J. theor. Biol. (1976) 62, 447-458
X-ray Diffraction Studies of Lecithin Bilayers J. TORBET AND M. H. F. WILKINS Medical Research Council Cell Biophysics Unit, Biophysics Department, King’s College, London WC2B 5RL
The intensitiesweremeasured of Bragg reflections of X-rays from oriented
periodic lamellar arrays of lecithin bilayers. The variation of the intensities with swelling of the lamellar system as water content increased was used to assign phases to the diffraction spectra. The assignment procedure needed to be an extension of the standard method since the bilayer thickness decreased as the specimen swelled. Electron density profiles for bilayers of dipalmitoyl and egg lecithin were derived
1. Introduction
Since the proposal of the lipid bilayer structure for membranes by Danielli & Davson (1934) and the accumulation of experimental evidence in favour of the proposal, the elucidation of the detailed structure of lipid bilayers has been of increasing interest as a step towards understanding the structure and functional mechanisms of biological membranes. Lecithins are major constituents of many biological membranes. X-ray diffraction studies have in the last few years begun to present a fairly unambiguous picture of the structure of the lecithin bilayer. The main uncertainties have derived from difficulty in assigning phases to the X-ray diffraction spectra from the bilayers. This paper gives an account of an X-ray diffraction study of dipalmitoyl lecithin (DPC) and of egg lecithin (EPC) and describes how we assigned phases using a method based on that of Perutz, 1954. It is often supposed that it is only possible to assign phases by using swelling if during swelling the structure remains constant except for the thickness of the solvent layer increasing. We have extended the method to the case where the structure changes in a simple way during swelling. This work grew out of earlier studies in this laboratory (Levine & Wilkins, 1971) and was briefly reported (Wilkins, 1972) in its preliminary stages. Other 147
448
J.
TORBET
AND
M.
H.
F.
WILKINS
X-ray diffraction studies which give similar electron density profiles include those by Lesslauer, Cain & Blasie, 1972 and Tardieu, Luzzati & Reman, 1972. Details of our work are in Torbet, 1973. By relating the profiles to model building we conclude that the dipole in the lecithin head group is in the plane of the bilayer. This is also indicated for an ethalonamine by studies at atomic resolution (Hitchcock, Mason, Thomas & Shipley, 1974). However, the orientation of the dipole for lecithin bilayers remains a matter of contention (e.g. see Lee, 1975).
2. Experimental Oriented bimolecular layers of L-a-dipahnitoyl lecithin (DPC) were produced by evaporating the solvent from a concentrated solution of the lipid in CHCl,:MlOH 1:l on a curved glass (l-2 cm radius) substrate, in a stream of nitrogen. Samples with excess water were produced by centrifuging a dilute dispersion in water at 150,000 g for 1 hr. The pellet was then forced down a 1 mm thin-walled glass capillary. The egg lecithin (EPC) was a gift from Mr N. Miller of the Agricultural Research Council Institute of Animal Physiology, Babraham, Cambridge. DPC was obtained from Sigma and purified in a silicic acid column eluted with EHCl,:MlOH 1 :l. X-ray diffraction patterns were recorded photographically in an Elliott point-focusing toroidal camera. Specimens were equilibrated with moist helium at 23°C or dried in uacuo. X-ray spacings were calculated after calibrating the specimen-to-film distance by placing calcite powder on the specimen. The X-ray beam entered tangentially into the curved specimen with the result that lowest-angle diffraction was more heavily absorbed than that at higher angles. This effect can cause errors but only for the fust Bragg order or two. To avoid calculating absorption effects, intensities from the oriented samples were checked by comparison with those from narrow cylindrical unoriented samples in which the incident beam passed centrally through the cylinder with the result that absorption did not vary significantly with angle.
3. Results and Interpretation The DPC specimens consisted of regularly stacked bilayers approximately parallel to the glass substrate. The specimens were fixed relative to the incident X-ray beam but some disorientation in the specimens ensured that the various Bragg orders were all reflected. If more than one phase was initially
X-RAY
DIFFRACTION
STUDIES
OF LECITHIN
BILAYERS
449
present, a single lamellar phase was obtained by annealing at high humidity. The intensities of the Bragg orders were measured for a range of humidities, reproducibility and reversibility being obtained. The lamellar spacing increased slightly as humidity increased and considerable changes in intensities were observed. The phases of the amplitudes were initially chosen as follows. A plot of the square roots of the intensities against distance in reciprocal space indicated (Fig. 1) that the amplitudes lay roughly on a smooth curve if the signs of the terms were suitably chosen (it was assumed that the structure was symmetrical and therefore that all phases, i.e. signs of amplitudes, were either positive or negative). This curve seemed to indicate the general form of the Fourier transform of the bilayer electron density profile minus the electron density
eqdrorewp%?posed 2 2
0 -2 -4 v 56.6a: O%RH o 57*5a;23% RH
-6
o 57.7
Remntructed
tmKforms
0.15
a-1
-
0 % AH
---
CO % AH
833%~~
0.20a-1
FIG. 1. Square roots of intensities of Bragg orders of a lamellar array of DPC bilayers plotted against corresponding reciprocals of Bragg spacings. The signs of the terms are those arrived at by the phasing procedure. For Bragg order 1 the points corresponding to the various humidities overlap. Reconstructed transforms are shown for the two extreme humidities: other transforms are intermediate as in Fig. 2(a).
