VOLUME 100, NUMBER 43, OCTOBER 24, 1996
© Copyright 1996 by the American Chemical Society
LETTERS C-C Bond Order Parameters from 2H and
13C
Solid-State NMR
J. P. Douliez,§,† B. Bechinger,† J. H. Davis,‡ and E. J. Dufourc*,§ Max Planck Institut fu¨ r Biochemie, 82152 Martinsried, Germany; Department of Physics, UniVersity of Guelph, Guelph, Ontario, Canada N1G 2W1; and Centre de Recherche Paul Pascal, CNRS, AV A. Schweitzer, 33600 Pessac, France ReceiVed: May 21, 1996; In Final Form: August 26, 1996X
In this letter we demonstrate the accuracy of the Ck-1-Ck bond order parameters, SCC k , when determined from the Ck-D (2H) bond order parameters, SCD , as experimentally measured on a fully deuterated chain. Two k different approaches were taken to determine the C1-C2 bond order parameter, SCC , of a palmitic acid chain 2 (k ) 1-16) embedded in a liquid crystal. First, solid-state 2H NMR experiments were performed on the perdeuterated chain in order to obtain its C-D bond order parameter profile. The recursion relation, CC CC CC -2SCD k ) Sk + Sk+1, between consecutive Sk , where k stands for the labeled carbon position was used to CC calculate S2 . Second, having included a quantity of palmitic acid specifically 13C-labeled at the C1 and C2 positions, the dipolar coupling between these carbons was measured using one- and two-dimensional 13C solid-state NMR spectroscopy. This coupling provides a direct and independent measure of SCC 2 , the order parameter of interest. Both methods agree within 4%.
Introduction The determination of C-C bond order parameters, SCC, in fatty acyl chains embedded in anisotropic media (biomembranes, liquid crystals) leads to the calculation of valuable conformational and dynamical properties such as conformational defects along the chain, probabilities of gauche conformers, and average hydrophobic chain length in phospholipid membranes.1 Such order parameters can be derived from experimental C-D or C-H order parameters as respectively determined from solidstate 2H NMR of perdeuterated chains2-6 or from protondetected local field experiments7,8 on nonlabeled samples. Recently, it has indeed been shown that C-C bond order †
Max Planck Institut fu¨r Biochemie. University of Guelph. § Centre de Recherche Paul Pascal. * To whom correspondence should be addressed. Tel (33) 56 84 56 38, fax (33) 56 84 56 00, email
[email protected]. X Abstract published in AdVance ACS Abstracts, October 1, 1996. ‡
S0022-3654(96)01457-8 CCC: $12.00
parameters can be calculated from the C-D bond order profile using an independent conformational model.1 In this approach, the terminal bond order parameter, SCC n , is determined by a simple coordinate transformation from the C-D of the methyl terminus to the Cn-1-Cn bond (which is also the rotation axis of the methyl group). Subsequently, the recursion relationship, CC 1 -2SCD ) SCC + Sk+1 , between consecutive SCC k k k , is used to calculate all of the C-C bond order parameters along the chain (having started from the methyl end). The validity of this equation has been tested by comparing the C-C bond order parameters calculated by this method with those obtained by a mean field dynamical model.9,10 However, since the calculation starts from one end of the chain and the order parameters are determined iteratively, the accuracy of the SCC k depends on the accuracy of the SCD and on the correct assignment of the C-D k bond order parameters, especially for positions near the carbonyl group where the SCD order profile exhibits a plateau region. Indeed, for perdeuterated chains in biomembranes, the positions © 1996 American Chemical Society
17084 J. Phys. Chem., Vol. 100, No. 43, 1996
Letters TABLE 1: Temperature Dependence of S2CC and the Dipolar Splitting, ∆νDa T (°C) SCC 2 ∆νD
(kHz)
30
35
40
45
50
1.98
0.30 1.85
0.27 1.67
0.23 1.43
0.20 1.28
SCC 2 are calculated using the recursion relation (see text) and the C-D bond order profile. The value at 30 °C cannot be determined accurately from our measurements and is not included. The uncertainty -2 in SCC 2 is (2 × 10 . The ∆νD measurement was made from the fatty acid carbonyl peaks near 200 ppm in the one-dimensional spectrum after assignment from the two dimensional correlation spectrum. The uncertainty is (50 Hz. a
Figure 1. Solid-state 2H NMR spectrum of perdeuterated palmitic acid in ZLI 1132 recorded with a quadrupolar echo sequence at 50 °C. The liquid crystal spontaneously orients parallel to the magnetic field. See text for details on the assignment of labeled positions. The accuracy in the measurement of quadrupolar splittings is about (250 Hz in the plateau region and about (50 Hz for other positions.
