are not pairwise additive. Theories of interactions between interfaces in liquids are reviewed by Marcelja (30).

    One spectacular example of the importance of discrete molecular effects is the phenomenon of "oscillating" forces. When the separation between interfaces is several molecular diameters, the exact value of the spacing may limit the possible configurations and bond orientations in the fluid. For two molecularly smooth, rigid surfaces, the force is expected to have a component of alternating sign. The zeros of that component occur at separations which correspond approximately to the thickness of integral numbers of layers of solvent molecules[14]. In fact regular variations ("oscillating" forces) with a wavelength comparable in size to that of the solvent molecule have been measured between molecularly smooth mica surfaces using the surfaces forces apparatus in aqueous solutions under solute conditions which reduced the magnitude of double layer forces (32). Such variations have not been reported (and are not expected) for bilayers, which are less smooth and less rigid than crystals of mica.

    Is the characteristic length determined by the liquid or the interface?

    In simple interpretations of the continuum theories, the degree of polarization (and hence Po) depends on the properties of the surface, whereas the decay length l of the perturbation depends on the properties of the medium. In the mid 1980s this was seen as being consistent with the early experimental results that the Po calculated for lipid-water mixtures varies enormously, whereas the values of the decay length l showed relatively little variation.

    As more systems were studied, a larger range of l was observed: from 0.08 to 2.4 nm (9). Although the magnitude of the decay length predicted by the simple theories falls within the range measured experimentally, the variation of l for different surfaces is inconsistent with one dimensional polarization models. There is a distinction to be made between the l used by the experimentalists (-1 times the slope of a plot of log(force) vs separation) and that used by the theoreticians (the characteristic length). For the experimentalist, Po in eqn 1 is a constant, and only the exponential term varies with y. For a theoretician, Po is related to the the surface polarization, and this may vary weakly with y, and thus contribute another term to the slope of a plot of log(force) vs separation. Such an example is analysed by Lis et al. (7, 8): when lamellar phases are dehydrated, the bilayers are compressed in the plane of the lamellae. It follows that the surface presented to the water, and thus the expected average polarization, is different at different values of y, and so the negative slope of log(force) vs separation will not equal the characteristic length.

    A further difference between the "characteristic length" of the theoretician and that of the experimentalist is that an experimental force-distance curve is due to the sum of all forces acting in the system, and not just that force being considered by the theoretician.

    Numerical analyses which include discrete molecular effects and which allow three dimensional variation of the polarization of water are more successful at explaining observed results: the strongly varying polarization in the plane of the surface disrupts the hydrogen bonding, but the amount of the disruption depends also on the proximity of another surface (see review by Marcelja, 30).

    Other theoretical studies have contested the nature of the force, proposing that these short range forces are not solvation forces at all. Belaya et al. (33) attribute the force to local electrostatic interactions, although the dielectric function used in this analysis has been questioned (34).

    Israelachvili and Wennerstrom (4, 23) have proposed a model for short range repulsive forces based on steric forces due to molecules which protrude from the bilayer due to thermal fluctuations. If the energy of a molecular protrusion is proportional to normal displacement, the Boltzmann distribution gives rise to an exponentially decaying force. These authors argue that this is one of three different thermally excited modes of normal motion of the surface which together provide the measured repulsion: the other two being the fluctuations of the membrane as a whole, and 'peristaltic' variations in the thickness of the membrane. These three forces they call entropic forces (23). This model predicts that the decay length is determined by the surface- solvent interaction rather than solely by the properties of the solvent, and thus would be expected to vary from lipid to lipid, as is found experimentally. This model does not account for the similar short range forces measured between mica sheets where fluctuations in the normal direction are presumably very small compared with those of bilayers where normal fluctuations could presumably be of larger range.

    Much of the difficulty in deciding the relative contributions of electrical, thermal and solvent forces is that of choosing the model for the solvent, the interface and the relevant model parameters. Israelachvili and Wennerstrom (23) make the important point that most models treat the amphiphile-water interface as a well-defined interface between two homogeneous continua. Where the calculations based on such a model differ from experimental data, the difference is attributed to the molecularity of the solvent. Israelachvili and Wennerstrom specifically include the molecularity of the interface by allowing a Boltzmann distribution of molecular protrusions. On the other hand, their model treats the solvent as a continuum, and in a sense it attributes the 'left over' force to protrusion by choosing an appropriate value for the parameter which determines the energy of protrusion from the interface. Thus the competing explanations have different simplified assumptions as starting points and give rise to different values of fitted parameters.