450
J.
TORBET
AND
M.
H.
I’.
WILKINS
of water. It was clear, however, that there was no single transform which fitted the data for all humidities: evidently the transform changed with humidity. We therefore did not have a situation where swelling the structure did not alter the bilayer profile and where (Pet&z, 1954) phases could be assigned by fitting all amplitudes on one smooth transform. Therefore, there was no standard and very straightforward method for establishing the phases. We therefore developed an approach as follows. The well-established method of phasing by swelling is based on the assumption that (a) a simple and unique solution is more likely to be correct than any one of a number of complicated alternative solutions and (b) a structure which remains constant with hydration is physically plausible. If no such solution exists we may look for one in terms of a structure which changes with hydration in a way that is (a) simple and (b) physically plausible. Our contention is that if we find a unique solution of this type it is reasonable to assume that it is correct. Figure 1 shows a plot of the amplitudes, the phases being those originally chosen and later checked according to the principle just described. The continuous transforms were calculated using a reconstructing technique (Sayre, 1952). This required a value for the zero order amplitude which, because the zero order is not observed, was calculated roughly from the molecular model of the bilayer described later. Fortunately in the regions of the larger values of reciprocal space, where the phase uncertainties exist, the transform is almost independent of the value of the zero order and hence of the form of the model used. Allocation of phases for the first four orders was unambiguous because the intensities of orders 2 and 3 changed uniformly with hydration and passed through zero. Continuous diffraction from dispersions of lipids indicated that there were no other zeros in this region of the transform (Wilkins, Blaurock & Engelman, 1971). A phase change, when the intensity passed through zero, in both cases provided a unique and simple solution in terms of a family of transforms in which the transforms expanded uniformly with increasing humidity. Similar effects with the intensity passing through zero were observed for orders 9, 10, 11 though the accuracy of measurement of intensities for these orders did not permit the intensity change to be delineated so clearly as for orders 2 and 3 and, as a result, assignment of a phase change was less certain. The intensities of orders 6 and 8 remained considerable at all humidities; this suggested that the transforms had maxima near those orders. Much uncertainty concerned possible phase changes near orders 5 and 7 which had very low or zero intensity at all humidities. It was likely that the transforms were tangential to the horizontal axis in these regions but such a form was compatible either with or without the transform having a phase change. The main problem therefore was to find whether
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
451
there was or was not a phase change near orders 5 and 7 (in other words, did the main transform bands on the two sides of each order have opposite or the same phase?), and also to check the somewhat uncertain phase changes near orders 9, 10, 11. It was fortunate that at 66% humidity all but three of the Bragg orders above 5 had negligible intensity with the result that only the phases of orders 6, 8, 11 needed to be determined. There were therefore only eight possible phase combinations to consider. One of these provided a solution which was a member of a family of transforms in which the transforms were related by a continuous and uniform change with humidity. The transform at smaller angles had already been shown to expand with humidity increase and this applied at the higher angles too if the phases in Fig. 1 were used. If it could be shown that this set of phases was unique in giving a simple change of transform with swelling, it could be chosen as being that most likely to be correct. It was necessary, therefore, to examine the alternative phase assignments to find if any of these might also give an appearance of simplicity and uniqueness. Figure 2 shows swelling behaviour with and without phase change near order 5 as referred to above. As we have said, without a phase change, the transform as a whole expands almost uniformly along the reciprocal space axis with increasing hydration [see Fig. 2(a)]. With a phase change (all phases above order 5 being reversed) the behaviour of the transforms was much more complicated [see Fig. 2(b)]. Consider, for example, the transform peak in the region of O-10 A-’ ; from 0% humidity to 100% the peak moves in one direction and then in the reverse direction for further increase of hydration. The change in form of the transform in the region of the zero near 0*09A-’ is complicated and suggests artificiality in fitting the data to the curves: without the phase change there is a clearly recognizable simplicity in the family of transforms; with phase change this is lacking. The same general phenomenon is obtained if the possibility of phase change near order 7 is investigated. Applying the criterion of uniqueness and simplicity one has therefore a reasonable basis for accepting that there are not phase changes near orders 5 and 7. If one attempts to change other phases the situation becomes even more complicated. Starting with possible phases, other than those in Fig. 1, for the orders at 66 % humidity one fails in any simple way to deduce the phases that would correspond at other humidities. In other words, there is no simple way of relating the observed intensities as the humidity is altered. This of course supports the original assignment of phases. This analysis may be summarized thus : the assigned phases give an especially simple family of transforms of quasi-sinusoida form; all other phases
452
4
J.
