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Hyaluronic acid: Molecular conformations and interactions in two sodium salts
J. blol. Biol. (1975) 95, 369-384
Hyahronic Acid : Molecular Conformations and Interactions in Two Sodium Salts J. M. Goss, D. W. L. HUKINS~, P. J. C. hITH W. T. WINTEE, STBUTHER ARNOTT Department of Biobgicd Sciences PUT&M University We& Lajayeite, In&. 47907, U.S.A. R. MOORHOUSE AND D. A. REES U&ever Research, Colworth/ Welwyn j5dmmtoy Oolworth Howe, Sbrnbrook Bedford MK44 lLQ, Englund (Received 19 November 1974) A detailed struotum for the t&ragoml form (a = b = O-989 nm, c, fibre axis, = 3.394 nm) of sodium hyaluronata has been obtained by analysing x-ray fibre diffraotion data using new molecular modelling techniques. Two polysacoharide ohaim pass through each unit cell, one at the corner and one at the oentre. The chains are anti-pars&l to one another. Each chain is a left-handed, 4-fold heliz of disaccharide units. There are intramolecular hydrogen bonds stabilising each glyoosidic linkage. Octahedrally co-ordinated sodium ions link, by 0 . . . Na+ . . . 0 bridges, neighbouring polysaccharide chains that are further linked by hydrogen bonds. No double-helix model (ss originally proposed for this struoture) has been found to be free of unacceptable non-bonded contacts or to fit the di&a&ion intensities as closely. The tatragoml form, which is stable at zero relative humidity, contains no deteotable water molecules. At higher relative humidities a related orthorhombic form is observed in which only the a dimension of the lattice is different (a = l-163 nm, b = O-989 run, c = 3.386 nm). In this form the hyaluronate helix is 2-fold with tetrasacoharide units conformationally similar to the 4-fold heliz of the tetragonal form. The Na+ . . . 0 binding and hydrogen bonds lost on expansion of the Stragonal lattice are all replaoed in the orthorhombic structure by bridges through water molecules, four of which assooiated with each btrasaccharide.
1. Introduction Hyaluronic acid is a glycosamiuoglycan present iu the iut~rcellular matrix of most vertebrate coxmective tissues and in some bacterial capsules. The molecule is a linear polydisacoharide of the form (-A-B-),, where A is glucurouic acid, B is N-acetylglucosamin e, and n can be as large as lo*. The linkages A-B and B-A are p(1 --f 3) and @(l --f 4). The structure is therefore analogous to the idealised structures of other glycosaminoglycaus such as chondroitiu (where B is galactosctmiue and t Present address: Department of Medical Biophysios, Manohester, Man&ester Ml3 QPT, England. 369
Stopford Building,
University
of
360
J. M. CUSS ET AL.
A is glucuronic
acid), dermatan (where B is galactosamine and A is iduronic acid), and keratan (where B is galactose and A is glucosamine). The polydisaccharide structure of hyaluronic acid is also analogous to the agar-carrageenan family of algal polysaccharides where A is 3,6-anhydrogalactose and B is galactose. The chemical similarities among the glycosaminoglycans evidently result in conformational similarities: in oriented films and fibres hyaluronic acid has been observed to have 2-fold or 3-fold helical forms (Atkins & Sheehan, 1972) similar to the 2-fold and 3-fold helical forms observed for chondroitin sulphates (Atkins et al., 1972; Arnott et al., 1973a; Isaac & Atkins, 1973) and dermatan sulphate (Arnott et al., 19733; Atkins L%Isaac, 1973) and to the 2-fold helix of keratan sulphate (Arnott et al., 1974a). All these helices have relatively long axial translations per disaccharide (h = 0.93 to 0.97 nm) corresponding to almost fully extended backbone conformations that preclude multistranded coaxial helical structures. Unlike the other glycosaminoglycans, hyaluronic acid has also been observed in 4-fold helical forms (Dea et al., 1973 ; Atkins & Sheehan, 1973) : one has h = O-928 nm and therefore corresponds to an extended single helix; the other has a markedly reduced value for h of about O-85 nm like c-carrageenan (b = 0.88 mu; Arnott et al., 1974b), K-carrageenan (F, = O-81 nm; Anderson et d., 1969) and agarose (h = 0.63 nm; Arnott et al., 1974c). For all the systems with short values of h, coaxial double-helical structures have been proposed (Anderson et d., 1969; Dea et al., 1973; Arnott et al., 1974c). In the models for L and K-carrageenan and agarose the coaxial helices are parallel (i.e. have the same chain sense), for hyaluronic acid they are antiparallel. Detailed model building and X-ray analyses (Arnott et al., 1974b,c) provide strong support for the L-carrageenan and agarose double helices. As a result of similar intensive studies we have now concluded that the double-helical model for the 4-fold (h = 0.85 nm) form of hyaluronic acid is incorrect and that the structure consists of single, left-handed chains. Results of nuclear magnetic relaxation studies on solutions of sodium hyaluronate (E. G. Finer, R. Moorhouse & D. A. Rees, unpublished results) can best be interpreted in terms of a partly ordered, partly disordered system. The fraction of ordered structure is not altered by changes in temperature or ionic strength, both of which are known to affect the rheological properties. An attractive possibility would have been to associate the ordered component with double-helix formation and the rheological properties with interactions between double helices. However, X-ray studies now give convincing evidence against a double helix in any condensed phase and it seems unlikely that the double helix exists in solution, where it would be stable to changes of ionic strength or temperature or moderate changes of pH, and yet fail to survive mild crystallization conditions.
2. Materials and Methods (a) Mat&d Samples of the sodium salt of hyaluronic acid (M, > 2 x 10E) isolated from human umbilioal chord were the Sifts of Dr Martin Mathews of the University of ChioaSo, Ill. and of Dr E. A. Balass of the Boston Biomedical Institute, Mass. Samples from rooster comb were also examined. (b) F&n preparation Hyaluronic acid films were prepared and oriented se described previously (Aruott et ad., 1974a) for keratan sulphate except that no heat wsa applied. The f&us stretched to 3 or 4
HYALURONIC
ACID
361
times their original length under 3.5 g tension at room temperature and relative humidity about 84%. Some samples were subsequently dried over silica gel. Densities of the tlhns were measured by flotation in a mixture of halogenated hydrocarbons.
(c) X-ray diffruction We used the same apparatus, operated under the same conditions, as in our work on keratan sulphate (Arnott et al., 1974a). The dried specimens were kept in an atmosphere of dry helium. The others were kept at 75% relative humidity with helium that had been bubbled through an 88% saturated solution of sodium nitrite. The diffraction patterns were calibrated by dusting the specimens with calcite (characteristic spacing 0.3035 run). The spacings of the Bragg reflections were measured on projected enlargements. Unit cell dimensions were refined by least-squares as described by Arnott & Hukins (1973). Intensities were measured as areas (A,) under radial microdensitometer traces across each spot. The areas were converted to relative structure amplitudes, ,P,, using the relationship
oF,a = A,R,(tan which provides approximate the cylindrical polar radius
20,)/(1
+ cos2 20,),
Lorentz, polarization and spot extension corrections. (R, is in reciprocal space of the X-ray reflection with Bragg angle e,.) (d) Model-building
and optimization
Following our usual strategy for building molecular models of helical polymers we treated the structure as a linked-atom system (Arnott & Wonacott, 1966) in which covalent bond lengths and angles have fixed standard values. The pyranose rings were fixed in the standard Cl chair conformation (Arnott & Scott, 1972) and the atoms of the acetamido group (except the methyl hydrogen atoms) were kept coplanar, leaving angles defining the glycosidic bridge conformations and the side-chain orientations as explicit variables. Helix continuity, symmetry (no. of residues/turn and chirality) and pitch were imposed by means of Lagrangrian constraints. To obtain helical molecules with the least steric compression we minimized @ (eqn (1)).
4 = &Cd,
-
dA2, d, < cd,
e, = O,d, 2 .d,. The first summation thus contains all varied non-bonded interatomic distances, d,, less than some specified minimum Od,. The second summation contains the Lagrange multipliers, &, and the constraint expressions, ah, that we wish to become zero. This approach bo minimizing non-bonded interactions was developed by Williams (1969) to determine packing of rigid molecules in a crystal. For this study we have adapted the method, using t,he linked-atom approach, for the determination of acceptable conformations of the flexible polymer chains. The values of the constants ic, and Od, were derived for each type of interatomic interaction from Buckingham energy functions of the type
E = - Bdm6 + Aexp(-d).
(2)
Values of B,A,p were taken from Chandrasekaran BE Balasubramanian (1969). Each Od, was set to be 0.02 m-n greater than the value of d corresponding to minimum E to ensure that all short contacts were driven to larger values. The values of k, were chosen so that a[k,(,d, - dr)a]/ad closely approximated aE/ad in the range d[E,,,] - 0.05 < d < [E,,,]. The values of k, and ,d, are given in Table 1. For isolated molecules all the d, are intramolecular contacts and the variables are the conformation angles mentioned above. For molecules in a lattice there may be additional d, from intermolecular contacts, and additional variables corresponding to the positions and orientations of molecules in each unit cell.
