5608
J. Phys. Chem. 1996, 100, 5608-5610
Interlamellar Transition Mechanism in Model Membranes Anchi Cheng and Martin Caffrey* Department of Chemistry, The Ohio State UniVersity, Columbus, Ohio 43210 ReceiVed: NoVember 22, 1995; In Final Form: February 13, 1996X
Time-resolved X-ray diffraction was used to monitor structure changes during a partial lamellar liquid crystal (smectic A)/lamellar gel (smectic B) transition in lipid multilayer vesicles in response to small pressure oscillations covering 4 decades in frequency. The data suggest that hydrocarbon chain ordering/disordering is tightly coupled to changes in lamellar unit cell length that occur during the phase change and are consistent with a bidirectional layer-by-layer transition mechanism best described by the Kolmogorov-Avrami kinetic model having an effective dimensionality of 1.
A layered or sheetlike arrangement is a ubiquitous motif in nature. It is found in such diverse materials as mollusk shells, stratum corneum of skin, myelin sheath of the nerve axon, chloroplast thylakoids, soaps, clays, and even synthetic polymers. The layered arrangement is particularly well developed in the assorted smectic or lamellar mesophases of the lyotropic and thermotropic liquid crystals. In this study, we have established the kinetics and deciphered the underlying mechanism of the interconversion between two lamellar phase variants considered to play a role in biomembrane structure and function. The fully hydrated neutral lipid, monoelaidin, which undergoes a reversible first-order lamellar gel (Lβ)/lamellar liquid crystal (LR) transition (Figure 1C), without the appearance of intermediates, was used in the study. During the Lβ-to-LR transition, the lipid acyl chains undergo an order-to-disorder conformational transformation that is evident in a wide-angle X-ray diffraction measurement as a change from a sharp reflection at 4.2 Å to a diffuse band centered at 4.6 Å (Figure 1B). The chain conformational rearrangement along with a change in lipid hydration causes a dramatic shift in the dimensions of the lamellar repeat unit from 64 Å in the Lβ phase to 53 Å in the LR phase (Figure 1A) which is apparent in the low-angle region of the diffraction pattern. Thus, time-resolved low- and wide-angle X-ray diffraction measurements can be used to monitor the dynamic structural changes in long- and shortrange order that accompany the Lβ/LR transition. In this study, a novel stationary relaxation measurement was made with the system poised at the midpoint of the transition while small oscillating pressure perturbations changed the relative amounts of the coexisting Lβ and LR phases of fully hydrated monoelaidin multilamellar vesicles (Figure 2). The experimental arrangement for the time-resolved diffraction data has been described.1 Briefly, an aqueous multilamellar vesicle dispersion of monoelaidin in an X-ray capillary tube was housed in an X-ray “transparent” beryllium cell. Static and oscillating pressures were applied to the sample by means of a syringe pump and a stepping-motor-driven volume oscillating device, respectively, with water as the pressure medium. Time-resolved X-ray diffraction measurements were made in the wide- and low-angle regions at the same time that sample temperature and pressure were recorded during the course of the pressure oscillation experiment. The amplitude and phase angle of the structure response were obtained by analyzing the time-resolved diffracted intensity data.2 The success of these measurements relied upon having a large enough signal-to-noise X
Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-5608$12.00/0
Figure 1. Low- (A) and wide-angle (B) X-ray diffraction and scattering from the LR and Lβ phases of hydrated monoelaidin at two points in time during a pressure oscillation measurement. The two time points represented in A and B are taken from the oscillation data presented in Figure 2.I at t ) 198 s and at t ) 233 s when the relative amount of the Lβ phase was at its maximum and minimum value, respectively. Data (circles) were fit (solid lines) with a maximum of three Lorenzian functions. Profiles are displaced vertically for clarity. s ()(2 sin θ)/λ) represents the scattering vector and is equal to the inverse of the repeat spacing, d. The individual Lβ and LR phases are shown schematically in C. The transition temperature, Tm, is 22 °C at ambient pressure and dTm/dP is 16 °C/kbar.
