INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND ANALYSIS DISCUSSION AND CONCLUSIONS APPENDIX REFERENCES

The majority of phospholipid acyl chains in animal cell membranes are saturated (only C---C bonds) or monounsaturated (one C==C bond) hydrocarbon polymers. Consequently, phospholipid bilayers with saturated or monounsaturated chains have been studied extensively, which includes the gel-to-liquid crystalline phase transitions that are prominent for saturated PC bilayers above 0°C in aqueous environments. Interestingly, to ensure that membranes of eukaryotic cells remain fluid (yet maintain strong, nearly impermeable interfaces), nature seems to have preferred cholesterol as a co-constituent even though polyunsaturation can also keep bilayers fluid to below water freezing temperatures. A simple rationale for not choosing polyunsaturated lipids is that they oxidize easily and would be chemically expensive to keep in membranes. But surprisingly, there are membranes rich in polyunsaturated lipids, as in brain tissue. Lipid polyunsaturation is not the only distinguishing feature of these special membranes; there are usually significant variations in chain lengths and differences in cholesterol content. Even so, we are compelled to ask how such labile and exotic lipids affect the material characteristics of membranes? Here, we report measurements of dynamic material propertiesmechanical rupture strength and water permeabilityof fluid diacyl phosphatidylcholine PC bilayers with equal chain lengths of 18 carbons and a wide range of unsaturation (1, 2, 4, or 6 double bonds per lipid). In a companion article (Rawicz et al., 2000), we present measurements of equilibrium elasticand thicknessproperties of the same PC bilayers. In both studies, we have used micropipette aspiration methods to directly measure membrane mechanical properties and permeability to water on giant-single bilayer vesicles. In this study, the results show that polyunsaturated PC bilayers are much more permeable and much weaker than the prototypical monounsaturated lipid bilayer.

Several techniques have been used to quantitate mechanical stretch properties of bilayers, which include the micropipette approach we have pioneered for giant vesicles (Kwok and Evans, 1981; Evans and Needham, 1987), photon correlation spectroscopy and dynamic light scattering of small vesicles under osmotic stress (Rutkowski et al., 1991; Hallett et al., 1993), cryoelectron microscopy of vesicles subjected to osmotic stress (Mui et al., 1993), nuclear magnetic resonance NMR and x-ray diffraction of strongly dehydrated multibilayer arrays (Koenig et al., 1997), plus others. Of these approaches, only the micropipette method can provide measurements of bilayer stretch on a single vesicle with a resolution of better than 0.1% relative change in area, test elasticity and reversibility, plus determine instantaneous tension and area dilation at rupture. In comparison to mechanical properties, permeability of bilayers to water has a long history embodied in numerous references describing a variety of measurements from osmotic filtration to isotope diffusion (Finkelstein, 1987, covers many of the important concepts and early work; recent contributions include Paula et al., 1996, and Huster et al., 1997). A prominent feature of water permeability measurements has been the significant variation in values obtained by different techniques and different laboratories. For instance, in early work on permeability of egg PC bilayers (similar to C18:0/1 PC tested here), the values of water permeability ranged from 10 to 50 µm/s (Fettiplace and Haydon, 1980). Likewise, permeability coefficients for osmotic filtration in some studies exceeded the values of permeability derived from tracer diffusion (Jansen and Blume, 1989) whereas in others, no difference was found between results with the two methods (Finkelstein, 1987; Ye and Verkman, 1989). More than experimental aesthetics, careful comparison of these two types of permeability measurement is expected to reveal important insights as to the mechanism of transport (Finkelstein, 1987; Paula et al., 1996; Xiang and Anderson, 1997). In our tests, the goal has been to expose the impact of polyunsaturation on permeability of single bilayers to water. Our approach has been to use micropipette aspiration of giant unilamellar vesicles and manipulation into a hyperosmotic environment as a simple technique to measure water filtration. The unique feature of the method is that it provides direct observation of water filtration across a single solvent-free and unsupported bilayer, which can be easily analyzed to obtain the coefficient for bilayer permeability to water.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND ANALYSIS DISCUSSION AND CONCLUSIONS APPENDIX REFERENCES