J. M. GUSS ET AL.
362
TABLE 1 Constants used in equations (1) and (3) to determine non-bonded ilzteractions Type of contact
kj or ,k, x 1Oa(nmm2)
c ...c
1.10
c ...0 C...N C...H C . . . Na 0 ...0 0 . ..N 0 . ..H N...N 0 . . . NE
1.62 2.17 2.18 1.00 1.66 2.21 1.66 2.97 1.00
N...H
2.14 1.00
N . . . Na H...H H . . . Na Na . . . Na
1.13 1.00 1.60
o---o O---N
11.70 11.70
0 . . . Ne
10.00
0.360 0.340 0.346 o-310 0.360 0.320 0.325 0.290 0.330
.i! 3 $
0.296 0.330 O-260 0.300 0.340 O-270 $ 0.290 *3 E 0.260 3
Cur computer program is also capable of simulating the attractive forces arising from hydrogen bonds or the interaction between a cation and atoms of its co-o&n&ion shell, and thereby mainteining distances between the atoms involved near prescribed standards. This situation arises when the distance, d,, between two non-bonded atoms of the proper types falls between speciSed limits *d, and & (Ad, < d, < &). Then, if & is the “ideal” contact distance and ,I%, the corresponding weight, for those interactions where these “special” functions apply the values of c, in eqn (1) become cj = k,(od, - d,Ia, 0 < d, < ,,d, or & 4 = Iw-4
- d,,“, ad, I d, 5 id,,
< d, < ,d,, (3)
c, = 0, d, 2 ,dj.
When 9 (eqn (1)) has been minimized, the final C l , is a measure of the sterio acceptability of a molecular model and its mode of packing. (e) Location of non-coualently bound atoms and ions Cations and water molecules present in structures of polyanionic polyseccharides presumably play an important role in the formation of stable intermolecular linkages through hydrogen bond or ionic bridge formation. A complete solution to a structure of this type involves the location of these components and refinement of their positions against X-ray intensities and packing data where possible. Since these cations and water molecules are not covalently bonded to the polysaccharide chains their possible locations are not immediately obvious. The method we have devised to find these involves giving each ion or water molecule a number of plausible starting positions throughout the structure then retbring its co-or&n&es to minimise the non-
HYALURONIC
363
ACID
bonded interactions (see section (d), above) 8nd to optimize its co-ordination with oxygens or participation in hydrogen bonding. In most cases this procedure gives a small number of possible sites, some of which can be discarded on the grounds of chemical unsuitability. Those that remain can then be assessed on the grounds of improved agrecmerit with the observed X-r8y structure runplitudes and successful formation of suitable interactions, e.g. hydrogen bonds or Na+ . . . 0. (f) X-ray refinement and Four&r sytihea~ The positions of these additional atoms and ions and the conformation of the polyanion may be refined jointly against X-ray and contact data maintaining the attr8ctive interactions discovered in the search procedure by minimizing Sa (eqn (4)). Q = C w,(,F,,, - F,,Ja + SX e, + .Z A,,@,.
(4) F, are the calcul8ted and ,F, the observed X-ray amplitudes. The weights applied 8re w,. The overall weight, S, 8pplied to the contact observations, was chosen on an empirical basis. First, 8 model was constructed using only the contact and not the X-ray data. This model was therefore the sterically most acceptable one that could be mrrde. In subsequent refinement cycles the X-ray data were included and successively reduced values of S were tested. For each value the short contacts were examined and the final value of S chosen was the smallest value thet led to no contacts unacceptable on a hard-sphere basis (Rees, 1969). (In the case of hyahnonste double helices we found no model acceptable on a hard-sphere basis 8nd therefore had to choose a value for S that led to no worsening of the shortest non-bonded contacts of the st8rting model.) Fourier syntheses of electron density were calculated in the usual way except that for overlapping reflections the intensity was divided equally among the contributing planes. Difference syntheses were calculated using W, (,F, - F,) as amplitudes. For centric projections 8ll W, were set equal to unity. Otherwise we used an approximation (eqn (6)) to Sim’s (1961) weighting scheme for acentric Fourier syntheses with phases calculated from an incomplete structure. W, = (,F,
x F,)/maximum(,F,,,
3. Ditlkaction
x F,,,).
(5)
Patterns
We have obtained three different but related diffraction patterns all corresponding to an hyaluronic acid chain repeat of four disaccharide residues with an average h of O-85 nm per disaccharide. The simplest pattern (Plate I(a)) is obtained from sodium hyaluronate specimens, stretched at high humidity, dried over silica gel, and X-rayed in an atmosphere of dry helium. The lattice is tetragonal: a = b = 0*989(2)nm, c (fibre axis) = 3*394(9)nm and meridional (001) reflections are observed only for 1 = 4%. The measured relative density (l-60) agrees well with that calculated for a unit cell containing eight disaccharide residues, eight sodium ions and not water molecules (1605). Thus, two regular 4-fold helical, polydisaccharide chains pass through each unit cell. At higher relative humidities (e.g. 75%) the unit cell remains rectangular but the a dimension is larger (a = 1*153(4)nm, b = 0*989(3)nm, c = 3*386(9)nm). There are now (002) reflections for I = 2n (Plate I(b)). The hyaluronate chain is therefore a 2-fold helix with tetrasaccharide units. However, since the general intensity distribution is very like that of the tetragonal form and the c dimension is essentially the same, it is likely that the molecular backbone conformations are little changed although the conformations of corresponding side-chains on adjacent disaccharide t The measured densities are not BOaoaurata that the exact number of water molecules present oea be prediated
with
oou6denoe.
In the subsequent
struoture
malyses
we indeed found no sites
for water in the tetragonal structure but 4 sites per tetrsaacaharide in the orthorhombic form.
J. M. CUSS
364
ET
AL.
residues may be somewhat different from one another. This is probably also the case for the co-ordination shells of the sodium ions. The measured relative density (1.45) corresponds to there being one water molecule-t per tetrasaccharide. The third crystal form from rooster comb sodium hyaluronate at high relative humidity also has a rectangular unit cell (la = l.l62(2)nm, b = O-984(3@, c = 3.331(6)nm) and an intensity distribution almost identical to Plate I(b) except that now there are meridional (002) reflections on every layer line indicating a further (but minor) perturbation of the original 4-fold helical symmetry.
4. Model-building Studies In general, analyses of fibrous structures require the creation and testing of plausible molecular and crystal models. To begin with we concentrated on the tetragonal crystal form, which contains regular 4-fold helical chains, and used the procedures described in Materials and Methods, section (d) that exploit only the spacings and not the intensities from the diffraction pattern.
(a)
(b)
FIG. 1. Possible modes of packing 2 ohains in the tetragonctl unit cell. (a) Single he&es. One passing through the corners of the lattice and an antiparallel chain through the centre. The relative trenslation of the 2 chains parallel to the helix axis is 2w. The orientations of the chains are pi and pa. If the lattice has tetragonal symmetry and pi # -pLz then the space group is either P4s (left-handed ah&s) or P4, (right-handed chains). If pi = -pa then the space group is P4e2,2 or P41212 in a non-standard setting. (b) Double helices passing through the corners of the lattice. (The radii of the 2 chains are shown dif%rently for illustration only). In this case if pi # -pa then the space group is again P4$ or P41. However if pi = -pa then the up and down-pointing chains of the double helix will be related by g-fold axes parallel to the cell edges and the space group becomes P4,22 or P4,22.
A priori we could have no preference for left (43) or right-handed (4,) helices. Preliminary models of each with a pitch of 3.394 nm were constructed by minimizing Q, (eqn (1)). Since two chains pass through each unit cell, we had also to determine whether the two chains had their axes coinciding (i.e. formed a double helix) or whether they were separated in a centred arrangement (Fig. 1). There was also the further question of whether the two chains were parallel or entiparallel. tSee footnote on page 363.
Cb)
ATE I. Diffraction patternsfrom sodium hyaluronate. The meridional direction is vertical At 0% relative humidity. At 75% relative humidity.
HYALURONIC
36b
ACID
(a) Hyalurmate chains paeked in a tetragonul array For each crystal model we varied the molecular parameters and the axial orientation (,u) of each chain and its displacement (w) (Fig. 1). All models containing parallel chains had severe non-bonded contacts that could not be relieved. Table 2A therefore contains the results only for the four kinds of antiparallel chain model obtained by minimizing @ (eqn (1)). These studies with our new computer model-building methods show clearly that coaxial, antiparallel, double-helical models whether built with left- or right-handed chains would involve a considerable degree of steric compression. The models with non-coaxial chains are markedly more acceptable and the model containing left-handed helices is superior to that containing right-handed helices. TABLE
2
Co?nparison of possible models for the tetrapnal structure A.
Coaxial
and non-coaxial or right-handed
chain models containing (4s) 4-fold helices
left-
Overshort+ contacts w4
Packing
(4,)
RS
R”
Non-coaxial
43
O-360
H:,, . . . CiBg)(0.210); %, . . . Cc, (0.241)
o-33
o-39
Non-coaxial
41
0.448
c%* * . C;, (0.273); c& . . . Op,, (0.264)
0.33
0.37
Coaxial
43
0.618
H;, . . . o&, (0.133); OS,. . . H& (0.199)
0.47
O-64
Coaxial
41
0.672
H$, . . . op,,, (@170); o:,,, * * * H& (0.174)
0.66
0.69
t Less than marginally allowed $ R and R” are crystallographic
in usual residuals
R = .Zj,F,
LeftModel
and right-handed Chains
.%
models
R-S, 1969) “hard sphere” analyses. calculated after scale factor refinement only:
(e.g.
- F,&?YoFm.