ratio (S/N) in the time-resolved X-ray diffraction data and upon the system responding linearly to the oscillating pressure perturbation. The data show that for all measured parameters, the system exhibits a satisfactory S/N and a linear response up to (16 bar, corresponding to a (19% mesophase conversion (Figure 2). The linearity in response to pressure change and the first-order nature of the phase transformation was also confirmed by slow (1 bar/min) pressure ramps in the range of the transition (data not shown). The lipid mesophase structure responses to the oscillating pressure perturbation are shown in Figure 3 in the form of response amplitude and phase-angle shift spectra. In both © 1996 American Chemical Society
Letters
J. Phys. Chem., Vol. 100, No. 14, 1996 5609
TABLE 1: Parameters Used in Fitting the Diffraction-Based Fractional Lr/Lβ Mesophase Conversion Response Amplitude Spectra to the Kolmogorov-Avrami Theorya mesophase structural feature
n
τ (s)
104A
104ξ
lamellar stacking (low-angle) chain order/disorder (wide-angle)
0.78 (0.76-0.81) 0.89 (0.81-0.99)
13 (12-14) 10 (8-13)
128 (fraction/bar) (122-134) 22 (arb units) (19-26)
4.4 (fraction/bar) (3.9-5.1) 1.7 (arb units) (1.4-1.9)
a The fractional mesophase conversion response amplitude at various frequencies was fit by |AFT{(ntn-1/τn)exp[-(t/τ)n]} + ξ| using a nonlinear χ2 fitting procedure where A is the maximal frequency-dependent response amplitude, FT{f(t)} represents the Fourier transform of the timedependent function f(t) which, in this case, represents the impulse-response function of the Kolmogorov-Avrami model11 and ξ is a constant assigned to the residual response evident in both the response amplitude and phase spectra at high frequencies. The numbers in parentheses represent parameter values evaluated at (1 standard deviation.
unit step response of a two-state phase transformation takes the form
X(t) ) 1 - exp(-(t/τ)n)
Figure 2. Simultaneously recorded pressure (A), temperature (B), and structure (C-F) response of fully hydrated monoelaidin in the LR/Lβ phase transition region to an oscillating pressure perturbation. Diffracted/scattering intensities from the Lβ lamellar (001) and wide-angle chain packing reflections are shown in C and E, respectively. The corresponding features of the LR phase are shown in D and F. Water alone contributed insignificantly to the diffracted/scattering intensity changes observed for the lipid-water system. The original data in the time domain, along with the corresponding power spectra, are shown in panels I and II, respectively. All spectra were normalized by setting the power level at the fundamental frequency to a value of unity. Experimental conditions include oscillation frequency, 0.0178 Hz (56 s/cycle); pressure amplitude, (15.7 bar; average temperature, 24.05 ( 0.01 °C; average pressure, 130.1 ( 0.1 bar. Linear behavior was exemplified by insignificant power contributions at harmonic frequencies (II, arrows mark harmonic frequencies).
spectra, the largest response amplitude and smallest response phase shift is observed at the lowest perturbation frequencies. At higher frequencies, the system can no longer track the perturbation resulting in a systematically reduced response amplitude and an enhanced response phase lag. The data show that the two structural changes measured have essentially identical response amplitude and phase shift spectra. This result supports the view that the changes in chain packing and in lamellarity that accompany the transformation are temporally and mechanistically tightly coupled. Many models have been used to describe a first-order phase transformation.3 In this study, we use the simple linear model of Kolmogorov and Avrami.4-7 According to this model, the
(1)
where X is the fraction of sample in the nascent phase, τ is the relaxation time of the process, and n is the effective dimensionality. The latter represents the sum of the time exponents in the expressions for the number of randomly distributed nuclei and the extended volume occupied by each nucleus experiencing unimpeded growth (see ref 8 for a more complete discussion of the model). The fit of the experimental data to this model is shown by the solid lines in Figure 3 and by the parameters listed in Table 1. Both structural aspects of the transition are best described with a value of n close to unity and a τ value of ca. 12 s. Because a small perturbation is used to drive partial mesophase interconversion, it is appropriate to assume that the number of nuclei in the system remains constant with time during the course of the measurement. For a fixed number of nuclei, a value of n ) 1 indicates that extended nucleus growth occurs at a constant rate. Taking into account the multilayered nature of the vesicles and the small perturbation used, we propose that the transformation takes