Département de Chimie, Centre de Recherche en Sciences et
Ingénierie des Macromolécules, Université Laval,
Québec, Québec G1K 7P4, Canada
Structural data can be obtained on proteins inserted in
magnetically oriented phospholipid membranes such as bicelles, which are most often made of a mixture of long and short chain
phosphatidylcholine. Possible shapes for these magnetically oriented
membranes have been postulated in the literature, such as discoidal
structures with a thickness of one bilayer and with the short acyl
chain phosphatidylcholine on the edges. In the present paper, a
geometrical study of these oriented structures is done to determine the
validity of this model. The method used is based on the determination
of the first spectral moment of solid-state 31P nuclear
magnetic resonance spectra. From this first moment, an order parameter
is defined that allows a quantitative analysis of partially oriented
spectra. The validity of this method is demonstrated in the present
study for oriented samples made of DMPC, DMPC:DHPC,
DMPC:DHPC:gramicidin A and adriamycin:cardiolipin.
 |
INTRODUCTION |
The spontaneous orientation of phospholipid
membranes in magnetic fields has often been considered problematic due
to the resulting change in the solid-state nuclear magnetic resonance (NMR) spectral lineshapes (Bayerl and Bloom, 1990
; Van Etcheld et al.,
1982; Killian and de Kruijff, 1986
). However, this phenomenon is now
widely exploited since it has been shown to improve the spectral
resolution (Sanders and Prestegard, 1990
; Vold and Prosser, 1996
).
Phospholipids spontaneously form unilamellar and multilamellar vesicles, which are usually spherical in an aqueous medium (Helfrich, 1973
; Pidgeon et al., 1987
), but some membranes, depending on composition, concentration, temperature, and the method of
preparation, tend to modify their shape in the presence of a magnetic
field (Seelig et al., 1985
; Speyer et al., 1987
; Jansson et al., 1990
; Qiu et al., 1993
). When sterols (Brumm et al., 1992
; Reinl et al.,
1992
) or proteins (Neugebauer et al., 1977
; Van Echteld et al., 1982
;
Pott and Dufourc, 1995
) are embedded in phospholipid membranes, the
orientation may be enhanced or modified.
The origin of the magnetic alignment for a given molecule is its
diamagnetic or paramagnetic anisotropy (Boroske and Helfrich, 1978
). If
a diamagnetic molecule is placed in a magnetic field, a magnetic moment
proportional to the diamagnetic anisotropy is induced. Most of the
time, the magnetic energy of one molecule is not sufficient to allow
its alignment. However, when several molecules are packed together,
there may be a reorientation of the aggregate relative to the field
(Qiu et al., 1993
). The diamagnetic anisotropy of an axially symmetric
molecule, 
, is defined by the difference between the diamagnetic
susceptibility parallel (
) and perpendicular
(
) to the main axis of the molecule. For molecules
with a negative 
, a perpendicular alignment will occur whereas
those with a positive 
will orient parallel to the field. For
example, in phospholipids, the hydrocarbon chains, which are considered
to be the reference axis, have a 
< 0 (Boroske and
Helfrich, 1978
), whereas glycerol ester carbonyls have a 
> 0 (Maret and Dransfeld, 1985
). Because glycerol carbonyls are about
perpendicular to the phospholipid hydrocarbon chains (Sakurai et al.,
1980
), they both tend to orient the long axis of the lipid at 90°
relative to the magnetic field. Peptide bonds also have a positive

(Worcester, 1978
). Because all peptide bonds contained in
or
helices are parallel to the helix axis, helical proteins will tend
to orient parallel to a magnetic field (Neugebauer et al., 1977
).
Proteins can also contain aromatic residues that are known to have
large negative 
(Maret and Dransfeld, 1985
). In particular, gramicidin A (GA) has 4 tryptophan residues in which the planes of the
aromatic rings are approximately parallel to the helix axis (Ketchem et
al., 1997
), favoring a parallel orientation. In the same way, an
aromatic molecule such as adriamycin (ADM) is expected, due to its
negative 
, to orient its plane parallel relative to a magnetic
field. In fact, it has been shown that the anthraquinone moieties of
ADM molecules are closely stacked together when they are present at
high concentration on the surface of a negatively charged
phospholipid membrane (Goormaghtigh and Ruysschaert, 1984
; De Wolf et
al., 1991
). Their magnetic susceptibilities are therefore added up,
which makes possible the orientation of the membrane. The orientation
of this membrane will depend on the angle formed by the ADM and
the normal to the bilayer. If the ADM molecule is tilted by 39°
(Goormaghtigh et al., 1987
), the membrane would orient its normal
parallel to the magnetic field.
The shape of phospholipidic membranes under high magnetic field is
usually prolate ellipsoid (Helfrich, 1973
; Speyer et al., 1987
). These
structures have been observed by electron microscopy (Brumm et al.,
1992
), 31P NMR (Pott and Dufourc, 1995
; Brumm et al., 1992
)
and 2H NMR spectroscopies (Reinl et al., 1992
;
Schaefer et al., 1998
). In addition, specific phospholipid mixtures are
known to form bicelles, which are discoidal micelles formed when a long
chain lipid (such as dimyristoylphosphatidylcholine (DMPC)) is mixed either with a short chain lipid (such as dihexanoylphosphatidylcholine (DHPC)) (Sanders and Schwonek, 1992
; Vold and Prosser, 1996
; Sanders and Prosser, 1998
), a bile salt such as sodium glycocholate (Ram and
Prestegard, 1988
), or the detergent
3-(cholamidopropyl)dimethylammonio-2-hydroxy-1-propanesulfonate (CHAPSO) (Sanders and Prestegard, 1990
; Hare et al., 1995
). In addition, it was recently observed that the addition of small amounts
of paramagnetic ions to pure bicelles results in systems in which the
director is oriented parallel to the magnetic field (Prosser et al.,
1996
). This phenomenon is due to paramagnetism and will not be
considered here.