R” = {I: w,(,F,
B.
either
refined
-
against
Overshort oontaats wd
Hyaluronate
4s
O-600
O$, . . . C& (0.260); HiBp). . . H&(0.183
Hyaluronate
41
0.666
HiS,, . , . O& %., * * * H;,,
Sodium hyaluronate
43
048
Op,, . . . C& (0.266); cd(6) . . . Ne (0.266)
(6)
Pm)“/ X w, .F,“}
(@168); (0-W
structure
*.
(7)
amplitudes
and contact
Hydrogen-bonds Intmhain Interohain
criteria R
R”
0$--o&; NB---OP,,,
o&--o&; O&---q&; op,--4,
0.307
0.364
None
O&---O&
0.304
0.366
o&--op,,; NB---O&
o&--o&; o&--o&; o&---o&
0.291
O-326
366
J. M. CUSS
ET
AL.
(ai
(b)
(d)
FIQ. 2. (a) and (o) Electron density projections with phases model having 1 ohein et the corner of the unit-cell. (a) is the The model used to compute the Fourier terms is superimposed (b) and (d) Difference electron density with phases from the
and amplitudes computed from s (100) and (a) the (001) projection. on the electron density. single-chain model and amplitudes
HYALURONIC
387
ACID
5. Fourier Synthesis of Electron Density We next considered the question of single-chain verszcs double-helical models by exploiting the X-ray intensities rather than stereochemical considerations. We postponed a decision as to the position of the second chain in the unit cell and calculated structure amplitudes and phases from a crystal model containing only one hyalmonate helix per unit cell. When these phases were combined with the observed structure amplitudes in Fourier syntheses of electron density, additional density was found corresponding to a similar second helix with its axis running centrally through each unit cell and not coincident with that of the first chain. Figure 2 shows the results of such experiments performed with observed amplitudes from the tetragonal crystal form. We obtained similar results in a similar, independent experiment with the orthorhombic crystal form. 6. Further Refinements of Tetragonal Structures In the third set of experiments we refined various models using equation (4) to optimize the fit between calculated and experimental X-ray structure amplitudes while maintaining minimum ateric compression. The stereochemically optimized model involving left-handed, coaxial helices had X-ray residuals R = O-48 and R” = O-57 before refinement and we found it impossible to reduce these substantially without producing many more unacceptable TABLE
3
Values of the refined parameters for the tetragonal structure PaSameter
Comment
value 106.9 -46.4
1 -+tlinkage s
- - 107.2 80.2
1 + 4 linkege
- 177.4
Hydroxymethyl
-79.1 -27.2 -91.4 18.1 0.04 nm=
ij ii’ u 8 m if 7 -
N-ctoetyl
Cerboxylats So&
fsQt@
Attenuation
t Relating observed and ordoulated BtNCtlllB amplitudes. $ Applied to the o&&ted amplitudes in the form exp(--B
fastor
sina e/xx) where h = 0.1642 -.
(,P, - P,). The projections are the ssme as (a) and (0). Another similar (antiparallel) single ohain with its axis at the oentrs of the unit oell is superimposed on the density. It should be noted thet the main ridges of electron density in (a) srs about 0.34 nm from the helix axis whioh ooinoides with the c-axis of the unit cell. In the difference Fourier synthesis in (b) the ridges srs only 0.17 nm from the sell edges and therefore donot indicate a similar h&x ooaxial with the tit. The ridges are, however, about 0.33 m-n from the oentre of the unit cell and it is this feat together with a shnilsr argument for (0) end (d) that oompels us to interpret this experiment as f&o favouring non-ooaxial &sins. 26
J. M. GUSS
368
TABLE
ET
AL.
4
Values of the observe@, ,I?,, and c&uhted$, F,, structure am$itudes for tetragonal sodium hyaluronate h
k
1
Jm
Pm
h
k
1
1 1 2 2 2 3 3 3 4
0 1 0 1 2 0 1 2 0
0 0 0 0 0 0 0 0 0
88 bt bt 8 17 88 29 31 18
0 12 6 61 9 0 23 18 17
1 1 2 2
0 1 0 1
4 4 4 4
9 14 40 15
9 28 24 23
1 1 2 2
0 1 0 1
5 5 5 6>
bt 8
10 6
27
33
1 1 2 2
0 1 0 1
1 1 1 1
12 24 38 49
18 20 36 66
1 1 2
0 1 0
6 6 6
18 bt 23
19 8 26
1 1 2 2
0 1 0 1
2 2 2 2
18 16 24 40
28 20 23 24
1 1 2
0 1 0
7 7 7
29 bt bt
27 6 6
1 1
0 1
3 3
17 bt
6 12
1 1 2 2 1 1
0 1 0 1 0 1
8 8 8 8 9 9
22 16 12 bt 22 27
7 17 24 8 23 17
0 1 0 1
10 10 10 10
bt bt bt 27
7 3 28 29
0 1
11 11
bt 20
4 3
88, System&o absence. bt, Intensity below observation&l threshold. Only those below-threshold within the outermost observed refleotion on any layer line are included. 8 Masked by the extended arc of (211).
.F?ll
F,
reflections
t The values of ,P,,, have been multiplied by the scale factor (Table 3). $ Atomic scattering faotors were from Intematid Tables for X-ray Crystallography
lying
(1962).
non-bonded contacts. Even when all attempts to maintain intramolecular hydrogen bonds were abandoned the residuals could not be reduced below R = 0.47 and R” = O-54. We therefore felt confident in rejecting further consideration of structures containing coaxial double helices on both stereochemical and X-ray grounds. In contrast the two remaining models with pairs of either right- or left-handed, antiparallel, non-coaxial hyaluronate helices had R = 0.33, 0.33 and R” = 0.37, O-39, respectively, even before further refinement, and R = O-31, O-30, R” = O-35, 0.36 after refinement of the polyanion conformations.
HYALURONIC
ACID
TABLE
369
6
Cartesian w-orohztes (x, y and z) for a disaccharide residue of sodium hyaluronate in the tetragonal lattice Atom
co, C Cal C (31 C (4) C(5) co, 00, %I 0,3,
0 0 0 0
(4) (6) ma) (661
H (11 H (1) H (3) H (4) H (61
C (11 C (9) C (3) C (41 C (6) C (61 0 (11 0 (3) 0 (4) 0 (55) 0 (61
H (1) H (11 H (51 H.4,
H (5) H G%a) H @b) N
C (7) C (61 0 (71
H (cm) H (EL, H (SC) H WI N&3
x (nm x 10’)
y (mn x 10’)
z (nm x 10’)
(residue A) -2686 -3796 -4276 -3098 -2009 - 762 -2190 -4867 -6217 -3616 -1612 - 736 81 -3074 - 3422 -4780 -2692 -2388
1669 2610 3664 4381 3466 4204 814 1669 4426 6246 2623 4660 4380 1132 3002 3073 4996 2907
Gluouronate 2239 2866 1869 1364 821 399 3216 3247 2610 299 1838 -802 1306 1361 3766 1023 2171 -63 N-acetylgluoosamine 387 -990 -920 148 1472 2647 299 -2190 342 1298 3792 742 - 1369 -681 - 169 1836 2697 2238 -1932 -3286 -4126 -3760 - 3688 -4324 - 6080 - 1600 -446
(residue B) -3112 - 3246 -2962 -3814 -3671 -4692 -3616 -3216 -3416 -3997 4400 -2076 -4266 - 1889 -4867 -2636 -4396 -6638 - 2323 -2671 - 1662 -3616 - 694 - 1906 -1413 - 1676 964
6671 7207 8698 9367 8613 9161 6246 9298 10712 7226 8482 6677 7062 8862 9342 8706 10223 9011 6633 6622 6889 7231 6847 4867 6420 6060 2480
The space-group symmetry k P4,2,2 in a non-standard setting, with the origin on the 4, axis. To form the 4 residues of the up-pointing chain the symmetry operations are x, y, z; y, -2, c/4 + 3; -2, -y, c/2 + z and -y, z, 3c/4 + z. To form the residues of the down-pointing ohaiu with helix axis at a/2, b/2, the symmetry operations are a/2 + x, b/2 - y, --z; a/2 - y, b/2 - x, c/4 - z; a/2 - x, b/2 + y, c/2 - z; al2 + y, b/2 + x, 3c/4 - z.
370
J. M. CUSS
ET
AL.
On the basis of the agreement between the observed and calculated structure amplitudes alone we cannot make a choice between right and left-handed mode1s.t However, we did decide to reject further consideration of right-handed helices on steric grounds, Their conformations involve a noticeably greater degree of steric compression than for left-handed helices and do not permit extensive hydrogen bonding. In marked contrast, refinement of the model containing left-handed helices gave an elaborately hydrogen-bonded structure in which all potential hydrogenbond donors were indeed involved in hydrogen bonding.
FIG. 3. The disaeoharide of hyahwoneta showing the atom labelling. A ia gluouronate and B is IV-acetylgluooaemine. The parentheses are omitted from the atom names for olarity. Subsequent reference8 to atoms are made in a form which speoi6es the residue in addition to the etomio type oxygen atom from residue A (gluouroneta). The suband number. e.g. O&, ia a oarboxylate ecripte i and i + 1 ere used to differentiate the non-equivalent residues of the tatrasacoharide in the orthorhombio struoture.