Lipids

Eight synthetic species of diacyl C18 PC lipids were obtained from Avanti Polar Lipids (Alabaster, AL) in chloroform and used without further purification. Seven were cis unsaturated: 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (C18:0/1_c9); 1-oleoyl-2-stearoyl-sn-glycero-3-phosphocholine (C18:1_c9/0); 1,2-dipetroselinoleoyl-sn-glycero-3-phosphocholine (diC18:1_c6); 1,2-dioleoyl-sn-glycero-3-phosphocholine (diC18:1_c9); 1-stearoyl-2-linoleoyl-sn-glycero-3-phosphocholine (C18:0/2_c9,12); 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (diC18:2_c9,12); and 1,2-dilinolenoyl-sn-3-phosphatidylcholine (diC18:3_c9,12,15). One was trans unsaturated: 1,2-elaidoyl-sn-glycero-3-phosphocholine (diC18:1_t9). The solutions were placed in amber glass screw-cap vials with Teflon-lined silicone septa. Especially important for the preservation of the oxidation-prone fatty acid chains (C18:0/2, diC18:2, and diC18:3), the vials were wrapped in aluminum foil and stored at 20°C under argon.

Vesicle preparation and assay of lipid oxidation

In our laboratories, the generic procedure for preparation of giant vesicles (15-30 µm diameter) is to rehydrate lipid films dried first from chloroform/methanol (2:1) onto the surface of a roughened Teflon disk (Needham et al., 1988). After deposition of the lipid film and evaporation of the organic solvent in vacuo, the Teflon disk is covered with a warm (37°C) sucrose solution (200 mOsm) and allowed to hydrate. To create a refractive index contrast between inside/outside of vesicles and to sediment vesicles in the microscope chamber, an aliquot of vesicles is diluted manyfold in an equiosmolar solution of glucose or electrolyte buffer. The refractive index gradient is used to enhance optical detection of the projection length inside the pipette as shown by the example in Fig. 1. Described below, accurate video tracking of the projection edge enables discrimination of <0.1% relative change in vesicle area or volume, even though optical measurements of total area and volume remain limited to a few percent accuracy by diffraction. For formation of vesicles from polyunsaturated lipids, slight modifications were made in the procedure. First, argon-purged, deionized water was used to make the hydration and suspension solutions. Second, the container with the polyunsaturated lipid film was wrapped in aluminum foil (to minimize exposure to light). The polyunsaturated lipids were allowed to hydrate for only three hours under argon and used immediately (normally, lipids are left to hydrate overnight then used the next day). At the beginning of the study, samples of the polyunsaturated lipids were tested for possible oxidative damage over the time scales associated with preparation and experiment by spectrophotometric assay (Kim and LaBella, 1987; New, 1990). The absorbance of a solution of 1 mM lipid in absolute ethanol was measured at ~230 nm using a Beckman DU-7500 diode-array spectrophotometer (Beckman, Fullerton, CA). Absorption at this wavelength indicated the presence of conjugated dienes in the hydrocarbon chain, which result from oxidation (Kim and LaBella, 1987; New, 1990). Lipid samples used soon after arrival from Avanti showed no detectable oxidative damage. Moreover, measurements of properties repeated with preparations from the same polyunsaturated lipid samples and from new samples purchased at later times gave identical results.

View larger version (88K): [in this window] [in a new window]   FIGURE 1   Video micrograph of a single bilayer vesicle (diameter ~20 µm) held by micropipette suction.

Mechanical expansion and rupture of vesicle bilayers

Micropipette suction was used to pressurize vesicles and stretch bilayers to rupture. Well-established from mechanics (Kwok and Evans, 1981), suction pressure P applied to a fluid-bilayer vesicle produces a uniform membrane tension _m, which is described by a simple geometric relation based on the pipette caliber (diameter) D_p and diameter D_v of the vesicle-spherical segment exterior to the pipette, i.e.,
The pipette suction (~10³ Pa) needed to expand the area of a ~20 µm vesicle is small compared to osmotic driving forces (~10⁵ Pa) required to kinetically displace water on the time scale of the experiment and small compared to the osmotic activity of the trapped sucrose (~5 × 10⁵ Pa). Thus, vesicle volume remains effectively fixed in the area expansion test. Increase of the aspirated projection length L_p inside the pipette provides a direct measure of the area expansion. Precise changes in area A with displacement L_p of the projection length in experiments were computed numerically as described in the Appendix. The proportionality between area and length is easily seen in the following first-order approximation:
Backed by this analysis, the following simple procedure was used to test membrane strength and maximum dilation. The vesicle was first prestressed under a tension of ~0.5 mN/m to incorporate hidden-excess area. Then, pipette suction was increased in stepseach held steady for several secondsuntil lysis occurred (total pressurization time of <1 min) at pressures of ~1-5 × 10³ Pa, where tensions reached the range of 3-10 mN/m for lysis, depending on the lipid.