Solid-state 31P NMR spectroscopy is an ideal
technique to follow the orientation of phospholipid membranes due to
the presence of only one phosphorus atom in each phospholipid and the
absence of phosphorus in most proteins. In addition, several
interactions studied by 31P NMR are orientation dependent,
such as the dipolar coupling and the chemical shift anisotropy (CSA)
(Seelig, 1978
; Smith and Ekiel, 1984
). Spectral simulations have been
done to extract the ratio of ellipsoid long/short axis from
experimental 31P (Pott and Dufourc, 1995
; Brumm et al.,
1992
) and 2H NMR spectra (Reinl et al., 1992
; Schaefer et
al., 1998
). In contrast, even though 31P and 2H
NMR spectroscopies have been applied to bicelles, no spectral simulation of such system has been done to our knowledge. However, the
shape of the bicelles has been investigated by Chung and Prestegard (1993)
based on field gradient studies and by Vold and Prosser (1996)
based on the ratios of the deuteron splittings for DHPC and DMPC.
In the present paper, a method is proposed that uses the first
spectral moment of 31P NMR spectra to obtain structural
details on magnetically oriented phospholipid membranes. More
specifically, it can be used to determine either the dimension of a
bicelle or the ratio of an ellipsoid long/short axis. All these
parameters are extracted from equations that are derived in the Theory
section. Different systems are studied to present several of the
possibilities mentioned above. First, DMPC forms ellipsoidal vesicles
in which the phospholipids have a perpendicular orientation relative to
the magnetic field. Moreover, a DMPC:DHPC mixture gives bicelles that
align the bilayer normal perpendicular to the magnetic field. Finally,
the lipids in membranes made of DMPC:DHPC and GA have a parallel
orientation relative to the field, such as those in a complex made of a
mixture of cardiolipin (CL) and ADM.
 |
THEORY |
In axially symmetric systems, 31P NMR chemical shifts
are defined as
|
(1)
|
where
is the angle between the principal axis of the chemical
shift tensor and the static magnetic field, and
iso is
the isotropic chemical shift. To simplify this equation, the CSA
parameter,
, and the isotropic chemical shift are expressed in
frequency units. Due to this chemical shift orientation dependence,
both the spectral lineshape of a static sample and the weighted-average frequency of a sample with fast molecular motions can be related to the
orientation distribution of the molecules in the sample. Therefore, if
partial orientation occurs during an NMR experiment, a modification of
either the lineshape or of the weighted-average frequency will also be
present. Thus, information about the orientation distribution can be
obtained from a detailed analysis of the spectral modification.
For static samples, a relationship between the spectral density,
S(
), and the angular distribution, P(
),
called the principle of differential conservation of the integral
(Schmidt-Rohr and Spiess, 1994
) is given by
|
(2)
|
That implies
|
(3)
|
In a randomly distributed sample, the angular distribution is
easily calculated and the weighted-average frequency is equaled to the
isotropic chemical shift, but, in lyotropic liquid crystals, partial
orientation can occur due to the diamagnetic anisotropy. In this case,
the orientational distribution has to be calculated. In the next
section, two cases of partial orientation will be considered, an
ellipsoid orientation distribution and a discoidal orientation
distribution called bicelles.
Angular distribution and spectral lineshape
The angular distribution for ellipsoids has already been
investigated by Pott and Dufourc (1995)
. Our approach is very similar to theirs but the following presentation is still necessary for a
better understanding of that used for bicelles. Also, the description of the origin of the ellipsoidal angular distribution will help to
define the effect of partial orientation on the first spectral moment.
Ellipsoids
Ellipsoids can be represented by the parametric equations,
|
(4)
|
where the semiaxes a and c and the angles
and
are represented in Fig. 1.
The ellipsoid is called either a prolate spheroid if the semiaxis
c is greater than the semiaxis a or an oblate spheroid if c is smaller than a. It can be seen
in Fig. 1 that, even if the angle that determines the NMR frequency is
(i.e., the angle between the axis of motional averaging and the
magnetic field), the ellipsoid is defined in terms of
and
.
Therefore, it is important to relate the distribution of probability
expressed in terms of
and
to the distribution of probability
expressed in terms of
.

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FIGURE 1
Geometrical representations of (A) an
ellipsoid, (B) a bicelle in the x'-y' plane,
and (C) a bicelle in the (x'y')-z' plane.
