J. Phys. Chem. 1988, 92, 2981-2987 the rate of this dehydration that determines the extent to which the subsequent thermal decomposition can take place. The rate of dehydration is faster the more hydrophobic the solute molecule is, regardless of its boiling point. When tetranitromethane acts as a scavenger of reducing radicals, the aci-nitroform anion is formed and N O z which subsequently hydrolyzes: C(NO&
+ e-
0.5H20
C(NOJ3-
+ 0.5N02- + 0.5N03- + H+
In the sonolysis very much more NOT plus NO3- ions are formed than C(NO2)3-. In additon, considerable amounts of N2, CO, and COzare produced. These findings confirm that tetranitromethane experiences a decomposition in sonolysis completely different from its radiolysis where it is simply a radical scavenger. The only product in sonolysis that could indicate that some radical scavenging took place is the C(NO2))- ion. However, even this product could have been formed thermally C(NO2)4
+
-
*C(N02)3 H z O
+ NO2' C(NOZ),- + H + + OH'
2981
the latter process being possible because of the extremely high electron affinity of the trinitromethyl radi~a1.l~ The decomposition of tetranitromethane occurs more slowly in water-alcohol mixtures, the retarding effect of propanol-2 being more pronounced than that of glycol or glycerin (Figure 6). This effect is explained by the lower temperatures in the cavitation bubbles as more and more alcohol molecules are present in them. The adiabatic compression of the bubbles produces less high temperatures in the presence of molecules having a low value of y, the ratio of specific heats. As the polyalcohols have lower vapor pressures than propanol-2, they damp the cavitations to a lesser degree. Acknowledgment. We thank Dr. Ch.-H. Fischer, Dr. H. Mockel, and Miss U. Michalzik for advice in analytical determinations, Mrs. H. Pohl for the assistance in the laboratory work, and Mrs. L. Katsikas for helpful discussions. This work was supported by the Deutsche Forschungsgmeinschaft. Registry No. PVP K90, 9003-39-8; TNM, 509-14-8; H3CCH20H, 64-17-5.
'C(NOz)3
(17) Frank, A. J.; Gratzel, M.; Henglein, A. Ber. Bunsen-Ges. Phys. Chem. 1976, 80, 593-602.
Proton Spin Relaxation Dispersion Studies of Phospholipid Membranes Eberhard Rommel, Friedrich Noack,* Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, D- 7000 Stuttgart 80, West Germany
Peter Meier, and Gerd Kothe Institut fur Physikalische Chemie, Universitat Stuttgart, Pfaffenwaldring 55, D - 7000 Stuttgart 80, West Germany (Received: November 3, 1987)
This paper presents measurements of the proton spin TI relaxation dispersion of phospholipid membranes of 1,2-dimyristoyl-sn-glycero-3-phosphocholine(DMPC) over a very broad Larmor frequency range (100 Hz I w/2* I 300 MHz). The results show that, in contrast to suggestions in the literature, collective molecular reorientations (order fluctuations) contribute to the proton relaxation process only at extremely low frequencies in the kilohertz regime, whereas the conventional high-frequency range is dominated by reorientationof individual molecules. The order fluctuationsare observed by a characteristic Tl(u) u' dispersion at low frequencies for both the liquid crystalline and intermediate phases of the model membranes, which is completely absent for the "crystalline" gel phase and for isotropic liquid phases of DMPC molecules.
-
Introduction In a series of papers on nuclear spin relaxation in the liquid crystalline phase of phospholipid membranes, Brown et al. recently analyzed the longitudinal relaxation time TI of 'H, 2H, I3C, and I4N spins in the standard high Larmor frequency range (10 MHz 5 w / 2 r 5 100 MHz) and suggested interpretation of the experimental results essentially by collective molecular reorientations in the membrane system, Le., by orderj7uctuations.'d The main argument for the presence of order fluctuations was the possibility to fit the data within the experimental error limits to a square-root (1) Brown, M. F. J . Mugn. Reson. 1979, 35, 203. (2) Brown, M. F. J . Chem. Phys. 1982, 77, 1576. (3) Brown, M. F.; Ribeiro, A. A.; Williams, G. D. Proc. Natl. Acad. Sei. U.S.A. 1983, 80, 4325. (4) Brown, M. F. J . Chem. Phys. 1984, 80, 2808. (5) Brown, M. F.; Williams, G. D. J . Biochem. Biophys. Methods 1985, 1 1 , 71. ( 6 ) Brown, M. F.; Ellena, J. F.; Trindle, C.; Williams, G. D. J . Chem. Phys. 1986, 84, 465.
