Calculated X-ray diffraction pattern from a quasi-hexagonal model for the
molecular arrangement in collagen Andrew Miller* and Defendente Tocchetti
European Molecular Biology Laboratory, Grenoble Outstation, c/o C.E.N,G., L.M.A., 85 X, 38041 Grenoble Cedes. France
(Received 14 January 1980; revised 14 March 1980)
The near-equatorial region of the medium-angle X-ray d!]fi'action pattern from native rat tail tendon contains sharp reflections which indicate that the collagen molecules are arranged in a crystalline manner within the fibrils. A succes~ful indexing ~?] these reflections would indicate the crystallographic unit cell in the fibrils while the intensities of the reflections are determined by the arran,qement of the collagen molecules within a unit cell. It is shown that the quasi-hexaqonal model proposed by Hulmes and Miller ~ with slight modifications accounts for the positions t~the reflections [i.e. their (R, Z) values]. Previous models used mainly the R-values of the reflections published by Miller and Parry 2. This model gives a better account t~]'the R-values of the reflections than previous models and, in addition, accounts.]br the Z-values and the intensities of the reflections. This represents the determination t?f the three-dimensional structure t?]'the collagen in a native animal tissue, rat tail tendon, to I nm resolution.
Introduction
In tendons the characteristic collagen structures are the fibrils. These are very long and of variable diameter a and, in mature animal tendons, are in the range 100-300 nm. Tendons are bundles of parallel and antiparallel fibrils and small-angle X-ray diffraction from dry tendons have meridional or near meridional reflections which index as orders of 64 nm 4. Under the electron microscope the origin of these X-ray reflections can be seen as a series of bands perpendicular to the fibril axis and regularly spaced at intervals of 64 nm along the fibril axis 5 - 7. The collagen molecules are 299 nm long and 1.3 nm in diameter. Apart from an N-terminal telopeptide of 16 amino acid residues and a C-terminal telopeptide of 25 residues, the whole molecule is a triple-strand rope in which each strand is a helical polypeptide s - l ° . The atomic arrangement in the dry collagen molecule has recently been refined 1 t. On the basis of electron micrographs of negatively stained fibrils, Hodge and Petruska 12 proposed the one-dimensional molecular arrangement shown in Figure 1. This has been confirmed at low resolution (5 nm) from the pattern of fine bands in electron micrographs of positively stained fibrils 13'41'42 and at higher resolution (1.6 nm) by a correspondence between the intensities of the observed X- ray meridional reflections and the sampled Fourier transform of the Hodge-Pet ruska arrangement of col- lagen molecules of known amino acid sequence projected on to the fibril axis~ 4,3 7. The X-ray diffraction pattern also showed that the 64.0 nm periodicity of the banding pattern in electron micrographs was 67.0 nm in native tendons 38. The one-dimensional molecular arrangement is thus well understood. Progress from this to knowledge
* P r e s e n t address : Laboratory of Molecular B i o p h y s i c s , D e p a r t m e n t of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK.
of the full three-dimensional molecular arrangement has been slow because of the nature of the relevant data. Unlike the analogous paramyosin fibrils 15, electron mic- rographs ofcoUagen fibrils have not shown unambiguous evidence of the lateral molecular arrangement, and direct visualization of the three-dimensional arrangement has
Z Y
5 \ / @ @ @ @ @ ( 9 @ @ - - - "
@ ® @ ® ® ® ®
e o o o 5 - G e o @ @ @',® @
t I I
G G o!G o o o o G-'+ G o o
q } ® @ ® @ ¢ ) @ ® Figure I The lateral arrangement of collagen molecules in the structure proposed by Hulmes and Miller 1. A collagen molecule of length 299 nm is represented by a rod divided into five segments labelled 1 5. Segments 1 ~, are 67 nm long and segment 5 is ~67/2 nm long. The three principal planes of the quasi- hexagonal lattice have spacings of 1.38. 1.33 and 1.26 nm, respectively. The resulting quasi-hexagonal lattice has a mono- clinic unit cell ofa = 3.9 nm, b = 2.67 nm and 7= 104.58 . One unit cell is outlined by broken lines. In the sheets of molecules parallel to the X-axis neighbouring molecules are staggered axially by l D and 4D with respect to each other (see Figure 4). In the sheets of molecules parallel to the Y and Z axes, neighbouring molecules are staggered axially by 2D and 3D with respect to each other
X-ray di[]?action fi'om model &r collaqen: Andrew Millet"
not yet proved possible. However, the medium-angle X- ray diffraction pattern, i.e. in the R-range 0.1 1.0 n m - (R = 2 sin 0/2, where 0 is half of the scattering angle, R and Z are defined as parallel to the equator and meridian, respectively, see Ref. 39), was shown to contain a series of equatorial and near equatorial reflections ~6'~ 7 which, in conjunction with associated row-lines, demonstrated that the collagen molecules were indeed arranged on a regular crystalline lattice. Since the fibrils are azimuthally dis- orientated, the X-ray diffraction pattern is equivalent to a crystal ' rotat ion' pattern. The R-values of these reflections were reported ~6 ~8 and on the basis of these a variety of different models have been proposed for the three- dimensional molecular arrangement 1,2 ,16 ~ 2 8 . Only
1 7 , 2 2 general discussion has been given to the Z values or intensities z4'28 of the reflections. In this paper, we cal- culate the (R, Z) positions of the near-equatorial re- flections as well as their intensities predicted by the quasi- hexagonal model of Huimes and Miller 1. These calcu- lations enable us to photowrite (see below) an I(R, Z) array and thus to produce a photograph of the X-ray diffraction pattern which the model would predict. This shows a good similarity to the observed X-ray diffraction pattern ~ 7, and the calculated and observed values of I(R, Z) in the near equatorial region also agree well.
Experimental
X-ray d![fraction The medium-angle X-ray diffraction patterns were
recorded on a focusing mir ror -monochromator camera linked to a rotating-anode X-ray generator (Elliott GX20) of source size 1 mm x 200 ~m. The mirror consisted of a glass block, usually coated with a thin layer of gold or nickel and bent so as to provide poor focusing in the vertical plane. An asymmetrically cut thin quartz crystal was used to isolate the ~ component of the CuK~ radiation from the X-ray source. The crystal was bent so as to provide good focusing in the horizontal plane. The size of the focus at the film was ~ 0.2 mm × 0.7 ram. The specimen, focus and film lay on the circumference of a circle of diameter 176 mm. The camera was therefore a cylinder with 176 mm diameter and a height of ~ 100 mm. The tendons in the specimen cell were held with their fibre axis horizontal, so all points on the meridian of the X-ray diffraction pattern were in focus.
