2H NMR lineshapes of immobilized uniaxially oriented membrane proteins

21

Solid State Nuclear Magnetic Resonance, 2 (1993) 21-36 Elsevier Science Publishers B.V., Amsterdam

2H NMR lineshapes of immobilized uniaxially oriented membrane proteins Anne S. Ulrich and Anthony Watts Department

of Biochemistry,

University

of Oxford,

South

Parks

Road,

Oxford

OX1

3QU,

UK

(Received 18 January 1993; accepted 9 February 1993) Abstract As a method for the structure determination of integral membrane proteins or other large macromolecular complexes, a solid state ‘H NMR approach is presented, capable of measuring the orientations of individual chemical bond vectors. In an immobilized uniaxially oriented sample, the bond angle of a deuterium-labelled methyl group relative to the axis of ordering can be calculated from the quadrupole splitting in the “zero-tilt” spectrum where the sample normal is aligned parallel to the spectrometer field direction. However, since positive and negative values of this splitting cannot be distinguished, there may appear to be two solutions, of which only one describes the correct molecular geometry. We show that it is possible to determine the bond angle uniquely between 0” and 90”, by analysing the lineshapes of a tilt series of spectra acquired over different sample inclinations. The lineshape equation describing such oriented ‘H NMR spectra will be derived (for asymmetry parameter TJ= 0) and discussed, with an illustration of the various linebroadening effects from which the orientational distribution function in the macroscopically ordered system can be determined. This strategy is then applied to specifically deuterium-labelled retinal in dark-adapted bacteriorhodopsin, prepared in a uniaxially oriented sample from purple membrane fragments. From the quadrupole splitting in the zero-tilt spectrum and by lineshape simulations, the deuteromethyl group at C,, on retinal is found to make an angle of 32”k 1” with the membrane normal, and the sample mosaic spread to be around f8”. The resulting orientation of retinal is in excellent agreement with its known structure in bacteriorhodopsin, and together with the results on other methyl groups it will be possible to construct a detailed picture of the chromophore in the protein binding pocket. Keywords:

‘H NMR; lineshape simulation; uniaxially oriented sample; bacteriorhodopsin;

Introduction Solid state NMR spectroscopy offers the possibility of investigating macromolecular systems which are immobile on NMR timescales or undergo restricted anisotropic motion, for example proteins that are embedded in a biological membrane. Unique information about local protein structure and dynamics [l-17] can be derived by examining the anisotropic interactions of specific reporter nuclei that have been introduced in the molecule through selective labelling. While protein dynamics may often be investigated with unoriented samples, for the determination of structural details, it is usually necessary to use

retinal structure

uniaxially ordered samples. In these oriented systems, the spatial dependence of the nuclear spin interaction is observed and translated into structural information in terms of molecular bond angles. Even though it may not always be feasible to elucidate the complete three-dimensional structure of a protein this way [9-11,171, many details may be resolved about a specific site of interest, such as a bound ligand or substrate in an active site [2,12], the protein backbone [4-7,15,16] or selected amino acid side chains [1,13,14]. Here, we discuss a solid state deuterium (2H> NMR method by which the orientation and conformation of a prosthetic group in a membrane protein can be determined from the measure-

22

ment of individual methyl group bond vectors. A deuterium-labelled methyl group in an immobilized uniaxially oriented sample gives rise to characteristic orientation-dependent 2H NMR lineshapes when measured at different sample inclinations in the spectrometer magnetic field. The quadrupole splitting in the simple “zero-tilt” spectrum alone, where the molecules are aligned with the direction of the spectrometer magnetic field, may not be sufficient to determine the bond angle unambiguously, when the sign of this splitting is indeterminate [1,2,.5,9,13]. Some previous NMR investigations faced with the problem of multiple solutions have applied restriction analysis as a method of excluding certain angles that are incompatible with known constraints on the molecular structure, but this requires additional knowledge about the system. We present the details of a novel strategy to obtain the unique deuterium bond angle between 0” and 90” relative to the sample normal, based on the analysis of the more complicated spectral lineshapes from the tilted sample. Having recently applied, but not yet described in detail, this approach to bacteriorhodopsin with a selectively ring-deuterated chromophore [2], we will now discuss the method comprehensively and use it to analyze a tilt series of 2H NMR spectra from the labelled polyene chain of the chromophore. From the different orientations of the measured deuteromethyl groups it is then possible to construct a three-dimensional picture of the local molecular structure, in this case of the chromophore within the protein binding pocket. Complementary neutron scattering experiments, also using deuterated and uniaxially oriented samples, provide an independent way of further localizing the absolute depth of the labelled segment within the membrane and thus to complete the picture of the three-dimensional local protein structure [18,19]. The same 2H NMR analysis can be applied equally well to the investigation of other types of oriented material such as polymers [20], oligonucleotides or DNA [21,22], as well as crystallites in a matrix [12,13]. In principle, the deuterium lineshape equation for uniaxially oriented samples describes all nuclear interactions (quadrupolar, dipolar, chemical shift anisotropy) with an axially

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symmetric anisotropy of (3 cos20 - 1). The approach described here may thus find general application in various other cases where the sign of the spectral splitting is not available, for example in the analysis of 14N quadrupolar spectra, or homonuclear and heteronuclear dipolar spin interactions between ‘H, 13C, or 15N in uniaxially oriented samples [9].