0022-3654/88/2092-2981$01.50/0
-
dispersion law, T l ( w ) which is known to be characteristic for director fluctuations in nematic liquid crystal^.^-'^ This view was first criticized by Marqusee et al.," on the one hand, because in lamellar phases one should expect smectic-typelZrather than nematic-type collective motions and consequently a linear frequency dependence, T,(w) w1 and, on the other hand, because the discrimination of such relaxation mechanisms from other molecular processes in liquid crystalline materials had previously required measurements to be taken over many decades of frequency. By means of field-cycling N M R techniques, which allow to extend the observation of Tl(w) from standard high to arbitrarily
-
( 7 ) Pincus, P. Solid State Commun. 1969, 7, 415. (8) Dong, R. Y . Isr. J . Chem. 1983, 23, 370. (9) Nagel, G.; Wolfel, W.; Noack, F. Isr. J . Chem. 1983, 23, 380. (10)Rorschach, H . E.;Hazlewood, C. F. J . Mugn. Reson. 1986, 70, 79. (11)Marqusee, J. A,; Warner, M.; Dill, K. A. J . Chem. Phys. 1984, 81, 6404. (12) Blinc, R.; Luzar, M.; Vilfan, M.; Burgar, M. J . Chem. Phys. 1975, 6 3 , 3445.
0 1988 American Chemical Society
2982
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
low values of w , the square-root law so far was always found in the kilohertz and not in the megahertz ranges98l2 Later objections to Brown's analysis arose from multipulse dynamic N M R studies of 2H-labeled membranes by Meier et al.,l33I4which could be interpreted quantitatively by a superposition of various individual molecular reorientations, without any need to take into account collective modes. Last, but not least, Brown overlooked previous investigations of phospholipid membranes by Kimmich et al.,l5-l7 where the 'H spin relaxation dispersion over a relatively broad frequency band (10 kHz Iw / 2 r I80 MHz) was demonstrated to be in qualitative agreement with rotametric and torsional motions of single alkyl chains (defect diffusion) and not with the square-root law of collective motions. Minor deviations from this interpretation, which indicated additional slower motions of the bilayer membranes, could be detected only near the lower end of the dispersion plots and thus suggested that the time scale for potential collective reorientations seen by the relaxation process must be very slow, even much slower than in the nematic liquid crystals studied up to Qualitatively, such a behavior is to be expected in view of the rather short total relaxation times of phospholipid membranes, which may easily conceal the square-root law contribution at high Larmor frequencies. It is also in accordance with conclusions drawn from rotating-frame NMR experiments in cell membranes, where anomalous effects are observed in the slow-motion and not in the fast-motion regime.'* Rotating frame measurements have also been performed in phospholipid membranes and reveal an unexpected angular dependence [Pope, J. M.; Walker, L.; Comell, B. A.; Separovic, F.; Mol. Cryst. Liq. Cryst. 1982,89, 1371. But these effects were not attributed to collective order fluctuations. In order to understand the discrepancy between the work of Brown et aLi6 and the results of other research groups,"-'* and also to compare the relaxing power of collective motions in phospholipid membranes with that known for simple thermotropic liquid we have studied the Larmor frequency dependence (dispersion) of the longitudinal IH spin relaxation time TI for multilamellar dispersions of 1,2-dimyristoyl-sn-glycero-3phosphocholine (DMPC) in heavy water ( D 2 0 ) over the broad range 100 H z Iw/2r I300 MHz, previously used to analyze collective reorientations of thermotropic systems. The phase behavior of DMPC-water mixtures has been studied by various techniques which all show that at maximum hydration (125% water) DMPC undergoes two transitions as a function of temperature, a main transition between the liquid crystalline (L,) and an intermediate phase (PF) and a so-called pretransition between the intermediate and a "crystalline" gel phase (Lp).19-22 The TI( w ) measurements by means of fast field-cycling technique^^^.^^ were performed for any of these phases in order to establish the significance of the different states of matter. It will be shown in the following that the experimental data for the liquid crystalline phase give clear evidence for an order fluctuation contribution to T l ( w ) only at extremely low Larmor frequencies. In other words: At conventional N M R frequencies in the megahertz range, collective reorientations are a negligible relaxation mechanism for 'H in phospholipid membranes. Similar results have recently been reported for the lamellar and hexagonal (13) Meier, P.; Ohmes, E.; Kothe, G. J . Chem. Phys. 1986, 85, 3598. (14) Meier, P.; Ohmes, E.; Kothe, G.;Blume, A,; Weidner, J.; Eibl, H.-J. J . Phys. Chem. 1 9 8 3 , 8 7 , 4904. (15) Kimmich, R.; Voigt, G. Chem. Phys. Lett. 1979, 62, 181. (16) Kimmich, R.; Scheuermann, A,; Schnur, G.; Spohn, K. H. Biophys. Strucr. Mech. 1981, 7 , 308. (17) Kimmich, R.; Schnur, G.; Scheuermann, A. Chem. Phys. Lipids 1983, 32, 27 1. (18) Comell, B. A.; Davenport, J. B.; Separovic, F. Biochim. Biophys. Acta 1982, 689,337. (19) Lee, A. G. Biochim. Biophys. Acta 1977, 472, 237. (20) Sackmann, E. Ber. Bunsen-Ges. Phys. Chem. 1978,82, 891. (21) Janiak, M. J.; Small, D. M.; Shipley, G.G. J . Bioi. Chem. 1979, 254, 6068. (22) Recently a further transition to a "crystalline" subgel phase has been observed after incubation at 273 K for several days. Finegold, L.; Singer, M. A. Biochim. Biophys. Acta 1986, 855, 417. (23) Kimmich, R. Bull. Magn. Reson. 1980, 1 , 195. (24) Noack, F. Prog. Nucl. Magn. Reson. Spectrosc. 1986, 18, 171.