Specimen preparation The series of sharp near-equatorial reflections in the
medium-angle X-ray diffraction pattern were first ob- tained from fibres that were dissected and then sealed immediately in capillary tubes in an effort to preserve the 'native" state ~. It was later discovered that these re- flections also appear if the tendons are dissected in 0.15 M NaC1 and then enclosed in a specimen cell above water a 7. Some specimens for the X-ray diffraction patterns de- scribed here were obtained with a cell in which both ends of the tendon could be held in a conical clamp. The fibres were then extended by ~3°0 so as to remove the crimp seen as a 200 #m periodicity along the fibre in a polarizing microscope. All fibres were removed from the rat tails by making two incisions in the tail skin ~ 4 cm apart and then pulling the fibres from the tail.
X-ray diffraction patterns of the orthomorphic state
and Dqlemlente Tocchetti
(see Results) were obtained from fibres dissected in ~ 0.5 M NaCI and then exposed to X-rays above water in a sealed cell. Fraser et al. 29 have obtained X-ray data from a state intermediate between native and orthomorphic by treating fibres with 0.3 M CsCI.
Computation The computations ofl(R, Z) were carried out on a Nord
10 computer.
Calculation ~/[R, Z). The values ofR =(hZa .2 + k2h .2 +2hka*h*cos~/*) ~;2 were calculated for reflections of order (h, k) (74~<h~<4; k~<3) using the values a*=0.265 nm -~, h*=0.387 nm -~ and 7*=75.42 . These values were taken from Ref. 1. The row-lines at these positions were assumed to be continuous and perpendicular to the two-dimensional reciprocal lattice defined by a*, h* and
The Z-value of each of the (h,k) reflections was esti- mated by calculating the Z-value of the intersection of the above row-lines with a tilted plane. This plane, referred to as F~, represented the Fourier transform of a molecule taken as a cylinder. Since the molecules are tilted at some 5' to the crystal (fibril) axis, the plane F~ is inclined at (90- 5) to the assumed row-line direction. The Z-value of the intersection of the row-line originating from the reciprocal lattice point (h, k) was given by:
-- tan r
where ~ is the angle between the molecular axis and the fibril axis and ~ is the angle between the axis of rotation producing the tilt and an arbitrary direction with tp = 0 in the equatorial plane and through the origin of the reciprocal lattice (see Fiqure 3 belowl.
Calculation ~71" I(R,Z). A collagen molecule was approximated by a cylinder of radius 0.49 nm. The unit cell base was taken with the a, b and ), values corresponding to the reciprocal unit cell given above. The real space cell has a = 3,903 rim, b = 2.667 rim, 7 = 104,58. In this cell, molecules were placed at positions with (x, y) coordinates (0, 0)(½, ~,,3~ ,~,12 ~,1~ ~,13 ~p4~ and (~, ~). All were given unit weight except that at (0, 0), which was given weight 0.5 to allow for the 'gap'. This therefore represents a projection along the direction of the molecular axis for a distance (67/cos 5 ) nm. One unit cell contains one collagen molecule in the form of its five segments (1)--(5) defined in Fiqure 1, one segment at each (x, y) position listed above. The interference function for one unit cell is therefore:
I(X, Y )=I ;+exp(25 i ) (X+3Y)+exp(25 i ) (2X+ Y,
This is multiplied by the Fourier transform of a cylinder:
[J l(2nR x 0.49)/(2nR x 0.49)] 2
and then sampled at the reciprocal lattice points (ha*, kh*). Several calculations were done to investigate the effect on the X-ray diffraction pattern if the four molecular segments in the 'gap' redistributed themselves to new (x, y)
10 Int. J. Biol. Macromol., 1981, Vol 3, February
X-ray di(fraction.l)'om model for collagen: Andrew Miller and Defendente Tocchetti
positions, not coincident with the (x, y) positions of the five molecular segments in the 'overlap' region, In this case, all nine (x, y) positions were given equal weighting.
Estimation of I(h,k)ob ~. It is difficult to estimate accurately the intensities of the observed reflections in the X-ray diffraction pattern for several reasons. Some of the reflections, such as that at R = 1/1.37 nm -1 and 1/1.33 nm- 1 are scarcely resolved in R while all the reflections lie on a substantial continuous diffuse scatter,
The X-ray diffraction patterns were microdensito- metered with a Joyce-Loebl microdensitometer. Linear records were made along the equator and along two lines parallel to the equator and separated by Z = 0.05 nm -1. The diffuse background scatter was approximated by a smooth curve connecting the regions between Bragg reflections, and the intensities of the Bragg reflections themselves taken as the area above this background. The intensities were on an arbitrary scale and different films from different exposure times were required to obtain the range of observed intensities.
All intensities were multiplied by a korentz factor equal to R and the equatorial reflections being multiple re- flections were weighted 0.5 compared with the off- equatorial reflections, which were weighted unity. The intensity in the region of R, 1/1.37-1/1.33 nm - 1 was not asymmetric along R, so the total intensity in this region was divided by two and each half assigned to the reflections estimated by Miller and Parry 2 to be at R = 1/1.37 and 1/1.33.
Photowritten diffraction patterns. The interference function was convoluted with a Gaussian function of half- width 0.2 nm ~ around each point of the Bragg reflection and then projected on R. The half-width of 0.02 nm-1 is estimated from the beam width in this direction. Since the beam is poorly focused in this direction, the width of the equatorial reflections parallel to R is dominated by the beam width and not by the coherent width of the crystallites in the collagen fibrils, The intensities obtained in this way were then convoluted with a Gaussian function of 0.03 nm -~ in Z to simulate the observed breadth of the reflection. A two-dimensional (R, Z) array was constructed thus and written on an Optronics Photowrite P1001. This instrument accepts as input a two-dimensional array of numbers and produces as output a two-dimensional photograph in which the brightness at any point corresponds to the number in the two-dimensional array at that point.
is rather sensitive to the moisture content of and the ionic strength within the fibre. In the native state, however, the intensity in this region is such that the reflections at larger R (1/1.33 nm 1) has a larger Z value than that at the lower R ( 1/1.37 nm- 1). The two reflections are never completely resolved from each other and the unresolved pair appear as a broad, slightly tilted reflection with the larger Z part of the reflection being further from the meridian than the lower Z part. This is of significance when compared with the same region of the X-ray pattern from fibres in the orthomorphic state.
Another point worthy of note is that the reflection at R = 1/3.8 nm -J usually does not have an equatorial com- ponent. However, this is not always the case and, again, this appears to be a part of the X-ray pattern which is very sensitive to the exact conditions of the specimen. Sometimes there is an equatorial component of intensity similar to that of the off-equatorial component which appears at Z = I/45.0 n m - 1.