    For this reason, the argument over the relative importance of the different components of the short-range repulsion is by no means resolved. Fortunately, this does not prevent us from discussing their implications for cryo- and anhydrobiology. The following discussion concerns any large repulsive force acting between amphiphilic surfaces (such as membranes and soluble macromolecules), independent of the origin of that force.

    How do large short-range forces affect water relations?

    Discussions of cellular water relations usually introduce two approximations: incompressibility of water and ideal (or predictably non-ideal) behaviour of solutions. Extreme dehydration is the situation under which these approximations are poorest. That of incompressiblity is the better of the two: the bulk modulus of water is approximately 2 Gpa (35), so the molar volume of water should be increased by 1% at suctions of 20 MPa. The total solute concentration in dehydrated tissues may be several kmol.m-3. Under these conditions it is difficult to estimate the activity coefficient, and of course it is expected to vary for different solutions in different tissues. The crudity of these approximations limits precise quantitative application of the equations derived therefrom, but this is often of little consequence because the relevant parameters cannot in many cases be measured with any greater precision.

    We begin with the treatment of water relations as it is applied at high water contents, and then examine the modifications necessary at low hydration. Equilibrium of water requires that its chemical potential mw be constant. With the assumption of constant molar volume of water Vw, it follows directly that a quantity called the water potentialbe constant in volumes of water that are in equilibrium (37).[15] (The water potential equals the chemical potential of water per unit volume, where the former is measured with respect to the standard state. It is approximately equal to the hydrostatic pressure P minus the osmotic pressure PI. The osmotic pressure in turn is approximately equal to (RT/Vw) ln(aw) where R is the gas constant, T the thermodynamic temperature, aw the activity of water). The osmotic pressure in the intermembrane solution includes component due to both the solutes and the membranes. We include all interactions between membranes in F, the force per unit area between them. That component PIs which is due to solutes may be written as

    PIs = RTN'/(V - b) (Eqn 2)

    where V is the volume of solution considered. The two fudge factors which make eqn 2 correct by definition are b, the "osmotically inactive volume" and N', the "effective number of moles of osmotically active solutes" in V. N' may be replaced with gN where N is the number of moles of osmotically active solutes and g is the activity coefficient, although this substitution is only helpful when one can estimate g. The "osmotically inactive volume" b is sometimes defined to include water of hydration. When the hydration force is explicitly included in an analysis, hydration of the membrane should not be included in b. (The inclusion of a single layer of water of hydration for the membrane in b is equivalent to defining the hydration force to be an infinite step function at a separation of twice the diameter of a water molecule.)

    In cryobiology, the water potential Ys of the extracellular solution is often known, being determined by the temperature at atmospheric pressure. In anhydrobiology the cellular water is often in equilibrium with the external atmosphere of known humidity. Substituting[16] eqn 2 gives

    Water potential = P - PI = P - RTN'/(V - b) (Eqn 3)

    In the approximation of an ideal solution, g = 1 and N' is replaced by N. This approximation is particularly poor at very low hydration.

    Consider the case where P = 0. Equation 3 then implies that, in the ideal limit, water potential and (V-b) are inversely proportional (sometimes called ideal osmotic behaviour). Thus, if the intracellular pressure is approximately zero, a plot of cellular volume vs reciprocal of water potential will be linear, with intercept b and slope RTN'. Cells and organelles in suspension exhibit this behaviour to a good approximation over a limited range of (relatively high) hydration (38, 39).

    In studies of water relations at relatively high hydration, P is either positive (for turgid cells in plants), zero (for flaccid tissue) or slightly negative (in the cytoplasm of non-turgid cells with relatively rigid cell walls). The most important implication of large, short-range forces is that they allow very large negative values of P (large suctions) under severe dehydration.

    At high levels of hydration, cellular membranes are separated by solution with inter- membrane spacings of nm or more. At these levels of hydration the solution volume is governed by osmotic pressure and external constraints. At low hydration, however, the membranes and other components are concentrated, and the interbilayer spacings may be less than a few nanometres. As membranes are brought into close proximity, further reductions in volume require closer approach of the non-aqueous components in general, and of membranes in particular. In highly membraneous regions of the cell, layers of membranes tightly squeezed together are seen in electron micrographs (40), and they resemble the lamellar phases in low hydration lipid-water mixtures.

