Quadrupolar Echo Deuteron Magnetic Resonance Spectroscopy in

7 Quadrupolar Echo Deuteron Magnetic Resonance Spectroscopy in Ordered Hydrocarbon Chains*

Downloaded by TUFTS UNIV on November 27, 2015 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0034.ch007

J. H . D A V I S , K . R. J E F F R E Y , * * M. B L O O M , and M . I. V A L I C

Department of Physics, University of British Columbia, Vancouver, B. C., Canada V6T 1W5 T. P. HIGGS Department of Chemistry, University of British Columbia, Vancouver, B.C., Canada V6T 1W5 Phospholipid hydrocarbon chain fluidity and the liquid cry stalline nature of the bilayer play an important role in the act ivity of biological membranes [1]. The molecular dynamics in these systems can be described by the order parameters Si and the correlation times τi for the different positions on the hydro carbon chains. The Si provide a convenient measure of the mean square amplitudes of the motion while the τi give the time scales over which these motions occur. Since the molecular motions in liquid crystalline systems are anisotropic, in contrast to those in ordinary liquids, the static electric-quadrupole and magnetic -dipole interactions are not completely averaged out [2]. The residual quadrupolar or dipolar splittings in the nuclear magnetic resonance spectrum are easily measurable and can be directly related to the order parameters S i . Relaxation time measurements can be used to determine the correlation times τi when the motions occur at frequencies less than or of the order of the Larmor frequency ω o . NMR, then, is well suited to the study of the molecular dynamics of these systems. The proton is, of course, the obvious nucleus to choose in an NMR study of these systems. However, since the dipolar interaction between protons along the chain produces a line broadening of roughly the same magnitude as the line splitting due to the nearest neighbour dipolar interactions, one normally observes a single broad absorption peak [3] and it is difficult to extract detailed information on the protons at different positions along the chain. The deuteron is uniquely suitable for studies of Si since its quadrupole moment leads to a split ting which, in most cases, is much larger than the linewidths *Research supported by the National Research Council of Canada and a special Killam-Canada Council Interdisciplinary Grant. **Permanent address: Department of Physics, University of Guelph, Guelph, Ontario, Canada NIG 2W1.

70

In Magnetic Resonance in Colloid and Interface Science; Resing, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.


7.

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Ordered

Hydrocarbon

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Chains

due to dipolar interactions between deuterons or to f i e l d inhomogeneities. Deuterium i s readily available and may be freely substituted for the hydrogen i n these molecules without drastic a l l y altering the dynamics of the system. Since the degree of motion experienced by inequivalent deuterons i s frequently quite different, the splittings, which depend on the amount of motional averaging, w i l l d i f f e r and, i n some cases, even i n a system with many different deuteron sites, the individual lines may be resolved. There are some experimental d i f f i c u l t i e s i n doing deuterium magnetic resonance, however. Foremost among these are the problems i n the chemical preparation of selectively deuterated samples. The preparation of perdeuterated samples i s often significantly easier and, i f the individual lines are well resolved, the use of these samples can provide very significant savings i n time since a l l of the positions along the chain can be studied at once. Further, the absence of protons with their relatively large magnetic moments sharpens the lines considerably. Another d i f f i c u l t y arises from the orientation dependence of the splittings. In many systems of biological interest, i t i s impossible to use oriented samples, so that information on the splittings must come from the study of unoriented samples· The resulting powder pattern spreads the signal intensity over a wide range. In principle, the study of such powder spectra does offer some advantages, however, providing that the broad spectra can be f a i t h f u l l y reproduced, since a single spectrum can give infor mation on a l l orientations at once. The instrumental d i f f i c u l t i e s encountered are due to the fact that i n conventional electromagnets the maximum deuteron resonance frequency i s about 15 MHz. This low frequency results i n r e l a t ively poor signal-to-noise, necessitating the use of extensive signal averaging, i n some cases requiring very long time to obtain a good spectrum. Often the deuterium powder spectra are very broad (up to ^ 100 - 200 kHz) implying that much of the information i s contained i n the very early part of the freeinduction-decay. Since the dead-time of most spectrometers operating i n this frequency range i s many tens of microseconds, much of the information about these broad components i s lost and cannot be f a i t h f u l l y reproduced. The usual application of pulsed Fourier transform spectro scopy involves the accumulation of the free-induction-decay (fid) following a single π/2 pulse applied at a frequency ω close to the sample's resonant frequency ω . The Fourier transform of this f i d gives the frequency spectrum of the sample. This technique can, of course, be applied to a quadrupolar system, such as a deuterated sample. The quadrupolar spectrum of a given deuteron (1=1) i s a doublet with lines at ω ± Ω. For ω = ω , the f i d of a collection of isolated deuteron spins having quadrupolar interactions i s given by 0

0

0


72

M A G N E T I C

g(Q)cosOtdQ.