|
|
The tangents to the surface of the ellipsoid,

and

, can be obtained by the partial
derivation of Eq. 4 relative to
and
,
|
(5)
|
|
(6)
|
Using the normalized cross product of the two tangents, a normal
unit vector is obtained,
|
(7)
|
The projection of the normal unit vector along z is
related to
via the equation,
|
(8)
|
Rearranging this equation, it is found that
and
are
related via the equation,
|
(9)
|
The angular distribution is related to a surface element,
ds, which is given by
|
(10)
|
An integration over
and the use of Eq. 9 gives the angular
distribution of an ellipsoid,
|
(11)
|
where r = c/a. Then, the lineshape of an
ellipsoid, prolate or oblate, can be determined using Eqs. 1, 3, and
11,
|
(12)
|
Oriented bicelles
In this model, the outer part of a bicelle is a torus and the
inner part is a circular plane. A representation of a bicelle can be
seen in Fig. 1. These two parts of the bicelle will be treated
separately. The parametric equations of a torus are
|
(13)
|
where the radii a and c and the angles
u and v are defined in Fig. 1. The tangents to
the surface of the torus,
u and
v, can be obtained by the partial
derivation of Eq. 13 relative to u and v,
|
(14)
|
|
(15)
|
Using the normalized cross product of the two tangents, a normal
unit vector is defined,
|
(16)
|
The lineshape for a bicelle oriented with its main axis (i.e., the
normal vector to the bilayer plane) parallel to the magnetic field will
first be derived in this section. To do so, we proceed as for the
ellipsoidal orientation by taking the scalar product of the normal unit
vector and the unit vector along z,
|
(17)
|
This equation gives directly the relationship between v
and
. Then, the surface area element is obtained from the tangents,
|
(18)
|
After an integration over u and using Eq. 17, the
density of probability of the torus is found,
|
(19)
|
Then, the lineshape of the outer part of a torus oriented with its
principal axis along z is determined using Eqs. 1, 3, and
19,
|
(20)
|
where r = a/c. Finally, the total lineshape of the
bicelle is
|
(21)
|
where the lineshape associated to the planes can be considered as
a delta function S
p(
) =
(
). The relative proportion of the
torus spectrum in the bicelle spectrum is defined as the area of the
outer part of a torus over the total area of the bicelle,
|
(22)
|
When fast motions relative to the 31P NMR time scale
occur, such as the rotation of the bicelle around its main symmetry
axis and the lateral diffusion of the lipids located in the edge
section of the bicelles, there is no more frequency distribution. In
such cases, the weighted-average frequency can be calculated,
|
(23)
|
For a bicelle oriented with its principal axis perpendicular to
z,
|
(24)
|
This equation does not give a direct relationship between two
angles and, therefore, it is not possible to use the same approach as
that used for the bicelle oriented with its normal parallel to the
magnetic field. However, using a delta function, a surface element
ds' can be defined as
|
(25)
|
which becomes
|
(26)
|
When c
0, this surface element corresponds to the
surface element of a sphere. Unfortunately, this equation cannot be
solved because it contains an elliptic integral. However, because
perpendicular bicelles spectra can be almost perfectly simulated by
considering the presence of lateral diffusion and tumbling as
demonstrated in the Result section, the static perpendicular bicelle
spectra were not simulated here. In the presence of rapid motions such as tumbling and lateral diffusion, the weighted-average frequency obtained for perpendicular bicelles can be calculated using Eq. 23 and
multiplied by a Stilt value of
0.5, as
described below.
Order parameters Sdist and
S1
As discussed above, if there is a change in the shape of the
orientation distribution, there is also a change in the
weighted-average frequency. Rearranging Eq. 23, it is possible to
define a distribution order parameter,
|
(27)
|
It should also be mentioned that the weighted-average frequency is
exactly the same as a first moment calculation, i.e., M1 = 

. Therefore, a calculation of
the spectral moments could be a measure of the orientation. Obviously,
this equation is only valid if the main axis of the distribution is
along z. If the system main axis is tilted relative to the
magnetic field axis, a new total order parameter can be introduced,
|
(28)
|
This new order parameter is denoted S1 to
emphasize that it comes experimentally from a first moment calculation.
It is possible to solve these order parameter equations for many
systems by considering their angular distributions. For a spherical
vesicle, S1 = 0. In the case of an
ellipsoid, assuming that the main axis is along z, the order
parameter S1 is
|
(29A)
|
If r < 1,
|
(29B)
|
whereas, if r > 1,
|
(29C)
|
For bicelles, because their main axis can be oriented at different
angles relative to the external magnetic field, it is more appropriate
to define a distribution order parameter using the distribution of
orientation and Eq. 22,
|
(30)
|
Then, the S1 order parameter is determined
from Eq. 28 using an Stilt value of 1 for
parallel bicelles and
0.5 for perpendicular bicelles. It is also
possible to use any other Stilt values for partially tilted bicelles.
 |
MATERIAL AND METHODS |
Material
DMPC, DHPC, and CL were obtained from Avanti Polar Lipids
(Alabaster, AL) and used without further purification. GA and ADM (doxorubicin hydrochloride) were obtained from Fluka (Ronkonkoma, NY)
and used without further purification.
Sample preparation
Aqueous dispersions of DMPC and CL were prepared in a 150 mM
NaCl and 10 mM EDTA solution and adjusted to pH 6.5. Samples containing
20% (wt/wt) of lipids were then heated to ~50°C for 10 min,
stirred on a vortex mixer, and cooled down at 0°C for 10 min. This
cycle was repeated at least five times just before the analysis. The
solution of ADM (0.01 g/mL) was prepared in 150 mM NaCl and 10 mM EDTA
and adjusted to pH 6.5. The appropriate volume of the ADM solution was
added to the CL dispersion to obtain a 2:1 CL:ADM molar ratio and then,
five freeze-thaw cycles were applied to the system. Samples of 2.7:1
DMPC:DHPC molar ratio were prepared in a 0.1 M KCl buffer. Then samples
containing 20% (wt/wt) of lipids were heated to ~35°C for 10 min,
stirred on a vortex mixer, sonicated, and cooled down at 0°C for 10 min. This cycle was repeated at least five times just before the
analysis. Samples of 10:4.3:1 DMPC:DHPC:GA molar ratio were prepared in trifluoroethanol. To obtain homogeneous peptide/lipid systems, the
samples were incubated at 52°C for 1 h and shaken on a vortex mixer at least a few times during the incubation cycle. After the
incubation, the organic solvent was evaporated with a nitrogen stream
followed by high vacuum pumping overnight. The samples were then
hydrated at 32% (wt/wt) with a HEPES buffer prepared at pH 7.0 and
were submitted to several cycles of heating (52°C), vortex-mixer,
sonication, and cooling (0°C).