2H NMR theory The deuterium nucleus is particularly wellsuited for the study of molecular geometry and dynamics in solids, and the fundamental aspects of 2H NMR have been reviewed extensively [14,23-261. The deuterium spectral lineshapes are dominated by the orientation-dependent quadrupole interaction of the Z = 1 spin with the electric field gradient at the labelled site, which for aliphatic segments is approximately axially symmetric about the C-D bond direction (asymmetry parameter T-Z= 0). Therefore, in the absence of motion, the resonance position v * of either of the two (*)-transitions is directly related to the angle 0 between the deuterium bond vector and the spectrometer magnetic field H, giving a quadrupole splitting AvJ8): At&I)

= u+- ZL = 3(e2qQ/h)/2.

(3 c0s2e - 1)/2

(1)

The static quadrupolar coupling constant (e2Qq/h) is approximately 170 kHz for C-D bonds [27]. Any motion of the C-D bond that is fast on the 2H NMR timescale (with a correlation time 7c < 10m7 s) causes partial averaging of this quadrupole interaction. This leads to a reduction in the value of the term (3 cos28 - 1)/2 by a factor of (3 cos2p - 1)/2, where p is the timeaveraged angle between the deuterium bond and the axis of motional averaging. A rapidly rotating (but otherwise immobilized) deuteromethyl group therefore has a threefold reduced splitting, where p = 109.5” reflects the tetrahedral geometry of the rotor axis, and 8 then represents the angle of this methyl group bond vector relative to the spectrometer field direction H. Any additional

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wobbling motion of this methyl group or of the whole protein framework will concomitantly lead to a further reduction in the observed splitting. The sensitivity of the experiment is enhanced when a methyl rotor is used as a molecular reporter, since the signal of a methyl-deuteron is confined into l/3 or less of the spectral width compared to that of a rigid C-D segment, and also the number of deuterons brings about an additional three-fold gain in absolute intensity. In the fast motional regime, it is thus the various modes of motional averaging which determine the scaling factor that relates the measured quadrupole splitting in kHz to the angular term (3 cos28 - 1). The exact value of this constant is equal to the splitting, Avcwder, of the lineshape maxima in the 2H NMR powder pattern obtained from an unoriented sample. Such a powder sample may be conveniently prepared by scrambling the oriented sample, however, it will be shown later that the value of Avgwder is also directly available from the oriented lineshapes alone. Either way, for the analysis of an individual oriented deuterium bond vector, the relationship of its spectral quadrupole splitting to its bond angle 0 is simply given by AvQ(6) = Avgwder. (3 cos28 1). If any of the C-D bond motions falls into the intermediate timescale of the 2H NMR experiment (1O-4 s < rc < lop7 s>, the time-dependent averaging between several discrete environments would lead to non-axially symmetric lineshapes [23], which complicates the analysis and will not be considered here. In practice, however, methyl groups are usually spinning rapidly enough (7, < lop7 s) even at low (a OOC) temperatures to guarantee axially symmetric lineshapes (77 = 01, and the fast dynamics furthermore alleviate the typical problems in solid state NMR measurements of short T2 and long TI relaxation times.

23

21-36

be directly determined using eqn. (1). Any distribution of the bond vector over different orientations in the sample, however, leads to a more complex spectral lineshape which contains all contributions weighted by their respective probabilities. Uniaxially oriented samples are readily prepared for a variety of systems and give rise to characteristic 2H NMR spectra that can be analyzed to find the orientation of the bond vector relative to the axis of ordering and to estimate the distribution function around this angle [2,3,13,20-221. In such a uniaxially ordered system there is no translational or rotational symmetry around the axis of alignment, but all deuterium bond vectors D lie uniformly along the rim of a cone with an angle y. Figure 1 illustrates this geometry for the case of an oriented sample at an arbitrary inclination (Y in the spectrometer magnetic field. The critical parameter which determines the spectral lineshape is the angle 8, summed and weighted over all the different values it may assume, as 4 is taken from 0” to 360”. In the case of perfect order the cone angle y is well defined, whereas in practice any slight disorder in the alignment of the microdomains within the sample leads to a distribution of values around y, as manifest in the mosaic spread of the sample. It is immaterial in the 2H NMR analysis whether these cones are facing up or down, since the quadrupole interaction is the same for angles 0 and (180’ - 0). Uniaxially oriented immobilized samples exhibit particularly simple 2H NMR spectra when aligned parallel to the direction of the applied magnetic field [2,3,10-141. When the sample normal N lies parallel to the spectrometer field H, that is at an inclination a = o”, then the crucial angle 0 coincides with the cone angle y. The resulting “zero-tilt” spectrum will therefore consist of two lines with a quadrupole splitting AvQ(y) [equal to AvQ(0) with 0 = y in eqn. (111 that is directly proportional to (cos2y):

Uniaxially oriented samples Av,( y) = Av&owder. (3 cos2y - 1) A single two narrow quadrupole bond angle

crystal 2H NMR spectrum consists of lines, with an orientation-dependent splitting from which the deuterium 0 relative to the axis of alignment can

(2)

With the known value of the proportionality constant Avgwder, the angle of the deuterium bond vector relative to the macroscopic axis of ordering

24

H

4-

Fig. 1. A uniaxially oriented sample shown at an inclination (Y relative to the spectrometer magnetic field H. All immobilized deuterium bond vectors (or deuteromethyl rotors) D of any one type lie uniformly along the rim of a cone with angle y around the membrane normal N. This axis coincides with the sample normal for the case of perfect orientation (zero mosaic spread) and it is defined parallel to the z-axis of the coordinate system which was used in the derivation of eqn. (9) describing the *H NMR spectral lineshape. The spherical polar coordinates of D are y (fixed) and 4, and one particular vector D is shown making an angle 0 with 2% All D vectors contribute to the spectrum and 4 is taken from 0 through to 360”. The corresponding variation in the value of 19,which determines the respective quadrupole splittings [eqn. Cl)], leads to the complex lineshape of eqn. (9).