F (t) x

RESONANCE

(1)


The d i s t r i b u t i o n f u n c t i o n g(0) f o r t h e deuteron quadrupolar f r e quencies i n an a n i s o t r o p i c l i q u i d c r y s t a l l i n e system i s obtained by summing over s p l i t t i n g f r e q u e n c i e s corresponding to a l l none q u i v a l e n t deuteron p o s i t i o n s i = l , 2 , . . . , N , and over the frequen c i e s a s s o c i a t e d w i t h the d i s t r i b u t e d of angles θ between the e x t e r n a l magnetic f i e l d and t h e c o n s t r a i n t v e c t o r or d i r e c t o r determined by the symmetry p r o p e r t i e s of the o r i e n t e d f l u i d .

v > =1 i e

K

s

(

i

i £ 2

i^)'

«)

2

where K i « e qiQ/tf i s the quadrupole c o u p l i n g constant f o r t h e i t h deuteron and the order parameter S i i s g i v e n by the ensemble average f

S

(3)

2

±

- J$(3cos ® -l) ±

i n v o l v i n g the angle ( Η ) ^ between the a x i s of symmetry of t h e e l e c t r i c f i e l d g r a d i e n t [ 4 ] , i . e . the C - D ^ bond d i r e c t i o n * * * , and the d i r e c t o r . For l a m e l l a r phases of the type s t u d i e d here, the d i r e c t o r i s perpendicular t o the planes of the l a m e l l a e . Since K± ^ Κ ^ 2π χ 1 . 7 x l 0 s " f o r a l l the methylene deuterons [6] and 0.25 i n the l a m e l l a r phases of soap s o l u t i o n s [7] and model p h o s p h o l i p i d b i l a y e r membranes [ 8 ] , F ^ ( t ) decays a p p r e c i a b l y i n a time of order (Ω^)"^- ~ 40 ys l e a d i n g t o some of the experimental problems described above. Now, suppose that a second p u l s e which r o t a t e s the magnet i z a t i o n by an angle θ and having r - f phase φ w i t h respect t o the f i r s t pulse i s a p p l i e d a t a time τ a f t e r the f i r s t p u l s e . A "quadrupole spin-echo" occurs a t t = 2τ due t o the r e f o c u s s i n g of the nuclear magnetization [ 9 ] . T h i s echo i s maximum when θ = π/2 and φ = π/2. Indeed, the r e f o c u s s i n g i s complete under these c o n d i t i o n s , a s i d e from e f f e c t s of r e l a x a t i o n and s t a t i c magnetic f i e l d inhomogeneities, so t h a t one can w r i t e the e x p r e s s i o n f o r the nuclear i n d u c t i o n s i g n a l i n the r e g i o n t ^ τ as 5

F (t) «{ J 2

1

g(Q)cos[a(t-2-)]dn > J R(t)

(4)

*** The a p p r o p r i a t e formula f o r S^ t a k i n g i n t o account t h a t the e l e c t r i c f i e l d g r a d i e n t tensor i s not q u i t e a x i a l l y symmetric about the C-D bond i s g i v e n elsewhere [ 5 ] .


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Chains

where R(t) represents the loss of transverse magnetization due to relaxation. Since the relaxation effects are produced primarily by magnetic dipolar interactions, which are much weaker than quadrupolar interactions for deuterons, or by very low frequency components of the fluctuating part of the quadru polar interactions, which are also usually much less effective than the dephasing effects of the distribution g(Q) of s t a t i c , l o c a l , quadrupolar frequencies for the anisotropic systems discussed here, i t i s usually possible to select a value of τ which i s much greater than the recovery time of a reasonably good r - f amplifier, but much less than the transverse relax ation time T . Under these conditions, i t i s possible to obtain a f a i t h f u l reproduction of the spectrum by calculating the Fourier Transform of F ( t ) starting at t = 2τ. It should be noticed that i f the transverse relaxation time of the i t h deuteron i s given by T , i . e . Ri(t) = exp(-t/T2i), the powder pattern lineshape i s given by