NMR experiments
The 31P NMR spectra were acquired at 121.5 MHz on a
Bruker ASX-300 (Bruker Canada Ltd., Milton, ON) operating at a
1H frequency of 300.0 MHz. Experiments were carried out
with a broadband/1H dual frequency 4-mm probehead. The free
induction decays (2 K data points) were recorded with a spin echo
sequence (2000 or 4000 scans) with a 4 to 7 s repetition time and
under conditions of proton decoupling. The 1H 90° pulse
length was typically 4.0 µs, corresponding to a rotating-frame frequency of about 63 kHz. The 31P 90° pulse length was 5 µs and the interpulse delay was set to 30 µs to avoid anisotropic
T2 effects on static spectra. The temperature was controlled to within ±0.5°C and the chemical shifts expressed in
parts per millions (ppm) were referenced relative to the signal of
phosphoric acid at 0 ppm. When not specified, a line broadening of 50 Hz was applied to the spectra. Magic angle spinning (MAS) 31P NMR spectra were obtained with a spinning speed of 6 kHz and a free induction decay of 4 K data points (1000 scans). No line broadening was applied to these spectra.
Simulations and calculations
Simulations and calculations were performed with the Grams 386 software (Galactic Industries Corp., Salem, NH) using the Array Basic
programming language. The simulated spectra were broadened by
convolution with a Gaussian function. The experimental spectral treatment was done using the UXNMR software from Bruker (Bruker Canada
Ltd., Milton, ON).
 |
RESULTS AND DISCUSSION |
Theoretical spectra
In this section, we will present the simulated 31P NMR
spectra for partially oriented membranes, using the formalism developed in the Theory section. The simulated spectra will then be used to
obtain the order parameters S1 and
S2, respectively related to the orientation and
the dynamics of membranes.
Figure 1 shows two types of partially oriented membranes, an
ellipsoidal vesicle in A and two views of a bicelle in
B and C. If partial orientation occurs in model
membranes, they will most likely adopt an ellipsoidal structure in
which a will be smaller than c due to the sign of
the lipid diamagnetic anisotropy (Boroske and Helfrich, 1978
). In this
kind of system, the majority of the phospholipids will be oriented with
their main axis,
, at 90° relative to the surface.
Such an ellipsoidal orientation implies either very large unilamellar
or multilamellar vesicles because phospholipids in an ellipsoid with a
very short semi-axis a will experience a fast angular
diffusion that would result in chemical shifts characteristic of a
hexagonal phase rather than the ones characteristic of lamellar phases
(Seelig, 1978
).
Figure 2 shows the simulated spectra of
ellipsoidal structures for r ranging from 5 to 0.2. At a
ratio of 5, the phospholipids are almost all oriented at 90° relative
to the magnetic field. The ratio of 1 corresponds to a spherical
vesicle, and, at a ratio of 0.2, the majority of the phospholipids is
oriented parallel to the magnetic field. The surprising point of these
simulated spectra is that a prolate ellipsoid gives a very small
distribution of frequencies in comparison with the broad distribution
occurring for an oblate shape. This can be seen in Fig. 2 by comparing
the spectra with r = 2.5 and 0.4.

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FIGURE 2
31P NMR spectral simulations of
ellipsoidal vesicles as a function of r with = 25 ppm, iso = 0 ppm and a Gaussian broadening
(FWHH = 1 ppm).
|
|
The second case of partial orientation is the bicelle, which is usually
made of a long acyl chain phospholipid that has been assumed to be on
the two circular planes, and of a short acyl chain phospholipid that
has been assumed to be on the rim of the bicelle (Sanders and Schwonek,
1992
; Vold and Prosser, 1996
). Bicelles made of only two circular
planes have also been proposed for systems composed of CHAPSO and DMPC
(Sanders and Prestegard, 1990
; Sanders et al., 1994
). In the present
study, the bicelles are modeled by the combination of the outer part of
a torus and of two circular planes (Fig. 1, B and
C). Simulations will be made using two different models. In
the first model, we will consider a constant molecular surface area, a
constant composition of phospholipids over the whole surface of the
bicelle and a negligible contribution of the lipid lateral diffusion.
In the second model, we will consider a rapid axial rotation of the
bicelles around their main axis in addition to a rapid lateral
diffusion of the lipids. In these two models, the bicelles are
considered to be made of a single bilayer in which the thickness is the
double of the radius of the edge, as illustrated in Fig.
1 C. The axis system of the bicelles is denoted
(x', y', z') to account for the difference with the laboratory frame (x, y, z). Two different orientations of
the main axis of the bicelles are modeled, a bicelle with its
z' axis along z and a bicelle with its
x' axis along z.
Figure 3 A reports the
simulation of 31P NMR spectra of static parallel bicelles
in which the effect of the orientation can be easily seen as an
increasing spectral component at 
. An important point
to note is that a highly oriented system, e.g., with an r
value of 0.5 corresponding to a bicelle thickness of 50 Å and to a
bicelle total diameter of 200 Å, gives a broad spectrum if the main
axis of the bicelle is oriented parallel to the magnetic field.