Rommel et al.
'P c
20"C.P,
5
30°C
IS
2 "C Lp
01 lo2
io3
10'
lo5
lo5
1c7
lo8
ici v Ib21
Figure 1. Frequency dependence of the 'Hspin relaxation time T , of D M P C in multilamellar dispersion (SO wt % D 2 0 ) . Top: liquid crystalline phase ( T = 30 "C). Bottom: intermediate phase ( T = 20 "C) and gel phase ( T = 2 " C ) . Also shown are measurements for an isotropic solution of D M P C in CDCI, (30 "C). The plots are theoretical model fits (see text).
mesophases of lyotropic soap systems.25
Experiments and Methods Sample Preparation. 1,2-Dimyristoyl-sn-glycero-3-phosphocholine (DMPC) was synthesized following the method described by Eib1.26 After thorough mixing of this material with pure D 2 0 in a weight ratio of 1:1, one obtains macroscopically unoriented, multilamellar dispersions of DMPC membranes in the L,, Ppt, or L, phase, depending on the temperature. Homogenization was achieved by repeated freezing (at liquid nitrogen temperature) and thawing (at room temperature) in combination with intense shaking of the ~ a m p l e s , ' ~Le., J ~ without sonication to suppress the formation of small vesicles as far as possible. Unfortunately, such vesicles could never be avoided completely as easily observed by the form and width of the N M R signals. In addition, to contrast the data with the behavior of nonmesomorphic, isotropic DMPC phases, we also considered solutions of the phospholipid in deuteriated chloroform (CDC13) and methanol (CD30D). In these solvents the lipids form inverse micelles. N M R Measurements. The measurements of the longitudinal 'H relaxation time TI as a function of Larmor frequency w = 2rv (100 Hz Iw / 2 r I300 MHz) and temperature T (273 K IT 5 318 K) were performed by means of three complementary N M R instruments: between 100 H z and 9 MHz with a homebuilt fast field-cycling device,27from 9 MHz to 84 MHz with a home-built frequency-adjustable pulsed spectrometer,% and at 300 MHz with a commercial Bruker CXP-300 spectr~meter.~~ Details about the underlying techniques, in particular the performance of field-cycling for measurements of the T, relaxation dispersion, have been described p r e v i ~ u s l y .It~may ~ ~ ~be~ worthwhile to note (25) Kiihner, W.; Rommel, E.; Noack, F.; Meier, P. 2. Naturforsch., A : Phys., Phys. Chem., Kosmophys. 1981, 42A, 127. (26) Eibl, H.-J. Chem. Phys. Lipids 1980, 26, 239. (27) Rommel, E.; Mischker, K.; Osswald, G.; Schweikert, K. H.; Noack, F. J . Magn. Reson. 1986, 70, 219. (28) Stohrer, M.; Noack, F. J . Chem. Phys. 1977, 67, 3729. (29) Muller, K.; Meier, P.; Kothe, G.Prog. Nucl. Magn. Reson. Spectrosc. 1985, 17, 211.
IH Spin Relaxation Dispersion Studies of Phospholipids that the unusually short low-field ‘H relaxation times of phospholipid membranes in the liquid crystalline phase ( T I 5 1 ms) essentially initiated the construction of the powerful field-cycling energy-storage network employed in this As a rule, the random error of the automatic, computer-controlled T I evaluations could be reduced to less than *8% by averaging both the signal amplitudes and the magnetization decay process up to 100 times (typically 10 times). An important premise for reliable data in view of the sample preparation was the capability of our apparatus to allow the measurement of the frequency dependence over almost the entire range with one single N M R sample tube (diameter, 10 mm; volume, 1 mL); only the 300-MHz instrument needed a different size (diameter, 5 mm; volume, 0.2 mL). At the beginning of the work, the T,(w) values a t frequencies lower than approximately 1 kHz showed a mysteriously large experimental which was found to originate from eddy currents induced in the vicinity of the probe through the field switching. After replacement of all metallic materials in this area by nonconductive components (with the exception of the radiofrequency coils), such perturbing effects disappeared completely on a time scale comparable to the shortest time T I and thus removed any unusual low-field scatter. Results Frequency Dependence of Relaxation Times. The form of the T , ( w ) relaxation dispersion sensitively depends on the type and structure of the various phospholipid phases. Figure 1 shows the results for DMPC-D20 mixtures containing 50% DzO. The relaxation curves refer to three different temperatures and in this way characterize the liquid crystalline (L,), intermediate (P,), and gel (L,) phases, respectively. Drastic changes in the T , ( w ) relaxation dispersion are observed. Except for the “crystalline” gel phase, T,(w)is strongly frequency dependent over almost the whole accessible Larmor frequency range. Both in the megahertz regime and in the kilohertz regime there exist more or less narrow invervals where T,(w) grows proportional to wl, but considering these regimes alone is not very meaningful. For clarity, the diagrams only show the behavior of the “solid-state” signal (FID 5 50 ps), produced by protons in multilamellar phospholipid membranes. In addition, there always exists a ”liquid-state” signal. The latter component (FID I 1 ms), probably originating from highly mobile protons in small vesicles or nonlamellar regions, does not exhibit the low-frequency dispersion described above. Rather, T,(w) of the “liquid-state” component is very similar to the data obtained