2

2

f

2i

where n± i s the number of deuterons having index i and A i s a normalization constant. This spectrum consists of a super position of Ν broad absorption curves, each with two sharp edges separated by a frequency àv± » Ω^(0)/2π = SK^S-jy (8π) corresponding to the ±π/2 orientations. Figure 1-a shows the quadrupolar echo observed i n a solution of 70% (by weight) perdeuterated potassium palmitate (CD3(CD2)l4C00K)t - 30% H 0 at 100°C. The f i r s t pulse rotates the equilibrium magnetization by π/2 and i s followed by the free-induction-decay. A time τ later the second pulse, also a π/2 pulse which is phase shifted by π/2 radians, i s applied. At 2τ the magnetization has refocussed and the entire signal i s observed (notice that the very sharp spike seen at t 2τ in the echo has been lost from the f i d due to the spectrometer dead time). The echo shown i n the figure, the result of 200 scans, when transformed gives the spectrum shown i n Figure 1-b. 2

x

t P a l m i t i c - d acid and β, Y-di(palmitoyld-d ) - L-ot-Lecithin were prepared according to published procedures [11,12]. 31

31


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M A G N E T I C

RESONANCE

(α) 2 mete


(b)

(0

Figure 1. (a) The quadrupolar echo in the lameUar phase of KP-d at Τ — 100°C occurring at t — 2r, where τ — 400 psec, from 200 scans with à dwell time of 10 psec. (b) The spectrum obtained from the Fourier transform of the quadrupohr echo. Spectral width is 50 kHz. (c) Computer simuhtion of the spectrum shown in b using Eq. (5). 3i

Even though the spectrum i s v e r y broad and c o n s i s t s of a l a r g e number of o v e r l a p p i n g powder p a t t e r n s , 14 of the 15 p o s s i b l e peaks are c l e a r l y r e s o l v e d and the b a s e l i n e i s f l a t . By c a r e f u l l y s e t t i n g the phases of the two p u l s e s and by s t a r t i n g the d i g i t i z a t i o n of the s i g n a l a t the exact c e n t e r of t h e echo no phase adjustments need t o be made on the transformed spectrum. Since the spectrum i s symmetric about ω the r f p u l s e s are a p p l i e d a t t h i s frequency causing the two h a l v e s of the spectrum t o be superimposed r e s u l t i n g i n a /2 improvement i n signal-to-noise r a t i o . F i g u r e 1-c i s a computer s i m u l a t i o n of t h i s spectrum from a s u p e r p o s i t i o n of 15 powder p a t t e r n s w i t h l i n e s h a p e s g i v e n by Equation ( 5 ) . T h i s s i m u l a t i o n g i v e s a f a i r l y a c c u r a t e r e p r e s e n t a t i o n of the spectrum l e a d i n g one t o b e l i e v e t h a t , even when many of the l i n e s o v e r l a p , an a c c u r a t e c h a r a c t e r i z a t i o n of the order parametersis p o s s i b l e . From such a c l e a r l y d e f i n e d spectrum, one can c o n f i d e n t l y o b t a i n the s p l i t t i n g s Δν^ as a f u n c t i o n of p o s i t i o n on the c h a i n , as shown i n F i g u r e 2, and from these d i r e c t l y determine the order parameters S^. A t lower temperatures the w e l l e s t a b l i s h e d " p l a t e a u " c h a r a c t e r i s t i c o f the order parameters 0



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4

6

8

10

Hydrocarbon

12

14

POSITION ALONG THE CHAIN

Chains

75

Figure 2. The peak positions rehtive to vo — 13.815 MHz, at Τ — 100°C for the spectrum shown in Figure 1(b), plotted against position along the hydrocarbon chain

of these systems [4,7,8] i s observed. However, the plateau is wiped out at high temperatures. The obvious pairing of the lines, as illustrated here, i s a result of the "odd-even effect" {10]. A more detailed description of the temperature dependence of the order parameters i s i n progress and w i l l be reported elsewhere. An example of a situation where the lines are not clearly resolved i s shown i n Figure 3. This spectrum i s for a 250 mg sample of chain-deuterated d i - p a l i t o y l phosphatidyl choline at 50 C. Since there are two chains i n this molecule which are not necessarily undergoing the same motions, as many as 30 overlapping powder pattern spectra can be expected from this sample. In order to f a i t h f u l l y reproduce this spectrum i t i s important that no information be lost due to spectrometer dead-time. Figure 3-a shows the spectrum as obtained by transforming the quadrupolar echo after accumulating 4000 scans. Figure 3-b i l l u s t r a t e s the effect of the loss of the i n i t i a l part of the f i d due to dead time. Here 4000 scans of the f i d were accumulated with a dead time of 50 μsec at 13.815 MHz with a spectral width of 50 kHz. The spectrum obtained from the transform, as given i n Fig. 3-b, i s severly distorted. The first-order phase correction which should be apglied to the spectrum i s simply (dead time/dwell time) χ 180 - 900 , and no zeroth order phase correction i s required. If the f i r s t five points i n the echo used for Figure 3-a are dropped, to correspond to a dead time of 50 μsec, and the transform i s carried out, as well as the same f i r s t order phase correction (900 ) as applied to the fid's spectrum, the spectrum appears as i n Figure 3-c. As expected, Figures 3-b,c are nearly In Magnetic Resonance in Colloid and Interface Science; Resing, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.