can be thus be determined. This method has been applied to magnetically oriented crystallites of heme proteins [12,13], drawn fibres and films of DNA [21,22] or polyethylene [20]. The measurement of the quadrupole splitting from the 2H NMR spectrum of a uniaxially oriented sample aligned parallel to the spectrometer field (cu = 01, however, is not necessarily sufficient to determine the deuterium bond vector uniquely. The calculation suffers from one drawback, in that positive and negative signs of Avo(y) from the zero-tilt spectrum cannot be discriminated, so that one splitting may yield two possible bond angles as a solution. This is the case for all cone

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angles y between 35” and 90”, which lie on opposite sides of the magic angle (54.7”) and respectively yield the same absolute value of AvO(y). To resolve this problem, we introduce an analysis based on the measurement of a tilt series over different inclinations of the oriented sample in the spectrometer magnetic field. At any sample alignment other than parallel to the field direction, the lineshapes are much broader and considerably more complex than the simple pair of resonances obtained in the zero-tilt spectrum at (Y= 0”. From Fig. 1 it can be seen that a tilted conical distribution of deuterium bond vectors encompasses a range of angles 0, which all contribute their correspondingly weighted pair of resonance lines to the overall spectrum. The resulting lineshapes can be computed for any choice of intramolecular bond angle y and sample inclination (Y (see below). By simulating the experimental spectra, or even by simply inspecting their characteristic features, it is then straightforward to discriminate the previously indistinguishable solutions from the zero-tilt spectrum and to determine the unique molecular bond angle between 0” and 90”. Only the absolute direction of the bond angle remains undefined, that is whether it is pointing above (y) or below (180” - y) the plane of ordering. With appropriate linebroadening functions in the lineshape simulation program, it is furthermore possible to take into account the effects of disorder in the sample, and thus to quantitate the orientational distribution function or mosaic spread of bond angles y about the sample normal [20-221. It should be noted that this 2H NMR lineshape analysis applies only to the immobilized samples described here, and not to oriented systems in which the molecules as a whole are undergoing fast long-axial rotation. That is because any motional averaging along the sample normal leads to a collapse of the broad lineshapes into a narrow pair of resonances for all sample inclinations (Y,with a quadrupole splitting that scales with (cos2a). In that case, the deuterium bond angle y can be calculated directly from the splitting in the powder pattern, Avgwder, and there would be no need to use oriented samples [15]. Nevertheless, the fundamental com-

25

A.S. U/rich, A. Watts /Solid State Nucl. Magn. Reson. 2 (1993) 21-36

plication still remains of there being potentially two values for the deuterium bond angle when calculated from the measured quadrupole splitting. In the light of the 2H NMR analysis presented here, this problem may be solved if an oriented sample was used and cooled down in order to suppress long-axial rotation [7,8,16,22]. If it can be shown from the quadrupole splittings at (Y= 0” that the molecular geometry is not significantly affected by the change in temperature or phase state, then the characteristics of the now immobilized system can be exploited as described here. In fact, for several axially averaged systems, such as gramicidin or a-tocopherol in phospholipid bilayers [1,5-7,281, 2H NMR investigations have already been designed around uniaxially oriented samples, despite the aforementioned suitability of unoriented powder samples for the determination of deuterium bond angles. That is because this provides the only possible way to separate local and global motions and to detect whether the molecular long-axis of averaging coincides with the sample normal, whereas the analysis of powder samples alone would leave considerable uncertainties in the description of molecular structure and dynamics.

Protein structure

For a comprehensive description of local protein structure, the deuterium-labelled groups may be exploited as molecular reporters to provide information not only about their own orientation, but also about the geometry of adjacent segments, notably when these are rigid structures such as planar rings or the protein backbone. Although the axial symmetry of the effective deuterium bond direction leaves the torsion angle around this bond undefined, it is nevertheless possible to construct a three-dimensional picture of the local site on a molecule from the measurement of several individual deuterium bonds, as long as their intramolecular geometry with respect to one another is known. This may be achieved by molecular-modelling approaches based on either the use of restriction maps [9,10] or analytical methods [4,28], as have been applied

to peptide backbone segments or other rigid molecules in lipid bilayers. Whilst previous 2H NMR investigations of immobilized oriented samples [12,13,21,22] have not focussed on the measurement of connected bond vectors to determine the three-dimensional molecular structure of the labelled site, we have recently explored this strategy using the integral membrane protein bacteriorhodopsin containing a deuteriumlabelled chromophore [2]. In this initial study, three deuteromethyl groups were simultaneously present in the same sample, which caused their resonances to overlap, so that the individual quadrupole splittings had to be deconvoluted first. Nevertheless, when the 2H NMR method is used to analyze a single deuteromethyl group at a time, as shown in the example below, the accuracy by which its bond angle can be determined is remarkably high, compared with other structural methods. Only the question concerning the absolute sidedness of the whole system cannot be answered by this ab initio 2H NMR method, although the relative directions of the individual bond vectors are implicit from their connectivities in the molecule. The 2H NMR measurements of deuteriumlabelled proteins are readily extended to the characterization of protein dynamics, such as backbone motions [5-7,15,26] and side chain dynamics [1,13,14] for which experiments are performed over a range of temperatures. Relaxation times provide information about fast (T,) and slow CT,) motions, while processes on the intermediate timescale of the experiment (10e4 s < ~~ < lo-’ s) are manifest in the diverse lineshapes with n # 0, for which equations are available elsewhere [23], even for the description of uniaxially oriented samples [29].