    Close approach of membranes is opposed by the very strong, short-range forces. This repulsive force between the bilayers is balanced in the aqueous inter-membrane phase by a negative pressure or suction. The importance of this negative P in cellular water relations at low hydration is implied by equation 3. When the water potential is sufficiently low that large repulsive forces are encountered: (i) V will be larger, and (ii) osmotic pressure PI will be smaller than predicted by eqn 3 with P = 0.

    The difficulty in measuring P directly[17] in situ means that when the volume at a given water potential is greater than predicted by eqn 3 using P = 0, this behaviour may be interpreted as non-osmotic behaviour, because the volume as a function of water potential appears to violate the law of Boyle and van't Hoff. The osmotic stress technique is such an example: P(x) is determined from the departure from "osmotic" behaviour by the water in the lamellar phase. In the case of no solutes, PIs = 0 and thus chemical equilibrium requires P = water potential. Newton's first law requires that P = -F and so the force per unit area F equals minus one times the water potential.

    In summary, reductions in water potential (caused by external freezing, hyperosmotic solutions or air drying) cause an increase in PIs and little change in P at high hydration. At low hydration, reductions in water potential cause P to become more negative but produce successively smaller changes in PIs. "Low" hydration in this sense means the hydration level at which hydration repulsion becomes non-negligible: i.e. when non-aqueous components approach within a couple of nanometres of each other. This happens when the water content is reduced to less than about 20%. The value at which this occurs will vary for different cells and among organelles in the same cell (see 41).

    Induced stresses and their effects

    Intermembrane repulsions and solution suctions of tens of MPa at low hydration are large in comparison with the pressures encountered in conditions of normal hydration. They are nevertheless small in comparison with the bulk modulus of liquids such as water and hydrocarbons (of order GPa). If these stresses were isotropic, one would expect small volume deformations of little mechanical importance, and some slight but perhaps physiologically important changes in protein configuration. The reason why these stresses are potentially capable of severe ultrastructural damage is that they and the strains they produce are highly anisotropic.

    The suction in the aqueous phase which balances the repulsive force between membranes acts to reduce the aqueous volume in all directions, so it tends to contract the membranes in their plane. This contraction is resisted by the elasticity of the membranes, which produces a lateral compressive stress in the membranes.

    How large are the stresses thus generated in membranes, and what are their significance for cell damage? An approximate answer to the first question can be obtained if several simplifying assumptions are made. If it is assumed that the thin layer of solution acts as an isotropic fluid (which approximation should be good for separations larger than a few solvent molecular diameters) and that the large, short-range force acts at the (volume-weighted) surface of the bilayer, then the balance of forces in the lateral direction requires that

    lateral pressure = - Py (Eqn 4)

    where P is the pressure in the aqueous phase and y is the intermembrane spacing. The lateral pressure thus used has dimensions of force per unit length and is -1 times the bifacial surface tension of the membrane[18]. It is equal to the compressive stress in the lateral direction integrated across the membrane.

    Several different strains may result from such stresses. The most ubiquitous is the deformation in which the membrane becomes thicker in the normal direction while the area per molecule in the plane of the membrane is reduced (7). The area modulus of membranes is in the range 200-400 mN/m, and the lateral pressures may be tens of mN/m (41), so the deform- ations may be considerable. There is, however, little reason to suspect that simple reductions of area are irreversible, so they may have little importance per se as a source of ultrastructural damage. Rather, it is the effect of these stresses on the phase properties of membrane components that are likely to be involved in such damage. Three types of phase behaviour have been implicated in cryo- and anhydro- biological damage: fluid lamellar - gel lamellar transitions, lateral phase separations in the lamellar phase, and lamellar to inverse hexagonal (hereinafter HII) phase transitions.