Orth~imorphic state. This state was discovered by Miller and Wray 17 and gives an X-ray diffraction pattern which, while closely resembling the pattern from a fibre in the native state, has very significant differences. In the near-equatorial region, the difference manifests itself in an off-equatorial splitting of the reflections at R = 1/1.27 nm-1 to Z=0.037 nm 1. At the same time, the broad relfection at R = 1/1.36 nm- 1 moves to a somewhat larger Z than that in the native state but, more interestingly, the apparent 'tilt' of the combined reflection alters so that the high Z part of the reflection is at a lower R value than the low Z part of the reflection. We interpret this in terms of a pair of reflections, one at R = 1/1.38 nm -~ and Z=0.047 nm 1 and the other at R=1/1.34 nm -1 and Z=0.036
1 D i n
7
Results
X-ray diffraction patterns Native state. The medium-angle near equatorial X-
ray diffraction pattern has been described 16.1 ~,2,18,22,19 The general features of the pattern which we use as the basis for our model are agreed upon (Figure 2). We summarize our own measurements in Table 1 and Figure 3. Some points are worth noting.
The off-equatorial intensity at around R = 1/I.36 nm- 1 was taken by Miller and Parry 2 as consisting of two reflections at R=1/1.37 nm 1 and 1/1.33 nm 1. The breadth of these reflections parallel to Z is considerable and so their Z values are difficult to estimate. Miller and Parry 2 gave Z--1/15.5 nm-1, while Fraser 3° implied Z = 1/20.0 nm 1. It would seem that this part of the pattern
Figure 2 la} Observed medium-angle X-ray diffraction pattern from native rat tail tendon. The equatorial and near-equatorial region is shown out to R = 1/1.2 nm- ~. The extreme left-hand edge of the plate is R =0. (b) Calculated medium-angle X-ray diffraction pattern from the model for the molecular arrange- ment in collagen described in the text. The same equatorial and near-equatorial region as in ta) is shown, ta) and (b) are on the same scale with their equators parallel and in register, to allow
.comparison between observed and calculated patterns
Int. J. Biol. Macromol., 1981, Vol 3, February I I
X-ray d!fi'raction Jrom model for colla.qen." Andrew Miller and De fi~nde,Tte Tocchetti
Table i Table of observed and calculated fIR,Z) for the equatorial and near equatorial reflections in the medium angle X-ray diffraction pattern from native rat tail tendon
I /R o I/'R~ R, R~ Z o Z~ /1 k (nm) (nm) (nm ) (nm 1) (nm l) (nm-l) 1,1 1~
Figure 3 Idealized diagram of the medium-angle X-ray diffrac- tion pattern from native rat tail tendon. The near-equatorial region is shown. The three stippled reflections are the most intense in the diagram. There are some minor differences between the pattern shown here and that reported as the observed pattern in Refs 22 and 25
Model derived fi'om the X-ray data Hexagonal hasisJbr model. The starting point for the
model is the assumption that the molecules are quasi- hexagonally packed. The R-spacings of the three intense reflections in the near-equatorial region a round R =0.8 nm 1 are taken as the distances between the three principal planes of a hexagonal array a. There are a variety of ways in which an assembly of D-staggered molecules can be arranged as a hexagonal lattice 3~'32 and here we take that class of models yielding the type of unit cell first proposed by Macfarlane 33. A section through this lattice is shown in Fiqure 1.
This arrangement may be thought of as follows. The length of a collagen molecule is L = 4.5 D where D = 67 nm. Hence the collagen molecule may be regarded as com- posed of four segments of length D, labelled (I), (2), (3) and (4) and a fifth segment of length D/2 labelled (5). Fiyure 1 may be considered as a section of height D through the structure. The circles represent molecules and the num- bers represent the appropriate segment of the molecule which occurs in the section. Thus the molecules along the axis marked X are staggered by D with respect to their neighbours to form a sheet shown in or thogonal section in
Figure 4a. It is clear that within a section of height D, there is a repeat of 5 × x (where x is the intermolecular distance) along the sheet in a direction (termed the X-axis in Figure 1) perpendicular to the molecular axis. The third dimen- sion is formed by stacking such sheets. A second sheet is stacked beside that in Figure 4a in axial register but shifted along the X-axis by 2.5 × D so that molecular segment (1) (Figure 4b) of the second sheet lies in between segments (3) and (4) of the first sheet and distance x from both. The third sheet is displaced with respect to the second in an identical manner and thus is coincident with the first sheet in the projection shown in Figure 4b. Note that within these sheets lying parallel to the X-axis in Figure 1, the molecules are staggered by 1D and 4D with respect to their neighbours and so the sheets themselves have a period of D when projected on to the direction of the molecular axis. The s trut ture could also be considered as having sheets of molecules parallel to the Y- and Z-axes in Figure 1. These sheets also have a D-period in projection but this is brought about by staggers of 2D and 3D between neighbouring molecules. The axes X, Yand Z correspond to the directions of the three principal planes of the hexagonal array of molecules. The unit cell in Figure l is that defined by Macfarlane 33 with a = 3 . 9 7 nm, h = 2 . 6 0 nm and ~,= 109. It should be noted that Macfarlane 33 illustrates the other possible choice in which two of the principal planes contain sheets of molecules staggered by 1D and 4D and the third contains molecules staggered by 2D and 3D (Figure 5). Both this choice, and that illustrated in Fiqure 1 are possible in the model of Hulmes and Miller 1. They illustrated that in Figure 1 but as we shall point out below that illustrated by Macfarlane is the more likely.
Quasi-hexagonal model. The above arrangement is, of course, perfectly hexagonal and it is not possible to obtain a fit between the R-values of the reflections predicted by such a model and the observed R-values 31. The derivation of the quasi-hexagonal model involves taking the intense reflections at R-values of 1/1.37, 1/1.33 and 1/1.26 n m - 1 as representing distinct values for the spacings between
12 Int. J. Biol. Macromol. , 1981, Vol 3, February
X-ray diffraction from model for collagen: Andrew Miller and Defendente Tocchetti
a b
I ' / I A A'
Figure 4 (a) Arrangement of collagen molecules in one of the sheets parallel to the X-axis in Figure 1. Neighbouring molecules are staggered by I D and 4D with respect to each other. The third dimension is formed by sheets like this stacking parallel to each other and displaced laterally by 2.5 × x, where x is the in- termolecular spacing in a sheet. (b) Projection through the 3-D stack of sheets. The full line molecules comprise sheets as in (a). The broken-line molecules form sheets parallel to that in (a) but displaced 1.3 nm from them in a direction perpendicular to the plane of the sheets, and displaced further by 2.5 × x in a direction parallel to the sheet plane and perpendicular to the molecular axis, so that the molecules labelled A is moved to A'. In the actual structure the molecules are also tilted, the direction of tilt being approximately out of the plane of this Figure. For precise direction of molecular tilt, see Fiqure 6
the principal planes and assuming the general unit cell shown in Figure 1. The Miller indices assigned to these reflections are thus fixed and three simultaneous equa- tions may be solved for a, b and "; of the unit cell in Figure 1. As Hulmes and Miller 1 have indicated, this leads to values of a=3 .903 nm, b=2 .667 nm and 7=104.58 °. These authors also showed that the R-values of the reflections predicted by this unit cell are in better agree- ment with the observed R-values than those predicted by any of the other models proposed (see In t roduct ion and Table 1). The three intermolecular distances in this model are 1.47, 1.52 and 1.59 nm, respectively.