However, because the broad component is due to the rim of the bicelle,
static parallel bicelles should give sharp NMR peaks for molecules
exhibiting fast axially symmetric motions inserted into their flat
sections, such as membrane proteins. Finally, the spectral difference
between parallel bicelles and oblate spheroids allows a discrimination
of the two types of organization, as discussed in a later section.

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FIGURE 3
31P NMR spectral simulations of bicelles
as a function of r with = 25 ppm,
iso = 0 ppm and a Gaussian broadening (FWHH = 3 ppm). (A) Static parallel bicelles. (B)
Parallel bicelles with axial tumbling and lateral diffusion.
(C) Perpendicular bicelles with axial tumbling and lateral
diffusion.
|
|
Figure 3, B and C, shows simulated parallel and
perpendicular bicelle spectra in which tumbling and lateral diffusion
have been considered. In this model, we supposed that the phospholipids that constitute the torus do not diffuse in the planes and vice-versa. This assumption has been made because experimental bicelles are constituted of two types of phospholipids that are believed to be
laterally phase separated. The relative proportion of the two peaks
observed in these spectra varies with the r shape parameter. This relationship is defined by Eq. 22 and is plotted in Fig.
4 A. Therefore, from an experimental
spectrum, it is possible to determine the size of the bicelle only by
integrating the two peaks. The frequency of the peak from the torus
part can also be related to the r shape parameter by
|
(31)
|
An Sdist order parameter can be calculated
from this weighted-average frequency using Eq. 27. This relationship,
plotted in Fig. 4 A, could also be a measure of the
r shape parameter. A value of 0.25 for the center of gravity
of the torus section of bicelles relative to the bilayer normal has
already been proposed in the literature (Vold and Prosser, 1996
) for
2H NMR spectra.

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FIGURE 4
(A) Relative proportion, , and
Sdist for the lipids in the torus part of the
bicelles. (B) S1 order parameter for
ellipsoidal vesicles, parallel bicelles, and perpendicular bicelles as
a function of the shape parameter r.
|
|
As discussed before, in oriented systems, it is possible to define an
order parameter from the first spectral moment measured experimentally,
which will be a measure of the orientation level. A system with a value
of S1 close to 1 (
0.5) indicates that all the
molecules are oriented with their main axis parallel (perpendicular) to
the magnetic field. Figure 4 B reports the variation of
S1 with the shape parameter r
assuming that the main axis of the oriented system is along
z for ellipsoids and either along or perpendicular to
z for bicelles.
A relative order parameter can also be defined, namely the ratio of the
spectral widths of an experimental spectrum to that of a reference
spectrum,
|
(32)
|
This order parameter, denoted S2 to
emphasize that it is related to the second spectral moment, can vary
from 1 for a system in which the dynamics are the same as those in a
reference system to 0 if the system becomes totally isotropic. Several
reference systems can be chosen, such as the CSA of DMPC multilamellar
vesicles when investigating bicelles made of DMPC and DHPC. This order parameter combines the effects of two other order parameters, a first
one that has already been introduced in the literature as
Sbilayers (Sanders and Schwonek, 1992
), which
denotes the presence of local motional averaging of the CSA, and a
second that we have previously named Stilt and
that some authors have introduced as Ssystem
(Sanders et al., 1994
), which relates the orientation of the main axis
of the system to the magnetic field axis. However, in the present
study, the main axis of each system is considered to be oriented either
parallel or perpendicular to z, which implies that a change
in S2 is considered as a change in the dynamic
properties (lateral diffusion, wobbling, tumbling) of the lipids rather
than an orientational change of the main axis of the oriented system (such as a tilt of the bicelles).
Experimental systems
To validate the spectral simulations and the use of the order
parameters presented in the previous section, several partially oriented lipid systems have been investigated. More specifically, we
have first investigated the partial orientation of pure DMPC multilamellar vesicles as a function of temperature and of hydration level. This system is known to be partially deformed in high magnetic fields, and the results of the present study will show that the partial
orientation can be quantitatively defined by the order parameter
S1. A similar approach will then be applied to
DMPC:DHPC bicelles, a lipid system known to orient with the lipids
oriented at 90° relative to the magnetic field. Finally, we will
investigate two cases of partial parallel lipid orientation, namely the
parallel orientation of DMPC:DHPC membranes in the presence of GA and
the partial orientation of CL membranes in the presence of ADM.
Pure DMPC
Figure 5 A presents the
31P NMR spectra of DMPC recorded at different conditions of
concentration and temperature to study their partial orientation in the
magnetic field. These spectra are characteristic of phospholipids in
the liquid-crystalline phase. At a concentration of 40%, the spectrum
is very close to the spectrum of a spherical distribution. However,
lowering the concentration results in a decrease of the intensity of
the lipids oriented at 0° relative to the magnetic field, which
confirms the presence of partial orientation. It is also possible to
note the appearance of an isotropic peak, which could be related to the
formation of smaller structures in which the tumbling and the lateral
diffusion correlation times become on the same order as the NMR
acquisition time. Even if hydration seems to have the most important
effect on the partial orientation, temperature also seems to induce a
change of the orientation distribution.