    The Crowes and co-workers (42-44) reported lateral phase separations in lamellę, and the co-existence of lamellar and HII in studies of vesicles made from components of sarcoplasmic reticulum. Freeze-fracture electron micrographs[19] of dehydrated samples contained areas of membranes in which there were high densities of intramembrane particles (interpreted as protein-rich phases) and other regions devoid of such particles (interpreted as protein-depleted phases) and thus implied lateral phase separations. The same micrographs showed arrays of cylinders. These were interpreted as arrays of inverse cylindrical micelles. The hexagonal symmetry of a closely packed array of cylinders resembles that of the HII phase, and so such ultrastructural features are often called HII phases[20]. Gordon-Kamm and Steponkus (45) reported similar geometries in electron micrographs of osmotically contracted plant protoplasts. The Crowes suggested that the formation of the HII phase implied membrane damage, because the topology of the HII phase is inappropriate for the semipermeable barrier which is the one of the chief functions of biological membranes. They also suggested that areas of lateral phase separations seen in these samples were a necessary precursor to the formation of the HII phase. They suggested that these lateral phase separations can lead to areas of almost pure lipid, some of which may be lipids (such as PE) which naturally form the HII phase. These lipids are then free to undergo the transition to the HII phase, thus disrupting the membrane. Phase transitions in membrane lipids, and phase separations among membrane components are discussed in the next section.

    Macromolecules which exhibit large, short-range repulsions are also exposed to mechanical stress by dehydration. In the case of an array of nearly cylindrical molecules, a compressive stress along the axis would be produced. Dehydration can produce a range of strains in macromolecules, including closing of channels. These and other examples are reviewed by Parsegian et al. (20).

    Membrane phase behaviour

    Fluid lamellar to gel lamellar transitions, lateral phase separations, and lamellar to HII transitions are all affected by the lateral stresses[21] imposed by dehydration. The lamellar fluid- gel transition involves a change in area per molecule, so the transition may be caused by a lateral stress, or the temperature at which it occurs may be a function of lateral stress. Lateral phase separations may occur in the presence of large, short-range forces because the strength of these interactions is very different for different components. The influence of such stresses on transitions between the lamellar and hexagonal phases is related to the quite different geometries of these phases. The aqueous volume in the HII phase has a higher surface to volume ratio than does that in the lamellar phase, and so transition to HII can relax compressive stresses in the interfacial plane.

    In the phase behaviour of a quasi-two dimensional structure such as a membrane, lateral pressure is analogous to pressure in three dimensions. The transition from fluid to gel entails a reduction in area, so a positive lateral pressure p raises the transition temperature, whereas a negative lateral pressure (i.e. a positive surface tension) lowers it. The most elegant and direct demonstrations of this are the experiments of Evans and Needham (22). These experiments use micropipette aspiration of unilamellar vesicles and thus allow the direct measurement of sections of the area-tension-temperature phase diagram for single membranes. The effect can also be inferred from studies in which the lateral pressure is not directly measured, because where the force is repulsive, increasing hydration implies decreasing lateral pressure (equations 1 and 4). For instance, studies of the lamellar fluid-gel transition in phosphatidylcholine using differential scanning calorimetry (47, 48) and nuclear magnetic resonance (49) show that the transition temperature decreases with hydration. Seddon et al. (50) have shown the same effect for phosphatidylethanolamines using X-ray diffraction.

    The magnitude of the effect of stresses on liquid-solid transition temperatures can be readily estimated. If the transition temperature is Tc when the lateral pressure p is zero, then the change in standard chemical potential mu0 for the transition from solid (S) to liquid (L) at temperature T is

    mu0S - mu0L = -L (1 - T/Tc) + p(aL - aS)

    whence Tc - T = Tc (aL - aS) p/L.

    To obtain an estimate, take the latent heat L = 5 x 10-20 J per molecule, and (aL - aS) = 0.2 nm2 (if p is the bilayer lateral pressure, then the appropriate area is the contribution to that of the bilayer, so monolayer values have been divided by 2). The transition temperature should be elevated by about 1 K for each mN/m of imposed lateral stress, in the linear limit. (For calculations of phase diagrams in (composition, temperature, lateral pressure) space, see 51, 52.)

    Lateral phase separations

    Hydration forces act differentially on membrane components. The magnitude of the interlamellar force at a given distance varies by more than an order of magnitude among different lipids (9). A consequence of this is that homogeneous mixtures may demix into separate phases during (isothermal) dehydration (6, 53, 54).