We then sought to complete this model containing left-handed hyaluronate helices by seeking likely sites for sodium ions and water molecules using the methods described in Materials and Methods, section (e). No water sites were detected but we found a single set of sites for sodium ions in which each sodium is co-ordinated to six oxygen atoms from three hyaluronate chains. Final refinement of the complete sodium hyaluronate structure improved both the stereochemistry and the fit with the X-ray amplitudes so that R and R" became O-29 and 0.33. This retiement was followed by a three-dimensional Fourier difference synthesis. The largest peaks in this were considered as possible water molecule sites but none was found that was both stereochemically reasonable and led to an improved fit with the X-ray amplitudes. The parameters of the final structure are given in Table 3. Observed and t This ia perfectly understandable when one considers that the of anomalous scattering) cannot distinguish between a structure we have observed ia that a left-handed I-fold hyeluronate helix image of B right-handed helix in such a way that regions of power ooinoide.
X-ray intensities (in the absence and its mirror image and what can be superposed on the mirror approximately equal scattering
HYALURONIC
ACID
I
(b)
(a)
4. Sohematie diagrams of the attraotive intermoleoular interactions in the tetragonel struoture. The numbers indiaete distanoes in nanometres. (a) The oontaots to the sodium ion. Helix I at (z = 0, y = 0) is anti-parallel to II at (z = -a/2, y = b/2) and III at (z = -a/2, y = -b/2). (b) The intermolecular hydrogen bonds. The helicea are the same aa in (a). The distances are between oxygen atoms. FIQ.
calculated structure amplitudes are given in Table 4. The atom labelling is shown in Figure 3 and the atomic co-ordinates are given in Table 6. The attractive noncovalent interactions (hydrogen bonds and Na . . . 0 contacts) are illustrated in Figure 4. 7. Description
of the Tetragonal Structure
(a) Polysacdaride chains The 6nal conformations at the glycosidic bridges are “fully allowed” for the 1 -+ 4 linkage and nearly “marginally allowed” (Rees, 1969) for the 1 -+ 3 linkage. (There is one short contact, 06) . . .C&, across this linkage which is O-266 nm compared to the marginally allowed value 0.270 mu.) The side-chain conformations are depicted in Figure 6. The hydroxymethyl group extends outwards to participate in inter-chain
(0)
(b) (cl showing the conformations of the side-chains and the values of the re6ned torsion angles in the tetragonel structure. (a) The wets&do group along the NE-C& bond; (b) the hydroxymethyl group along the C&-C& bond; (c) the aarboxylate group along the C&-C& bond. FICA 5. Projeotions
372
J. M.
GUSS
ET
AL.
hydrogen bonding. The acetamido group has an orientation about 30” different from that in N-acetylglucosamine (Johnson, 1966). This allows formation of an P-H---O&,] hydrogen-bond (length 0.278 nm) across the 1 -+ 4 linkage. There is a hydrogen bond (length O-253 mu) stabilizing the 1 -+ 3 linkage also-between O& of N-acetylglucosamine and O& of glucuronate. The conformation of a single chain is shown in Figure 6.
1 Fm. 6. A single hyclluronate ohain from the tetragon~l struoture. The hydrogen-bonds NEof 0.278 run, and 0$-H---0$, , of 0.253 nm, are shown. The nitrogen atoms are H---O&, shown as solid circles. This and subsequent drawings were made using oomputer program ORTEP (Johnson, 1965).
(b) CMra. packing a& cation associa;tion in the tetragonal etructzcre The left-handed helical chains are packed in the square lattice with the molecules passing through the corners antiparallel to those passing through the centres. The mutual orientation of chains corresponds to the higher symmetry of space-group P4,2,2. (No significant reduction in .Q resulted from the relaxation of the condition p1 = --pa (Fig. l(a).) Neighbouring chains along the cell edge separated by 0.989 nm and O&---H-O& hydrogen bonds (Figs 4(a) and are linked by O&-H---0$ 7(a)). In addition neighbouring antiparallel chains are linked by O&-H---O&, hydrogen bonds (Figs 4(b) and 7). The network of hydrogen bonds linking adjacent chains is supplemented by Na + . . . 0 bridges. A sodium ion bound to the two carboxyl oxygens of a residue in a corner chain is also bound to O&, OS, and O& of a centre chain and to O$, of another corner chain (Figs 4(b) and 7), completing a distorted octahedral shell (Figs 4(a) and 8).
(4
do.9l39
nm -+
:
h
(b)
I.399 nm __,
Pro. 7. Views of tho rafined tetragonal structure of sodium hyaluronate. Chains at the cell corners are shown emphasized. Hydrogen bonds are shown by dashed lines and Na+ . . . 0 contacts by dotted linea. (For clarity only some of these interactions have been shown.) (a) View along the (100) direction. The centre chain (open bonds) is translakd n/2 behind the corner chains. Only the contacts to the sodium ion NA, which binds to all 3 chains in this Figure, are shown. The a and c dimensions are indicated. (b) View along the (110) direction. The 2 corner chains are at diagonally opposit,e corners of the unit cell. The helix axes of the 3 chains shown are coplanar. Contacts to sodium ions which interact with 2 chains are shown. The 6th co-ordination positions (to chains not in this Figure) are indicated.
+-
k-f+@
374
J. M. GUSS
ET AL.
FIG. 8. Details of the sodium ion environment in the tetragonal struoture. !Cbis ia an enlargement of e se&ion of Fig. 7(a) showing the lebeh of atoms bound to the sodium ion.
8. The Orthorhombic
Structure
In developing a model for the orthorhombic structure we made the basic assumption that the structure is closely related to that of the tetragonal form. This conservation is suggested by the in@niScant change in the fibre repeat, distance (3.394 nm in the tetragonal and 3.386 nm in the orthorhombic form) and by the close similarity of the overall intensity distributions in the diffraction patterns (Plate I). In addition transitions between the two forms are accomplished easily under mild conditions of dehydration or humidification, suggesting that not only is the polyanion conformation largely preserved but so also are many of the intermolecular hydrogen bonds and Na+ . . . 0 interactions. There is no obvious explanation as to why only one of the two lateral spacings should be preserved in the transition, but, this in itself certainly means that a number of the intermolecular contacts will be maintained if there are no large changes in relative orientation and translation of the polyanions. (a) Posit&x&g the sodium ions and water moleczdEes Initially we refined a model whose starting point was the polyanion component in the same relative orientation to the a cell edge as in the tetragonal form. Retieme& of only the relative chain orientations (p) and translations (w) resulted in a model with no overshort contacts and which gave good agreement between the observed and calculated X-ray amplitudes (R = 0.36 and R” = O-42)?. The unidirectional expansion of the lattice parallel to (100) causes the separation of the helix axes of neighbouring antiparallel chains to increase from 0.699 nm to 0.769 nm and of adjacent up-pointing chains separated by a to increase from 0.989 nm to 1.153 nm. This results in the breaking of the O&---O& and O&---O& hydrogen bonds in the (100) direction and in the disruption of the previous 6-fold co-ordination about the sodium ions. Consistent with the orthorhombic symmetry, the repeating unit of the helix is now a tetrasaccharide in which the two successive disaccharides, conformationally identical in the tetragonal structure, will now be different and make d&rent intermolecular contacts. A refinement optimizing the contacts to the two sodium ions (see Materials and Methoda, section (d)) contirmed that neither disaccharide could now form the same t A model with coaxial
double helices had R = 0.49 and R" = OG at this stage.
HYALURONIC
376
ACID
six intezactions with sodium ions as in the tetragonal structure. One sodium ion, NqI), could make either of two sets of five interactions (Fig. 9(a) and the other, NaCoj, either of two sets of four interactions (F’ig. 9(b)). All the possible combinations of the sodium ion co-ordination sites were considered, and for each structure amplitudes were calculated. Possible water molecule positions were derived using the method described earlier (Materials and Methods, section (0)). I
NatI) I
I
I
I
Oh,+,OC%,+, o~)i+l I ops.,, I op,*,; I Of&,+, No (I)
(0)
Na (2)
G);
I
1
I
Of: );
OP. ), 1
I
$3, I
O&J,,+, I Na (2)
O&7,;+, J
(b) FIO. 9. Preliminary aseignmenta of binding sites for the 2 sodium ions in the orthorhombio Btruoture. (a) Nat11 may bind to either of the 2 sets of 5 oxygen &XIM from the 6 found in the tetragonal structure. In the final model 1 additional water mole&e binds to Ne(,,. (b) Na(g, may bind to 4 oqgen atoms of the polysecohsride backbone. Neither possibility inoludea O&. In the final model 3 water moleoules also bind, 1 to Nao, and 2 to Naca,.
TABLET
V&be8 of th rejined pwmeters for th orthorhombk &uc.ture P8rameter
Value
21
It
comment
120.2 - 62.2
112.3 - 60.6
-Ill*6 - 80-8
-110.1 - 76.8
- 154.6
- 167.4
- 97-7 63.3
-78.1 40.4
N-acetyl
-31.6
- 92-7
Carboxylate
66.2 0.1 nma t For disaooharide $ For disaaohaxide $ Not refined.
residue i + 1. residue i.
1 +tlinkage 0
c c. Hydroxymethyl i 5
s So& factor Attenuation
fmtor§
376
J. M.
GUSS
ET
AL.