Lineshape derivation

The calculation of NMR lineshapes for partially ordered systems can be based on either the use of Wigner rotation matrices or on the analytical derivation of an expression that describes the spectral intensity envelope [20,25,29]. Here, the latter approach will be used to derive the line-

26

A.S. Ulrich, A. Watts /Solid State Nucl. Magn. Reson. 2 (1993) 21-36

shape equation for a deuterium bond in an immobilized uniaxially oriented sample, where the asymmetry parameter is 77 = 0. Mathematically, the spectral lineshape corresponds to the probability density p(l) which is a function of the reduced resonance frequency I, centred about the spectral origin ~a: &=

(v,-

vo)/Avt;owde’=

k(3 cos28 - 1)/2

From (3) we define cow

= [(2~+1)/3]‘/~=~(~+)

(6)

and from (4) we simplify the ratio COD

=

(COS((Y)

-

COS(Y)

/(sin(a)

sin(y)]

c05fe))

= A/B

(7)

so that correspondingly (3)

sin( 4) = (1 - A2/B2)1’2 Only one of the two (+)-transitions is calculated, say the l+-range (- l/2 I l+~ l), and the overall spectral envelope is then obtained by superimposing its mirror image l-. The vectors and angles used for the lineshape derivation are defined in Fig. 1, where the effective immobilized deuterium vectors D (in the example below the deuteromethyl group bond vectors) are shown to lie along the rim of a cone with an angle y around the normal N of the uniaxially oriented sample. At a fixed inclination (Y of the sample relative to the magnetic field H, the exact resonance position 5, corresponding to any one deuterium nucleus depends in a complex manner on the value of 4, as this angle varies between 0” and 360“ (see Fig. 1). This dependence, expressed in terms of f3 alone, gives the lineshape from eqn. (3). Angle 0 is defined by the two unit vectors H and D in Fig. 1 and is calculated from their scalar product of the two vectors in the X, y, z-coordinate system: cos(fl) =H*D/(H)(D)