Molecular tilt aml evaluation of (R, Z ) f o r near- equatorial reflection.s. Let us rehearse the arguments of Miller and Wray ~" that the collagen molecules are inclined (by 4 5 ~) to the fibril axis. The intense reflections at R-values of 1/1.37 and 1/1.33 n m - 1 are off-equatorial at Z values of 0.055 n m - 1 and 0.065 n m - 1 , respectively, while the intense reflection at R = 1/1.26 n m - a is at Z =0.
That the occurrence of intense reflections at such large values of Z is not due to short coherent lengths of untilted collagen molecules is demonstrated by the fact that the scattered intensity in the equatorial and near-equatorial region is confined to a fan-shaped region with the origin as apex of the fan. Untilted molecules of short coherent length would produce a band of intensity with its limits parallel to the equator. Nemetschek and Hosemann 22 also have argued that the molecules are tilted.
Since the molecular tilt must take place in a specified direction with respect to the lattice proposed in the model, the model may be tested by seeing if a direction of tilt can be discovered which would account for the observed Z- values of the various reflections. Hulmes and Miller ~ pointed out that if the molecules were tilted in a plane parallel to the sheets of molecules separated by 1.26 nm, then this would predict the intense reflection at R = 1/1.25 nm -1 as equatorial , those at 1/1.37 nm -1 and t/1.33 n m - 1 as equally off-equatorial and the reflection at 1/1.73 nm 1 as in practice, on-equatorial .
We have calculated the Z-values of all the reflections predicted by the model lattice with molecules inclined at angles in the 3.5-6.Y to the fibril axis. The angle between an arbitrary reference plane and the plane in which the molecules are inclined was varied. The angle between the reference plane and the plane parallel to the sheets of molecules spaced by 1.26 nm was 76 °. In these calculations we assumed that the row-lines predicted by the model lattice were perpendicular to the equator. We also took the t ransform of the molecule in the equatorial region to be a disc of infinitesimal thickness in the Z direction. When the molecules were tilted by, say 5 °, in a plane in real space, we rotated the disc by 5 ° about an axis perpendicular to this plane, through the origin of recipro- cal space and in the equatorial plane. We then calculated the Z-value of the intersections between this rotated disc and the row-lines predicted by the model lattice.
Z Y
\ / 5 G ® ® @ @ @ ® ® 4
@ @ ( 9 @ @ @ @ 3
( 9 @ @ @ @ @ @ @ 2 @ @ @ @ @ @ @ I
( 9 @ @ @ @ @ @ @ @ @ ( 9 @ @ @ @
@ ( 9 @ @ @ @ @ @ Figure 5 As Fiqure 1 but showing an alternative arrangement of the molecules. In this Figure, the sheets parallel to the X-axis contain molecules with axial staggers of 2D and 3D with respect to each other. In the sheets parallel to the Y- and Z-axes, neighbouring molecules are staggered axially by I D and 4D with respect to each other. If covalent crosslinking only occurs between the 1D/4D staggered molecules, then this arrangement would allow a three dimensionally crosslinked fibril. However, the arrangement in Figure I would only allow the sheets parallel to the X-axis to be stabilized by crosslinks: these sheets, being related by 2D/3D staggers could not be crosslinked together
Int. J. Biol. Macromol. , 1981, Vol 3, February 13
h 2 5
X-ray d![J?action from model]or collacten: Andrew Miller and
J JJ
/ /
T o
\ / \ %
Figure 6 Diagram of the reciprocal lattice corresponding to the real lattice in Fi.qure 1. The lattice has a* =0.26 nm -~, h* = 0.39 nm-~ and 7*= 75.42 . The broken line through the origin and labelled @ = 80 represents the axis of rotation ~bout which the molecular transform is tilted by 5.2 to the meridian in native collagen. Reciprocal lattice points lying on or near this line will appear as equatorial reflections in the X-ray pattern. The broken line labelled ¢ = 50 is the corresponding axis of rotation in the orthomorphic state when the tilt angle is 5.75 . The full line through the origin and labelled ff =0 is the axis to which the ~p angle is referred
These calculations indicated that when the plane in which the molecules were tilted was inclined at 8 0 to the reference plane (for sense of rotat ion see Fiqure 6) and the molecules were inclined at 5 .2 to the fibril axis, the best fit was obtained between the predicted and the observed Z- values of the various reflections. We shall see later that this procedure of estimating the Z-values of the reflections is strictly valid only for the three intense reflections at R = 1/1.37, 1/1.33 and 1/1.26 nm - ~; for the other reflections however, the evaluation of Z is correct to ± 1/2 × 67.0 nm ~ (i.e. +0.007 nm 1).
It is interesting to note how, at qJ = 8 0 , the Z value of the 1/1.37 nm -1 reflection is less than that of the 1/1.33 nm i reflection since this accounts for the tilted ap- pearance of the observed double reflection. The reflections at 1/1.26 and I/1.73 n m - 1 are at sufficiently low values of Z that, given the crystalline disorientation of + 1.5 ' , they will appear as equatorial reflections. This discussion is, of course, for the 'native' X-ray diffraction pattern.
The 'o r thomorphic ' X-ray diffraction pattern differs most markedly from the 'native' pattern in the near- equatorial region in that the reflection at 1/1.26 nm ~ is now split across the equator. Since all of the observed reflections maintain their R-posit ions compared with the 'native' pattern (apart from a uniform swelling in real space of 0.88'!ii) this splitting can only be brought about by altering ~, the angle of the plane in which the molecules are inclined. We have varied ~ and the molecular tilt angle and obtain a good fit with the observed and predicted Z- values of the reflections when ~ = 5 0 and the molecules are inclined at 5 .75 to the fibril axis. In particular, the Z- value of the reflection at 1/1.37 nm 1 is now greater than that at 1/1.33 nm -1, account ing for the tilt of the combined reflection appearing in a direction opposite to that in the native case. The reflection at 1/1.73 n m - 1 is effectively equatorial, the reflection at 1/1.89 nm 1 at a Z- value similar to that of the "native" case while the Z-values of the reflection at 1/3.8 nm ~ increases with respect to that in the "native" case. All of these points accord with the observed X-ray diffraction patterns.