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FIGURE 5
(A) Experimental 31P NMR
spectra. (B) r Shape parameter for DMPC as a
function of temperature and concentration (wt/wt %).
|
|
These spectral deformations were investigated by an orientation
calculation. Information about the orientation in this system could be
obtained only if the isotropic and anisotropic chemical shifts are
evaluated precisely. The isotropic chemical shifts were obtained from
MAS spectra but are not reported here, and the chemical shift
anisotropy was evaluated directly on the static spectra. The CSA can be
obtained in different ways, such as evaluating the second spectral
moment. However, simulations have proven that an extremely accurate
measurement of the CSA is not necessary for the orientational
calculations (results not shown) and we have therefore evaluated this
parameter by taking the chemical shift at 90% of the maximum spectral
intensity. Our results indicate that both the CSA and the isotropic
chemical shift vary linearly with temperature, with a transition at the
gel to liquid-crystalline phase transition (results not shown). Then,
an ellipsoidal parameter, r, was evaluted from the first
spectral moment using Eq. 29 and plotted as a function of the
phospholipid concentration for two temperatures in Fig.
5 B. The ratio of the semi-axes c/a increases with temperature and DMPC concentration, indicating a higher
orientation at high temperature and low concentration. This is related
to the membrane elasticity, which increases with an increasing
temperature and decreasing concentration.
Bicelles
The second system investigated in the present study is made of
DMPC and DHPC at a molar ratio of 2.7:1. This system is supposed to
form discoidal structures that orient their main axis at 90° relative
to the magnetic field. Figure
6 A shows the spectra
obtained as a function of temperature. Below 25°C, the spectrum is
composed of an isotropic peak that can be attributed to DHPC and of a
broad spectrum that can be attributed to DMPC (Sanders and Schwonek, 1992
). The intensities of the two subspectra correspond approximately to the molar fraction of DMPC and DHPC used in the sample preparation. From 25° to 35°C, the spectra indicate that the system becomes more
and more oriented, i.e., the intensity corresponding to a perpendicular
orientation of the phospholipids increases greatly. A second
smaller peak, characterized by a different chemical shift, is also
present and its chemical shift decreases with temperature.

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FIGURE 6
(A) Experimental 31P NMR
spectra. (B) S1 and
S2 order parameters and (C)
S1t order parameter and t for
DMPC:DHPC (2.7:1 molar ratio) as a function of temperature.
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|
In a previous section, we have demonstrated that, as some authors have
suggested (Sanders and Schwonek, 1992
; Vold and Prosser, 1996
), the
smaller peak is due to phospholipids in the edges of the bicelle, most
likely the short-chain lipid DHPC. However, the relative intensity of
the two peaks changes with time, which indicates that these two peaks
might not be solely attributed to DMPC and DHPC. At temperatures above
40°C, the smaller peak disappears at the expense of an isotropic
peak. This corresponds to a well-known property of bicelles,
namely the existence of a magnetic phase transition at 40°C (Sanders
and Schwonek, 1992
). At temperatures above 40°C, the proportion
of phospholipids with a 90° orientation seems to increase with
temperature and the intensity of the isotropic peak decreases.
The order parameters S1 and
S2 have been calculated for these spectra using
pure DMPC multilamellar vesicles as the reference system. More
specifically, S1 is calculated from the first
spectral moment. In a previous section, we have demonstrated that, even in the presence of two distinct peaks, S1 can be
calculated if the peaks have the same isotropic chemical shift. This
seems very likely because DMPC and DHPC have the same headgroup. In
addition, even if the two peaks are not solely attributed to DMPC or
DHPC, no fine structure is observed in the two peaks, again suggesting similar isotropic chemical shifts and CSA for the two lipids. Figure
6 B shows the variation of S1 as a
function of temperature. S1 has a value of 0 at
20°C, representing no orientation and, as the temperature increases,
S1 decreases to
0.45 at 35°C, representing an almost complete perpendicular orientation of the lipids. Then, S1 increases to
0.35 at 50°C and decreases
to
0.40 at 65°C. The greatest orientation is therefore at 35°C
with a transition between 40 and 50°C. These results indicate that
bicelles are well oriented between 30 and 40°C. This temperature
range is similar to that obtained by other groups (Sanders and
Schwonek, 1992
; Losonczi and Prestegard, 1998
; Ottiger and Bax, 1998
)
that demonstrated that bicelles are well oriented between 30 and
40-45°C. The slight difference observed in the upper limit
temperature might be due to a slight sampling heating effect resulting
from the high proton decoupling power used in the present study.
The results presented above indicate that S1 is
a good tool for representing the magnetic orientation of phospholipids
because it is directly related to the shape of the membrane. Another
order parameter that can be measured on these spectra is
S2, which is related to the dynamics in the
system relative to a reference system. In this case, the reference
system is pure DMPC. S2 is plotted as a function
of temperature in Fig. 6 B. In the supposed temperature
range of existence of the bicelles (<40°C), the order parameter
indicates that the system is less ordered than is pure DMPC. This is in
agreement with the formation of small structures such as bicelles. At
high temperatures, S2 is equal to 1, indicating that the averaging of the chemical shift tensor is similar to that
obtained for pure DMPC. The spectra are also broader and S1 higher, showing that the system is most
likely constituted of bigger structures less oriented than the bicelles
at low temperature. These comments are based on the assumption that the
Stilt of the bicelles equals
0.5. In this
system, the parameter S2 therefore provides
important and complementary information about the dynamics in the system.