One model was clearly superior in that it possessed the following features: (i) an extensive hydrogen-bond network; (ii) the closest relationship to the tetragonal structure; (iii) direct interaction between the cations and carboxylate anions and (iv) the best X-ray agreement indices (R = O-30 and R” = O-38). In the refinement of this model the cations and water molecules were considered as independent entities additional to the linked-atom description of the hyaluronate chains but subject to the repulsive and attractive forces described previously. A fmal refinement varying backbone and side-chain conformations and packing of the TABLE
7
Value-s of the observedt, J?,, and cddatccted, I?,, structure amplitudes for orthorhombic sodiunz hyalwonate h
k
1
,Fm
Fm
h
k
1
0F In
F,
1 0 1 2 0 2 1 3 2 3 0 1 3 4
0 1 1 0 2 1 2 0 2 1 3 3 2 0
0 0 0 0 0 0> 0 0 0 0 0 0 0 0
aa S& bt bt
0 0 13 46
3 3 3 3 3 3>
6 14 21 42
62
0 1 1 0 1 2
bt 27 bt bt
49
1 0 1 2 2 0
62
69
46 sa bt 63 se 47 bt 34
44 0 14 23 0 36 26 22
1 0 1 2
0 1 1 0
4 4 4 4
bt bt 34 36
2 12 47 17
1 0 1 2
0 1 1 0
1 1 1 1
bt bt 46 36
10 4 42 26
1 0 1 2 2 0
0 1 1 0 1 2
6 6 6 6 6 6>
bt bt 31 bt
6 16 23 26
40
34
1 0 1
0 1 1
2 2 2
21 28 39
21 21 33
2
30
24
6 6 6 6 6 6>
17 9 14 21
0
0 1 1 0 1 2
bt bt 36 bt
2
1 0 1 2 2 0
34
23
2 0
1 2
2 2>
66
48
1 0
0 1
7 7>
44
49
1 0 1
0 1 1
8 8> 8
20
7
33
16
1 0
0 1
9 9>
68
37
a, System&o ebsence. bt, Intensity below observ&tionel
threshold.
t The v&~ea of ,,F,,, have been multiplied
by the scale factor
(Table 6).
HYALURONIC
ACID
377
polyanions, the cation and water positions and the X-ray scale factor resulted in a structure for which Robs is 0.29 and Rnobs is 0.33 with a value of 8 = 0.2. Final values of the parameters of this structure are given in Table 6, observed and calculated structure amplitudes in Table 7, atomic co-ordinates are given in Table 8. The attractive interactions are illustrated in Figure 10.
I - "ij,,..,
“KM,,, ,.-
“‘L33
=.0.267
“I6
0 ‘..
I
FIU. 10. Schematic diagrams of the attraotive i&era&ions in the orthorhombic structure. (a) and (b) The contacts to the sodium ions. Parallel he&es I and V are it (z = 0, y = 0) and (z = a, y = 0). The other ohains are anti-parallel to these. Helix II is at (z = -a/2, y = a/2), III at (z = -a/2, y = -a/2) and IV is at (z = a/2, y = b/2). (c) and (d) The intermoleoular hydrogen bonds. The helices are the same as in (a) and (b). In (d) the water molecule, W,,,, co-ordinated to helices I and V is the one whose co-ordinates are listed in Table 8 and which binds to the sodium ion, Na ta,, shown. The related moleoule, W,,,, is included to show the completion of the hydrogen bonds between helioes II and IV.
L-l
378
J. M. CUSS
ET
TABLE
AL.
8
Cartes&n co-ordinates for a tetrasaccharide f-es&e of sodium hyaluronate in the orthorhombic lattice Atom
z (Ml
x 104)
y (nm x 10’)
Gluouronete C (11 C (1) c (31
C (41 cm
C tea 0 (11 0 (2) 0 (31 0 (4) 0 (5) 0 (80) 0 (86) H (11 Hm, H (3) H (44 J%,
C (71 C (8) 0 (7) H (aa) Hwm, H (80) H(N)
636 -747 -671 369 1698 2744 637 - 1949 673 1617 4067 1021 -1167 -399 19 2093 2649 2696 -1668 -3021 -3828 - 3624 - 3344 -3886 -4843 - 1303
cm c (2) c (3)
Gluouronete - 2477 - 3703 -4237
c (41 C(5)
C (61 O(l) O(3) O(4)
0 (51 0 WL) H (11 H(a) H (3) H(4) Hw
H wll H (Bb) N
x 10”)
(residue A,)
2633 3166 2111 1641 1203 832 3663 3611 2668 637 2270 -380 1784 1761 4071 1263 2461 326
-2333 -3519 -3990 -2826 - 1662 -430 - 1866 -4668 -6010 -3222 -1281 -336 334 -2641 - 3226 -4417 - 2600 - 1960
IV-aoetylgluooswnine C (11 C (91 C (3)
2 (ml
1642 2442 3441 4303 3421 4219 841 1649 4272 6116 2638 4610 4486 1061 2978 2902 2828
(residue B,) -2944 -3094 -2941 -3893 -3722 -4721 -3222 -3219 -3628 -3914 - 4269 - 1934 -4084 -1906 -4930 -2713 -4890 -6672 - 2086 -2286 - 1182 -3261 -867 -326 - 1646 - 1313
(residue A‘ + 11 -2246 - 2822 - 1846
6472 7094 9181 8463 8902 6116 9181 10667 7042 8634 6673 6846 8867 9069 8641 9986 6609 6694 6967 7129 6020 6646 6740 6084
10018 10714 11762
HYALURONIC
Atom
C (4) C(6) C (6) 0 (1) 0 (3) 0 (3) O(4)
0 (6) 0 (60) 0 cab) H (1) H (1) H (3) H (4) H (6)
x (nm x 10’) Clucuronate -3126 -1917 -736 -1949 -4698 - 6298 -33574 - 1480 - 1030 386 -2769 - 3434 -4639 -2832 -2187 N-aoety&hooaamine
C (11 cm
C (3) C (4) C (6) C (6) (1) :
(3) 0 (4.) 0 (6) 0 (6) H (1) Ho, H(a) H (4) Ho,
H (30) H cab) N cm
C(a) O(7) H (80) H (3b) H (8C) H (N) N%l, %a, W(l)
w(a) W(a) W(4)
- 3400 -3486 -3446 -4612 -4394 - 6600 -3674 -3663 -4360 - 4472 -6102 -2439 -4421 -2463 - 6608
- 3433 -6770 - 6380 -2371 -2612 - 1388 -3702 -962 -1672 -647 -1607 - 1087 2161 396 4363 -3301 4133
ACID
y (mu x 10’)
(residue Al+ l)-con&wed -1430 -932 -609 -3219 -3122 - 2460 -382 - 1938 -197 -797 - 1328 - 3769 -966 -2290 -18 (residue B, + 1) -681 770 696 -396 -1690 -2676 -382 1866 -701 - 1413 - 4020 - 1069 1273 226 42 -2176 -22696 -2460 1629 2968 3722 3493 3213 4748 3766 1266 940 -603 1334 -1981 664 1777
379
2 (ml
x 104)
12706 11921 12811 9181 9743 12486 13664 10994 13963 12289 9480 11206 11246 13326 11371
14928 16626 17136 17681 16783 17099 13664 17771 18966 lb376 16839 lb168 lb339 17436 17424 17010 18163 16480 lb166 14936 14473 lb092 13600 14196 16286 16033 2449 10498 10464 10186 748 4319
Wo, to W,,, refer to the oxygen atoms of the water molecules. The crystallographioally nonequivalent residues of the tetraswcharide are labelled i and i + 1. The spaae-group symmetry is P2,2,2, in a non-standard setting. The 2l axis parallel to a passes through z = 0, y = 0 and the 2r ti parallel to z is in the a = 0 plane. To form the 2 residues of the up-pointing ohain the symmetry operations we x, y, a and -x, -y, c/2 + z. For the down-ohain the symmetq operations are a/2 + 2. b/2 - y, --z and a/2 - z, b/2 + y, c/2 - z.
J. M. GUSS
380
ET
AL.
Despite the good overall agreement with the X-ray amplitudes a number of reflexions on the equator and layer line 1 = 3 that are below the threshold for observation have large calculated amplitudes. This could be due to there being water molecules in sites we have not detected (perhaps because they are not occupied in every unit cell). (b) Polysm&&de
chai?asof the orthorhombic structure
Refinement of the backbone conformation angles in the orthorhombic structure resulted in values differing on average by only 5” (maximum 14”) from those in the tetragonal structure. As a result of these changes the short contacts, O&---C&, across the 1 -+ 3 linkages were improved to 0.270 nm and 0.271 nm. The hydrogen bonds across the linkage now have lengths of O&~-H---Of’,,i+l 0.269 run; 0.257 nm; O&+,-H---O& 0.292 nm; N;-H---O&,; NfL-H---o&)d+l o-295 nm. Somewhat larger shifts occurred in the side-chain conformations (Fig. 11). This was expected since the side chains are intimately involved in the interchain packing. The orientation angles for the two non-equivalent carboxylate groups of the tetrasaccharide unit differ by about 60”.
H(N)’
(d)
HB(6b)
(e)
FIQ. 11. Projections showing the conformations Conventions are the same &s for Fig. 6. (a), (b) and (c) are for residue i. (d), (e) and (f) em for residue i -I- 1.
of the side chains in the orthorhombic
structure.