TORBET
0.04
0.06
AND
M.
0.08
H.
F.
0.10
WILKINS
0.12
0.14
o-14
0.16
0.16
c = :
0.04
o-06
0*08
0.10 Reciprocal
o-12
O-18
space (%-‘I
FIG. 2. The families of reconstructed DPC transforms for (a) no phase change in the region of 0.09 A-1 (asshown in Fig. l), (b) a phase change in that region. The transforms within a family are simply related in (a) and not in (b). (a) * * * * * . , 0% RH; -, 58 2; RH; -.-.-, 84%RH; ---, excess water.(b) ***..*, O%RH;-----,23%RH; . 66% RH; -.-.-, 100% RH; ---, excess water.
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
453
destroy the quasi-sinusoidal form and give much more complicated families of transforms. The simplicity of change within the family of transforms is of course reflected in the corresponding family of electron density profiles (Fig. 3) derived from the transforms. The procedure so far described for assigning phases makes no use of assumptions about the structure of the bilayer itself (except for the rough calculation of the zero order). One may, however, use such assumptions to test the correctness of the phases. One would expect the electron density profile of a bilayer to show a region of uniform electron density corresponding to the methylene part of the hydrocarbon chains, a lower region where the terminal methyl groups are concentrated, and a higher region for the head region. Profiles were calculated for the eight phase combinations (Fig. 4). Only one gave a profile of the expected type; this corresponded to the phase assigned by the swelling procedure. We did not find it possible to account for the other profiles in terms of a bilayer structure; however, the errors of measurement of the higher diffraction orders are such that choice between some of the profiles, e.g. the two lowest profiles in Fig. 4, is not very significant. The swelling behaviour shown in Fig. 3 is physically reasonable: there is a recognizable water layer which increases in width as humidity increases and in parallel the thickness of the bilayer decreases, which is in line with the known behaviour of bilayers (e.g. Tardieu et al., 1973).
A further test of the correctness of the phase assignment is to see if a molecular model can be built which will account for the precise form of the profile. This was found to be the case; the profile calculated from the model corresponded very closely to that observed (Fig. 5). The model was built before the structure of crystalline dilauroyl ethanolamine (Hitchcock, Mason, Thomas & Shipley, 1974) was available. The main stereochemical guides were as follows. The ester c-o-c-c //O group (Chothia & Pauling, 1971) was kept coplanar as in the crystal structure of tricaprin (Jensen & Mabis, 1966). The o-c-c group had a gauche conformation and the -N phosphodiester linkage was gauche gauche (Sundaralingham, 1972). The phosphodiester choiine conformation was similar to that in GPC (Abrahamson & Pascher, 1966) and GPC. Cd Cl2 crystals (Sundaralingham & Jensen, 1965). The terminal methyl groups formed a layer in a plane in the centre of the bilayer and the phosphate-choline dipoles lay in the bilayer plane. It was not found possibIe to build a model, without an in-plane dipole, which accounted for the observed profile of the dry DPC bilayer. Since the profile of the head group showed no sign of change of conformation with hydration it seemed likely that the dipole remainedin-plane in hydrated bilayers. However,
454
LUKUET
AND
M.
H.
F.
WlLKlNb
12 alders d=!56-6
8
O%RH Ilorders d=WOft
23% RH IO ordm d=57*5 8
56%
RH
12 orders d=57-7
%
100 % RH I I orders d=56-68
Vesicles in excess waler IO orders d=64*0 a
L
40
Distance
from centre
of biloyer
a
Fro. 3. Electron density pro& of the DPC bilayer at various relative humiditie (BH) (phases are as in Fig. 1). Note that as the humidity increases the width of the water layer increases and that of the bilayer decreases. d is the spacing in A. The number of Bragg orders wed in calculating the pro6ks is shown. Fro. 4 (oppoSite).Electron density profiles of a DPC bilayer (only half a bilayer is shown) for the eight phase combinations for the 66% relative humidity data. The prow lab&d L‘correct” is obtained with the assigned phas*l as in Fig. 1; the other profiks are labekd with those orders which have their phases reversed.