To go further in the analysis of the system, we have used the proposed
shape of the bicelles discussed in the Theory section to obtain the
r (a/c ratio) value from the relative proportion of the two
peaks at 35°C. Using Eq. 22, we found a value of 0.07, indicating
that the semi-axis c is 15 times the value of the semi-axis a. Assuming that the bicelle thickness is 50 Å, the total
diameter of the bicelle is ~750 Å. In contrast, it is possible to
determine the r shape parameter from the total
S1 value at 35°C. Using Eqs. 28 and 30, we
found that r = 0.05, indicating that the semi-axis c is 20 times the value of the semi-axis a, which
gives a bicelle diameter of ~1000 Å. Therefore, these two different
methods give approximately the same diameter, which corresponds to the
proposed diameter for discoidal structures in lyotropic liquid-crystals (Forrest and Reeves, 1981
). Another way to determine the r
shape parameter is from the S1 of the edge
phospholipids. This value is plotted as a function of temperature in
Fig. 6 C. The first remarkable feature is the linear
relationship between S1 and temperature between
25° and 45°C. However, it is surprising that all the
S1 values are below
0.125, the limit value. A
way to explain this phenomenon is to suppose an exchange between the
phospholipids in the torus and in the planes of the bicelles. The
resulting order parameter could be represented by
|
(33)
|
In this equation, t represents the proportion of time
spent by a phospholipid in the torus. This calculation has been
performed on the data presented in Fig. 6 A and the results
are plotted in Fig. 6 C. These results show that the
phospholipid lateral diffusion becomes more important with increasing
temperature. In addition, they suggest that the phospholipids in the
edges of the bicelle are partially phase separated from the lipids in the planes, but that a fast exchange process exists between them. Vold
and Prosser (1996)
have investigated the same system by 2H
NMR and showed, using labeled DHPC, that this phospholipid is located
solely in the edges of the bicelle. This difference can be easily
explained by the longer timescale of 31P NMR relative to
2H NMR.
Parallel lipid orientation
One potential limitation in using the magnetically oriented
bilayers described in the two previous sections for structural studies
is that, because this system is characterized by a negative orientational order parameter (S1
0.5), a well-resolved NMR spectrum with sharp lines will only be
obtained if the molecule of interest undergoes fast axially symmetric
motions. Otherwise, the NMR spectra will exhibit cylindrical powder
patterns (Prosser et al., 1998
). For this reason, the alignment of
phospholipid bilayers with their director parallel to the magnetic
field (i.e., with S1 = 1) has been the goal
of several research efforts. Recently, it was observed that the
addition of small amounts of paramagnetic ions such as Eu3+
or Yb3+ to DMPC/DHPC bicelles results in systems in which
the director is oriented parallel to the magnetic field (Prosser et
al., 1996
). Another way to obtain a parallel lipid orientation without
these paramagnetic effects would be the addition of a molecule
(protein, peptide, or drug) with a large positive 
(Sanders et
al., 1993
). This avenue was used in the present study. More
specifically, we have first prepared bicelles in the presence of the
transmembrane peptide GA due to its high content in aromatic residues
and to its helical conformation. Figure
7 A shows the spectra of
DMPC:DHPC:GA as a function of temperature and time. These spectra
clearly show the appearance of a spectral component at

both with increasing temperature but also as a
function of the time spent in the magnet.

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FIGURE 7
(A) Experimental 31P NMR
spectra and (B) S1 and r
for DMPC:DHPC:GA (10:4.3:1 molar ratio) as a function of temperature
and time. The spectra have been recorded every four hours at the
following temperatures: (a) 25°C, (b) 30°C,
(c) 35°C, (d) 40°C, (e) 45°C,
(f to l) 50°C.
|
|
The comparison between the spectra presented in Fig. 7 A
and the simulated spectra presented in Figs. 2 and 3 indicates that the
shape of the partially oriented system is closer to a static parallel
bicelle than to a parallel ellipsoid. To obtain more quantitative
information about this orientation phenomenon,
S1 and S2 were calculated
using pure DMPC multilamellar vesicles as the reference system. The
S2 value is constant at 0.7 for all spectra.
Thus, it can be considered that these systems are less ordered than
pure DMPC. This is in agreement with the disordering effect also
observed in 31P NMR spectra of unoriented DMPC lamellar
vesicles in the presence of GA (Bélanger, A. and Auger, M.,
unpublished results). Fig. 7 B presents the
S1 calculation that provides quantitative
information about the orientation of the lipid systems. Hence,
S1 goes up to 0.55 in the last spectrum, which
is representative of a high orientational order. In addition, Fig.
7 B shows the r (a/c) ratio obtained from the
order parameter S1. For the highly oriented system at the end of the experiment, the calculation of the diameter from the r value indicates that the bicelle has a diameter
four times bigger than its thickness. This observation is in agreement with the proposed size of bicelles (Vold and Prosser, 1996
).
Parallel lipid orientation without DHPC? the CL:ADM
complex
Another oriented system with the lipids parallel to the magnetic
field is the CL:ADM complex at a 2:1 molar ratio. ADM is a highly
aromatic molecule used currently in chemotherapy as an antineoplastic
agent. This molecule is known to interact strongly with negatively
charged lipids such as CL, a phospholipid found in the negatively
charged cardiac cellular membranes. ADM has been shown to cause cardiac
arrest if taken at high dosage. A model of interaction for this system
has been proposed in the literature in which the ADM molecules are
stacked on the membrane at an angle of 39° relative to the bilayer
normal (Goormaghtigh et al., 1987
). This arrangement is characterized
by a large value of 
which favors its magnetic orientation.
Figure 8 A shows the spectra
of the CL:ADM complex at a 2:1 molar ratio as a function of
temperature. Significant magnetic orientation occurs in this system as
the temperature increases, which is in agreement with the model of
interaction proposed for this complex. Comparing these lineshapes with
those presented in Figs. 2 and 3 indicates that these spectra could
again be associated to a bicellar organization. However, the resolution
is not as good and the spectrum is broader, characteristic of a
distribution of CSA. Another satisfactory model could be an
intermediate system composed of spherical vesicles with flat sections
where the phospholipids are oriented parallel to the magnetic field.