HYALURONIC
ACID
381
(c) Chain packing and cation association8 in the orthorhombic stmctwre The relationship (pl = -t+) between the polysaccharide chains implies the symmetry P2,2,2,. Relaxing the relationship again yields no significant reduction in Q. A schematic diagram of the interchain contacts involving hydrogen bonds is shown in Figure 10(b). The overall result is that the same chains are linked in essentially the same manner in both tetragonal and orthorhombic structures, with water molecules bridging the gaps caused by the extension of the lattice in the orthorhombic form. For one disaccharide of the repeating tetrasaccharide unit, the corner-to-corner hydrogen bond, O&+,-H---O&, is retained with little change in length from the tetragonal structure. Calculation of the angles C&,-O&i---O~~,+l (155”) and C&+I-O&i+l---O&i+l (121’) suggests that Ocej is the more probable interaction found in the tetragonal form is replaced donor. The O&i+l-H---O&+l by a bridge through a water molecule O&+,---W~y~---O~7),+,. This same water molecule completes the co-ordination shell about Na,,, and can also accept a hydrogen bond from O&. For the other disaccharide both the equivalent interactions are through water molecules O&, ---w(,,---o&i For and O& ---Wc2j---O&,+,. both disaccharides the hydrogen bonds between antiparallel chains are the same as in the tetragonal structure, though slightly longer. Three-dimensional Fourier difference synthesis also indicates a fourth water molecule WC*, interacting with O& and O&~~t+I of antiparallel chains. The inclusion of this water molecule caused & substantial (15%) reduction in calculated values of F(200) and P(203) : apparently these reflections are relatively sensitive to minor changes in the overall distribution of electron density. The network of hydrogen bonds is further supplemented by contacts to the sodium ions which involve a number of different polysaccharide chains (Fig 10(a)). One sodium ion, Nat,,, is involved in contacts to three hyaluronate chains and a single water molecule. The second sodium ion, Nacz,, makes only four contacts to the original six oxygen atoms but is also co-ordinated to two water molecules. One of these, Wcz,, is hydrogen-bonded to O&, so that this linkage, Na . . . O& in the tetragonal structure is restored via a water bridge, Nao, . . , W,,,----O&. The overall chain packing is shown in Figure 12.
9. Discussion and Conclusions We have described a general strategy for analysing fibrous polymer structures where the X-ray diffraction data alone (because of their characteristically small number and limited resolving power) require to be supplemented by stereochemical information. Using the linked-atom least-squares approach we maintain standard bond lengths and bond angles and (in this instance) standard pyranose ring shapes. The polymer conformation and packing are then varied to minimize steric compression (represented by overshot non-bonded contacts) or to optimize the fit with X-ray amplitudes or to do both simultaneously. Potential hydrogen bonds are recognised and can be removed from the list of repulsive interactions and even, when desired, maintained near standard lengths. Additional non-polymeric components such as cations and water molecules, detected by systematic trial of likely sites or in Fourier syntheses of electron density, can be added to the structure and their
1
t
3.39 nm 3.39
+
t
o&9
(al
nm ---*
“Ill
I
t
I.153 nm +
(b)
A
FIU. 12. Viewe of the rafined orthorhombia struoture of sodium hyaluronate. Conventiona are the game as for Fig. 7. The sodium ions are shown &B NAI and NA2. (a) View along the (100) direction; (b) view along the (010) dire&ion; (a) view along the (110) direotion.
HYALURONIC
ACID
343
positions and contacts optimized simultaneously with the refinement of the polymeric part of the structure. We have applied this strategy to a tetragonal form of sodium hyaluronate that contains little or no water. Various models for the polyanion have been considered. We have rejected an antiparallel double helix on three grounds: first, we have found it impossible to build any model that is free of considerable steric compression; second, even when we concede what would normally be unacceptable steric compression, the fit between the observed and model X-ray amplitudes is very poor; third, Fourier difference syntheses with single chain models providing the approximate phases indicate that the second chain in the unit cell is not coaxial with the f&t. In contrast, structures with non-coaxial chains are not sterically compressed and the fit with the X-ray amplitudes is as good as we have found for other fibrous structures. Structures with left-or right-handed helices fit the X-ray amplitudes equally well, but only left-handed helices lead to an extensively hydrogen-bonded structure in which every pot’ential donor indeed participates in hydrogen bonding. In this structure there is a unique set of sodium ion sites where sodium is octahedrally coordinated with six oxygen atoms from three hyaluronate chains. WC have also made an investigation of R more hydrated sodium hyaluronate structure that has orthorhombic symmetry but is apparently very similar in many respects to the tetragonnl form. In the orthorhombic structure we have located the sodium ions and some additional water molecules-four per tetrasaccharide. In both structures the similar molecular conformations are stabilized intramolecularly by O-H---O hydrogen bonds across the 1 -+ 3 glycosidic linkages and N-H---O hydrogen bonds across the 1 -+ 4 linkages, and intermolecularly by a network of hydrogen bonds and 0 . . . Na+ . . . 0 bridges. The dehydrated, tetragonal form contains no detectable water and the oxygen atoms in the octahedral co-ordination shells of the sodium ions are perforce part of the polyanion structures. (Three polysaccharide chains conhribute oxygen atoms to the co-ordination shell of any sodium ion.) In the high humidity, orthorhombic form at least four water molecules per tetrasaccharide appear to have been intruded. (Two are bound to one of the two sodium ions associated with each tetrasaccharide unit and one to the second sodium.) The polyanion conformations, hydrogen bondings and ionic bridges between chains are very similar to those in the tetragonal structure except that a few of the direct’ interactions between chains have been replaced by water bridges. The work at Purdue w&9 supported by grants to one of us (S. A.) from the National Science Foundation (7420505) and National Institutes of Health (GM20612). Two other authors (J. M. G. and W. T. W.) were fellows of the U.S. Arthritis Foundation and another author (D. W. L. H.) was a Jane Coffin Childs Memorial Fellow.
REFERENCES Anderson, N. S., Campbell, J. W., Harding, M. M., Rees, D. A. & Samuel, J. W. B. (1969). J. Mol. Biol. 45, 85-99. Arnott, S. & Hukins, D. W. L. (1973). J. Mol. Biol. 81, 93-106. Arnott, S. & Scott, W. E. (1972). J. Chem. Sot. Perkin Tram. II, 324-335. Arnott, S. & Wonaeott, A. J. (1966). Polymer, 7, 157-166. Arnott, S., Guss, J. M., Hukins, D. W. L. & Mathews, M. B. (1973ct). ScievLce, 180, 743-745. 26
J. M. GUSS ET
384
AL.
Arnott,
S., Guss, J. M., H&ins, D. W. L. & Mathews, M. B. (1973b). Biochem. Biophys. Res. Ccmmun. 54, 1377-1383. Arnott, S., GUSI, J. M., Hukins, D. W. L., Dea, I. C. M. & Rees, D. A. (1974a). J. Mol. Biol.
Arnott, Arnott,
88, 175-185.
S., Scott, W. E., McNab, C. G. A. & Rees, D. A. (1974b). J. Mol. Biol. 90, 253-268. S., Fulmer, A., Scott, W. E., Dea, I. C. M., Moorhouse, R. & Rees, D. A. (1974c).
J. Mol.
Atkins, Atkins, Atkins, Atkins,
E. E. E. E.
Biol.
D. D. D. D.
T. T. T. T.,
90, 269-284.
& Isaac, D. H. (1973). J. MOE. Biol. 80, 773-779. & Sheehan, J. K. (1972). Nature New Biol. 235, 253-256. & Sheehan, J. K. (1973). Science, 179, 562564. Gaussen, R., Isaac, D. H., Nandanwar, V. & Sheehan, J. K. (1972). J. Polymer Sci. B, 10, 863-865. Chsndrasekaran, R. & Balasubramanisn, R. (1969). Biochim. Biophys. Acta, 188, l-9. Dea, I. C. M., Moorhouse, R., Rees, D. A., Arnott, S., Guss, J. M. & Balazs, E. A. (1973). Science, 179, 660-562. International Tabb for X-ray Crystallography (1962). Vol. 3, Kynoch Press, Birmingham. Isaac, D. H. & Atkins, E. D. T. (1973). Nature New Biol. 244, 252-253. Johnson, C. K. (1965). Report ORNL-3794, Oak Ridge National Laboratory, Tennessee. Johnson, L. N. (1966). Acta Crystullogr. 21, 885-891. Rees, D. A. (1969). J. Chem. Sot. B, 217-226. Sim, G. A. (1961). In Computing Methods and the Phase Problem in X-ray Crystal Analysis (Pepinsky, R., Robertson, J. M. & Speakman, J. C., eds), pp. 227-235, Pergamon Press, New York. Williams, D. E. (1969). Actu Crystullogr. sect. A, 25, 464-470.
Hyahronic Acid : Molecular Conformations and Interactions in Two Sodium Salts J. M. Goss, D. W. L. HUKINS~, P. J. C. hITH W. T. WINTEE, STBUTHER ARNOTT Department of Biobgicd Sciences PUT&M University We& Lajayeite, In&. 47907, U.S.A. R. MOORHOUSE AND D. A. REES U&ever Research, Colworth/ Welwyn j5dmmtoy Oolworth Howe, Sbrnbrook Bedford MK44 lLQ, Englund (Received 19 November 1974) A detailed struotum for the t&ragoml form (a = b = O-989 nm, c, fibre axis, = 3.394 nm) of sodium hyaluronata has been obtained by analysing x-ray fibre diffraotion data using new molecular modelling techniques. Two polysacoharide ohaim pass through each unit cell, one at the corner and one at the oentre. The chains are anti-pars&l to one another. Each chain is a left-handed, 4-fold heliz of disaccharide units. There are intramolecular hydrogen bonds stabilising each glyoosidic linkage. Octahedrally co-ordinated sodium ions link, by 0 . . . Na+ . . . 0 bridges, neighbouring polysaccharide chains that are further linked by hydrogen bonds. No double-helix model (ss originally proposed for this struoture) has been found to be free of unacceptable non-bonded contacts or to fit the di&a&ion intensities as closely. The tatragoml form, which is stable at zero relative humidity, contains no deteotable water molecules. At higher relative humidities a related orthorhombic form is observed in which only the a dimension of the lattice is different (a = l-163 nm, b = O-989 run, c = 3.386 nm). In this form the hyaluronate helix is 2-fold with tetrasacoharide units conformationally similar to the 4-fold heliz of the tetragonal form. The Na+ . . . 0 binding and hydrogen bonds lost on expansion of the Stragonal lattice are all replaoed in the orthorhombic structure by bridges through water molecules, four of which assooiated with each btrasaccharide.