O-
\ O-
d o-
O-
.
0
O\
0
O
I
0
5 Distmce
IO
15 from bikyer
20 centre
25
X
456
J.
TORBET
AND
M.
H.
F.
WILKINS
FIG. 5. Electron density pro&s of DPC bilayer as calculated from the model and as derived from the diffraction measurements. Thermal disorder has been taken into account by applying a temperature factor of B = 100. -, calculated; -----, observed.
since the X-ray scattering from the choline group is not much different than that of water, one cannot very reliably deduce its position directly from the X-ray data. Neutron diffraction locates the choline group more clearly (Worcester & Franks, 1976) and confirms that the dipole is in-plane in a hydrated lipid bilayer. Data on egg lecithin (EPC) bilayers relate satisfactorily to those on DPC. The higher Bragg orders for EPC all appear near maxima of the transform peaks (thus differing from the case of DPC where some orders are near transform minima), yet the data fit transforms very similar to those obtained for DPC. Electron density profiles derived from such transforms are shown in Fig. 6. The swelling for EPC is small but it gives some indication that the phase assignment is correct. We suggest, however, that the main basis for phase assignment in this case is the analogy with DPC bilayers. When EPC is very thoroughly dried there is a structural transition, the liquid-type arrangement of the hydrocarbon chains changing to a crystalline type like that in DPC. For such dry EPC bilayers the Bragg orders sample the transform in much the same manner as for dry DPC except that order 5 is quite strong. Yet again a transform of the DPC type fits the data. The fact that it is again possible to fit these data to the DPC type of transform is further cotirmation that the DPC phase assignment is correct. A profile derived from the dry EPC transform is shown in Fig. 7; it bears, of course, a close resemblance to the DPC protie.
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
457
47 % RH dC06 8.
66 % RH d=WO a
9296RI-l d*5kI fi
loo % RH +51.3
a
100% RH z/=51*5 A
i 1 40
1
I
1
30
20
IO
Distance
1
0
from centre
methyl groups I
I
I
J
IO
20
30
40
of bilayer
8,
FIG. 6. Electron density profiles of EPC bilayers at various humidities. There is a slight reduction of bilayer thickness as humidity is increased. All curves are calculated using eight Bragg orders except for the vesicles where only five orders were used.
J.
TORBET
AND
20
IO
M.
H.
F.
WILKfNS
20 2
15
5 z. IO b 2 3z 5 % 4.%
o
s -5 CL Y iij -10 -15 0
IO
20
Ll
30
A Fro. 7. Electron density profile of dehydrated corresponding to those derived for DPC.
EPC
bilayers,
calculated
using
phases
One of us (J. T.) held a Medical Research Council Training Scholarship during this work. We are grateful to several colleagues, in particular Y. K. Levine and A. E. Blaurock, for advice and discussion. REFERENCES s. & hSCHER, I. (1966). ACtQ. crysf. 21, 79. CH-, C. & PAUNG, P. (1971). Nuture, Lmd. 299,281. DANIELLI, J. F. & DAWN, H. (1934). J. Cell Camp. Physiol. HITCI+XCK, P. B., MASON, R., THOM.Q,K. M. & SHIPLEY, G. Sci. U.S.A. 71, 3036. JENSEN, L. H. & MABIS, A. J. (1966). Actu Cryst. 21, 770. LEE, A. G. (1975). Prog. Biophys. molec. Biol. 29, 3. i%BRAHAMSGN,
5, 495. G. (1974). Proc. mtn. Ad.
LBSSLAUER, W., CAIN,J. E. & BLASIE, J. K. (1972).Proc. natn. Acad. Sci. U.S.A. 69,1499. LEVINE,
Y. K. & WILKINS,
M.
H. F. (1971).
Nature New BioIogy 230, 69.
PERUTZ, M. F. (1954).Proc. R. Sot. A. 225, 264. SAYRE, D. (1952).Actu. Cryst. 5, 843. SUNDARALINGHAM, M. & JENSEN, L. H. (1965). Science, N. Y. 150, 1035. %ND~GHAM, M. (1969). Biopoiymers 7, 821. SUNDARALINGHAM, M. (P972). Ann. New York Acud. Sci. 195, 355. TARDIEIJ, A., LuZZATI, V. & &MAN, F. C. (1973). J. molec. Biol. 75, 711. TORBJXT, J. (1973). X-ray Diffraction Studies of Lipid Bimok&ar Layers. PhD
University of London. WILKINS,M. l-i. F. (1972). Ann. New York Acad. Sri. 195, 291. Wo~ixrza,
D.