De[endente Tocchetti
The 0.95 nm layer-line. The clearest evidence that the sharp reflections in the near-equatorial X-ray diffraction pattern originate from a crystalline arrangement of collagen molecules is the fact that row-lines emanat ing from some of these reflections, sample the 1/0.95 n m 1 layer_line 16.1v. This layer-line is, of course, the first-order Bessel function layer-line from the helical collagen mole- cule. In this region of the X-ray diffraction pattern from 'native' tendon, it is evident that the row-line emanat ing from the 1/'3.8 nm-1 near-equatorial reflection has two arms. The angle between the arms is 6 17.2% This row-line splitting is negligible in the near-equatorial region.
Fraser e t 0l. 29 have shown that the angle between the arms of this row-line is the same as the angle between the two near-meridional zero-order row-lines. This indicates that the lattice is sheared in a direction parallel to the fibril axis. The Z-value of the intersection of the inner row-line with the 1/0.95 n m - 1 layer-line (i.e. on the low R side) is smaller than the Z-value of the intersection with the outer row-line. This again indicates that the molecular axis is inclined to the fibril axis and, furthermore, reveals that the directions of the molecular tilt is opposite to the tilt (from the normal to the fibril axis) of the vector connecting
3 ~ equivalent sites in the sheared structure -. The molecular tilt, as projected on to the 3.8 mn vector, is 2.2' in the simplified model lattice compared with 3.2 from the observed Z-values on the 1/0.95 nm 1 layer-lines. However, as we shall see later, the simplified model could lead to predictions of Z which are _+ 0.007 nm 1 in error and the tilt difference is within this error.
When the transition to the ' o r thomorphic ' form occurs, the angle between the arms of the first-order row line decreases to zero and the single row-line intersects the 1/0.95 n m - 1 layer-line to produce two reflections with the same R value but with different Z-values I 7,1s Fraser et al. 2~ have discovered an intermediate state in which the angle between the arms of the first-order row-line is 3 . They find that there is a decrease in the Z-values of the intersection of this row-line with the 1./0.95 nm-1 layer- line. As pointed out by Hulmes and Miller 1 this is thc behaviour expected from the proposed model.
The inner arm of the 1/3.8 n m - 1 row-line in the native structure intersects the 1/0.95 nm 1 layer-line in a reflection which is narrow (+0.01 nm -1) in the Z- direction. The crystal disorientation in the specimen gives the reflection the shape of an arc. The arc spans 0.28 < R < 0 . 2 3 5 nm i and this allows an estimate of the maximum disorientation as + 1.5.
Et~aluation o] the intensities qf' the rellectioms predicted by the model. The collagen in tendons is shown from X- ray diffraction to have three-dimensional crystallinity. Normally, in the X-ray analysis of a crystal of a small molecule the dimensions and space-group of the unit cell are first determined from the geometry of the reciprocal lattice and then the structure is determined by compar ison of the observed X-ray intensities with those predicted by a model for the structure. In the case of a fibrous macromolecule, however, the unit cell in one direction at least is often within the molecule, so measurement of the geometry of the reciprocal lattice already yields a model. In spite of this, full confirmation of the validity of a model awaits a detailed compar ison between the observed and predicted intensity distribution within the X-ray diffraction pattern. This we now do.
Essentially, what we do is to calculate an intensity
14 Int. J. Biol. Macromol. , 1981, Vol 3, February
X-ray diffraction from model for collagen: Andrew Miller and Defendente Tocchetti
corresponding to each reflection of (R, Z) described above. The unit cell chosen for the intensity calculation has the a, b and 7 values described above. This defines the unit cell base. The fractional coordinates (x, y) of the molecules within this cell were taken 1 3 2 ! as (0, 0) (~, ~), (~, ~), (3, 4) and 4 2 (g, ~). Each molecule was weighted unity except that at (0, 0) which was weighted 0.5 to allow for the 'gap'. Each molecule was considered as a cylinder of radius 0.49 nm. This radius was chosen because the first zero of the function J, (2nRr)/(2nRr) where r=0 .49 nm occurs at R = 0.8 n m - ~, which coincides with the observed minimum equatorial intensity in the X-ray diffraction pattern. The Fourier transform of the above cylinders was multiplied by the two-dimensional interference function for the molecular positions [equation (1)]. This two-dimensional function was then sampled by the reciprocal lattice of the model. This calculation gives an approximation to the diffraction pattern predicted from one three-dimensional unit cell projected along the molecular axes through a distance 67.0/cosq~ (where ~p is the angle between the molecular axis and the fibrillar axis) on to a base of dimensions close to a =3.903 nm, b =2.667 nm and 7' = 104.58. This unit cell contains one collagen molecule in the form of five molecular segments labelled (1)-(5) in Figure 1. Justification of this as an approximate calcu- lation of the intensities of the reflections is given below. The error in R due to the fact that the molecules are inclined by 5 ~ to the axis of the fibril leads to an error of <0.5'~, in the calculation of I(R, Z).
Table 1 consists of a list of the calculated and observed intensities of all the equatorial and near-equatorial re- flections within the range studied. In summary, this resulted in the prediction of the intensities of the re- flections which agreed well with the general distribution of intensities in the observed X-ray pattern. The broad maximum at R = 1/1.3 nm -1 was due to the interference between the principal planes of the quasi-hexagonal lattice and the sharp Bragg reflections came from the regularly arranged 'gaps' defining the 3-D unit cell.
It has been pointed out 35 that since the gap and overlap regions are about equal in length (D/2), it could be that the lateral arrangement of molecules within the gap and overlap regions differ. We have tested this idea by calculating the X-ray diffraction pattern for models in which the overlap region is packed quasi-hexagonally as described above, but in the gap region the molecules are redistributed to give a more even distribution of molecules than is obtained by leaving regular gaps. In projection down the molecular axis, this would still produce the same monoclinic unit cell as above, but the intermolecular interference functions differ and so different intensities for the reflections are predicted. We found that any deviation from quasi-hexagonal packing with gaps (i.e. the mole- cules following the same linear path through the gap region as the overlap region) destroys the good agreement between observed and predicted intensities of the reflections.