= -sin( (.y) sin(y) cos(+) + cos( a) cos( y) withH=(

(4)

~~~)andD=[‘:“~~~~~’ I

Given that ~(4) = l/2 r, and with the differentials from (4) and (3), one obtains p(i’+> =bW = I1/2~.

-Wd@dVdll sin( e)/( sin( cy) sin(y) sin( 4))

. l/{ 3 sin( 0)

cos(e)}

1

(5)

= ( B2 - A2) 1’2/B

(8)

Substituting into (5), and factorizing the denominator with due attention to trigonometric relations, finally yields the lineshape equation:

P(S+) a [x(5+)1-1 *{[x- co+ +r>l *[co@- Y)-x(i+)l}-1’2 (9) with cos(a + Y)

- Y)

It is necessary that 0 I cy5 90” and 0 5 y s 90”. Note also that x(5+> < 0 for 0 > 90”, and that cos(a +y) 90”. With ,&+I= [c&J++ 1)/3P2 as defined in (6), eqn. (9) contains three singularities, (A), (B), (C), which represent peaks in the (4’+)-lineshape at the corresponding spectral positions: (A) P)

x(C+> = co+ x(f+) = co+

cc>

x(5+)

+ Y> -Y)

=o

The occurrence of a singularity can be visualized from Fig. 1 using geometric arguments. It is clear that with a smoothly changing 8, the bond vectors become crowded near the maximal and the minimal value of 8, namely e,, = ((Y + y) and f& = I cx- y I. The increased probability of these angles is thus reflected in an increased intensity at the corresponding positions (A) and (B) in the (5+)-l ineshape. Similarly, the spectral density corresponding to angles near 0 = 90” is increased due to the cos(B) dependence of i, so that another singularity (C) occurs at l+= - l/2 when the cone of bond vectors bisects the plane perpendicular to the spectrometer field in Fig. 1.

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Lineshape discussion Representative theoretical 2H NMR spectra are calculated from eqn. (9) above, without line-

27

broadening, and shown in Fig. 2 (normalized to height rather than area). The two tilt series illustrate the effect of progressively stepping cy by 10” increments, for two different molecular bond an-

sample inclination:

>

>

-1 -‘I* 0 7, 1 r -1 -‘I, 0 ‘I, 1 5 Fig. 2. Two theoretical tilt series of oriented *H NMR spectra, calculated from eqn. (9) without linebroadening and normalized to height. Spectra are displayed relative to the reduced resonance frequency ( [see eqn. (3)], and the lineshape arising from only the i+ range, out of the two nuclear (+)-transitions, is drawn shaded. In the zero-tilt spectrum at a sample inclination (Y= O”, the two different molecular bond angles, y = 38” (left column) and y = 78” (right column), give rise to identical quadrupole splittings of Av, = 7/8 units in c, but with opposite sign. On incrementing the sample inclination LY by steps of lo”, the two tilt series are distinguished by their characteristically different lineshapes, which are governed by the relative positions of the singularities (A), (B) and (0 from the lineshape eqn. (9).

28

A.S. Ulrich,

gles y. The representative examples of y = 38” (left column) and y = 78” (right column) give rise to indistinguishable zero-tilt spectra at a sample inclination (Y = 0“ (uppermost spectra), with ( Av,(y) I = 7/8 units in 5, but they correspond to a positive and negative splitting, respectively. Differences in the lineshapes become apparent when tilting the sample away from (Y= O”, and the two values of y can now be distinguished from the characteristic patterns of the relative peak positions throughout the tilt series. The spectral positions of singularities (A) and (B) depend on the value of y and they also vary in a distinctive way with the sample tilt angle (Y, as given by the limiting values 8,, = ((u + y) and emin = I (Y- y I. Singularity (Cl, on the other hand, remains invariant at l= it l/2 corresponding to 8 = 90” which only occurs for higher sample incli-

intrinsic linebroadening:

l.OkHz

/“?

I

I

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nations of the tilt series where (a + y) > 90”. Focussing on one of the two (&)-transitions, say on the shaded areas corresponding to J, in Fig. 2, it is seen that the ([+)-lineshape of the zero-tilt spectrum with LY= 0” consists of a single peak at ~(5) = cos(y). When the sample is tilted away from (Y= O”, the spectral lineshape is described by a smooth curve suspended between the two singularities (A) and (B), although the function is not symmetrical in itself. At higher sample inclinations, where (a + y) > 90”, a third singularity emerges at (Cl which will thereafter always constitute the left edge of the ((+I-lineshape (shaded areas). While the right edge still corresponds to (B), with increasing sample tilt angle the central singularity (A) progressively moves away from (Cl towards the other side, and finally merges with (B) when (Y= 90”. It is seen from each of the two

mosaic spread:

,fi

I

A. Watts /Solid

I

-1 -Vz 0 ‘/* 1

>

r

*6”

>

-1 -‘/* 0 ‘/, 1 6 Fig. 3. Calculated oriented 2H NMR spectra for various degrees of intrinsic linebroadening (left column) and of mosaic spread (right column), normalized to height. For all spectra, the underlying lineshape without any broadening (upper left spectrum) is taken from Fig 2 [bond angle y = 78”, sample inclination (Y= 50”, singularities (A), (B) and (C)l, and for the illustration of the mosaic spread (right column) an intrinsic linewidth of 1 kHz was used.

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different tilt series in Fig. 2 that the overall spectral width reaches its maximum (5 = + 1) when the sample inclination (Y is set equal to the value of the cone angle y. That is because only at this tilt angle do there exist bond vectors parallel to the magnetic field direction with 0 = 0”. This observation suggests that y could actually be found directly from a narrowly spaced tilt series of spectra, simply by determining the tilt angle (Y at which the spectral width is greatest. This approach would not even require knowledge of Avgwder for the calculation of y with eqn. (3), which would usually have to be measured separately from a specially prepared powder sample. On the other hand, it is now seen that this value Avpowder is readily available anyway from the fixed Q singularities (C) at 4’ = k l/2 in all oriented spectra recorded at high sample inclinations where (Y> 90” - y. The corresponding splitting is always well-resolved in the experimental spectra, unlike the other singularities (A) and (B) which get broadened or even smeared out by the effects of disorder in the sample, as discussed below. The appearance of an experimental 2H NMR spectrum differs considerably from that of the theoretical examples shown in Fig. 2, as a result of various linebroadening effects. An intrinsic linewidth is implemented in the lineshape calculation by placing a Lorentzian curve over every point in the lineshape function, to represent the lifetime of the deuterium transition together with any exponential multiplication of the fid applied in the data-processing. The effective spin-spin relaxation time, T2*, may conveniently be assumed to be orientation-independent throughout the tilt series, as long as it is possible to fit the corresponding powder pattern smoothly with a constant linebroadening. The second source of the observed linebroadening is the mosaic spread, which represents the misalignment of the microdomains in the sample, which contribute slightly different lineshapes to the total spectrum. A series of sub-spectra is thus computed for incremental inclinations around the set value of (Y, and summed with an appropriate weighting function, which is assumed here to be a Gaussian distribution. Figure 3 illustrates the effect of a varying

21-36

29