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FIGURE 8
(A) Experimental 31P NMR
spectra and (B) S1 as a function of
temperature for the CL:ADM (2:1 molar ratio) system. A line broadening
of 150 Hz was applied to these spectra.
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|
Figure 8 B shows the results of the order parameter
calculations for the ADM:CL system. The value of
S1 increases gradually with temperature.
However, the orientation does not become as high as that observed in
the DMPC:DHPC:GA system. Using pure CL multilamellar vesicles as the
reference system, the value of S2 is ~1 at all
temperatures, indicating that the dynamics in this system are close to
those of the pure CL system. These observations are in agreement with a
broader distribution of orientations that is probably not associated to
a perfect bicellar system. The r shape parameter has not
been calculated because it is impossible to assume a perfect bicellar
shape for this system.
Perspectives
The concept of magnetic orientation is not really new. However, a
lack of methods to evaluate this phenomenon is evident in this area of
research. Some authors (Forrest and Reeves, 1981
) proposed order
parameters to evaluate the extent of magnetic orientation, but these
parameters are not really appropriate. More specifically, the
measurement of the orientation via an order parameter such as
S2, as described above, is interesting but not
complete. This order parameter could be indicative if a tilt of the
bicelles or ellipsoids relative to the magnetic field axis is assumed. However, in general, it is more appropriate to suppose that the main
axis of the deformed membrane is along or perpendicular to the magnetic
field. In these cases, such order parameters will provide interesting
information about the dynamics in the system. Therefore, the definition
of another order parameter is really important. In the previous
section, we proposed a new order parameter, S1,
derived from the measurement of the first spectral moment.
Spectral moments are well defined in the literature and are very easy
to measure (Abragam, 1961
). Therefore, an orientation parameter derived
from this type of measurement is suitable. In fact, a change in the
spectral lineshape due to partial orientation will affect the spectral
moments. In principle, it could be possible to obtain
orientation-dependent measurements from each of the spectral moments
(M1, M2, M3, M4,
...). However, the moments higher than the first one are very
dependent on the spectral line broadening and only
M1 is not affected by symmetrical broadenings,
such as Lorentzian or Gaussian broadenings. Therefore, only the use of M1 is possible, even if
M1 is dependent on both the CSA and the isotropic chemical shift. With an evaluation of
on a well-defined static spectrum and of
iso from a MAS spectrum, a really
precise evaluation of S1 is possible.
Because of the increasing use of both parallel and perpendicular
bicelles as model membrane systems, the characterization of their
shape and size is important. A model has recently been proposed based
on 2H NMR measurements and on the calculation of the
relative areas of the planes and edges of the bicelles (Vold and
Prosser, 1996
). There are also extensive studies of the position of
DHPC on the edges of the bicelles by 2H and 31P
NMR spectroscopy (Sanders and Schwonek, 1992
; Vold and Prosser, 1996
).
However, there are no simulated spectra of such bicelles in the
literature, and therefore, an attempt to simulate both the
perpendicular and parallel orientation of bicelles seems valuable.
The experimental spectra obtained for bicelles with their main axes
oriented parallel to the magnetic field are in agreement with simulated
spectra, suggesting the validity of this model. For perpendicular
bicelles made of DMPC and DHPC, the presence of a second peak with a
frequency different from
iso is a convincing proof of
the validity of the bicelle model. In addition, both the relative
intensity of the two peaks and the S1
calculation give the same r shape parameter, which
corresponds to the proposed diameter of the bicelles. Finally, the
values of S1 obtained for the phospholipids in
the edges of the bicelles suggest that there is a phase separation
between the lipids in the planes and the torus of the bicelles and that
there is a fast exchange process between them. These results from
31P NMR are in agreement with those obtained from
2H NMR measurements (Vold and Prosser, 1996
).
 |
CONCLUSION |
A new order parameter, S1, has been
proposed in the present study to obtain quantitative information about
the orientation of phospholipidic systems. This new tool can be helpful
both to investigate the shape of lipid membranes and to study the
effect of several parameters (temperature, hydration, addition of
proteins or drugs, etc.) on the orientation of phospholipidic systems. A second order parameter, S2, can provide
complementary information about the dynamics in an oriented system.
31P NMR spectra have been simulated for both ellipsoid and
bicellar systems in which the lipids are oriented either parallel or
perpendicular to the external magnetic field. In addition, the
S1 and S2 order parameters have been determined from the experimental spectra obtained
for several systems.
More specifically, the general influence of temperature and
concentration on orientation has been clearly demonstrated for pure
DMPC multilamellar vesicles. In addition, the orientation and shape of
bicelles made of DMPC:DHPC, in which the lipids are oriented
perpendicular to the magnetic field, has been determined as a function
of temperature. We have also shown in this study that the addition of
GA to the DMPC:DHPC system induces an orientation of the lipids
parallel to the magnetic field that seems to favor the formation of
bicelles. Adriamycin also induces an orientation of the lipids at 0°
relative to the magnetic field in CL bilayers, even in the absence of
the short chain lipid DHPC. This indicates that a partial positive
ordering can be obtained in lipid systems without the addition of
paramagnetic ions and can be well characterized by the order parameter
S1 derived from the first spectral moment.
We are grateful to Mario Laviolette for numerous helpful
discussions and for recording the DMPC:DHPC bicelle spectra, and to Dr.
James H. Davis for helpful comments about the revised manuscript. This
work was supported by the Natural Science and Engineering Research
Council (NSERC) of Canada and by the Fonds pour la Fo