L. & FRANKS,
N. P. (1976).
J. nwlec. Biol. 100, 359.
Thesis,
X-ray Diffraction Studies of Lecithin Bilayers J. TORBET AND M. H. F. WILKINS Medical Research Council Cell Biophysics Unit, Biophysics Department, King’s College, London WC2B 5RL
The intensitiesweremeasured of Bragg reflections of X-rays from oriented
periodic lamellar arrays of lecithin bilayers. The variation of the intensities with swelling of the lamellar system as water content increased was used to assign phases to the diffraction spectra. The assignment procedure needed to be an extension of the standard method since the bilayer thickness decreased as the specimen swelled. Electron density profiles for bilayers of dipalmitoyl and egg lecithin were derived
1. Introduction
Since the proposal of the lipid bilayer structure for membranes by Danielli & Davson (1934) and the accumulation of experimental evidence in favour of the proposal, the elucidation of the detailed structure of lipid bilayers has been of increasing interest as a step towards understanding the structure and functional mechanisms of biological membranes. Lecithins are major constituents of many biological membranes. X-ray diffraction studies have in the last few years begun to present a fairly unambiguous picture of the structure of the lecithin bilayer. The main uncertainties have derived from difficulty in assigning phases to the X-ray diffraction spectra from the bilayers. This paper gives an account of an X-ray diffraction study of dipalmitoyl lecithin (DPC) and of egg lecithin (EPC) and describes how we assigned phases using a method based on that of Perutz, 1954. It is often supposed that it is only possible to assign phases by using swelling if during swelling the structure remains constant except for the thickness of the solvent layer increasing. We have extended the method to the case where the structure changes in a simple way during swelling. This work grew out of earlier studies in this laboratory (Levine & Wilkins, 1971) and was briefly reported (Wilkins, 1972) in its preliminary stages. Other 147
448
J.
TORBET
AND
M.
H.
F.
WILKINS
X-ray diffraction studies which give similar electron density profiles include those by Lesslauer, Cain & Blasie, 1972 and Tardieu, Luzzati & Reman, 1972. Details of our work are in Torbet, 1973. By relating the profiles to model building we conclude that the dipole in the lecithin head group is in the plane of the bilayer. This is also indicated for an ethalonamine by studies at atomic resolution (Hitchcock, Mason, Thomas & Shipley, 1974). However, the orientation of the dipole for lecithin bilayers remains a matter of contention (e.g. see Lee, 1975).
2. Experimental Oriented bimolecular layers of L-a-dipahnitoyl lecithin (DPC) were produced by evaporating the solvent from a concentrated solution of the lipid in CHCl,:MlOH 1:l on a curved glass (l-2 cm radius) substrate, in a stream of nitrogen. Samples with excess water were produced by centrifuging a dilute dispersion in water at 150,000 g for 1 hr. The pellet was then forced down a 1 mm thin-walled glass capillary. The egg lecithin (EPC) was a gift from Mr N. Miller of the Agricultural Research Council Institute of Animal Physiology, Babraham, Cambridge. DPC was obtained from Sigma and purified in a silicic acid column eluted with EHCl,:MlOH 1 :l. X-ray diffraction patterns were recorded photographically in an Elliott point-focusing toroidal camera. Specimens were equilibrated with moist helium at 23°C or dried in uacuo. X-ray spacings were calculated after calibrating the specimen-to-film distance by placing calcite powder on the specimen. The X-ray beam entered tangentially into the curved specimen with the result that lowest-angle diffraction was more heavily absorbed than that at higher angles. This effect can cause errors but only for the fust Bragg order or two. To avoid calculating absorption effects, intensities from the oriented samples were checked by comparison with those from narrow cylindrical unoriented samples in which the incident beam passed centrally through the cylinder with the result that absorption did not vary significantly with angle.
3. Results and Interpretation The DPC specimens consisted of regularly stacked bilayers approximately parallel to the glass substrate. The specimens were fixed relative to the incident X-ray beam but some disorientation in the specimens ensured that the various Bragg orders were all reflected. If more than one phase was initially
X-RAY
DIFFRACTION
STUDIES
OF LECITHIN
BILAYERS
449
present, a single lamellar phase was obtained by annealing at high humidity. The intensities of the Bragg orders were measured for a range of humidities, reproducibility and reversibility being obtained. The lamellar spacing increased slightly as humidity increased and considerable changes in intensities were observed. The phases of the amplitudes were initially chosen as follows. A plot of the square roots of the intensities against distance in reciprocal space indicated (Fig. 1) that the amplitudes lay roughly on a smooth curve if the signs of the terms were suitably chosen (it was assumed that the structure was symmetrical and therefore that all phases, i.e. signs of amplitudes, were either positive or negative). This curve seemed to indicate the general form of the Fourier transform of the bilayer electron density profile minus the electron density
eqdrorewp%?posed 2 2
0 -2 -4 v 56.6a: O%RH o 57*5a;23% RH
-6
o 57.7
Remntructed
tmKforms
0.15
a-1
-
0 % AH
---
CO % AH
833%~~
0.20a-1
FIG. 1. Square roots of intensities of Bragg orders of a lamellar array of DPC bilayers plotted against corresponding reciprocals of Bragg spacings. The signs of the terms are those arrived at by the phasing procedure. For Bragg order 1 the points corresponding to the various humidities overlap. Reconstructed transforms are shown for the two extreme humidities: other transforms are intermediate as in Fig. 2(a).