intrinsic linebroadening (left column) and mosaic spread (right column) on the spectral lineshape, using as a representative example one of the spectra from Fig. 2 (cone angle y = 78”, sample inclination (Y= 50”). The progressive increase in purely the intrinsic linewidth from zero to 2.5 kHz (left column) shows that the typically encountered intrinsic linewidth in solid state 2H NMR of a few kHz is already sufficient to obscure details in the spectrum. The consequence of a mosaic spread contribution in addition to an intrinsic linewidth of 1 kHz is illustrated in the right column of Fig. 3, where the mosaic spread is incremented from zero to + 15”. It is seen that both the central maximum and the outer shoulders of the spectral lineshape are smeared out with increasing disorder in the sample, while the peaks at 5 = + l/2 remain unaffected. That is because the positions of the underlying singularities at the centre (A) and at the shoulders (B) of the spectrum in Fig. 3 are sensitive to on the local tilt angle a, which varies over the imperfectly aligned microdomains in the sample. For macroscopically oriented samples with a high degree of disorder, the lineshape will ultimately revert into a powder pattern for all sample inclinations, and this trend is already noticeable in Fig. 3 for the higher mosaic spread values. The accuracy to which bond angles can be evaluated by this *H NMR method is much dependent on the precise measurement of the quadrupole splitting from the two peaks in the zero-tilt spectrum recorded at a sample inclination LY= o”, and this accuracy is thus affected by the spectral linebroadening. To assess the contributions of the intrinsic linebroadening and the mosaic spread on the sharpness of the peaks, the cos(8) dependence of IJ needs to be taken into account. That is, across the spectral range of resonance frequencies 5, the corresponding values of 8 become crowded near the edges where 6’ = 0” and 90”, which concomitantly leads to an increased error margin in the conversion of Av, for bond angles near y = 0” or 90”. On the other hand, this effect is partially offset by the inverse correlation between the resolution of the underlying bond angle and the observed linewidth due to the mosaic spread contribution. That is, for sam-

30

pies with the same mosaic spread but different bond angles y, the absolute linewidth would appear much narrower for values of y near 0” or 90” (with 0 = y at (Y= 0”) than for an intermediate angle y. Therefore, as a combined result of the two linebroadening effects, the accuracy of this *H NMR method is only weakly dependent on the actual orientation of the methyl group in the molecule. For well-oriented samples one may expect to obtain remarkably accurate data, of potentially higher resolution of the local protein structure than that given by other structural methods such as electron diffraction [30], neutron scattering [18,19], FT-IR [31] or dichroic measurements [32,33]. For instance, in the case of a deuteromethyl group quadrupole splitting around +40 kHz (see experimental example below, with a mosaic spread of f So), an error of k 1 kHz in the measurement of this splitting produces an uncertainty of less than + 1” in the calculation of the bond angle y. Beyond a simple inspection of the experimental *H NMR spectra, computer simulations are fundamental to a thorough and accurate data analysis. A complete tilt series of spectra recorded over several angles thereby provides a highly comprehensive set of data, from which the internal consistency of the concluded parameters can be substantiated and the overall reliability of the method judged. As a first step, the quadrupole splitting is measured from the zero-tilt spectrum, and the value of the constant Avgwder is obtained from the splitting of the powder pattern or directly from the oriented spectrum recorded at cx= 90” (see above). The calculated value of y from eqn. (31, or its two possible solutions which need to be distinguished, can then be validated and refined by visually optimizing the fit of the simulated lineshapes for the various tilt angles to the experimental tilt series. It is possible to deduce values for both the intrinsic linewidth and the mosaic spread directly from the tilt series, by incrementally varying these two independent broadening parameters to find the one combination that produces the best linefits. However, in order to avoid any ambiguity in assessing the relative contributions, it is convenient to determine the intrinsic linewidth independently from

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the powder spectrum of the same labelled specimen. That is because only in this case does the observed linewidth represent the intrinsic linebroadening alone (with no contribution from the mosaic spread), so that the value of this parameter can be extracted by linefitting the powder pattern and subsequently be used in the simulations of the oriented *H NMR lineshapes. Also, it may even be possible to get an estimate of the mosaic spread from independent 31P NMR measurements of the phospholipid component in the oriented sample [1,2,34].

Experimental

example

The motivation for the *H NMR analysis presented here stems from the need for a structural characterization of proteins in biological membranes. Due to their amphiphilic nature, proteins of this class are inherently difficult to crystallize and they are usually too large to be investigated in detergent micelles by solution NMR methods. Bacteriorhodopsin (BR) constitutes a suitable model system for exploring the potential of this novel solid state *H NMR method as an alternative structural tool, since the protein is remarkably stable and highly abundant in the purple membrane (PM) of Halobacterium halobium [35]. BR is also one of the few integral membrane proteins for which a three-dimensional model has been established. Recently, cryo-electron microscopy has yielded an electron-densi map with a resolution of 2.7 A in-plane and 10 A vertically [30], which reveals seven transmembrane a-helices as well as the retinal chromophore lying buried in the centre. To understand the function of the BR, a lightdriven proton pump [35,36], it is important to focus on the chromophore itself, since the lightinduced isomerization of retinal constitutes a key step in the translocation of protons across the membrane, which proceeds through a channel in the protein and via the retinal Schiff base. Although the detailed structure and geometry of retinal within the protein binding have not yet been fully resolved by electron microscopy, the three-dimensional location of its long-axis could

31

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be established in a series of neutron scattering experiments [18,19]. These measurement of the depth and in-plane position of individual deuterium-labelled segments along the retinal molecule in the membrane highlight the complementary use of selectively deuterated and macroscopically oriented protein samples for both neutron scattering and the *H NMR method. Further information about the chromophore structure has also been obtained using a variety of biophysical techniques, such as optical dichroism [32,33], FT-IR [31,36] and rotational resonance NMR [37] amongst others. The molecular structure of retinal in its all-truns (6S)-truns conformation, which it is known from these studies to assume within the protein binding pocket, is drawn in the inset of Fig. 4 *. In the development of the *H NMR method presented here, these known results provided valuable references to assess the validity and accuracy of this independent structural approach. The aim of our *H NMR investigation is thus to collect a comprehensive set of the methyl group bond angles for retinal, and to use these to construct ab initio the three-dimensional picture of the whole chromophore within BR. The three methyl groups on the cyclohexene ring of retinal have already been investigated this way [2], and here we present some previously unpublished experimental data on retinal deuterated at C,, in the polyene chain. For the *H NMR experiments, BR was grown in a retinal-deficient (JW5) strain of Hulobucterium hulobium as described [18]. Synthetic retinal was incorporated with one selectively deuterated methyl group, C20, which is marked in the inset in Fig. 4. Since BR occurs naturally as a dense two-dimensional array in the form of PM patches, uniaxial films with a good orientation of the immobilized protein can be obtained by controlled evaporation of a PM suspension [19]. Approximately 110 mg of the labelled BR in *H-depleted water were distributed over the surface of