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Figure 3. (a) The spectrum for DPLd atT = 50° obtained from the quadrupolar echo after accumulation of 4,000 scans (spectral width of 50 kHz), showing several resolved lines as well as the characteristic plateau. The scale has been expanded by a factor of four in the base line region to illustrate the shoulder, the signal-to-noise ratio, and the flat base line, (b) The spectrum obtained under the same conditions as in (a) but using the fid with a dead time of 50 psec, properly phase corrected, (c) The same spectrum, obtained by discarding the first five points in the quadrupolar echo (dwell time is 10 psec) and making the same phase correction as in (b). st


RESONANCE


7.

DAVIS

E T A L .

Ordered Hydrocarbon

Chains

i d e n t i c a l . The d i s t o r t i o n apparent i n these s p e c t r a i s a r e f l e c t i o n of the i n f o r m a t i o n l o s t d u r i n g the spectrometer dead time, and f u r t h e r adjustments of the phase knobs c a n only g i v e m i s l e a d i n g r e s u l t s . Because of the improvements i n s i g n a l - t o - n o i s e and spectrum f i d e l i t y a l a r g e v a r i e t y of experiments which were p r e v i o u s l y v e r y time-consuming become q u i t e manageable. Temperature dependent s t u d i e s of the quadrupolar s p l i t t i n g s and r e l a x a t i o n times i n these systems a r e p r e s e n t l y underway and w i l l be r e p o r t e d in the Symposium. An apparent r e l a t i o n s h i p between the temperature dependence of the hydrocarbon c h a i n order parameters and the water (D£0) order parameters w i l l be d i s c u s s e d . A l s o , the v a r i a t i o n of the r e l a x a t i o n times along the c h a i n i n d i c a t e s the i n f l u e n c e of c o l l e c t i v e motions. The a p p l i c a t i o n of t h i s technique t o n a t u r a l membranes i s expected t o be p a r t i c u l a r l y rewarding. ACKNOWLEDGMENTS We wish t o thank Dr. E.E. B u r n e l l and Dr. A. MacKay f o r helpful discussions.

LITERATURE CITED [ 1] Chapman, D., Quart. Rev. Biophys., (1975), 8, 185. [ 2] Lawson, K.D., and Flautt, T.J., J. Am. Chem. Soc., (1967), 89, 5489; Charvolin, J., and Rigny, P., J. Chem. Phys., (1973), 58, 3999. [ 3] Lawson, K.D., and Flautt, T.J., Mol. Cryst., (1966), 1, 241 and J. Phys. Chem., (1968), 72, 2066; Wennerstrom, Η., Chem. Phys. Letters, (1973), 18, 41. [ 4] Charvolin, J., Manneville, P., and Deloche, Β., Chem. Phys. Letters, (1973), 23, 349. [ 5] Wennerstrom, Η., Persson, Ν., and Lindman, Β., ACS Symposium Series, (1975), 9, 253. [ 6] Burnett, L.J., and Muller, B.M., J. Chem. Phys., (1971), 55, 5829. [ 7] Mely, Β., Charvolin, J., and Keller, P., Chem. Phys. Lipids, (1975), 15, 161. [ 8] Seelig, A., and Seelig, J., Biochem., (1974), 13, 4839. [ 9] Solomon, I., Phys. Rev., (1958), 110, 61. [10] Marcelja, S., J. Chem. Phys., (1974), 60, 3599; Pink, D.A., J. Chem. Phys., (1975), 63, 2533. [11] Dink-Nguyen, Ν., and Stenkagen, E.A., Chem. Abstracts, (1967), 67, 63814. [12] Cubero-Robles, Ε., and Van Den Berg, D., Biophys. Biochem. Acta., (1969), 187, 520.


Quadrupolar Echo Deuteron Magnetic Resonance Spectroscopy in

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