    The distribution of membrane proteins is often used to identify phase separations. Membrane proteins are large molecules and they may protrude from the membrane surface. Thus proteins in a membrane are expected to have stronger interactions (of all sorts) than have lipids in the same membrane at a given intermembrane separation. The lateral separation of intrinsic membrane proteins in dehydrated vesicles and in the membranes of dehydrated protoplasts cited above has (at least) two possible explanations. Either the large repulsion among proteins causes the membrane to separate into a protein-rich phase and a protein-depleted phase, or else the membrane lipids separate into two distinct phases in which the proteins have differential solubility.

    The difference in the repulsive interaction among different species of lipid molecules can give rise to dehydration-induced lateral separations in lipid membranes. This has been observed in model systems: POPC and POPE[22] have very different hydration characteristics: POPC lamellae produce a much larger repulsion at a given separation than do POPE lamellae. In excess water and above the thermotropic phase transition temperatures of both, these two lipids are completely miscible. At 315 K and 10% water content, however, they separate into two fluid phases with different repeat spacings (55-57)[23].

    Hexagonal phases

    In their important early work on the structure of lipid-water phases, Luzatti and co- workers (59-62) showed that some lipid-water mixtures undergo a transition from lamellar to inverse hexagonal (HII) phase. The HII phase usually occurs at high temperatures, low water contents or a combination of both[24] (see review by Rand, 64). At sufficiently low hydrations, the transition temperature for some species may occur at sub-zero temperatures and the HII phase is thus relevant to cryobiology. In an electron micrograph study, Gordon-Kamm and Steponkus (45) correlated damage to protoplasts in suspension with the frequency of observation of arrays of cylinders resembling the HII phase (see footnote 20).

    Gruner and co-workers (65-69) have constructed thermodynamic models of the HII phase transition. They consider three effects which involve molecular geometry. First, the lipid-water interface has a spontaneous curvature, and for HII forming lipids this favours a surface slightly concave from the water side. Second, there is a large van der Waals attraction among the hydrocarbon tails of the lipids. Because of this attraction, any geometry which requires a vacuum in the hydrocarbon region of a phase must have a high energy, and so the length of a hydrocarbon chain thus specifies the maximum possible distance from the interface of any point in the hydrocarbon region. This effect forbids large cylinders. Finally, the formation of small cylinders requires dehydration and thus is only favoured at large suctions.

    The importance of aqueous solutes

    The Crowes and co-workers (70-72) and others (73) have implicated the presence of sugars (in particular the sugar trehalose) in the stability of membranes at low hydration. Trehalose, for instance, has been reported to preserve the functional integrity of vesicles prepared from sarco- plasmic reticulum.

    Aqueous solutes in high concentration have several effects.

    i) They lower the water activity. From eqn 3 this means that at any given chemical potential of water the pressure is less negative (i.e. the suction is smaller) and so the stress in membranes and macromolecules is smaller.

    ii) They increase the volume of the aqueous solution at any given chemical potential of water.

    This means that the separations among membranes and macromolecules are larger. From eqn 1 one would naively expect that this would reduce hydration forces, but the presence of solutes in large concentrations is likely to change hydrogen bonding in water (and thus l) and to change the water ordering near the interface (and thus Po). It is therefore not clear how much (or even whether) this effect would reduce hydration forces because the appropriate experiments have not, to our knowledge, been performed. An important effect of increased solution volume is that, all else equal, it opposes the formation of the HII phase24.

    iii) Some sugars have specific interactions with membrane-forming lipids. This has been observed by infra-red spectroscopy. It is possible too that such solute-lipid interactions may change the spontaneous curvature and/or curvature modulus of the interface. These effects are expected to change the lamellar-HII phase diagram. All else equal, HII formation would be opposed by any solute interaction which expands the interface, makes the spontaneous curvature less concave (from the water side) or which increases the curvature modulus. If the attraction between a solute and a lipid headgroup were comparable in strength to that between water and the headgroup, then at low water content (high solute concentration), the solute would replace the "water of hydration".

    iv) High concentration of solutes increases the viscosity of the solution (the viscosity is also increased at low temperature). If the viscosity is sufficiently high (1 to 100 TPa s), supersaturated or supercooled solutions may result and vitrification occurs (74). Water diffusion[25] out of a cell or organelle then becomes negligible and the resultant hydration may be rather higher than the equilibrium value. This higher hydration (all else equal) would impose smaller stress in membranes and macromolecules. The non-equilibrium solution may however freeze if sufficiently supercooled, or it may phase separate. The propensity of the solutes to crystalise or to nucleate ice formation then becomes important. The importance of glass formation in cryobiology is discussed by Franks et al. (74). A summary of the significance of glass formation in anhydrobiology is given by Burke (75).