for isotropic liquid solutions of DMPC in CDCl,, which are also shown in Figure 1 for comparison. Note that in such isotropic phases all the proton signals are found to be liquidlike. A qualitative inspection of the various T l ( w )plots reveals some systematic distinctions which are most helpful to develop a quantitative model for the underlying molecular reorientations. In particular, it clearly shows where the order fluctuation mechanism is a significant contribution and where it is not. We emphasize the following features: (i) The relaxation dispersion of the D 2 0 mixtures is strongest in the liquid crystalline (L,) phase and weakest in the gel (L,) phase. It extends over nearly the whole covered frequency range and vanishes only at rather low frequencies (w/27r 5 lo3Hz). (ii) The relaxation dispersion generally indicates at least two regimes separated by a plateau of T,(w) at medium frequencies (w/27r 105-106Hz). The transition is more conspicuous in the L, phase than in the P, or L, phases. (iii) The low-frequency relaxation dispersion in the liquid crystalline state shows a broad interval where T l ( w ) is proportional to w I . Such a linear frequency dependence is also observable in the intermediate phase, but it is completely absent in the “crystalline” gel phase. (iv) The low-frequency relaxation dispersion disappears for both the isotropic DMPC solutions and for the liquidlike signal component of the lamellar phases. However, the related highfrequency dispersion profiles (w/27r > lo7 Hz) are very similar to those measured by the solidlike signals. We learn from (i) that the relaxation mechanism in the liquid crystalline phase must be different from that in the other phases;
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2983 T
c -
)-Po
La-
01
315
I
,
I
3 2 3 2 5 3 3 335
----
-1--L3
I I
I I
I
I
I
[“C]
l
l
1
,
3 1 315 3 5 355 3 6 365 103/T [K-’]
Figure 2. Temperature dependence of the ’ H spin relaxation time T I of DMPC in multilamellar dispersion (50 wt % D20)at various proton Larmor frequencies u = w/27r (A, 84 MHz; & 8.9 MHz; 0,1 MHz; X, 100 kHz; 0,10 kHz; 0,1 kHz). Dashed lines indicate different phase transitions. Left: liquid crystalline phase. Center: intermediate phase. Right: gel phase. The plots are theoretical model fits (see text).
(ii) tells us that there exist at least two kinds of molecular processes with unlike time scales; (iii) suggests that the slow process is most likely a smectic-type collective fluctuation, and (iv) strongly supports such a concept. The listed phenomena have essentially been observed for a number of comparable samples prepared in the course of this work, although the complex homogenization procedure never led to exactly the same T , ( w ) data for corresponding mixtures. Temperature Dependence of Relaxation Times. The variation of T I with temperature T , shown in Figure 2 for the L,, P,, and L, phases, reveals further details of the effects seen by T , ( w ) . As a rule, T I (7‘) decreases with decreasing temperature, and both the absolute relaxation times and the slopes of T , ( T )are slightly discontinuous a t the phase transitions. However, only the L, to P, transition is easily recognized, and obviously the details for the L, phase are more complex than those for the Pr or L, phases. Important aspects are the following: (i) The temperature dependence in the L, phase involves a shallow minimum at low and medium frequencies, which provides data very sensitive to the dynamic model parameters. (ii) The temperature dependence in all phases is generally stronger at higher than at lower Larmor frequencies. Hence again we see the relaxation mechanism in the liquid crystalline phase to be significantly different from that in the intermediate and gel phases and the existence of at least two kinds of molecular reorientations with unlike time scales. Moreover, (i) clearly demonstrates that the low-frequency relaxation does not reflect only one single process.
Analysis Relaxation Model. In this section we develop a relaxation model for phospholipid membranes in the liquid crystalline phase. The measurements described above leave no doubt that order fluctuations strongly contribute to the proton T I relaxation time, but only at rather low Larmor frequencies. Above all, this concept ~ lo5 Hz is supported by the observation that below v = w / 2 r there exists a T , ( w ) w1 dispersion regime for the liquid crystalline and intermediate phases, which disappears for the “crystalline” gel state and which is completely absent for isotropic solutions. However, the complex temperature dependence of T I (7‘) in the liquid crystalline phase also indicates that the collective relaxation mechanism is different from that known for simple nematic or smectic liquid crystal^.^^^^ Obviously, the rich experimental details, revealed by Figures 1 and 2, cannot be interpreted quantitatively by a relaxation model restricted to one single process, say by the T,(w) w1i2 or T,(w) w1 laws favored by Brown et al.1-6 or Marqusee et al.” A satisfactory model for phospholipid membranes in the liquid crystalline state must eludicate the existence of at least two distinct dispersion regimes separated by a plateau, the disappearance of
-
-
-
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
Rommel et al.