* Since the orientation of methyl group bond angles is unaltered in the 13-ci5 15syn isomer, its presence in the darkadapted ground state of BR will be of no further concern here, but see refs. 2, 3.

Avo = 46 kHz I I

0 2 a=90”

-40 -20

0 20 40 km Fig. 4. Tilt series of experimental 2H NMR spectra from selectively deuterated bacteriorhodopsin in a uniaxially oriented sample at room temperature, with lineshape simulations (dashed lines) superimposed. The central resonance seen at all sample inclinations (Y is due to residual HDO. The protein contains retinal in its all-trans conformation as shown in the inset, specifically deuterium-labelled on the marked methyl group at C,,. From the quadrupole splitting AvQ(y) = 46+ 1 kHz in the zero-tilt spectrum ((Y = O”), the bond angle of the deuteromethyl group relative to the membrane normal N was calculated to be y = 32”+ 1” and confirmed by the lineshape simulations generated from Fig. 5.

18 small glass plates (8 mm X 30 mm X 0.15 mm, or 5 mm X 30 mm X 0.15 mm) cut from microscope cover slips. After slow drying (> 48 h), the plates were assembled pairwise using small spacers and glue at either end, with the membrane films apposing each other. A parallel stack of

32

these sandwiches was then placed longitudinally into a lo-mm NMR tube, together with a piece of sponge containing saturated KC1 to maintain the humidity (> 80%) within the sealed unit. The tube could be rotated manually within the horizontal solenoid, allowing the sample inclination to be set with a precision of +3”. All ‘H NMR spectra were acquired on a Bruker MSL 400 spectrometer at a deuterium frequency of 61 MHz, using a quadrupole-echo pulse sequence [24] with full phase-cycling, a r/2 pulse width of 6.5 ps, echo-delay times of 20-30 ps, and a repetition time of 200 ms. An exponential multiplication with a 2 kHz linebroadening factor was applied to the fid’s and all spectra were symmetrized in order to improve the signal-to-noise ratio. For the calculation of the spin-lattice relax-

A.S. Ulrich, A. Watts /Solid State Nucl. Magn. Reson. 2 (1993) 21-36

ation time constant, T,, from the heights of the fid’s as a function of the variable time delay, 6 data points were acquired using an inversion recovery experiment with a quadrupole-echo sequence and curve fitted to a single exponential function. Cooling of the sample during the lowtemperature acquisitions was achieved using a liquid nitrogen boil-off, which maintained the temperature stable within k 1°C over > 12 h. The computer program for generating the oriented ‘H NMR lineshapes was written in PASCAL and simulations were performed on a SUN workstation, where each calculation took from a few seconds up to a couple of minutes, depending on the degree of linebroadening applied. Figure 4 shows representative experimental *H NMR spectra from the deuterated retinal in an

Fig. 5. Tilt series of experimental ‘H NMR spectra (left column) at -60°C from deuterated bacteriorhodopsin (see Fig. 41, together with the best-fit lineshape simulations (right column). This data analysis, over 7 spectra from different sample inclinations between a = 0” and 90”, revealed a bond angle of y = 32” + l”, an intrinsic linebroadening of 2 kHz, and a mosaic spread of around f8”. The same parameters also apply the data acquired at room temperature (see Fig. 4).

A.S. Ulrich, A. Watts /Solid State Nucl. Magn. Reson. 2 (1993) 21-36

oriented, dark-adapted PM sample, together with the lineshape simulations superimposed (dashed lines) that were generated in the subsequent data analysis. The tilt series was acquired at room temperature over four different sample inclinations ((Y = o”, 30”, 60”, 90”), with about 4 X lo5 scans per spectrum. The experimental lineshapes are seen to be dominated by a broad central peak from residual HDO in the sample, which obscures the underlying characteristic spectral features. Therefore, a second tilt series was measured at - 6O”C, shown in Fig. 5, where the water in the sample is frozen out and not observed under the experimental conditions due to its long T, and short Tz relaxation times. The seven experimental spectra at -60°C (left column, Fig. 5) have a better signal-to-noise ratio than those at room temperature (Fig. 4), despite being acquired with only half the number of scans per spectrum. Since the lineshapes are virtually unchanged for the two different temperatures, the spectral analysis was based on the low-temperature tilt series, to which the simulations were fitted (see below). The equivalence of the two data sets, with the exception of the HDO signal, is demonstrated by showing the resulting set of lineshape simulations from -60°C (right hand column of Fig. 5) superimposed over the experimental spectra at room temperature (dashed lines in Fig. 4). The temperature-independence of the 2H NMR lineshapes indicates that the protein is completely immobilized within the purple membrane sample, and that the chromophore does not undergo any wobbling motions within the binding pocket even at physiological temperature, as has been shown previously 1381. Therefore, it may be assumed that methyl group rotation is the only motion that contributes to the spin-lattice relaxation, which may thus be described by a single effective motional correlation time T,. Measurement of the spin-lattice relaxation time, T,, gave a value of about 64 k 5 ms at - 6o”C, where T, must already lie within the fast motional regime on the 2H NMR timescale. To a first approximation it is [25] l/T, = 3n-‘/2(e2qQ/ hj2TC, which yields a value for the rotational correlation time 7, at - 60°C of around 30-40 ps.

33