Osmotic filtration of water from single vesicles

To measure bilayer permeability to water, single vesicles were selected by a micropipette and transferred to an adjacent microscope chamber with ~10% higher solute concentration. In the new environment, water was driven out of the vesicle by strong osmotic forces (>10⁵ Pa) to achieve equilibrium. The time course of vesicle dehydration was tracked and analyzed to obtain the transport coefficient for water filtration. To transfer a vesicle through the small air gap that separated the microscope chambers, the vesicle was maneuvered into the entrance of another larger pipette. The microscope stage was then translated to leave the sheltered vesicle in the second chamber, where it was brought out into the new environment. Typically, vesicles were transferred from a chamber that contained a 200 mOsm glucose solution to a chamber that contained a hypertonic (220 mOsm) glucose solution. However, specific tests were also performed at twofold higher osmolarities to verify the expected proportionality between filtration rate and level of osmolarity. Transfer back to the original chamber was used to verify that the water exchange was recoverable and that no sucrose solute escaped or glucose solute entered the vesicle. Throughout the test, the vesicle was held under small fixed suction pressure to control bilayer tension (~1 mN/m). Thus, changes in vesicle volume occurred at constant area and were computed precisely from displacements of the projection length inside the pipette, as described in the Appendix. The proportionality between change in volume V and displacement L_p of the projection length is demonstrated by the first-order approximation:
Displacement of the projection length of an aspirated vesicle under osmotic dehydration is shown in Fig. 2

View larger version (90K): [in this window] [in a new window]   FIGURE 2   Video micrographs of a single bilayer vesicle during the course of dehydration in a water filtration experiment. The increase in aspiration length inside the pipette is proportional to the reduction in vesicle volume.

	RESULTS AND ANALYSIS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND ANALYSIS DISCUSSION AND CONCLUSIONS APPENDIX REFERENCES

Water permeability

Measurements of aspiration length versus time after transfer of vesicles to a hypertonic environment were used to quantitate water filtration over the course to a new state of osmotic equilibrium. Fig. 3 shows the time dependence of vesicle dehydration followed by rehydration (when returned to the original chamber), which illustrates both approach to osmotic equilibrium and reversibility. The kinetics of the time course were analyzed with the standard phenomenological law for water transport across a semipermeable membrane and the dilute concentration approximation for osmotic activity (Finkelstein, 1987). As such, the rate of change in vesicle volume per unit of surface area A is governed by the bilayer permeability coefficient P_f and the outside-inside difference c in osmolarity, according to
where _w is the molar volume of water (18 ml/mol). Because the membrane is impermeable to solutes (on the time scale for water filtration), the instantaneous osmolarity of the vesicle interior is set by the number of moles m of solute and the volume, i.e., c = m/V. Scaling instantaneous volume by the final equilibrium volume V, we obtain a dimensionless kinetic equation for the time course to the new equilibrium state,
with definitions of V* = V/V and c equal to the final osmolarity. Relative to the dimensionless volume V_o^* at time t = 0, the time course obeys the following transcendental equation:
with the time rate of decay set by k = A(P_fc_w)/V.

View larger version (15K): [in this window] [in a new window]   FIGURE 3   Evolution of vesicle volume with time in a water filtration experiment. The first phase shows dehydration in response to transfer from a 200 mOsm glucose solution into a hyperosmotic (220 mOsm) glucose solution. The second phase demonstrates the full recovery of volume after return to the original solution around ~300 s. Here, the vesicle bilayer was composed of C18:0/1 PC and tested at 18°C. From measurements of vesicle dimensions inside and outside the pipette, the area of the vesicle was calculated to be ~1940 µm2, and the volume was ~11,200 µm3.

Using a nonlinear fitting algorithm, this equation was matched to the time-dependent change in volume of each vesicle tested, which yielded the time constant 1/k for approach to osmotic equilibrium. From each value of the decay constant we obtained an apparent measure of the permeability coefficient (P_fapp). As seen above, the time constant for volume changes scales inversely with the osmolarity of the environment. This intrinsic feature was verified in separate tests where a twofold increase in osmolarity reduced the time constant by exactly a factor of one-half, as expected. Measurements of apparent water permeability (P_fapp) were performed on at least 10 vesicles for each type of lipid. The results (±SD) are listed in Table 1 and plotted as a histogram in order of increasing unsaturation in Fig. 4. The apparent permeabilities were found to increase modestly with mono- and dimono-unsaturation, but incorporation of alternating cis-double bonds led to a significant augmentation of permeability. The semi-log plot in Fig. 5 demonstrates that log(apparent permeability) varies linearly with the reduced temperature of each lipid relative to the gel-liquid crystalline phase transition temperature reported in the literature (Table 1).