the low-frequency relaxation dispersion in the case of isotropic solutions or “crystalline” states, and last but not least the complex temperature effects on T , despite the rather small mesophase intervals. Some of these features concerning the high-field relaxation have already been recognized and discussed by Kimmich et al.,l5-I7 and they were mainly attributed to reorientations of single molecules involved in defect diffusion processes. Our novel conclusions are essentially based on the existence of the measurements at lower frequencies, where the characteristic phenomena of order fluctuations fully Therefore, as a starting point to interpret the data, it is reasonable to combine the two concepts. However, as an alternative to kimmich’s defect diffusion approach, we employed a less specific model for the individual molecular reorientations,3p33 which avoids several assumptions not appropriate for the liquid crystalline phase.34 When we tried to fit such a superposition of two processes to our T l ( w ) and T l ( T )measurements in a self-consistent way, it was easily recognized that a combination of only two relaxation mechanisms did not yield satisfactory results. In particular, the Tl(T ) minimum detected at lower frequencies proved incompatible with this simple combination. Additional processes had to be taken into account to achieve a consistent description of the measurements, a circumstance which was already observed by Kimmich et al.15-17This finding, of course, complicates the quantitative analysis but fortunately does not unduly influence the evaluation of the order fluctuation contribution. In view of the numerous motional degrees of freedom of phospholipid molecules, it is difficult to select the additional reorientations that may be relevant to the overall relaxation rate. However, it is reasonable to consider above all the effect of translational motions completely neglected so far. Measurements of the self-diffusion in phospholipid bilayer^^^-^' suggest that translational molecular jumps have a time constant comparable to the upper part of our Larmor period range and thus should give a frequency-dependent T I( w ) . Furthermore, self-diffusion in a curved bilayer membrane induces molecular rotations, which may also give a frequency-dependent TI,because according to dielectric s t ~ d i e ssuch ~ ~ ,molecular ~~ rotations can be rather slow. Following these arguments we present a quantitative evaluation of the data of the liquid crystalline phase in terms of relaxation by smectic order fluctuations of groups of molecules (relaxation internal and overall molecular rotations of rate 1/ T1(oF)),II,12 individual molecules (relaxation rate 1/ ZfMR)),3w33 lateral diffusion of molecules in the bilayer plane (relaxation rate 1/ T1(LD))$4-46 and translationally induced rotations of molecules on curved bilayer regions (relaxation rate l / T1(TR)).47This model implies a correction of Brown’s approach’-6 and a refinement of both Marqusee’s” and Kimmich’~’~-’’ treatment.
Neglecting all potential correlation^^^ between the four relaxation rates (which may be critical if the reorientation times are similar) and restricting the calculations to purely exponential signal decays (observed experimentally), the superposition of the competing contributions can be expressed as 1/T,(w) = l / T , ( O F ) ( w ) + l / T I ( M R ) ( W ) + l/T1(LD)(W) 1/T1(TR)(w)
2984
(30) Woessner, D. E. J . Chem. Phys. 1962, 37, 647. (31) Woessner, D. E.; Snowden, B. S.; Meyer, G. H . J . Chem. Phys. 1969, 50, 719. (32) Lipari, G.; Szabo, A. J . A m . Chem. SOC.1982, 104, 4546. (33) Lipari, G.; Szabo, A. J . A m . Chem. SOC.1982, 104, 4559. (34) Ferrarini, A.; Moro, G.; Nordio, P. L., submitted for publication in J . Phvs. Chem. (35) Scandeila, C. J.; Devaux, P.; McConnell, H. M. Proc. Acad. Sei. U . S . A . 1972, 69, 2056. (36) Trauble, H.; Sackmann, E. J . A m . Chem. Soc. 1972, 94, 4499. (37) Wu, E.-S.; Jacobson, K.: Papahadjopoulos, D. Biochemistry 1977,16, 3936. (38) Fahey, P. F.; Webb, W. W. Biochemistry 1978, 17, 3046. (39) Rubenstein, J. L. R.; Smith, B. A,; McConnell, H. M. Proc. Natl. Acad. Sci. U . S . A . 1979, 76, 15. (40) Kuo, A. L.; Wade, C. G. Biochemistry 1979, 18, 2300. (41) T a n ” L. K.; McConnell, H . M. Biophys. J . 1985, 47, 105. (42) Kaatze, U.; Henze, R.; Pottel, R. Chem. Phys. Lipids 1979, 25, 149. (43) Pottel, R.; Gopel, K. D.; Henze, R.; Kaatze, U.: Uhlendorf, V. Biophys. Chem. 1984, 19, 233. (44) Beckert, D. Ann. Phys. (Leipzig) 1967, 20, 220. (45) Vilfan, M.;h m e r , S . Phys. Rev.A 1980, 21, 672. (46) Korb, J.-P.; Winterhalter] M.; McConnell, H . M. J . Chem. Phys. 1984., 80.. 1059. (47) kumer, S.; Vilfan, M. J . Phys. (Les Ulis. F r . ) 1985, 46, 1763
+
(1)
