INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION REFERENCES

Lipid energetics are important in cell signaling, protein transport, metabolic regulation, endocytotic and exocytotic events, viral fusion, and other cellular processes (Nagle and Scott, 1978). Isolated lipids form a veritable menagerie of liquid crystal structures when hydrated and their phase behavior is valuable for studying biological membranes (Tardieu et al., 1973). In recent years, a great deal of attention has been given to the lamellar/inverse-hexagonal (L-H_II) phase transition, because an understanding of this transition is believed to be vital to understanding membrane fusion (Kuzmin et al., 2001) and interactions with membrane proteins (Brown, 1997). The close regulation of membrane lipid composition by a wide variety of organisms provides strong support for this view (Hazel and Williams, 1990).

The first step in determining thermodynamic properties of a system is to measure the phase diagram as a function of relevant variables, such as the temperature. By symmetry considerations, the L-H_II transition is expected to be first order, and, therefore, at constant pressure should occur at a well-defined temperature, T_LH. A very commonly studied lipid that undergoes the L-H_II transition is 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE), which is used both because it is readily available and because T_LH is conveniently between 0°C and room temperature (Rand and Fuller, 1994). DOPE is also of considerable biological interest and affects a range of cellular functions including protein translocation (Rietveld et al., 1995).

T_LH of fully-hydrated DOPE (DOPE in coexistence with a bulk water phase) has been measured by a variety of methods, including differential scanning calorimetry (DSC), nuclear magnetic resonance (NMR), x-ray diffraction (XRD), Fourier-transform infra-red spectroscopy (FTIR), and fluorescence (FL) as detailed in Table 1. Despite the years of interest on this lipid and multiple experimental techniques, the resultant literature values range from 4 to 16°C (Koynova and Caffrey, 1994). This wide range of uncertainty about the true transition temperature limits the utility of DOPE thermodynamic data. Similar ambiguities plague almost all mesomorphic lipid phase transitions, with the result that the phase diagrams of most lipid-water systems are poorly known.

View this table: [in this window] [in a new window]   TABLE 1   Determinations of the L:HII phase transition temperature

The wide range of published T_LH values is a consequence of the kinetically hindered nature of the L-H_II transition, with the consequence that the temperature at which the transition occurs is dependent upon the rate at which the temperature is changed. Even temperature changes of only a small fraction of a degree per day are insufficient to obtain the true equilibrium phase (Tate et al., 1992), which limits the use of almost all methods used to directly determine T_LH. The physical basis for the kinetic barriers between the lamellar and inverse hexagonal phases arise from the very different geometry of the water-lipid interfaces in the two phases (Fig. 1). There is no simple path for the lipid-water interfaces to transform between the phases without tearing and reorganizing, which implies that the transition involves substantial exposure of the hydrocarbon chains to water. Such topologically hindered transitions are very common with biomembrane lipids and, more generally, are also seen with other amphiphilic systems, such as diblock copolymers. These phase transitions typically exhibit hysteresis, that is to say, the apparent phase transition temperature upon heating is higher than upon cooling. Another characteristic is that the amount of hysteresis generally increases with the degree of segregation of the amphiphile molecules, which may be readily understood in terms of the free energy cost of exposing one part of the amphiphile to the environment of the other. Thus, short lysolipids tend to exhibit less hysteresis than long-chain lysolipids, which, in turn, have less hysteresis than long-chain diacyl lipids (Tenchov, 1991).

View larger version (50K): [in this window] [in a new window]   FIGURE 1   Lipid organization in the lamellar liquid (L) and (HII) phases (Tate, 1987). In both phases, lipid molecules are arranged such that the polar headgroups (circles) form an interface separating the water (gray region) from the oily hydrocarbon tails.