place layer-by-layer and propagates from existing nuclei in the multilamellar vesicle (inset in Figure 3A) and that growth within the plane of a given layer is too fast (see ref 9) to be characterized on the time scale of the measurements. The values of n reported are close to, but consistently less than, unity. This suggests that the layerby-layer transition mechanism involving growth in one dimension is not entirely interface controlled where n ) 1 and that diffusion (presumably water) plays some, but not a dominant, role in the transition. Strictly speaking, in a closed multilamellar vesicle, each lipid bilayer does not contain the same amount of material. Therefore, growth rate of the extended nucleus will have some finite time dependence. However, this effect is minimized when the layered nuclei grow bidirectionally toward the inside and the outside of the vesicle. Consistent with the observation that n ≈ 1 in the current application is time-resolved dilatometry data obtained on several interlamellar mesophase transitions in phospholipid multilamellar vesicles where the measured value of n was found to range from 0.8 to 1.3.10 In this study, a small oscillating pressure perturbation was used to drive the periodic interconversion of two lamellar phases. The kinetics and mechanism of the transition were established by monitoring changes in two structural features of the transforming phases during the course of the measurement which covered four decades in pressure oscillation frequency. The data support a bidirectional layer-by-layer transition mechanism characterized by an effective dimensionality of 1. While the results and conclusions presented herein apply to interconversions between smectic or lamellar mesophases, the method introduced can be used to investigate more complex transitions involving mesophases periodic in two and three dimensions, such as the hexagonal and cubic phases. More generally, the
5610 J. Phys. Chem., Vol. 100, No. 14, 1996
Letters
Figure 3. Perturbation frequency dependence of the structure response amplitude (A, low- and C, wide-angle diffraction) and phase-angle shift (B, low-, and D, wide-angle diffraction) in the LR/Lβ mesophase transition region of fully hydrated monoelaidin. The response amplitudes were normalized by the pressure oscillation amplitude while the phase-angle shift was computed by comparing the time-dependence of the diffracted intensity variation and oscillating pressure perturbation. A total of 11 samples were used to minimize X-radiation damage effects.12 For all samples, maximum accumulated dose was limited to 210 krad where no significant chemical breakdown of the lipid was found. The data were collected at 24.05 ( 0.02 °C and 130 ( 1 bar with a pressure oscillation amplitude of (11 to ( 6 bar in the LR/Lβ phase transition region. The data (circles) were fit (solid lines) to the Kolmogorov-Avrami kinetic theory model. The best fitting parameters are reported in Table 1. The fitting sought to minimize the χ2 of the response amplitude only, and the solid lines in B and D are the corresponding phase-angle shift calculated from the fit. The inset in A is a schematic representation of the unimpeded growth of a nucleus in the proposed layer-by-layer phase transformation in part of a closed multilamellar vesicle. Arrows point in the direction of growth which is bidirectional away from the original nucleus.
method should find application in deciphering kinetics and mechanisms of processes that show an interpretable change in X-ray diffraction/scattering in response to a pressure perturbation. Acknowledgment. This work was supported by grants from the NIH (DK 36849 and DK 46295) and Rohm & Haas. We thank the X9B staff at NSLS, a DOE facility, for their help and support. We also thank R. L. Biltonen, J. Nagle, and S. Tristram-Nagle for valuable comments on an early version of this letter. References and Notes (1) Mencke, A.; Cheng, A.; Caffrey, M. ReV. Sci. Instrum. 1993, 64, 383. (2) Mencke, A. P.; Caffrey, M. Biochemistry 1991, 30, 2453.
(3) Gunton, J. D.; San Miguel, M.; Sahni, P. S. The Dynamics of First Order Phase Transitions. In Phase transitions and critical phenomena; Domb, C., Lebowtz, J., Eds.; Academic Press: New York, 1983; Vol. 8; p 269. (4) Avrami, M. J. Chem. Phys. 1939, 7, 1103. (5) Avrami, M. J. Chem. Phys. 1940, 8, 212. (6) Avrami, M. J. Chem. Phys. 1941, 9, 177. (7) Kolmogorov, A. N. Bull. Acad. Sci. U.S.S.R., Phys. Ser. 1937, 3, 555. (8) Doremus, R. H. Rates of phase transformations; Academic Press: New York, 1985. (9) van Osdol, W. W.; Johnson, M. L.; Ye, Q.; Biltonen, R. L. Biophys. J. 1991, 59, 775. (10) Yang, C. P.; Nagle, J. F. Phys. ReV. A 1988, 37, 3993. (11) Ye, Q.; van Osdol, W. W.; Biltonen, R. L. Biophys. J. 1991, 60, 1002. (12) Cheng, A.; Hogan, J. L.; Caffrey, M. J. Mol. Biol. 1993, 229, 291.
JP953431Q