where, according to standard theory, the individual relaxation rates l/Tl(‘I) ( i j = OF, MR, LD, and T R ) depend on characteristic intensity spectra Jl(il) and JZcij)via23,24 1/ T l ( g ) ( w ) = (9/8)r4h2(~o/4..)2[Jl(’,)(w) J,(‘J)(2w)]
+
+
= (y2B,2 w,oc2)l/2 (2) In eq 1 and 2 7,h , p,,, B,, and wloc denote the proton magnetogyric , magnetic permeability ratio, Planck’s constant divided by 2 ~the of vacuum, the external Zeeman field, and the local Larmor frequency correction, respectively. Explicitly, the considered intensity spectra are, in the case of order fluctuationsL’Sl2 Jp(OF)(pw) = PA(’‘)( 1/ w ) w
A(oF) = ( 1 / 5 ) k T S z / ( K x r 6 )
(3)
in the case of molecular rotations3G33 r
in the case of lateral d i f f ~ s i o n ~ ~ - ~ ~
and in the case of translationally induced rotations4’
A(TR)= (4/15)SZ/r6 (6) These expressions essentially follow the notations used in the literature: k , S, K , x , r, TR,, TR,,,T ~ RT, L D , B,,, &,,n, d, and T T R denote the amplitude factors, Boltzmann’s constant, the effective order parameter of the proton-proton vector, the coherence length of the order, the effective proton-proton separation, the rotational correlation times for anisotropic overall motions perand parallel (11) to the main molecular axis, the pendicular ( I ) effective correlation time for internal rotations, the time constant for translational molecular jumps, numerically evaluated geometry factors and damping constants, the surface spin density, the translational closest spin approach, and the correlation time for translationally induced rotations, respectively. For details we refer to the original papers. In order to keep the number of model parameters as small as possible, we always used the simplest form of the individual relaxation rates and introduced refinements only in case of experimental evidence. Model Fitting. By means of computer fitting techniques it was possible to describe all the experimental T , ( w ) and T , ( T ) plots (48) Freed, J. H. J . Chem. Phys. 1977, 66, 4183.
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2985
*HSpin Relaxation Dispersion Studies of Phospholipids
TABLE I: Optimized Model Parameters for Various Contributions to 'H Spin Relaxation Time TI of DMPC in Multilamellar Dispersion (Liquid Crystalline Phase) dij)a
relaxation mechanism molecular rotations (MR)C lateral diffusion (LD)' translationally induced rotations (TR)g smectic order fluctuations (OF)h
~l,/2~b
x 108 1.8 x 109 2.0 x 109 8.9 X lo6 1.2 x 107 7 x 106 2.2
C,'MR' c2(MR)
cp) OLD) OTR)
E$
(303 K)'
7,j 7R1 rRll
71R TJ+D
5 x lo-'
ERl
5 x 10-9 2 x 10-10 5 x
ERI,
50 50 20 50
EIR
ELD ETR
~ T R 5 x 10-6 150 OOF) 1500 "In units of s - ~ . See eq 7; analytical expression for O°F),OLD), and CTR) are given in eq 3, 5, and 6 . Hz. See eq 2. C I n s. rRL,TRII = rotational correlation times for anisotropic overall motion; 7 I R = effective correlation time for internal motion; TLD = time constant for translational molecular jumps; 7 T R = correlation time for translationally induced rotations. d E i j = activation energies (in kJ/mol) for the motional correlation times, according to eq 8. 'See ref 30-33. /See ref 44-46. gSee ref 47. hSee ref 11 and 12.
quantitatively in terms of the introduced relaxation model. However, only the strong relaxation dispersion together with the pronounced temperature dependence in the liquid crystalline phase really allowed a critical separation of the four mechanisms. Therefore, our present analysis will mainly be restricted to this most interesting phase. For the fitting procedure, eq 1 and 2 were suitably rewritten in the form
....
61') = (9 / 8)y4h2(p,/4?r)2A(u)
with normalized intensity spectra f(d)(w,rij) defined by eq 2-6. Equation 7 explicitly shows the different kinds of adjustable parameters, namely, amplitude factors oil)and motional correlation times T ~ Note ~ . the most helpful circumstance that the amplitudes d l j ) , unlike the other fitting parameters, depend linearly on the relaxation rate. The Ti(w) plots were calculated by evaluating the selected theoretical expressions and optimizing the model parameters so that deviations between the experimental data points and the theoretical predictions vanished or became small compared to the experimental scatter. Such a fit to a relaxation dispersion curve does not need any assumptions about the temperature dependence of the underlying quantities. These variations with temperature were found experimentally by making the T,(w) and T,(T) fits consistent with each other. In this way it was observed that, within the temperature range of the liquid crystalline phase, the variations of the amplitude factors 611) were negligible compared to the effects produced by the correlation times rij,which could be described by Arrhenius laws rij =
LD
(7) 01
' ' , ' 1 ' 1 1 1
io2
'',"...'