450
J.
TORBET
AND
M.
H.
I’.
WILKINS
of water. It was clear, however, that there was no single transform which fitted the data for all humidities: evidently the transform changed with humidity. We therefore did not have a situation where swelling the structure did not alter the bilayer profile and where (Pet&z, 1954) phases could be assigned by fitting all amplitudes on one smooth transform. Therefore, there was no standard and very straightforward method for establishing the phases. We therefore developed an approach as follows. The well-established method of phasing by swelling is based on the assumption that (a) a simple and unique solution is more likely to be correct than any one of a number of complicated alternative solutions and (b) a structure which remains constant with hydration is physically plausible. If no such solution exists we may look for one in terms of a structure which changes with hydration in a way that is (a) simple and (b) physically plausible. Our contention is that if we find a unique solution of this type it is reasonable to assume that it is correct. Figure 1 shows a plot of the amplitudes, the phases being those originally chosen and later checked according to the principle just described. The continuous transforms were calculated using a reconstructing technique (Sayre, 1952). This required a value for the zero order amplitude which, because the zero order is not observed, was calculated roughly from the molecular model of the bilayer described later. Fortunately in the regions of the larger values of reciprocal space, where the phase uncertainties exist, the transform is almost independent of the value of the zero order and hence of the form of the model used. Allocation of phases for the first four orders was unambiguous because the intensities of orders 2 and 3 changed uniformly with hydration and passed through zero. Continuous diffraction from dispersions of lipids indicated that there were no other zeros in this region of the transform (Wilkins, Blaurock & Engelman, 1971). A phase change, when the intensity passed through zero, in both cases provided a unique and simple solution in terms of a family of transforms in which the transforms expanded uniformly with increasing humidity. Similar effects with the intensity passing through zero were observed for orders 9, 10, 11 though the accuracy of measurement of intensities for these orders did not permit the intensity change to be delineated so clearly as for orders 2 and 3 and, as a result, assignment of a phase change was less certain. The intensities of orders 6 and 8 remained considerable at all humidities; this suggested that the transforms had maxima near those orders. Much uncertainty concerned possible phase changes near orders 5 and 7 which had very low or zero intensity at all humidities. It was likely that the transforms were tangential to the horizontal axis in these regions but such a form was compatible either with or without the transform having a phase change. The main problem therefore was to find whether
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
451
there was or was not a phase change near orders 5 and 7 (in other words, did the main transform bands on the two sides of each order have opposite or the same phase?), and also to check the somewhat uncertain phase changes near orders 9, 10, 11. It was fortunate that at 66% humidity all but three of the Bragg orders above 5 had negligible intensity with the result that only the phases of orders 6, 8, 11 needed to be determined. There were therefore only eight possible phase combinations to consider. One of these provided a solution which was a member of a family of transforms in which the transforms were related by a continuous and uniform change with humidity. The transform at smaller angles had already been shown to expand with humidity increase and this applied at the higher angles too if the phases in Fig. 1 were used. If it could be shown that this set of phases was unique in giving a simple change of transform with swelling, it could be chosen as being that most likely to be correct. It was necessary, therefore, to examine the alternative phase assignments to find if any of these might also give an appearance of simplicity and uniqueness. Figure 2 shows swelling behaviour with and without phase change near order 5 as referred to above. As we have said, without a phase change, the transform as a whole expands almost uniformly along the reciprocal space axis with increasing hydration [see Fig. 2(a)]. With a phase change (all phases above order 5 being reversed) the behaviour of the transforms was much more complicated [see Fig. 2(b)]. Consider, for example, the transform peak in the region of O-10 A-’ ; from 0% humidity to 100% the peak moves in one direction and then in the reverse direction for further increase of hydration. The change in form of the transform in the region of the zero near 0*09A-’ is complicated and suggests artificiality in fitting the data to the curves: without the phase change there is a clearly recognizable simplicity in the family of transforms; with phase change this is lacking. The same general phenomenon is obtained if the possibility of phase change near order 7 is investigated. Applying the criterion of uniqueness and simplicity one has therefore a reasonable basis for accepting that there are not phase changes near orders 5 and 7. If one attempts to change other phases the situation becomes even more complicated. Starting with possible phases, other than those in Fig. 1, for the orders at 66 % humidity one fails in any simple way to deduce the phases that would correspond at other humidities. In other words, there is no simple way of relating the observed intensities as the humidity is altered. This of course supports the original assignment of phases. This analysis may be summarized thus : the assigned phases give an especially simple family of transforms of quasi-sinusoida form; all other phases
452
4
J.