Full three-dimensional cell. The base of the unit cell was determined from the R-values of the X-ray reflections in the equatorial region. If this base lay in the plane perpendicular to the fibre axis, then the row-lines in the diffraction pattern would be perpendicular to the equa- torial plane. In fact, in the native pattern the row-lines are not at right angles to the equatorial plane. The row-line which cuts the equator at R =0.26 n m - 1 has been studied
in some detail 17'1s'29. It makes an angle of 87 ° with the equatorial plane and the near-meridional or zero-order row-line is parallel to it. This means that the angle between the base of the unit cell and the equatorial plane is 3'. The direction of maximum inclination is along the 3.8 nm vector and fibre axis. The effect of this shear is negligible in the near-equatorial part of the X-ray diffrac- tion pattern but becomes evident at Z =0.1 n m - 1. In the orthomorphic state the row-lines are perpendicular to the equatorial plane and so there is no shear: the unit cell base lies in the plane perpendicular to the fibre axis.
In summary, the unit cell base has been determined. This predicts a two-dimensional reciprocal lattice, the R- values of which agree well with the R-values of the observed X-ray reflections 1. This unit cell ba,se predicts a row-line originating from each reciprocal lattice point. In the orthomorphic case, these row-lines are perpendicular to the equatorial plane: in the native state the row-lines are inclined at (90-3y to the equatorial plane.
To define the full three-dimensional reciprocal lattice, we must determine the layer-lines (more accurately, layer- planes) which intersect the array of continuous row-lines to produce a three-dimensional lattice. In real space this means we must discover a third vector, roughly parallel to the fibril axis, which, with the two vectors in the unit cell base, defines the three-dimensional unit cell. If the col- lagen molecules were parallel to the fibril axis, then the third vector would most naturally be that relating one collagen molecule to another within a Hodge Petruska sheet, i.e. displaced laterally by some 1.5 nm and axially by 67.0 nm. However, it is known that the molecules are inclined to the fibril axis by 5.25 ° (see above). This is equivalent to the lateral displacement of the molecules, which are axially displaced by 67.0 nm. Since the mole- cular tilt is known and the direction of the tilt with respect to the lattice is also known, it is possible to predict the vector connecting closest molecules displaced by 67.0 nm. However, the precision with which this vector can be predicted is limited by the precision with which we know the angle of tilt of the molecule. This type of unit cell is 67.0 nm high and of unit cell base as described above (Quasi- hexagonal model). The angles 0c and fl are determined by the third vector connecting closest molecules displaced axially by 67.0 nm and this, in turn, is determined by the molecular tilt. The effect on the diffraction patterns is to produce a series of layer-planes spaced by Z = 1/67.0 nm-~. These planes intersect the true meridian at Z- values which are integral multiples of 1/67.0 nm -1. However, the planes are not necessarily parallel to the equatorial plane but are inclined to the equatorial plane in a manner determined by :~* and [3*. In principle, diffrac- tion can only occur in directions specified by the in- tersection of this set of layer-planes with the row-lines coming from the unit cell base. In practice, the crystal disorientation of + 1½ ~" means that such layer-planes will only be resolved when R <0.57 n m - 1 Thus evidence of the layer-plane spacing can only be expected on the row- line at R = 1/3.8 nm-1. The row-lines at R = 1/1.26 nm-1 a n d l / 1 . 2 4 n m l are too weak and that at R=1 /19 nm 1 too close to the limit of R to provide clear information on the Z-sampling. The row-line at R=1/3.8 nm 1 has reflections at Z = 1/45 nm I and 1/22 nm-1. These are slightly broadened in Z by _+ 0.01 nm-~ in well-oriented specimens. The displacement of these reflections in Z from integral integers of 1/67 rim- 1 is sufficient to indicate that the layer-lines are not parallel but inclined to the equa-
Int. J. Biol. Macromol., 1981, Vol 3, February 15
X-ray d~[i'action.from model for collagen: Andrew Miller
torial plane, but their breadth parallel to Z is too great to allow the determination of a precise value for the angle of inclination.
There are implications from the true three-dimensional unit cell for the calculation of R, Z and I(R, Z) which we report above. We have assumed row-lines which are normal to the equatorial plane and which are continuous in Z. The effect of the first assumption is negligible in the near-equatorial region. At Z=0.1 nm -1 at R = 1 nm -~, the error in R due to this approximation is 0.0005 nm- 1, which is below the natural breadth of the reflections (_+0.01 nm-i) . The second assumption ignores the 1/67 n m - ' sampling along Z, so each Z value is subject to a maximum error of _+1/2×67 nm -~, i.e. _+0.0075 nm -~.
The calculations of I(R, Z) were carried out for the projection along the molecular axis. Thus, the molecules were all weighted unity except for that at (0, 0) which was weighted 1/2 to allow for the gap. The Fourier transform of a molecule taken as a cylinder lies in a plane and has circular symmetry. This plane, which we call FM, is tilted with respect to the equatorial plane. When the model of the whole fibril is viewed along the molecular axis, the true unit cell base is not apparent because of the superposition of many unit cells and all that is apparent is a lattice of quasi-hexagonally packed molecules, all information about displacements parallel to the molecular axis being lost. In reciprocal space this implies that the only three- dimensional lattice reflections which lie precisely on the tilted F , are the reflections corresponding to the three principal planes of the quasi-hexagonal lattice, viz. those at R = 1/1.37, 1/1.33 and 1/1.26 nm- 1. However, F,, is not infinitesimally wide in Z. The region 5 of the collagen molecule is only 0.5 x 67 nm in length and so F,, will be at least -4- 0.03 nm- i in breadth. Furthermore, it is possible that the axes of the collagen molecules do not follow absolutely straight lines through the unit ceil. This would contribute to an R-dependent broadening in the Z-spread of F M. Finally, the coherent length of a collagen molecule is probably limited to around 15 20 nm.
These three points (gap, molecular disorientation within the fibril and finite coherent length of collagen helix) all imply that F M has a finite breadth in Z. The profile of F w in Z will be roughly a Gaussian curve with half-width at least 0.03 nm-1. Since the gap and the disoriented molecules of finite coherent length are arranged on the 3-D lattice, F,, will be sampled by the 3-D reciprocal lattice. Only the row-lines corresponding to the three principal planes of the quasi-hexagonal lattice will intersect the coincidence of the layer-planes and the plane of maximum F~ (i.e. maximum as measured parallel to the Z-axis). The row-lines from non-principal planes will, in general, intersect the layer-planes at a non-maximal value of F,~ (i.e. non-maximal parallel to the Z-axis). The effect of these considerations on our method of calculating I(R, Z) is that we will overestimate the intensities of the non-principal planes compared with the principal planes since, in our calculations, we only use the values of F,~ at its maximum (parallel to the Z-axis).