On this timescale, and with even faster dynamics at room temperature, it is thus justified to assume the fast motional approximation (7, < lop7 s) and put 77 = 0 in the lineshape calculations. At both temperatures at which spectra were recorded, the zero-tilt spectrum measured at a horizontal sample inclination ((.y= 0’) exhibits two distinct resonances with a well-defined quadrupole splitting Av,(y) of 46 + 1 kHz (Figs. 4 and 5, uppermost spectra). The proportionality constant is Avcwder = 40 + 1 kHz, as previously determined from the powder spectrum of a similarly labelled retinal in BR [2], and which is also manifest in the invariant splitting at high sample inclinations ((w > 60”) in Fig. 5, as explained above. Using eqn. (3), the quadrupole splitting of 46 f. 1 kHz thus yields a bond angle of y = 32” + 1” for the deuteromethyl group C,, on retinal relative to the membrane normal, as schematically indicated by the orientation of the molecular bond vector in the inset in Fig. 4. It is apparent that in this case with Avo(y) > Avgwder there exists only one solution for y, and the bond angle is thus already unambiguously calculated. In view of these fortunate circumstances, the 2H NMR lineshape analysis is not actually applied to its full potential here, which would be to discriminate positive and negative quadrupole splittings. Indeed, the examination of the experimental tilt series in Fig. 5 serves primarily as a demonstration of the validity of the predicted lineshapes and of the simulation approach presented here. Nevertheless, the spectral tilt series can be now be analyzed to give the mosaic spread of the sample, and to confirm the internal consistency of all parameters throughout the series of different sample inclinations. It is expected that the experimental tilt series would reveal the greatest spectral width at the 30” sample inclination where Q = y, in order to be consistent with the deduced bond angle of y = 32”, as discussed above. Careful inspection confirms that this is indeed the case as far as the underlying singularities are concerned. However, it is apparent that some of the other spectra also extend up to the maximum I= -t 1 as a result of the various linebroadening effects. These contributions are readily taken into account by per-

34

forming a series of lineshape simulations, and the remarkable differences in the experimental lineshapes provide a good basis for individually fitting all seven spectra. The excellent match of the simulated spectra with the experimental data confirms that the deuteromethyl group on retinal in BR lies at an angle y = 32” f 1” relative to the membrane normal, as already concluded from the quadrupole splitting in the zero-tilt spectrum. The intrinsic linebroadening in the oriented sample was independently evaluated from the 2H NMR powder pattern of a similarly labelled BR sample as reported [2]. An orientation-independent intrinsic linewidth of 2 kHz was deduced by lineshape simulations of this powder pattern, and the same value also consistently yielded the best fits in the oriented spectra shown in Fig. 5. This 2 kHz linewidth actually correlates with the externally applied linebroadening factor in the exponential multiplication of the fid’s, which is thus the dominant contribution to the intrinsic linewidth in these solid state spectra. Using a lower exponential multiplication factor in the data processing, however, would not bring out any further spectral details but rather deteriorate the signal-to-noise ratio, because the sensitivity is low in these biological 2H NMR samples. Lineshape simulations that were fitted to deduce the mosaic spread of the macroscopically oriented sample, give a consistent value of around *So for all spectra in the tilt series. Thus the disorder amongst the membrane patches is indeed well characterized by a Gaussian distribution of local tilt angles over the sample normal. Comparison with our previous results on a similarly deuterated BR sample, which had a mosaic spread of f 10” as found by both independent 31P and 2H NMR [2], indicates that the quality of orientation was improved here, by a more controlled sample preparation and the use of spacers to align the individual glass plates. Conclusions The 2H NMR lineshape analysis that was introduced and discussed, has been successfully applied to deuterium-labelled retinal in dark-

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adapted bacteriorhodopsin in a uniaxially oriented protein sample. The bond vector of the C,, methyl group on the polyene chain was found to lie at an angle of 32” + 1” relative to the membrane normal, as calculated from the quadrupole splitting of the zero-tilt spectrum (cu = O”) and confirmed by lineshape simulations of a tilt series of experimental spectra. This bond angle is in excellent agreement with the known inclination of the retinal long-axis of around 65”-71” relative to the membrane normal [18,31-331, since the methyl group makes a right angle with this axis (see inset of Fig. 4) and the molecular plane of the conjugated system is known to lie approximately vertically in the membrane [31,32]. This good agreement with the known structure of retinal in bacteriorhodopsin supports the validity of the novel 2H NMR approach and illuminates its greater potential for accuracy than that offered by other structural methods. Similar measurements of further methyl group bond vectors on retinal, of which the three groups on the cyclohexene ring have already been investigated [2], will make it possible to construct a detailed picture of the whole chromophore in the protein binding pocket. The orientation and molecular conformation, including any twist or curvature, of the chromophore can thus be determined ab i&o and without recourse to model compounds or any other information on the system. This investigation is the first of its kind where a single methyl group was detected and analyzed by 2H NMR in a protein of this size. Due to the relatively large molecular weight of bacteriorhodopsin (26 kDa) there were only approximately 1O-5 mol deuterons present in the sample, which thus necessitated considerable acquisition times to overcome the intrinsically low signal-to-noise ratio. However, it would be possible to double or triple the amount of protein (approximately 110 mg> accommodated in the sample volume, and the use of a flat coil [39] would further enhance the sensitivity by improving the filling factor. These possibilities illustrate the potential for the investigation of other membrane proteins, which may be larger or less densely packed in the bilayer, and of which a limited number is already found naturally in large quanti-

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A.S. Ulrich, A. Watts /Solid State Nucl. Magn. Reson. 2 (1993) 21-36

ties. It might then be straightforward to bind a specifically deuterated substrate, drug or ligand [2,12]. Proteins may also be labelled biotechnologically with certain deuterated amino acids [14,17], or by using site-directed mutagenesis to target specific sites of interest, and chemical modification of the intact protein offers the possibility of introducing deuteromethyl groups onto or - SH residues [13]. Macrospecific -NH, scopically oriented samples can be obtained from labelled membrane fragments by sedimentation or centrifugation methods [40], or from a membrane dispersion on glass plates by annealing or mechanical shear [34]. Proteins may also be ordered by high magnetic fields when accommodated in an appropriate matrix [7,12,13,411 and subsequently frozen for immobilization and acquisition of the tilt series. The general 2H NMR strategy presented here is naturally also applicable to many materials other than biological membranes, such as liquid crystals, polymers, or small crystallites within a suitable matrix. Many of these compounds are available in large quantities and readily deuterium-labelled, and are thus successfully being investigated by this and other solid state NMR methods. Nevertheless, due to the general complexity of biological membranes, for which other techniques do not provide sufficient detail, the structure determination of integral membrane proteins may still be regarded as one of the major challenges for future investigations by solid state NMR.

Acknowledgements We thank Professor M.P. Heyn and Ingrid Wallat (Freie Universitat Berlin, Germany) for valuable discussion and for kindly providing the sample. This work was supported by the EC, SERC Grant GR/F/69400, SERC Grant GR/ F/80852, and an SERC studentship (fees only) to A.S.U.

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