The goal of this study is to accurately determine T_LH for DOPE by examining the systematic behavior of the directly measured, apparent rate-dependent transition temperature, T_A(r), upon the rate of temperature change, r. This approach was inspired by analogous studies on block copolymer systems (Ryu and Lodge, 1999). The method, which has been developed here, is generally applicable to other lipid systems.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION REFERENCES

Sample preparation

DOPE was obtained from Avanti Polar Lipids (Alabaster, AL) and used without additional purification. A clean stock solution of DOPE was prepared by solubilization in spectrophotometry grade cyclohexane obtained from Fisher Scientific (Fair Lawn, NJ) (100 mg DOPE:1 ml cyclohexane) and stored at 70°C. Lipid purity was checked before and after data collection by thin layer chromatography.

Individual samples were prepared by lyophilizing 5 mg of DOPE in a narrow (d = 2.5 mm) glass tube. Ten microliters of deionized water was added, and the sample homogenized by five freeze-thaw-mixing cycles. In each cycle, samples were frozen at 70°C, warmed to room temperature, centrifuged for 5 min and mechanically mixed for 5 min with a 10-µL Drummond Microdispenser (Broomall, PA). The resultant lipid gel was transferred to an acid-cleaned 1 mm glass x-ray capillary (Charles Supper, Natick, MA) and 5 µL excess water added on top before sealing with a layer of vacuum grease backed with an epoxy plug. A small air bubble was used to separate lipid and the sealing materials. Prior to data collection, samples were cycled an additional 5 times between 20°C and 20°C. Each cycle lasted for approximately 10 min.

Thermal cycling protocol

Previous studies of DOPE phase behavior showed that sample history is reset by cooling well into the L phase (Shyamsunder et al., 1988). Each thermal cycle commenced with 30 min equilibration at T_min = 20°C. X-ray diffraction data were gathered as the temperature was progressively incremented (T = 0.1°C) to T_max = 20°C. After 30 min equilibration at T_max, the temperature was decremented back to T_min. For both temperature increments and decrements, the maximum and minimum rates of temperature change were r = 6.25 × 10² and 5.9 × 10⁵°C/s, respectively. For slow scans, the sample temperature was ramped at an intermediate scan speed of r = 2.5 × 10⁴ for |T  T_LH| > 5°C. Temperature stability was better than 0.05°C as measured with a second resistance temperature detector (RTD) used in place of the sample.

X-ray scattering

Small angle x-ray scattering (SAXS) data were obtained using an RU-200 Cu rotating anode X-ray generator (Rigaku, The Woodlands, TX) directed through a nickel filter and single Franks mirror (q_min = 0.025 Å¹). The flux at the sample was 2 × 10⁷ Cu K x-rays ( = 1.54 Å) per second (Tate, 1987). The sample stage temperature was measured with a platinum RTD sensor (Omega Inc., Stamford, CT) and regulated with a water-cooled Peltier device operating within the beamline vacuum. Eight-second exposures provided sufficient scattering intensity and the read-out from the home-made CCD area detector (Tate et al., 1997) also took 8 s. This set the maximum thermal scan rate at 16 s per temperature step.

Visualizing phase transitions

Because the sample consists of many small, randomly-ordered crystallites, the scattering intensity per unit area, I(q), may be averaged radially as a function of the scattering vector magnitude, q = 4 sin()/, where 2 is the total scattering angle. The H_II phase scatters into peaks with a q-spacing ratio of 1::2 while the L phase scatters into peaks with a ratio of 1:2:3.

Sample diffraction for a thermal scan was visualized with false-color images as shown in Fig. 2. Using color to represent I(q), scattering is recorded as a function of q and temperature, T. Horizontal slices show the evolution of scattering at a given q mode, whereas vertical slices of the image show sample ordering at a particular temperature. The scattering signatures of the lamellar and hexagonal phases are distinct.