","',,'
' " " ' 1 1 1
io3
lo5
ioL
MR '',,,,,,'
''l."''l
io6
io7
' ' l L L
lo9
io8
v[Hzl
Figure 3. Comparison of the experimental and calculated 'H spin relaxation dispersion T I ( w / 2 ~ )of DMPC in multilamellar dispersion (50 wt % D20) at T = 30 OC (liquid crystalline phase). The solid lines represent best fit simulations, employing the relaxation model of eq 7 and 8 and the parameters of Table I. The individual relaxation contributions are indicated by broken lines. T
60
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I
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,
,
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,
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72
with preexponentials and activation energies Eijas new fitting parameters ( R = molar gas constant). The quality of the model fits is illustrated by the solid lines in Figures 1 and 2. Details of the individual relaxation contributions for the Laphase are represented in Figures 3 and 4, and the related parameters are listed in Table I. Apparently, the best fit simulations agree favorably with the experimental data. Both the T,(w) and the T,(T) analyses reveal that the relaxation dispersion profile of phospholipid membranes in the liquid crystalline phase is essentially governed by two mechanisms, namely, individual ~ 1 molecular reorientations (MR) a t high frequencies ( w / 2 k MHz) and collective order fluctuations (OF) at low frequencies (0/27r 5 1 MHz). However, deviations from the Ti(w) wI law clearly show a third contribution in the range lo4 Hz < w / 2 < ~ lo6 Hz, which is even better recognized by the Tl(7') minimum of the temperature-dependent measurements. In our model this process is attributed to slow rotations induced by translational diffusion (TR) in curved bilayer regions. The fourth contribution, namely, lateral diffusion (LD) itself, is not a significant relaxation process. However, it must be present to allow for the more important T R mechanism. To facilitate the comparison with known studies of phospholipid membranes, in particular to make clear which details of our analysis are significant and which are not critical, we performed additional curve fits for some similar, yet microscopically different
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2986 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
expressions for both anisotropic overall and internal motions and various forms of two-dimensional diffusion in membrane layIn all cases the available experimental data did not allow ers.an unambiguous discrimination of the alternatives, because the simulated relaxation dispersions proved very similar. However, none of the models worked satisfactorily without the order fluctuation term at low Larmor frequencies.
Discussion What do we learn from the measurements and the curve fits? First of all, the quantitative analysis confirms our qualitative estimations that order fluctuations in membranes are slow and not an important relaxation mechanism at frequencies above 10 MHz as assumed by Brown et a1.I“ This is most critically seen by comparing the results with the data for the ”crystalline” gel or isotropic liquid phase. Second, it clearly demonstrates that there exist both slow and fast additional contributions to the total relaxation rate, which are hard to distinguish even by relaxation dispersion measurements. Let us now consider the significance of the four underlying contributions in more detail, with emphasis on the liquid crystalline phase. Order Fluctuations. The order fluctuation mechanism (OF) in the liquid crystalline phase is not only supported by the T I u1regime above the local field cutoff frequency ulW/2a 1500 Hz but also by the evaluation of the amplitude factor A(oF) in eq 3. Using experimentally determined values of the order paS1 = 0.2 13,49*50and an effective proton-proton separation rameter I r = 1.9 X m25and putting the coherence length equal to the bilayer thickness ( x zz 6 X m),19-21one obtains for T = 303 K an average elastic constant K = 5 X lo-” N , Le., approximately the value reported in the l i t e r a t ~ r e . ~ I -Since ~ ~ this constant is expected to be much larger in the “Crystalline” gel phase, it is plausible that collective reorientations are not observed in this phase (see Figure 1). For the intermediate phase the situation is more complicated, as two different components are detected in the *Hand I3CN M R spectra with spectral characteristics, corresponding to those observed in the liquid crystalline phase and gel phase, respective1y.13J4,55Apparently, the microscopic heterogeneity of the intermediate phase,56still containing a liquid crystalline component, is responsible for the occurrence of order fluctuations in this phase. Molecular Rotations. As clearly seen from the curve fits in Figures 3 and 4 (liquid crystalline phase), director fluctuations are a negligible relaxation mechanism in the megahertz range in contrast to the conclusions of Brown et a1.I” Instead, isolated molecular rotations (MR) almost fully account for the observed relaxation dispersion above v = w / 2 a 10 MHz and the related temperature variation. Such motions are specified in terms of three different correlation times T R , , T ~ and~ T , ~ characterizing ~ , anisotropic overall rotation, parallei or perpendicular to the main molecular axis, and internal isomerization, r e s p e c t i ~ e l y .From ~~~~ Table I we infer that isomerization occurs with correlation times T~~ r s, in agreement with values obtained from previous 2H T I relaxation studies at fixed frequency ( w / 2 a r 50 MHz).13,57,58By employing specifically deuteriated phospholipids and 2H NMR, it was possible to establish a mobility gradient for this motion with decreasing along the hydrocarbon
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(49) Seelig, A.; Seelig, J. J. Biochemistry 1974, 13, 4839. (50) Petersen, N. 0.;Chan, S. I. Biochemistry 1977, 16, 2657. (51) Brochard, F.; Lennon, J. F. J . Phys. (Les Ulis,Fr.) 1975, 36, 1035. (52) Schneider, M. B.; Jenkins, J. T.; Webb, W. W. J . Phys. (Les Ulis, Fr.) 1984, 45, 1457. (53) Engelhardt, H.; Duwe, H . P.; Sackmann, E. J . Phys. Lett. 1985,46, L-395. (54) Beblik, G.;Servuss, R.-M.; Helfrich, W. J . Phys. (Les Ulis, Fr.) 1985, 46, 1773. (55) Wittebort, R. J.; Schmidt, C. F.; Griffin, R. G. Biochemisrry 1981, 20, 6068. (56) Falkovitz, M. S.; Sed. M.; Frisch, H. C.; McConnell, H. M. Proc. Nail. Acad. Sci. U . S . A . 1982, 79, 3918. (57) Brown, M. F.; Seelig, J.; Habeden, U. J. Chem. Phys. 1979, 70, 5045. (58) Siminovitch, D. J.; Ruocco, M. J.; Olejniczak, E. T.; Das Gupta, S . K.; Griffin, R. G . Chem. Phys. Lett. 1985, 119, 251.