in the plateau region cannot be well resolved and it is usually assumed that SCD is constant for these positions, whereas experiments with selectively labeled lipids have revealed small variations in the C-D bond order parameters.2,3,11 However, fully deuterated systems are much easier to synthesize so it is essential to test experimentally the accuracy of the SCC k values calculated from such perdeuterated systems. It is interesting to note that Morrow and co-workers12 recently proposed a similar approach in which information related to C-C bond orientation can be inferred from perdeuterated-chain SCD values using an iterative process beginning at the methyl group. In what follows the C1-C2 bond order parameter, SCC 2 , of a perdeuterated palmitic acid chain (k ) 1-16) embedded in a liquid crystal was first calculated using the above recursion equation and the C-D bond order parameter profile, SCD k , as obtained from solid-state 2H NMR experiments. Second, the 13C -13C dipolar coupling of the same palmitic acid specifically 1 2 13C-labeled was measured using one- and two-dimensional 13C solid-state NMR spectroscopy, hence providing a direct and independent measure of SCC 2 . Materials and Methods The solid-state NMR samples were prepared by dissolving 40 mg of [1,2-13C]palmitic acid and 10 mg of palmitic acid-d31 in approximately 500 mg of a nematic liquid crystal, ZLI-1132 (E. Merck, Darmstadt, Germany). This mixture spontaneously orients with its director parallel to the static magnetic field. Several cycles through the isotropic phase transition (above 65 °C) and vigorous vortexing were used to guarantee a uniformly mixed sample. Quadrupolar and dipolar splittings were measured as a function of temperature between 30 and 50 °C on Bruker MSL 200 and AMX 400 spectrometers.13 Results and Discussion Figure 1 shows the deuterium spectrum obtained at 50 °C. Quadrupolar splittings were measured for each of the doublets in the spectrum. The assignments of the different labeled positions were performed on the basis of previously published data.4,14 The C-D bonds exhibiting the largest splittings, of
Figure 2. One-dimensional solid-state 13C NMR spectrum recorded with 1H decoupling at 30 °C. The strong overlap between the fatty acid peaks and those of the (natural abundance) liquid-crystal peaks in the methylene region does not permit the unambiguous assignment of all peaks. The dipolar coupling between the two fatty acid 13C labels is measured with an accuracy of (50 Hz after the chemical shifts of the fatty acid peaks have been unambiguously assigned in the 2D correlation experiment (Figure 3).
approximately 40 kHz are assigned to the 2 (or R-CD2) methylene position, i.e., that next to the carboxyl group. At temperatures below 45 °C two signals are observed (not shown). This indicates that the two deuterons on this carbon are not equivalent, as was also found for diacyl phosphatidylcholines.2,15 The recursion relation used in calculating SCC has to be 2 slightly modified in this case.1 The large, broad peaks with a splitting of 38 kHz were assigned to the deuterons attached to carbons 3-11, corresponding to the well-known plateau region of the hydrocarbon chain. In contrast, the splittings assigned to positions 12-16 decrease monotonically as the methyl terminus is approached. As in the case of axially symmetric reorientation the quadrupolar splittings are directly related to the C-D bond order parameters, SCD k , and the assignment of the doublets allows us to determine the order parameters for all positions along the chain. In the plateau region, where the corresponding peak has a width of about 250 Hz, the accuracy -3 in the determination of SCD k is about (1 × 10 , while for the other well resolved positions it is estimated to be about (5 × 10-4. Following the C-C bond order parameter formalism,1 the SCC k were calculated from the C-D bond order profile. For the sake of clarity, only SCC 2 is reported in Table 1 as a function of temperature. Note that SCC 2 could not be estimated accurately at 30 °C therefore it is not included in the table. As observed for the deuterium order parameters, SCC 2 also decreases with temperature, reflecting the increase in fatty acyl chain disorder. order profile of the It should be mentioned that the SCC k palmitic acid chain exhibits a behavior similar to that of biomembranes.1 Indeed, in both systems an odd-even effect is calculated is observed in the plateau region.9 Since SCC 2 order profile using a recursion relation, its from the SCD k accuracy is approximately (2 × 10-2 due to the accumulation of errors during its calculation.
Letters
J. Phys. Chem., Vol. 100, No. 43, 1996 17085
Figure 3. Two-dimensional correlation spectrum for the palmitic chain selectively labeled at positions 1 and 2. The dipolar interaction leads to magnetization transfer as in conventional separated local field experiments. The diagonal accounts for the autocorrelation contribution, whereas cross correlation peaks, at the intersection of the C1 and C2 chemical shifts, arise because of the dipolar coupling between carbons 1 and 2. The square pattern obtained permits the unambiguous assignment of the peaks in the carbonyl region of the 1D spectrum.