View this table: [in this window] [in a new window]   TABLE 1   Rupture tension *m and apparent permeability Pfapp to water measured at 21°C on single-bilayer vesicles made from polyunsaturated PC bilayers

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Coefficients of apparent water permeability for polyunsaturated PC bilayers measured by osmotic filtration at 21°C.

View larger version (16K): [in this window] [in a new window]   FIGURE 5   Log(apparent water permeability) versus reduced temperature Tr = (T  Tm)/Tm for polyunsaturated PCs at 21°C. The reduced temperatures are based on the literature values listed in Table 1 for gel-to-liquid crystalline phase transition temperatures (Tm).

Because of diffusion through unstirred layers adjacent to the bilayer, the prominent increase of permeability seen for the most unsaturated lipids (diC18:2 and diC18:3) was expected to be even more pronounced than revealed by the measurements of P_fapp. Conservatively, the added impedance is estimated by the ratio of a diffusion length set by the vesicle radius R_v = D_v/2 (~10 µm) to the diffusivity D_w of water (~3 × 10³ µm²/s), which implies that 1/P_fapp  1/P_f + R_v/D_w (Finkelstein, 1987; Goldstein and Dembo, 1995). Based on this approximation, unstirred layers should be significant for a ~20-µm-size vesicle made from diC18:3 PC because the estimated value of P_f ~ 284 µm/s is much larger than the measured value P_fapp ~ 146 µm/s. To test the significance of unstirred layers, a separate set of experiments was performed where the apparent permeabilities of diC18:3 vesicles were measured over the widest possible range of vesicle sizes 2R_v ~15-60 µm. The reciprocal values 1/P_fapp are plotted as a function of radii in Fig. 6. Surprisingly, the data in Fig. 6 show a more modest increase in apparent permeability with reduction in vesicle size than predicted by the simple model. Based on the linear fit to the data shown in Fig. 6, the unstirred layer impedance was found to be ~(0.0001 s/µm²)R_v, which is threefold lower than the value given by R_v/D_w. Thus, the permeability coefficients corrected for unstirred layers would increase from P_fapp ~ 90 µm/s to P_f ~ 100 µm/s for diC18:2 and from P_fapp ~ 146 µm/s to P_f ~ 170 µm/s for diC18:3, with negligible impact on the permeability coefficients measured for the more saturated PCs.

View larger version (15K): [in this window] [in a new window]   FIGURE 6   Measurements of apparent water permeability for single vesicles composed of diC18:3 PC (at 18°C) plotted as a function of vesicle radius. The linear regression line implies the unstirred layer impedance is ~0.0001 s/µm2 × Rv.

Rupture strength

Ramped upward until the vesicle ruptured, pipette suction was used to establish the tension limit for bilayer strength. The rate of tension loading was ~0.1 mN/m/s. Cumulated from tests of at least 10 vesicles for each lipid type (listed in Table 1), Fig. 7 presents a histogram of the rupture tensions _m^* (±SD) for PC bilayers arranged in order of increasing unsaturation. For bilayers with up to one unsaturated-double bond per chain, rupture strength varied little from _m^* ~ 10 mN/m. However, rupture tensions of bilayers with two or more alternating cis-double bonds (C==C---C==C) in one or both chains dropped precipitously to _m^* ~ 5 mN/m for C18:0/2, diC18:2, and even weaker_m^* ~ 3 mN/mfor diC18:3. Moreover, the direct stretch moduli of the bilayers were found to vary by <±10% from a mean value of K_A = 243 mN/m (see Rawicz et al., 2000); so the fractional changes in area of bilayers at rupture * = _m^*/K_A also dropped commensurately from a value of *  0.04 to *  0.02 (or *  0.012 for diC18:3). Clearly, two or more alternating cis-double bonds make the bilayer distinctly weaker than bilayers of mono- and dimono-unsaturated PCs.

View larger version (19K): [in this window] [in a new window]   FIGURE 7   Lysis tensions for vesicles with polyunsaturated PC bilayers.