    Several solutes, such as trehalose, sucrose, raffinose and glucose have been shown to inhibit desiccation damage to different degrees, while some others such as inositol appear to have little effect (70, 72, 76, 77). The inhibitory effects are therefore not simply due to the osmotic or volumetric effects (points i and ii above). These authors also used infrared spectroscopy to study the interaction between sugars and phosphate moieties in the lipid headgroups. They made the observation that those sugars which can inhibit desiccation damage exhibit strong interactions with the phosphate molecules in the lipid head groups, and that trehalose shows the strongest interaction.

    Another relevant parameter which varies for different solutions is the temperature at which vitrifications occurs. Attention has been focussed on trehalose, which shows the greatest protective capabilities, but which exists in only small quantities in some organisms. The next most effective of the sugars studied is sucrose. It exists in larger quantities in many organisms, but may crystallize in only moderately supersaturated solutions. Solutions of sucrose containing other dissolved sugars support greater supersaturation and it has been suggested that while sucrose may act as the principal vitrifier, other sugars, such as raffinose, may contribute by preventing sucrose crystallization (78-80).

    How does the presence of such solutes modulate short range forces and their effects? These solutes have a hydrogen bonding geometry that is different from that of water, and their polarizability is different. At low hydration, hydrated solutes may form a substantial volume fraction of the solution at the membrane surface. In this condition the polarization and solvent structure theories of hydration forces would predict substantial alteration of the effect. Solutes would also affect the protrusion forces of the Israelachvili and Wennerstrom model (4, 23) via their effects on the surface tension and (less directly) on the curvature moduli.

    This raises the question: do certain solutes act to stabilize membranes by reducing the repulsion at a given distance, and thus reduce the internal stresses in the membrane? If so, the partitioning of the solute at the interface, as well as its hydrogen bonding structure, would help to determine its effectiveness at maintaining membrane structure. The experiments that would help answer these questions have yet to be done. Perhaps that is another reason why cyrobiologists and anhydrobiologists should take a greater interest in large, short-range forces.


    The very large forces encountered at close separation, although usually irrelevant to the biology of the highly hydrated state, are important in cryobiology and anhydrobiology for at least three reasons:


    We thank Jacob Israelachvili, Karen Koster, Stjepan Marcelja, Adrian Parsegian and Peter Rand who kindly made available their unpublished papers. We also thank them for their helpful comments on an earlier draft of this paper, but imply no blame for anything in this one.
  • This paper was published as Cryo-Letters 13, 23-36 (1992).

    Joe Wolfe / /61-2-9385 4594 (UT+10,+11 Oct-Mar)