Figure 2 displays the one dimensional 13C spectrum recorded with 1H decoupling at 30 oC. Overlapping peaks from the various sites on the palmitic acid chain and the liquid crystal are observed. Although 80% of the palmitic acid is selectively labeled with 13C, the (1.1%) natural abundance of this nucleus yields a significant contribution from the liquid crystal because the weight ratio of liquid crystal to palmitic acid is about 10to-1. Due to the complex composition of this commercial liquid-crystalline phase (ZLI 1132) it is not possible for us to assign all of the peaks in the spectrum. However, the strong dipolar coupling between the two adjacent 13C labels on the fatty acid enable us to unambiguously identify the palmitic acid carbonyl doublet near 200 ppm. There should be a corresponding doublet in the methylene region of the spectrum with the same dipolar splitting; however, the overlap with the many liquid crystal peaks makes the identification of these peaks difficult. For this reason, we performed the two-dimensional correlation experiment (analogous to 2D-COSY) shown in Figure 3, at
13 Figure 4. SCC 2 as a function of temperature, measured from C NMR (O) and calculated using the C-C bond order parameter formalism and the C-D order profile (b), as discussed in the text. The experimental data are listed in Table 1. The accuracy of the two SCC 2 determinations is (8 × 10-3 and (2 × 10-2, respectively.
17086 J. Phys. Chem., Vol. 100, No. 43, 1996 30 °C. The dipolar coupling results in a transfer of magnetization similar to that in separated local field or proton-detected local field experiments.7,8,16 Cross-correlation peaks appear at the intersection of the C1 and C2 chemical shifts. The square pattern obtained allows the unambiguous identification of the labeled residues in the 1D spectrum from which the dipolar coupling is measured. The square patterns obtained in the cross peaks of this 2D experiment also permit an estimate of the dipolar coupling, but having made the assignments, measurement of the dipolar splittings is more accurate in the 1Dexperiment ((50 Hz). The dipolar splittings are given as a function of temperature in Table 1. From these data one may 17 also calculate SCC 2 , taking the average orientation of the long molecular axis to be along the liquid-crystal director (aligned parallel to the external static magnetic field). The 100 Hz width of the peaks in the 1D spectrum results in an accuracy in -3 SCC 2 (determined from the dipolar splitting) of (8 × 10 . Figure 4 shows the C1-C2 bond order parameter, SCC 2 , determined by both methods, as a function of temperature. The two methods agree nicely over the temperature range measured from 0.30 to 0.20 (on (35-50 °C). The decrease of SCC 2 raising the temperature from 35-50 °C) is well outside the uncertainty in the measurements. Even though as many as 10 chain positions are unresolved in the plateau region (in the 2H spectra), the accuracy of the recursion method is quite good. The smaller plateau region in biological and model membrane systems will give even more accurate results. Because chain perdeuteration is generally much easier than specific 13C labeling of lipids, this provides a useful and simple means for determining C-C bond-order parameters in lyotropic
Letters and/or thermotropic systems. Knowledge of C-C bond-order parameters can be used to determine conformer probabilities and the number of gauche defects per chain as well as the average hydrophobic chain length.1 The C-C bond-order parameter formalism therefore contributes to our understanding of the conformational and dynamical properties of aliphatic chains. References and Notes (1) Douliez, J. P.; Le´onard, A.; Dufourc, E. J. Biophys. J. 1995, 68, 1727. (2) Seelig, A.; Seelig, J. Biochemistry 1974, 13, 4839. (3) Oldfield, E.; Gilmore, R.; Glazer, M.; Gutowsky, H. S.; Hshung, J. C.; Kang, S. Y.; King, T. S.; Meadows, M.; Rice, D. Proc. Natl. Acad. Sci. U.S.A. 1978, 75, 4657. (4) Davis, J. H. Biochim. Biophys. Acta 1983, 737, 117. (5) Meier, P.; Ohmes, E.; Kothe, G. J. Chem. Phys. 1986, 85, 3598. (6) Morrison, C.; Bloom, M. J. Chem. Phys. 1994, 101, 29. (7) Hong, M.; Schmidt-Rohr, K.; Pines, A. J. Am. Chem. Soc. 1995, 117, 3310. (8) Nakai, T.; Terao, T. Magn. Reson. Chem. 1992, 30, 42. (9) Douliez, J. P. Ph.D. Thesis, Bordeaux I University, 1995. (10) Ferrarini, A.; Nordio, P. L.; More, G. J.; Crepeau, R. H.; J. H., F. J. Chem. Phys. 1989, 91, 5707. (11) Schindler, H.; Seelig, J. Biochemistry 1975, 14, 2283. (12) Morrow, M.; Singh, D.; Lu, D.; Grant, C. W. M. Biophys. J. 1993, 64, 654. (13) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (14) Davis, J. H.; Jeffrey, K. R. Chem. Phys. Lipids 1977, 20, 87. (15) Engel, A. K.; Cowburn, D. F.E.B.S. Lett. 1981, 126, 169. (16) Waugh, J. S. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 1394. (17) Abragam, A. Principles of Nuclear Magnetism; Oxford University Press: London, 1961.
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