Rommel et al. which is not resolved by the proton measurements. However, the average activation energy of EIR = 20 kJ/mol, evaluated in this study, compares well with 2 times the potential barrier height encountered in rotational isomerization about C-C bonds.63 Similarly, the correlation times for overall rotation range from to IO-’s, exhibiting a nearly constant anisotropy ratio of T R , / T R ~ , = 10, which is consistent with theoretical estimations from the length and breadth of the DMPC molecule. The high motional activation energies ERlIz E R L = 50 kJ/mol reflect the intermolecular character of these motions, namely, reorientations of the phospholipid molecules as a whole. In view of the manifold proton-pair orientations and proton-pair separations, involved in the amplitude factors AI(MR)of eq 4, we do not give an explicit evaluation of these parameters; the present proton N M R measurements cannot distinguish between unlike proton locations and thus only allow us to fit some average spin-pair vectors with no specific microscopic meaning. For the same reason our experiments are not capable of distinguishing critically between the considered model of molecular rotations (MR), developed by W o e ~ s n e r ~and ~ - ~S ’z a b ~ ,and ~~?~~ the defect diffusion description, worked out by Kimmich.l3-l7 Both treatments yield curve fits of comparable quality with only minor distinctions in the high-frequency region.64 Nevertheless, the present simulations indicate, that the defect diffusion model is more appropriate for the gel than for the liquid crystalline phase. Lateral Dvfusion. As already mentioned, lateral self-diffusion (LD) in the bilayer plane does not constitute a major relaxation process and hence cannot be determined reliably (see Figure 3). Nevertheless, it was included in the fitting procedure mainly because of its importance for the related T R mechanism. The relevant time constant for the two-dimensional diffusion process is the average time between two successive lateral jumps, TLD. For the DMPC membranes in the liquid crystalline phase this time s at T = 303 K (see constant was determined to TLD = 5 X Table I). Assuming a meansquare jump length of d2 = 64 X IO-” m2 65 , one obtains a translational diffusion coefficient of D = (1/4)~,~-’& = 3 X 10-I2m2 s-*, a value that fits well with other experimental data.35-41 The amplitude factor A(LD)was then m and a surface proton density n calculated with d = 8 X = 1.2 X 1019m-2.19-21It is evident from Figure 1 that the significance of lateral diffusion increases from the L, to the L, phase, since the relaxation times T I at low frequencies are still short in spite of the much smaller order fluctuation contribution. Translationally Induced Rotations. Since lateral self-diffusion could not explain the unusual relaxation behavior, clearly visible in the T I (r ) data (see Figure 2 ) , it was necessary to introduce an additional slow mechanism. We considered a reorientation process, recently suggested by Zumer and Vilfan?’ namely, translationally induced rotations by diffusion of molecules along a curved interface (TR); such a motion is to be expected in lamellar phases with aggregates of finite length. The effectiveness of this mechanism depends on the radius of curvature R,which can be estimated from the correlation time of the translationally induced With T T R = rotations T T R , using the relation R = 5X s, obtained from the curve fits at 303 K, and D = 3 X m2 s-I we find a curvature of R r m, which corresponds to the radius of very small vesicles.66 We therefore conclude that the effective bilayer curvature has little to do with the curvature of the large particles in unsonicated multilamellar dispersions.66 Rather, the effective bilayer curvature is associated with “curved (59) Mantsch, H. H.; Saito, H.; Smith, I. C . P. Prog. Nucl. Magn. Reson. Spectrosc. 1971, 11, 211. (60) Bloom, M.; Smith, I. C. P. In Progress in Protein-Lipid Interactions; Watts, A,, DePont, J . J . H . H., Eds.; Elsevier: New York, 1985; p 61. (61) Davis, J. H. Chem. Phys. Lipids 1987, 40, 223. (62) Mayer, C.; Muller, K.; Weisz, K.; Kothe, G. Liq. Cryst., in press. (63) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience: New York, 1969. (64) Rommel, E. Thesis, University of Stuttgart, 1988. (65) Sachse, J. H.; King, M. D.; Marsh, D. J . Magn. Reson. 1987, 71, 385. (66) Jain, M. K.; Wagner, R. C. Introduction to Biological Membranes; Wiley: New York, 1980.
J. Phys. Chem. 1988, 92, 2987-2990 defects” of the lamellar structures having much larger dimensions. Since only a small fraction of the DMPC molecules is located in such defects, the amplitude factor Am)in eq 6 has to be weighted with t f i fador. The fraction comesponds to the ratio of “arvd” and “total” bilayer surface. From the experimentally observed amplitude C