TORBET
0.04
0.06
AND
M.
0.08
H.
F.
0.10
WILKINS
0.12
0.14
o-14
0.16
0.16
c = :
0.04
o-06
0*08
0.10 Reciprocal
o-12
O-18
space (%-‘I
FIG. 2. The families of reconstructed DPC transforms for (a) no phase change in the region of 0.09 A-1 (asshown in Fig. l), (b) a phase change in that region. The transforms within a family are simply related in (a) and not in (b). (a) * * * * * . , 0% RH; -, 58 2; RH; -.-.-, 84%RH; ---, excess water.(b) ***..*, O%RH;-----,23%RH; . 66% RH; -.-.-, 100% RH; ---, excess water.
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
453
destroy the quasi-sinusoidal form and give much more complicated families of transforms. The simplicity of change within the family of transforms is of course reflected in the corresponding family of electron density profiles (Fig. 3) derived from the transforms. The procedure so far described for assigning phases makes no use of assumptions about the structure of the bilayer itself (except for the rough calculation of the zero order). One may, however, use such assumptions to test the correctness of the phases. One would expect the electron density profile of a bilayer to show a region of uniform electron density corresponding to the methylene part of the hydrocarbon chains, a lower region where the terminal methyl groups are concentrated, and a higher region for the head region. Profiles were calculated for the eight phase combinations (Fig. 4). Only one gave a profile of the expected type; this corresponded to the phase assigned by the swelling procedure. We did not find it possible to account for the other profiles in terms of a bilayer structure; however, the errors of measurement of the higher diffraction orders are such that choice between some of the profiles, e.g. the two lowest profiles in Fig. 4, is not very significant. The swelling behaviour shown in Fig. 3 is physically reasonable: there is a recognizable water layer which increases in width as humidity increases and in parallel the thickness of the bilayer decreases, which is in line with the known behaviour of bilayers (e.g. Tardieu et al., 1973).
A further test of the correctness of the phase assignment is to see if a molecular model can be built which will account for the precise form of the profile. This was found to be the case; the profile calculated from the model corresponded very closely to that observed (Fig. 5). The model was built before the structure of crystalline dilauroyl ethanolamine (Hitchcock, Mason, Thomas & Shipley, 1974) was available. The main stereochemical guides were as follows. The ester c-o-c-c //O group (Chothia & Pauling, 1971) was kept coplanar as in the crystal structure of tricaprin (Jensen & Mabis, 1966). The o-c-c group had a gauche conformation and the -N phosphodiester linkage was gauche gauche (Sundaralingham, 1972). The phosphodiester choiine conformation was similar to that in GPC (Abrahamson & Pascher, 1966) and GPC. Cd Cl2 crystals (Sundaralingham & Jensen, 1965). The terminal methyl groups formed a layer in a plane in the centre of the bilayer and the phosphate-choline dipoles lay in the bilayer plane. It was not found possibIe to build a model, without an in-plane dipole, which accounted for the observed profile of the dry DPC bilayer. Since the profile of the head group showed no sign of change of conformation with hydration it seemed likely that the dipole remainedin-plane in hydrated bilayers. However,
454
LUKUET
AND
M.
H.
F.
WlLKlNb
12 alders d=!56-6
8
O%RH Ilorders d=WOft
23% RH IO ordm d=57*5 8
56%
RH
12 orders d=57-7
%
100 % RH I I orders d=56-68
Vesicles in excess waler IO orders d=64*0 a
L
40
Distance
from centre
of biloyer
a
Fro. 3. Electron density pro& of the DPC bilayer at various relative humiditie (BH) (phases are as in Fig. 1). Note that as the humidity increases the width of the water layer increases and that of the bilayer decreases. d is the spacing in A. The number of Bragg orders wed in calculating the pro6ks is shown. Fro. 4 (oppoSite).Electron density profiles of a DPC bilayer (only half a bilayer is shown) for the eight phase combinations for the 66% relative humidity data. The prow lab&d L‘correct” is obtained with the assigned phas*l as in Fig. 1; the other profiks are labekd with those orders which have their phases reversed.