1. Introduction Hyaluronic acid is a glycosamiuoglycan present iu the iut~rcellular matrix of most vertebrate coxmective tissues and in some bacterial capsules. The molecule is a linear polydisacoharide of the form (-A-B-),, where A is glucurouic acid, B is N-acetylglucosamin e, and n can be as large as lo*. The linkages A-B and B-A are p(1 --f 3) and @(l --f 4). The structure is therefore analogous to the idealised structures of other glycosaminoglycaus such as chondroitiu (where B is galactosctmiue and t Present address: Department of Medical Biophysios, Manohester, Man&ester Ml3 QPT, England. 369
Stopford Building,
University
of
360
J. M. CUSS ET AL.
A is glucuronic
acid), dermatan (where B is galactosamine and A is iduronic acid), and keratan (where B is galactose and A is glucosamine). The polydisaccharide structure of hyaluronic acid is also analogous to the agar-carrageenan family of algal polysaccharides where A is 3,6-anhydrogalactose and B is galactose. The chemical similarities among the glycosaminoglycans evidently result in conformational similarities: in oriented films and fibres hyaluronic acid has been observed to have 2-fold or 3-fold helical forms (Atkins & Sheehan, 1972) similar to the 2-fold and 3-fold helical forms observed for chondroitin sulphates (Atkins et al., 1972; Arnott et al., 1973a; Isaac & Atkins, 1973) and dermatan sulphate (Arnott et al., 19733; Atkins L%Isaac, 1973) and to the 2-fold helix of keratan sulphate (Arnott et al., 1974a). All these helices have relatively long axial translations per disaccharide (h = 0.93 to 0.97 nm) corresponding to almost fully extended backbone conformations that preclude multistranded coaxial helical structures. Unlike the other glycosaminoglycans, hyaluronic acid has also been observed in 4-fold helical forms (Dea et al., 1973 ; Atkins & Sheehan, 1973) : one has h = O-928 nm and therefore corresponds to an extended single helix; the other has a markedly reduced value for h of about O-85 nm like c-carrageenan (b = 0.88 mu; Arnott et al., 1974b), K-carrageenan (F, = O-81 nm; Anderson et d., 1969) and agarose (h = 0.63 nm; Arnott et al., 1974c). For all the systems with short values of h, coaxial double-helical structures have been proposed (Anderson et d., 1969; Dea et al., 1973; Arnott et al., 1974c). In the models for L and K-carrageenan and agarose the coaxial helices are parallel (i.e. have the same chain sense), for hyaluronic acid they are antiparallel. Detailed model building and X-ray analyses (Arnott et al., 1974b,c) provide strong support for the L-carrageenan and agarose double helices. As a result of similar intensive studies we have now concluded that the double-helical model for the 4-fold (h = 0.85 nm) form of hyaluronic acid is incorrect and that the structure consists of single, left-handed chains. Results of nuclear magnetic relaxation studies on solutions of sodium hyaluronate (E. G. Finer, R. Moorhouse & D. A. Rees, unpublished results) can best be interpreted in terms of a partly ordered, partly disordered system. The fraction of ordered structure is not altered by changes in temperature or ionic strength, both of which are known to affect the rheological properties. An attractive possibility would have been to associate the ordered component with double-helix formation and the rheological properties with interactions between double helices. However, X-ray studies now give convincing evidence against a double helix in any condensed phase and it seems unlikely that the double helix exists in solution, where it would be stable to changes of ionic strength or temperature or moderate changes of pH, and yet fail to survive mild crystallization conditions.
2. Materials and Methods (a) Mat&d Samples of the sodium salt of hyaluronic acid (M, > 2 x 10E) isolated from human umbilioal chord were the Sifts of Dr Martin Mathews of the University of ChioaSo, Ill. and of Dr E. A. Balass of the Boston Biomedical Institute, Mass. Samples from rooster comb were also examined. (b) F&n preparation Hyaluronic acid films were prepared and oriented se described previously (Aruott et ad., 1974a) for keratan sulphate except that no heat wsa applied. The f&us stretched to 3 or 4
HYALURONIC
ACID
361
times their original length under 3.5 g tension at room temperature and relative humidity about 84%. Some samples were subsequently dried over silica gel. Densities of the tlhns were measured by flotation in a mixture of halogenated hydrocarbons.
(c) X-ray diffruction We used the same apparatus, operated under the same conditions, as in our work on keratan sulphate (Arnott et al., 1974a). The dried specimens were kept in an atmosphere of dry helium. The others were kept at 75% relative humidity with helium that had been bubbled through an 88% saturated solution of sodium nitrite. The diffraction patterns were calibrated by dusting the specimens with calcite (characteristic spacing 0.3035 run). The spacings of the Bragg reflections were measured on projected enlargements. Unit cell dimensions were refined by least-squares as described by Arnott & Hukins (1973). Intensities were measured as areas (A,) under radial microdensitometer traces across each spot. The areas were converted to relative structure amplitudes, ,P,, using the relationship
oF,a = A,R,(tan which provides approximate the cylindrical polar radius
20,)/(1
+ cos2 20,),
Lorentz, polarization and spot extension corrections. (R, is in reciprocal space of the X-ray reflection with Bragg angle e,.) (d) Model-building
and optimization
Following our usual strategy for building molecular models of helical polymers we treated the structure as a linked-atom system (Arnott & Wonacott, 1966) in which covalent bond lengths and angles have fixed standard values. The pyranose rings were fixed in the standard Cl chair conformation (Arnott & Scott, 1972) and the atoms of the acetamido group (except the methyl hydrogen atoms) were kept coplanar, leaving angles defining the glycosidic bridge conformations and the side-chain orientations as explicit variables. Helix continuity, symmetry (no. of residues/turn and chirality) and pitch were imposed by means of Lagrangrian constraints. To obtain helical molecules with the least steric compression we minimized @ (eqn (1)).
4 = &Cd,
-
dA2, d, < cd,
e, = O,d, 2 .d,. The first summation thus contains all varied non-bonded interatomic distances, d,, less than some specified minimum Od,. The second summation contains the Lagrange multipliers, &, and the constraint expressions, ah, that we wish to become zero. This approach bo minimizing non-bonded interactions was developed by Williams (1969) to determine packing of rigid molecules in a crystal. For this study we have adapted the method, using t,he linked-atom approach, for the determination of acceptable conformations of the flexible polymer chains. The values of the constants ic, and Od, were derived for each type of interatomic interaction from Buckingham energy functions of the type
E = - Bdm6 + Aexp(-d).
(2)
Values of B,A,p were taken from Chandrasekaran BE Balasubramanian (1969). Each Od, was set to be 0.02 m-n greater than the value of d corresponding to minimum E to ensure that all short contacts were driven to larger values. The values of k, were chosen so that a[k,(,d, - dr)a]/ad closely approximated aE/ad in the range d[E,,,] - 0.05 < d < [E,,,]. The values of k, and ,d, are given in Table 1. For isolated molecules all the d, are intramolecular contacts and the variables are the conformation angles mentioned above. For molecules in a lattice there may be additional d, from intermolecular contacts, and additional variables corresponding to the positions and orientations of molecules in each unit cell.
J. M. GUSS ET AL.
362
TABLE 1 Constants used in equations (1) and (3) to determine non-bonded ilzteractions Type of contact
kj or ,k, x 1Oa(nmm2)
c ...c
1.10
c ...0 C...N C...H C . . . Na 0 ...0 0 . ..N 0 . ..H N...N 0 . . . NE
1.62 2.17 2.18 1.00 1.66 2.21 1.66 2.97 1.00
N...H
2.14 1.00
N . . . Na H...H H . . . Na Na . . . Na
1.13 1.00 1.60
o---o O---N
11.70 11.70
0 . . . Ne
10.00
0.360 0.340 0.346 o-310 0.360 0.320 0.325 0.290 0.330
.i! 3 $
0.296 0.330 O-260 0.300 0.340 O-270 $ 0.290 *3 E 0.260 3
Cur computer program is also capable of simulating the attractive forces arising from hydrogen bonds or the interaction between a cation and atoms of its co-o&n&ion shell, and thereby mainteining distances between the atoms involved near prescribed standards. This situation arises when the distance, d,, between two non-bonded atoms of the proper types falls between speciSed limits *d, and & (Ad, < d, < &). Then, if & is the “ideal” contact distance and ,I%, the corresponding weight, for those interactions where these “special” functions apply the values of c, in eqn (1) become cj = k,(od, - d,Ia, 0 < d, < ,,d, or & 4 = Iw-4
- d,,“, ad, I d, 5 id,,
< d, < ,d,, (3)
c, = 0, d, 2 ,dj.