View larger version (70K): [in this window] [in a new window]   FIGURE 2   log(I(q)) plotted in false color as a function of q and T for (A) heating and (B) cooling at a rate of r = 2.86 × 104°C/s. A vertical slice at temperature T shows the scattering from the sample at that temperature. The phase composition of the sample may be directly determined from the scattering pattern. For the heating scan (A), the L-L transition occurs at T  9°C and the L-HII transition at T  6°C. Upon cooling (B), the HII-L transition is at T  0.5°C and the L-L transition occurs at T  12°C.

Determining apparent transition temperatures

Figure 2 shows that transitions occur over a finite range of temperature. The fraction, f, of the sample in a given phase is proportional to the x-rays scattered into diffraction peaks of that phase. Figure 3 shows the integrated scattering of the H_II phase peaks for heating and cooling. The scattered intensity for a given phase component is normalized relative to the signal when 100% of the sample is in that phase. The finite temperature range, T_A, for conversion demands a functional definition of the apparent transition temperature, T_A. For the purposes of this analysis, T_A is defined as the temperature when 50% of the sample has entered the final phase. T_A is defined using the 75% occupancy of the initial and final phases. For heating, at T = T_A  T_A, 75% of the sample is in the initial phase, but, when T = T_A + T_A, 75% of the sample is in the final phase. These points are all marked on Fig. 3. For each thermal cycle, an apparent transition temperature for heating, T_A and for cooling, T_A is assigned along with transition widths T_A and T_A.

View larger version (29K): [in this window] [in a new window]   FIGURE 3   Normalized intensity of HII phase peaks versus temperature for heating () and cooling () at r = 2.86 × 104°C/s. On heating, 50% conversion occurs at TA = 6.11 ± 0.64°C, whereas, on cooling, TA = 1.03 ± 0.76°C. The transitions are marked with solid lines and the 25-75% range is marked with dotted lines.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION REFERENCES

Figure 4 shows T_A as a function of r. For a given scan rate, the apparent transition temperature on heating, T_A, and apparent transition temperature on cooling, T_A, were found to be independent of sample used or number of thermal cycles. Transition hysteresis is pronounced but the weak dependence on scanning rate rules out Arrhenius-type kinetics. The broad range of applied temperature rates and the symmetry between heating and cooling hysteresis permits a determination of T_LH by extrapolation.

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Apparent transition temperature, TA, versus rate of heating/cooling, r. Heating scans are marked as () and cooling scans are marked as (). Error bars represent the 25% and 75% mark of the transition. The fitted line is of the form, TA = TLH ± r where TLH = 3.33 ± 0.16°C,  = 0.2401 ± 0.0060 and  = 18.41 ± 0.71°C1s.

Determination of T_LH

Determining the limits, lim_r0T_A(r) = T_LH or lim_r0T_A(r) = T_LH directly requires a specific model for hysteresis. Much can be determined, however, without resorting to particular models. At the limit r = 0, T_A(r) = T_A(r). T_A and T_A are likely to satisfy the relation,

(1)

making T_A a single-valued function of T_A. The intersection of this derived function, T_A(T_A), with the line T_A = T_A is the transition temperature, T_LH.

Figure 5 is a plot of T_A versus T_A for each thermal cycle. Cooling data range from 6.7°C < T_A < 1.6°C whereas transitions on heating occurred between 5.3°C < T_A < 13.4°C. To determine T_LH, the curve T_A(T_A) must be extrapolated 20% beyond the measured range. The function is well approximated by a straight line and a least-squares fit is shown on Fig. 5. Extrapolating the fit yields T_LH = 3.33 ± 0.16°C. Direct measurements only limit the transition temperature to 1.6°C < T_LH < 5.3°C, and even at low scan speeds T_A exhibited a width of T_A = 0.8°C.

View larger version (19K): [in this window] [in a new window]   FIGURE 5   Apparent transition temperature on heating, TA, versus apparent transition temperature on cooling, TA. A linear extrapolation of TA (solid line) to intersect the line TA = TA (dashed line) gives a transition temperature of TLH = 3.33 ± 0.16C. The slope of the extrapolation is 0.961 ± 0.051.