O-
\ O-
d o-
O-
.
0
O\
0
O
I
0
5 Distmce
IO
15 from bikyer
20 centre
25
X
456
J.
TORBET
AND
M.
H.
F.
WILKINS
FIG. 5. Electron density pro&s of DPC bilayer as calculated from the model and as derived from the diffraction measurements. Thermal disorder has been taken into account by applying a temperature factor of B = 100. -, calculated; -----, observed.
since the X-ray scattering from the choline group is not much different than that of water, one cannot very reliably deduce its position directly from the X-ray data. Neutron diffraction locates the choline group more clearly (Worcester & Franks, 1976) and confirms that the dipole is in-plane in a hydrated lipid bilayer. Data on egg lecithin (EPC) bilayers relate satisfactorily to those on DPC. The higher Bragg orders for EPC all appear near maxima of the transform peaks (thus differing from the case of DPC where some orders are near transform minima), yet the data fit transforms very similar to those obtained for DPC. Electron density profiles derived from such transforms are shown in Fig. 6. The swelling for EPC is small but it gives some indication that the phase assignment is correct. We suggest, however, that the main basis for phase assignment in this case is the analogy with DPC bilayers. When EPC is very thoroughly dried there is a structural transition, the liquid-type arrangement of the hydrocarbon chains changing to a crystalline type like that in DPC. For such dry EPC bilayers the Bragg orders sample the transform in much the same manner as for dry DPC except that order 5 is quite strong. Yet again a transform of the DPC type fits the data. The fact that it is again possible to fit these data to the DPC type of transform is further cotirmation that the DPC phase assignment is correct. A profile derived from the dry EPC transform is shown in Fig. 7; it bears, of course, a close resemblance to the DPC protie.
X-RAY
DIFFRACTION
STUDIES
OF
LECITHIN
BILAYERS
457
47 % RH dC06 8.
66 % RH d=WO a
9296RI-l d*5kI fi
loo % RH +51.3
a
100% RH z/=51*5 A
i 1 40
1
I
1
30
20
IO
Distance
1
0
from centre
methyl groups I
I
I
J
IO
20
30
40
of bilayer
8,
FIG. 6. Electron density profiles of EPC bilayers at various humidities. There is a slight reduction of bilayer thickness as humidity is increased. All curves are calculated using eight Bragg orders except for the vesicles where only five orders were used.
J.
TORBET
AND
20
IO
M.
H.
F.
WILKfNS
20 2
15
5 z. IO b 2 3z 5 % 4.%
o
s -5 CL Y iij -10 -15 0
IO
20
Ll
30
A Fro. 7. Electron density profile of dehydrated corresponding to those derived for DPC.
EPC
bilayers,
calculated
using
phases
One of us (J. T.) held a Medical Research Council Training Scholarship during this work. We are grateful to several colleagues, in particular Y. K. Levine and A. E. Blaurock, for advice and discussion. REFERENCES s. & hSCHER, I. (1966). ACtQ. crysf. 21, 79. CH-, C. & PAUNG, P. (1971). Nuture, Lmd. 299,281. DANIELLI, J. F. & DAWN, H. (1934). J. Cell Camp. Physiol. HITCI+XCK, P. B., MASON, R., THOM.Q,K. M. & SHIPLEY, G. Sci. U.S.A. 71, 3036. JENSEN, L. H. & MABIS, A. J. (1966). Actu Cryst. 21, 770. LEE, A. G. (1975). Prog. Biophys. molec. Biol. 29, 3. i%BRAHAMSGN,
5, 495. G. (1974). Proc. mtn. Ad.
LBSSLAUER, W., CAIN,J. E. & BLASIE, J. K. (1972).Proc. natn. Acad. Sci. U.S.A. 69,1499. LEVINE,
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PERUTZ, M. F. (1954).Proc. R. Sot. A. 225, 264. SAYRE, D. (1952).Actu. Cryst. 5, 843. SUNDARALINGHAM, M. & JENSEN, L. H. (1965). Science, N. Y. 150, 1035. %ND~GHAM, M. (1969). Biopoiymers 7, 821. SUNDARALINGHAM, M. (P972). Ann. New York Acud. Sci. 195, 355. TARDIEIJ, A., LuZZATI, V. & &MAN, F. C. (1973). J. molec. Biol. 75, 711. TORBJXT, J. (1973). X-ray Diffraction Studies of Lipid Bimok&ar Layers. PhD
University of London. WILKINS,M. l-i. F. (1972). Ann. New York Acad. Sri. 195, 291. Wo~ixrza,
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Thesis,