Discussion
It appears to be a general feature of the structure of fibrous proteins that the crystailinity of the assembly of molecules in a fibre is much better developed in the direction parallel to the fibre axis than perpendicular to it. Collagen exemplifies this very well. The meridional reflections are
and Defendente Tocchetti
intense, sharp and with no measurable diffuse scatter between them. The equatorial reflections are weak, dif- ficult to obtain and, in native fibres, always accompanied by diffuse scatter between the Bragg reflections. This means that in the lateral direction there are two aspects of the structure to be defined. These are (a) the regular, crystalline and (b) the nature of the lateral disorder which gives rise to the diffuse scatter. This paper is about (a).
The fact that at least some of the fibrils have 3-D crystallinity is significant since it implies that there is some specificity in the lateral aggregation of molecules. The specificity of the axial shift between collagen molecules is well developed and its origin has been shown to reside in the amino acid sequence of the triple helical part of the molecule 34. Attempts to find a specificity in the azimuthal interaction which dight define the lateral packing of the molecules have not led to a generally accepted solution. However, the existence of Bragg reflections in the equa- torial and near-equatorial'regions implies that the lateral intermolecular interaction has a degree of specificity which results in these sharp reflections. As mentioned above, these reflections do not always occur, so it may be inferred that the geometrical order readily breaks down. Since the collagen molecules are crosslinked by covalent crosslinks, the regular topology in intermolecular con- nections will be preserved even when the geometrical regularity is lost. It is not possible, therefore, to deduce from an inability to observe the Bragg reflections that a regular topology of lateral interactions is absent.
At present, the origin of the lateral regularity is not known. A bundle of smooth parallel cylinders would pack hexagonally. The 2-D lateral unit cell could arise from the axial distribution of amino acids if, for example, a ID stagger was preferred over a 2D stagger. Alternatively it could arise from the azimuthal distribution of amino acids round the molecule. The molecular symmetry could be responsible for the quasi-hexagonal packing as could the intermolecular crosslink formation. Now that there is a fairly precise model for the 3-D molecular arrangement it will be possible to try to discriminate between these putative factors.
It is worth emphasizing the type of crystallinity which corresponds to the calculations reported here. The essen- tial points we test are the unit cell (base) dimensions, the molecular tilt and the positions of the molecules within the unit cell. However, we have not, in these calculations, distinguished which of the molecular segments 1 5 occur at which points within the cell. The actual distribution must be such as to produce the above unit cell but specify the arrangement no further. Put otherwise, we know the unit cell defined by the distribution of 'gaps' (i.e. molecular segment (5) but we do not know the relative arrangement of segments (1)--(5) within the unit cell. Hulmes and Miller (1979) illustrated a possible arrange- ment, and here in Figures 1 and 5 we illustrate two possible arrangements though there are others.
Figure 1 shows a possible lateral distribution of the collagen molecules which accords with the X-ray pat- tern ~. The sheets parallel to the X-axis contain molecules staggered by 1D and 4D with respect to their neighbours in the sheet. Covalent crosslinks have been established as linking molecules staggered by 4 D 36 s o that the sheets parallel to the X-axis could be stabilized in this way provided 1 D staggered molecules are similarly crosslinked. However, at present, crosslinks have not been established which link molecules staggered by 2D or 3D. Thus there is
16 Int. J. Biol. Macromol., 1981, Vol 3, February
X-ray diffraction.from model for collagen: Andrew Miller and Defendente Tocchetti
at present no evidence to suggest that the sheets parallel to the X-axis in Figure 1 could be crosslinked together by inter-sheet crosslinks and thus stabilize the whole 3-D fibril. However, a molecular arrangement equally in agreement with the X-ray pattern is that in Figure 4. This contains one set of sheets with 2D and 3D staggers (parallel to X-axis and two sets of sheets (parallel to Yand Z axes) with 1D and 4D staggers. If these latter two sets of sheets were covalently crosslinked this would result in crosslinking both within and between these sheets and result in a covalently crosslined 3-D network. For this reason the arrangement in Figure 5 may be considered more likely than that in Figure 1, though it could be that further knowledge of crosslinking could revise this.
In this paper we make a stringent test of the quasi- hexagonal model of Hulmes and Miller 1 for the molecular packing of collagen in tendons. Aspects of our model have occurred as features in other models proposed for the molecular packing in collagen. Hexagonal packing was once widely accepted 2°'43 and studies using molecular probes have been used to support this mode of pack- ing 44-46. Macfarlane was the first to suggest a mode of hexagonal packing which would generate a unit cell similar to the one we use. It was shown that the Macfarlane cell did not predict the R-values of the observed X-ray reflections 31 and none of the other proposals for the molecular packing in collagen has made use of Macfarlane's model 1'2'16- 28. Hulmes and Miller I showed that a specifically modified form of the Macfarlane cell would predict the R-values of the X-ray reflections better than any other model. Tilted molecules have been suggested in models 2°'22 which involved tetragonal or quasi-tetragonal unit cells, but the latter had a density higher than that in dry films of (gly-pro-pro),. The tilt was involved to explain the Z-values of the reflections just as we have done here. However, the molecular tilt 2z was coupled with the lattice shear (this latter producing split row-lines) in a manner not involved in our model. Other models proposed involve two- strand 19"2'*, four-strand 26, five-strand 17 and eight- strand 22 microfibrils, tetragonal packing 2'28, quasi- tetragonal packing 22 and liquid crystal packing 4°. A test of any model is to compare the observed X-ray diffraction pattern with that predicted by the model. Previous efforts to derive models for the molecular arrangement in collagen from the X-ray diffraction patterns have relied mainly, though not exclusively, on the R-values 2 of the sharp reflections in the near-equatorial region of the medium angle X-ray diffraction pattern. Here we attempt to account for the (R, Z) positions and the intensities of the reflections in this region. The agreement obtained be- tween the observed I(R, Z) and that calculated from a slightly modified version of the model gives support for the model. Detailed intensity calculations for other models have not yet been made. The present model even gives a better agreement between the observed and predicted R- values of the reflections than any of the other models referred to in the Introduction. There are ways in which the work reported here can be improved. The triple helical molecule could replace the cylindrical approximation used here and then allowance made for the fact that the molecules are immersed in an aqueous medium. A calculation based on the true three-dimensional unit cell could replace the approximate method we have employed above for the model derived from the X-ray data. However, it is likely that such improvements will produce
only minor changes in the parameters of the model. In accounting for the R-values of the reflections, we use
three parameters (a, b and 7) to account for 20 obser- vations. When molecular tilt is added to explain the Z- splittings, we use five parameters (z and ~ in addition) to account for 40 observations. Attempts to construct models with further variable parameters will certainly be. possible but would lose conviction. A more secure way forward is to record more of the X-ray diffraction pattern and use this to test and extend the present model. However, this is essentially the method of trial and error and is therefore model dependent. The phases of the X-ray reflections have been determined indirectly. The direct methods of phase determination are difficult to apply to large structures such as collagen. Visualization of the collagen lattice by electron microscopy of thin transverse sections of tendons would be a most satisfactory test of our model.