Cycle hysteresis

There are many mechanisms that cause hysteresis in first-order phase transitions, each producing a functional dependence on scanning rate. Figure 6 shows loop hysteresis |T_A(r)  T_A(r)| as a function of r. Reduction of the scan rate by 1.06 × 10³ only diminished |T_A  T_A| by a factor of 4.5 ± 1.0. Hysteresis over the entire range is well fit by the equation,

(2)

where  = 18.4 ± 0.7C¹s and  = 0.2401 ± 0.0060. The root mean square variation for a given cycle from the power-law fit is only 6.4%.

View larger version (16K): [in this window] [in a new window]   FIGURE 6   Loop hysteresis, |TA  TA|, versus rate of heating or cooling, r. The log-log plot fit has a slope of 0.2401 ± 0.0060 and an intercept of 36.8 ± 1.4°C. Slowing thermal scan speed by 16× reduces transition hysteresis by only 2×.

Symmetry of heating and cooling

The L  H_II and H_II  L kinetic pathways may be compared by studying T_A(r) and T_A(r) as shown in Fig. 4. Remarkably, both transitions fit the functional form,

(3)

where T_LH = 3.33 ± 0.16°C,  = 0.2401 ± 0.0060, and  = 18.41 ± 0.71°C¹s. Neither L  H_II nor H_II  L kinetics show significant systematic deviation from this power-law relationship.

Transition width

T_A has a clear dependence on scan rate r. The transition width, T_A, is not so predictable, as Fig. 7 illustrates. On average, T_A should be a monotonic increasing function of r. No such broad trend is evident, although, for heating rates above r = 10²°C/s, the transition width does seem to grow.

View larger version (16K): [in this window] [in a new window]   FIGURE 7   Width of transition, TA, versus rate, r, for heating () and cooling (). No universal trend is prevalent, suggesting that sample inhomogeneity may dominate transition width.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION REFERENCES

Comparison to previous values

By extrapolation, T_LH = 3.33 ± 0.16°C for fully hydrated DOPE. The finite transition width T_A observed for all thermal ramping speeds is the dominant source of uncertainty in determining T_LH. Results summarized in Table 1 place a lower bound of 0.5°C, and data from Tate et al. (1992) (shown in Table 2) suggest an upper bound of 4°C. The current determination is consistent with other reports and provides confidence in a more precise value of T_LH.

Determining hysteretic transitions

Metastable states and hysteretic transitions are prevalent in biology, but determining the location of hysteretic transitions is experimentally challenging (Tenchov, 1991). For a fixed thermal scan rate, the phase transition occurs rapidly at a temperature, T_A, that is reproduced on every scan. Furthermore, reducing scan rate only has a small effect on T_A. This can give the impression that the system is close to equilibrium when in truth |T_A  T_LH| is large, as is easily demonstrated for reversible hysteretic transitions.

The DOPE L-H_II transition is remarkable for the symmetry between forward and reverse hysteresis. In the general case, the empirical form of T_A(r) suggests r must be varied by well over an order of magnitude for even a rough estimate of hysteresis. This places x-ray scattering, NMR, and other "absolute" measures of phase at an advantage over DSC and other differential techniques that restrict the range of scan speeds. Transitions of this type must be tested over a very wide set of equilibration times.

DOPE transition kinetics

Most studies of L-H_II phase kinetics for DOPE have utilized large temperature and pressure jumps to aid the search for transition intermediates (Erbes et al., 2000). Conversion rates depend heavily on jump size for large jumps. Ramping data only partially describes phase conversion kinetics as it convolutes the effects of the individual steps involved. A common hypothesis is that phase conversion pathway is independent of rate so that,

(4)

where f is the fraction in the new phase, h(f) is the conversion mechanism function, and g(T  T_LH) is the rate of conversion (Kennedy and Clark, 1996). The combination of this model with the measured form of T_A(r) (Eq. 2) requires that,

(5)

where   0.25. Regardless of the ansatz used in Eq. 4, at slow rates, phase conversion kinetics demonstrably follow a power-law term. Tate et al.'s (1992) study of conversion kinetics under small temperature jumps (Table 2) supports this conclusion. Many rate-limiting mechanisms could produce a power-law relationship, but the data cannot be reconciled with the exponential behavior of single activation barrier models (Kennedy and Clark, 1996).