	DISCUSSION AND CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND ANALYSIS DISCUSSION AND CONCLUSIONS APPENDIX REFERENCES

Water permeability

Because of the sensitivity to changes in vesicle volume, aspiration into a micropipette provides a precise method to measure the transport coefficient (permeability) for water filtration across a single bilayer. Tested experimentally, impedance to filtration from unstirred layers was found to be much less (~0.0001 s/µm² × R_v) than predicted by the ratio of vesicle radius to water diffusivity (~0.0003 s/µm² × R_v). As such, a bilayer permeability coefficient of ~200 µm/s defines a reasonable upper bound accessible to measurement by the micropipette technique in the absence of some type of convective mixing (e.g., using an auxiliary pipette to blow solution past the vesicle). Calculated from the time course of osmotic filtration for each vesicle, the apparent permeabilities at 21°C varied modestly between 28 and 42 µm/s for mono- and dimono-unsaturated PC bilayers. Within this range, there were only subtle variations associated with position and trans or cis configurations of the double bond. However, the most striking result was that two or more alternating cis-double bonds along a chain led to major increase in apparent permeability of bilayers to water (~49 µm/s for C18:0/2, ~90 µm/s for diC18:2, and ~146 µm/s for diC18:3 at 21°C). A similar impact of unsaturation on water permeability was found by Huster et al. (1997). However, their values of permeability coefficient differ significantly from our measurements in Table 1. Using NMR spectroscopy to follow exchange of ¹⁷O across membranes of ~100-nm-size vesicles, the measurements of Huster et al. give values of ~123 µm/s for C18:0/1, ~97 µm/s for diC18:1, and ~261 µm/s for the asymmetric C18:0/3 at 21°C. The puzzling feature is the large (~3-fold) discrepancy between their values and our values for the mono- and dimono-unsaturated PC bilayers under conditions where unstirred layer effects were completely negligible in both types of experiments. A similar discrepancy exists between our measurement of permeability coefficient (~42 µm/s at 21°C) for diC18:1 and the value of ~150 µm/s obtained by Paula et al. (1996), albeit measured at 30°C. Based on the activation energies for diC18:1 given in Huster et al. (1997), the value at 21°C would only reduce to ~91 µm/s, which remains far from our value of 42 µm/s. In comparison, Finkelstein measured the permeability of planar egg PC bilayers to water at 25°C and obtained a value of ~22 µm/s, which is consistent with the value of ~28 µm/s we found for the closely related C18:0/1 at 21°C. Most intriguing, the values of log(apparent permeability) from our measurements yield a linear correlation with the reduced temperatures of these lipids relative to the gel-liquid crystalline phase transition temperatures reported in the literature, as shown in Fig. 5. The exponential rise in permeability with increase in reduced temperature implies that free volume in the hydrocarbon region increases significantly under thermal expansion of area per lipid above the gel-liquid crystalline phase transition. This is consistent with the concept emphasized by Xiang and Anderson (1997) that the partition of solutes (water) in the hydrocarbon region is strongly effected by chain-ordering, which diminishes progressively with reduced temperature in bilayers.

Rupture strength

Measured under a ramp of tension at a rate of ~0.1 mN/m/s, mono- and dimono-unsaturated PC bilayers ruptured at nearly the same level of tension, ~10 mN/m. But as seen in Fig. 7, there was an major drop in bilayer strength to ~3-5 mN/m when the number of unsaturated bonds in one or both hydrocarbon chains was increased from one to two or more. Although these measurements at a single rate provide a comparative assay of bilayer strength, it is important to recognize that strength is a dynamic material property that will change with the period of time subjected to different levels of tension set by tension loading rate. This follows from the accepted view that rupture of a fluid membrane emanates from formation of unstable pores. The theory for rupture pore nucleation was first proposed by Deryagin and Gutop (1962) for breakdown of thin films and is a 2-D version of the classic theory for cavitation in 3-D liquids introduced by Zeldovich (1943) a generation earlier. In this dynamical theory, the membrane is modeled as a simple elastic continuum where the energetics of an open hole (radius r) involve a constant-edge energy  (energy/length) × hole perimeter 2r and the applied mechanical potential _m (r²) as expressed by E(r) = (2r)  _m(r²). From the model, we see that edge energy is the material property responsible for membrane strength. More subtly, however, membrane rupture is a kinetic process where the events are governed by thermally activated nucleation and thus depend on a tension-mediated energy barrier, E* = ²/_m, which changes with time. Hence, time of exposure to changing levels of tension is important in the determination of bilayer strength. Too lengthy to report here, we have recently tested the dependence of rupture tension on the time scale used to apply tension to a vesicle for most of these unsaturated PC bilayers (Evans and Ludwig, 2000). Although the results confirm the kinetic nature of the rupture process when examined over 10,000-fold change in time scale, the measurements of rupture tension varied little in the range of plus/minus an order of magnitude above/below the rate of ~0.1 mN/m/s used in this study. Thus, the lysis tensions given in Table 1 and Fig. 7 represent the levels of strength to be expected for polyunsaturated PC bilayers with 18-carbon chains in most practical situations.