    See alsoBiophysical Cryobiology and Anhydrobiology


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  • Footnote 1 In turgid plant tissues, however, the plasma membrane and the inner surface of the cell wall are kept very tightly together by moderate (~MPa) hydrostatic pressures. back to text
  • Footnote 2 The term "stress" is often used metaphorically in biology. In this article it is used in its usual physical meaning of deforming force per unit area. back to text
  • Footnote 3 Although double layer forces are due to electric effects, one might argue that the forces themselves are not electric. If two similar surfaces approach, the volumes on either side of the plane of symmetry are electrically neutral. Rather the force is osmotic: the concentration of ions at this plane is changed (usually increased) and this changes the solvent activity (usually decreased) and this gives an osmotic pressure (usually repulsive). back to text
  • Footnote 4 Due to the interaction of transient dipoles.back to text
  • Footnote 5 Others attribute it to properties of the surfaces: more on this anon. back to text
  • Footnote 6 Large suctions are not usually possible in macroscopic volumes of water because the water cavitates. Cavitation is unlikely in the water in lamellar phases (or in geometrically similar intracellular structures) for two reasons. First, the cavitation nucleii are rarely present in such small volumes. Second, the thickness of the aqueous regions (a few nanometres or less) is small compared to the critical radius for cavitation for all but very large suctions. back to text
  • Footnote 7 LeNeveu et al. (2) use P for the repulsive force per unit area between membranes. The italic P is used here because P is used later to mean hydrostatic pressure, which is a more venerable convention. back to text
  • Footnote 8 The calculation is in fact more involved than simple subtraction, and the use of odd and even order standing waves allows determination of the refractive index as well. back to text
  • Footnote 9 These are not mutually exclusive. Any forces that depend non-linearly on separation will be magnified if the surfaces move about their equilibrium position. Surfaces exhibiting thermally excited modes on any scales would lead to larger measured solvation forces than would planar surfaces. back to text
  • Footnote 10 This poses the problem: what to call these very large forces? "Strong Forces" has already been taken, and in any case they are not that strong. They are, however, bloody big - indeed Israelachvili (personal communication) approves of "Bloody Big Forces" as a neutral and appropriate appelation. back to text
  • Footnote 11 Note that the free energy of an aqueous interface is often dominated by the entropic term resulting from restricted hydrogen bond configurations at the interface. back to text
  • Footnote 12 Strictly speaking, this argument would include interfacial interactions as hydration forces because all contribute to the free energy of approach. The hydration force is identified by elimination: it is the force remaining after all other effects are accounted for, or it is that part of the force whose explanation requires consideration of the structure of the solvent. back to text
  • Footnote 13 The "hydration" or "solvation" force applies not only to lipid-water systems, but to any liquid between polarising surfaces. back to text
  • Footnote 14 Boscovich argued in 1763 (31) that forces between bodies should oscillate with separation. back to text
  • Footnote 15 Sometimes a further component called the matric potential is included in the water potential . Passioura (36) points out that the definition of the matric potential usually involves a peculiar definition of either hydrostatic pressure or osmotic pressure. back to text
  • Footnote 16 In this equation, the component of osmotic pressure which is due to the presence of the membrane is, once again, implicitly included in P and not in PI. back to text
  • Footnote 17 Of course the surface forces apparatus measures the force directly, but it can only be used for model systems. back to text
  • Footnote 18 An extended single membrane in excess solution will buckle rather than support a positive lateral pressure. In lamellar phases subject to low hydration, buckling would not relax the stress and is opposed by inter- membrane repulsion. back to text
  • Footnote 19 The results from electron microscopy should however be used cautiously, as the sample preparation methods used can introduce artifacts which mimic low hydration phase behaviour, and can cause membrane damage. The Crowes supported their electron microscopic studies with studies of lipid motion and orientation using 31P Nuclear Magnetic Resonance. back to text
  • Footnote 20 The distinction between a stack of inverted cylindrical micelles and a region of inverse hexagonal phase is an important one at the experimental level. A simple homogeneous mix of lipids and water may give a hexagonal phase with a high degree of long range order, and thus a clear X-ray diffraction pattern. A relatively small collection of inverse cylindrical micelles in a deyhdrated cell may have similar local geometry, and is therefore often called HII, but it will have only short range order and so its geometry cannot be readily obtained from X-ray diffraction. back to text
  • Footnote 21 Membrane phase properties are also dependent on temperature, of course. Thermotropic phase behaviour has been extensively reported elsewhere (see e.g. the review by Williams, 46) and need not be discussed in a review of short range forces. back to text
  • Footnote 22 Palmitoyloleoylphosphatidylcholine and palmitoyloleoylphosphatidylethanolamine respectively. back to text
  • Footnote 23 Tamura-Lis et al. (58) also report a fluid-fluid phase co-existence which may be a result of the same phenomenon. back to text
  • Footnote 24 Though see also Gawrisch et al. (63) who report a transition from HII to lamellar to HII with increasing temperature or with increasing hydration. back to text
  • Footnote 25 Vitrification therefore also severely restricts metabolic processes which require diffusion, and thus explains the near total suspension of animation in the dehydrated or frozen state. back to text
    This paper was published in Cryo-Letters 13, 23-36 (1992). For more recent reviews, see
  • Wolfe, J. and Bryant, G. "Cellular cryobiology: thermodynamic and mechanical effects" International Journal of Refrigeration, in press; and
  • Wolfe, J. and Bryant, G. (1999) "Freezing, drying and/or vitrification of membrane-solute-water systems" Cryobiology, 39, 103-129.