Determination of rate-limiting steps

Phase conversion in DOPE may be limited by nucleation, inaccessible intermediate states for domain growth, or barriers to bulk water transport. This study shows that, whatever the detailed mechanism, the same rate-limiting process applies over three orders of magnitude of conversion rate! The precise identity of the rate-limiting mechanism should be revealed by study of conversion kinetics under altered conditions.

Tristram-Nagle et al. (1994) determined nucleation to be important in sub-gel formation of DPPC with a two-temperature-jump protocol. An identical procedure could be used for DOPE. Limitations imposed by water transport should have two characteristic signatures. Above 22°C, the H_II phase is energetically preferred over the L phase at all hydrations (Gawrisch et al., 1992) so more rapid heating should show a dramatic increase in conversion speed above 22°C if water transport is rate limiting. An alternative approach would be to study samples with reduced water concentrations. At a concentration of 11 ± 1 water molecules per lipid (Gawrisch et al., 1992) there is no change in hydration between L and H_II phases that would limit conversion speed. Finally, the role of intermediates can be tested by adding small quantities of lyso-lipids and other impurities (Gruner et al., 1988). Regrettably, sample preparation can markedly alter phase conversion kinetics (Epand and Lemay, 1993), so such studies will be quite challenging.

Ice formation

Sanderson et al., (1993) demonstrated the importance of ice formation in lipid:water samples. This experiment has shown that the bulk freezing point of water is not significant for the L-H_II phase transition under slow-to-moderate conversion. Ice formation should cause an asymmetry in hysteresis between heating and cooling and cause an abrupt change in L repeat spacing. Neither effect was observed. Bulk ice formation might explain the two abrupt changes in lamellar repeat spacing in the L-L transition as shown in Fig. 8. However, Epand and Epand (1988) report a two-step liquid-gel transition for DEPE at slow scan rates (T_trans > 35°C), so ice formation is not an essential explanation in our experiment.

View larger version (104K): [in this window] [in a new window]   FIGURE 8   Scattering intensity for cooling scan at r = 3.70 × 103°Cs1. There are two abrupt changes in D-spacing in the vicinity of the L:L transition (T  12°C).

	CONCLUSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION REFERENCES

Experiments upon lipid liquid crystals are greatly complicated by hysteresis and metastability. Using linear temperature ramps, this study has shown that the L:H_II phase transition in a bulk sample of DOPE is highly reproducible. When the sample is heated or cooled at a fixed rate, r, the apparent phase conversion temperature, T_A(r), is well defined, and conversion occurs over a relatively small temperature range, T_A(r). By measuring T_A(r) over three orders of magnitude of r, an accurate extrapolation of the L:H_II transition temperature was possible and was found to be T_LH = 3.33 ± 0.16°C.

The functional form of T_A(r) proved to be particularly interesting. Hysteresis was identical for heating and cooling following the equation,

(6)

This power-law dependence is unexpected and conflicts with the exponential form of single-activation barrier kinetics. The study provides no direct insight into the rate-limiting step in topological transitions, although the precise characterization of phase conversion kinetics for fully hydrated DOPE is an excellent basis for further investigations. Although hysteresis can be very significant in lyotropic phase transitions and may cause substantial errors when determining thermodynamic parameters, this study shows that a careful analysis of rate-dependent trends can accurately eliminate almost all of the rate dependence from the transition-temperature determination.