Acknowledgements We are grateful to Claude Masurel for preparing the photographs, and to Drs R. D. B. Fraser, D. J. S. Hulmes and T. P. Macrae for helpful comments.
References 1 Hulmes, D. J. S. and Miller, A. Nature (London) 1979, 282, 878 2 Miller, A. and Parry, D. A. D. J. Mol. Biol. 1973, 75, 441 3 Parry, D. A. D., Craig, A. S. and Barnes, G. R. Proc. Roy. Soc. (B)
1978, 203, 293; Parry, D. A. D., Barnes, G. R. and Craig, A. S. Proc. Roy. Soc. (B) 1978, 203, 305
4 Bear, R. J. Am. Chem. Soc. 1942, 64, 727 5 Hall, C. E., Jakus, M. A. and Schmitt, F. 0. Y. Am. Chem. Soc.
1942, 64, 1234 6 Schmitt, F. O., Hall, C. E. and Jakus, M. A. J. Cell. Comp. Physiol.
1942, 20, 11 7 Wolpers, C. Kiln, Wochenschr. 1943, 22, 624 8 Ramachandran, G. N. and Kartha, G. Nature(London) 1955,176,
593 9 Rich, A. and Crick, F. H. C. Nature (London) 1955, 176, 915
10 Cowan, P. M., McGavin, S. and North, A. C. T. Nature (London) 1955, 176, 1062
12 Hodge, A. J. and Petruska, J. A. in 'Aspects of Protein Structure' (Ed. G. N. Ramachandran) Academic Press, London, 1963, p. 289
13 Doyle, B. B., Hulmes, D. J. S., Miller, A., Parry, D. A. D., Piez, K. A. and Woodhead-Galloway, J. Proc. Roy. Soc. (B) 1974, 187, 37
14 Hulmes, D. J. S., Miller, A., White, S. W. and Doyle, B. B. J. Mol. Biol. 1977, 110, 643
15 Elliott, A. J. Mol. Biol. 1979, 132, 323 16 North, A. C. T., Cowan, P. M. and Randall, J. T. Nature (London)
1954, 174, 142 17 Miller, A. and Wray, J. S. Nature (London) 1971, 230, 437 18 Wray, J. S. DPhil Thesis University of Oxford (1972) 19 Burge, R. E. in "Structure and Function of Connective Tissue and
Skeletal Tissue' (Eds. S. Fetton Jackson et al.) Butterworths, London, 1965, p. 2
20 Ramachandran, G. N. in "Treatise on Collagen', lEd. G. N. Ramachandran) Academic Press, London, 1967, Vol. l, Ch. 3
21 Petruska, J. A. in 'Comp. Mol. Biol. of Extracellular Matrices' (Ed. H. C. Slavin) Academic Press, London, 1972, p. 431
22 Nemetschek, T. and Hosemann, R. Kolloid-Z.Z. Polym. 1973, 251, 1044
23 Fraser, R. D. B., Miller, A. and Parry, D. A. D. J. Mol. Biol. 1974, 83, 281
24 Woodhead-Galloway, J., Hukins, D. W. L. and Wray, J. S. Bioehem. Biophys. Res. Commun. 1975, 64, 1237
25 Hosemann, R., Dreissig, W. and Nemetschek, T. J. Mol. Biol. 1974, 83, 275
26 Veis, A. and Yuan, L. Biopolymers 1975, 14, 895
Int. J. Biol. Macromol., 1981, Vol 3, February 17
X - r a y d! l f rac t ion f r o m model.l~)r colla,qen: A n d r e w Millet" and
27 Woodhead-Galloway, J. Acta Crystalloqr. (B) 1976, 32, t880 28 Woodhead-Galloway, J. Actu Crystallo#r. (B) 1977, 33, 1212 29 Fraser, R. D. B. and Macrae, T. P. J. Mol. Biol. 1979, 127, 129 30 Fraser, R. D. B. in "Proc. First Cleveland Symposium on
Macromolecules" (Ed. A. G. Walton) Elsevier, Amsterdam, 1977, p. 1
31 Miller, A. in ~Biochemistry of Collagen' IEds. G. N. Ramachandran and A. Reddi) Academic Press, London, 1976, Ch. 3
32 Miller, A. Proc. Third John lnnes Symposium 1976, p. 59 33 Macfarlane, E. F. Search 1971, 2, 171 34 Hulmes, D. J. S., Miller, A., Parry, D. A. D,, Piez, K. A. and
Woodhead-Galloway, J. J. Mnl. Biol. 1973, 79, 173 35 Piez, K. A. and Miller, A. Ji Supramnlecular Str. 1975.2, 121 36 Tanzer, M. L. in ~Biochemistry of Collagen' [Eds. G. N.
Ramanchandran and A. Reddi) Academic Press, London, 1976,
Delemlen te T o c c h e t t i
Ch. 4 37 Claffey, W. Biophys. J. 1977, 19, 63 38 Tomlin, S. G, and Worthington, C. R. Proc. Roy. Soc. (A) 1956,
235, 189 39 Fraser, R. D. B., Macrae, T. P., Miller, A. and Rowlands, R. J.
J. Appl. Crystallogr. 1976, 9, 81 40 Hukins, D. W. k. and Woodhead-Galloway, J. 4th European
Crystalloqruphy Meetin.q Oxford 1977, PI, 140 41 Chapman, J. A. and Hardcastle, R. Conn. Tissue Res. 1974, 2, 151 42 Meek, K. M., Chapman, J. A. and Hardcastle, R. B. J. Biol. Chem.
1979, 254, 10710 43 Kuhn, K. Essays in Biochemistry 1969, 5, 57 44 Katz, E. P. and Li, S. T. Biochem. Biophys. Res. Commun. 1972, 46,
1368 45 Katz, E. P. and Li, S. T. J. Mol. Biol. 1973, 73, 351 46 Katz, E. P. and Li. S. T. J. Mol. Biol. 1973, 80, t
18 In t . J. Biol . M a c r o m o l . , 1981, V o l 3, F e b r u a r y