When 9 (eqn (1)) has been minimized, the final C l , is a measure of the sterio acceptability of a molecular model and its mode of packing. (e) Location of non-coualently bound atoms and ions Cations and water molecules present in structures of polyanionic polyseccharides presumably play an important role in the formation of stable intermolecular linkages through hydrogen bond or ionic bridge formation. A complete solution to a structure of this type involves the location of these components and refinement of their positions against X-ray intensities and packing data where possible. Since these cations and water molecules are not covalently bonded to the polysaccharide chains their possible locations are not immediately obvious. The method we have devised to find these involves giving each ion or water molecule a number of plausible starting positions throughout the structure then retbring its co-or&n&es to minimise the non-
HYALURONIC
363
ACID
bonded interactions (see section (d), above) 8nd to optimize its co-ordination with oxygens or participation in hydrogen bonding. In most cases this procedure gives a small number of possible sites, some of which can be discarded on the grounds of chemical unsuitability. Those that remain can then be assessed on the grounds of improved agrecmerit with the observed X-r8y structure runplitudes and successful formation of suitable interactions, e.g. hydrogen bonds or Na+ . . . 0. (f) X-ray refinement and Four&r sytihea~ The positions of these additional atoms and ions and the conformation of the polyanion may be refined jointly against X-ray and contact data maintaining the attr8ctive interactions discovered in the search procedure by minimizing Sa (eqn (4)). Q = C w,(,F,,, - F,,Ja + SX e, + .Z A,,@,.
(4) F, are the calcul8ted and ,F, the observed X-ray amplitudes. The weights applied 8re w,. The overall weight, S, 8pplied to the contact observations, was chosen on an empirical basis. First, 8 model was constructed using only the contact and not the X-ray data. This model was therefore the sterically most acceptable one that could be mrrde. In subsequent refinement cycles the X-ray data were included and successively reduced values of S were tested. For each value the short contacts were examined and the final value of S chosen was the smallest value thet led to no contacts unacceptable on a hard-sphere basis (Rees, 1969). (In the case of hyahnonste double helices we found no model acceptable on a hard-sphere basis 8nd therefore had to choose a value for S that led to no worsening of the shortest non-bonded contacts of the st8rting model.) Fourier syntheses of electron density were calculated in the usual way except that for overlapping reflections the intensity was divided equally among the contributing planes. Difference syntheses were calculated using W, (,F, - F,) as amplitudes. For centric projections 8ll W, were set equal to unity. Otherwise we used an approximation (eqn (6)) to Sim’s (1961) weighting scheme for acentric Fourier syntheses with phases calculated from an incomplete structure. W, = (,F,
x F,)/maximum(,F,,,
3. Ditlkaction
x F,,,).
(5)
Patterns
We have obtained three different but related diffraction patterns all corresponding to an hyaluronic acid chain repeat of four disaccharide residues with an average h of O-85 nm per disaccharide. The simplest pattern (Plate I(a)) is obtained from sodium hyaluronate specimens, stretched at high humidity, dried over silica gel, and X-rayed in an atmosphere of dry helium. The lattice is tetragonal: a = b = 0*989(2)nm, c (fibre axis) = 3*394(9)nm and meridional (001) reflections are observed only for 1 = 4%. The measured relative density (l-60) agrees well with that calculated for a unit cell containing eight disaccharide residues, eight sodium ions and not water molecules (1605). Thus, two regular 4-fold helical, polydisaccharide chains pass through each unit cell. At higher relative humidities (e.g. 75%) the unit cell remains rectangular but the a dimension is larger (a = 1*153(4)nm, b = 0*989(3)nm, c = 3*386(9)nm). There are now (002) reflections for I = 2n (Plate I(b)). The hyaluronate chain is therefore a 2-fold helix with tetrasaccharide units. However, since the general intensity distribution is very like that of the tetragonal form and the c dimension is essentially the same, it is likely that the molecular backbone conformations are little changed although the conformations of corresponding side-chains on adjacent disaccharide t The measured densities are not BOaoaurata that the exact number of water molecules present oea be prediated
with
oou6denoe.
In the subsequent
struoture
malyses
we indeed found no sites
for water in the tetragonal structure but 4 sites per tetrsaacaharide in the orthorhombic form.
J. M. CUSS
364
ET
AL.
residues may be somewhat different from one another. This is probably also the case for the co-ordination shells of the sodium ions. The measured relative density (1.45) corresponds to there being one water molecule-t per tetrasaccharide. The third crystal form from rooster comb sodium hyaluronate at high relative humidity also has a rectangular unit cell (la = l.l62(2)nm, b = O-984(3@, c = 3.331(6)nm) and an intensity distribution almost identical to Plate I(b) except that now there are meridional (002) reflections on every layer line indicating a further (but minor) perturbation of the original 4-fold helical symmetry.
4. Model-building Studies In general, analyses of fibrous structures require the creation and testing of plausible molecular and crystal models. To begin with we concentrated on the tetragonal crystal form, which contains regular 4-fold helical chains, and used the procedures described in Materials and Methods, section (d) that exploit only the spacings and not the intensities from the diffraction pattern.
(a)
(b)
FIG. 1. Possible modes of packing 2 ohains in the tetragonctl unit cell. (a) Single he&es. One passing through the corners of the lattice and an antiparallel chain through the centre. The relative trenslation of the 2 chains parallel to the helix axis is 2w. The orientations of the chains are pi and pa. If the lattice has tetragonal symmetry and pi # -pLz then the space group is either P4s (left-handed ah&s) or P4, (right-handed chains). If pi = -pa then the space group is P4e2,2 or P41212 in a non-standard setting. (b) Double helices passing through the corners of the lattice. (The radii of the 2 chains are shown dif%rently for illustration only). In this case if pi # -pa then the space group is again P4$ or P41. However if pi = -pa then the up and down-pointing chains of the double helix will be related by g-fold axes parallel to the cell edges and the space group becomes P4,22 or P4,22.
A priori we could have no preference for left (43) or right-handed (4,) helices. Preliminary models of each with a pitch of 3.394 nm were constructed by minimizing Q, (eqn (1)). Since two chains pass through each unit cell, we had also to determine whether the two chains had their axes coinciding (i.e. formed a double helix) or whether they were separated in a centred arrangement (Fig. 1). There was also the further question of whether the two chains were parallel or entiparallel. tSee footnote on page 363.
Cb)
ATE I. Diffraction patternsfrom sodium hyaluronate. The meridional direction is vertical At 0% relative humidity. At 75% relative humidity.
HYALURONIC
36b
ACID
(a) Hyalurmate chains paeked in a tetragonul array For each crystal model we varied the molecular parameters and the axial orientation (,u) of each chain and its displacement (w) (Fig. 1). All models containing parallel chains had severe non-bonded contacts that could not be relieved. Table 2A therefore contains the results only for the four kinds of antiparallel chain model obtained by minimizing @ (eqn (1)). These studies with our new computer model-building methods show clearly that coaxial, antiparallel, double-helical models whether built with left- or right-handed chains would involve a considerable degree of steric compression. The models with non-coaxial chains are markedly more acceptable and the model containing left-handed helices is superior to that containing right-handed helices. TABLE
2
Co?nparison of possible models for the tetrapnal structure A.
Coaxial
and non-coaxial or right-handed
chain models containing (4s) 4-fold helices
left-
Overshort+ contacts w4
Packing
(4,)
RS
R”
Non-coaxial
43
O-360
H:,, . . . CiBg)(0.210); %, . . . Cc, (0.241)
o-33
o-39
Non-coaxial
41
0.448
c%* * . C;, (0.273); c& . . . Op,, (0.264)
0.33
0.37
Coaxial
43
0.618
H;, . . . o&, (0.133); OS,. . . H& (0.199)
0.47
O-64
Coaxial
41
0.672
H$, . . . op,,, (@170); o:,,, * * * H& (0.174)
0.66
0.69
t Less than marginally allowed $ R and R” are crystallographic
in usual residuals
R = .Zj,F,
LeftModel
and right-handed Chains
.%
models
R-S, 1969) “hard sphere” analyses. calculated after scale factor refinement only:
(e.g.
- F,&?YoFm.
R” = {I: w,(,F,
B.
either
refined
-
against
Overshort oontaats wd
Hyaluronate
4s
O-600
O$, . . . C& (0.260); HiBp). . . H&(0.183
Hyaluronate
41
0.666
HiS,, . , . O& %., * * * H;,,
Sodium hyaluronate
43
048
Op,, . . . C& (0.266); cd(6) . . . Ne (0.266)
(6)
Pm)“/ X w, .F,“}
(@168); (0-W
structure
*.
(7)
amplitudes
and contact
Hydrogen-bonds Intmhain Interohain
criteria R
R”
0$--o&; NB---OP,,,
o&--o&; O&---q&; op,--4,
0.307
0.364
None
O&---O&
0.304
0.366
o&--op,,; NB---O&
o&--o&; o&--o&; o&---o&
0.291
O-326
366
J. M. CUSS
ET
AL.
(ai
(b)
(d)
FIQ. 2. (a) and (o) Electron density projections with phases model having 1 ohein et the corner of the unit-cell. (a) is the The model used to compute the Fourier terms is superimposed (b) and (d) Difference electron density with phases from the
and amplitudes computed from s (100) and (a) the (001) projection. on the electron density. single-chain model and amplitudes
HYALURONIC
387
ACID
5. Fourier Synthesis of Electron Density We next considered the question of single-chain verszcs double-helical models by exploiting the X-ray intensities rather than stereochemical considerations. We postponed a decision as to the position of the second chain in the unit cell and calculated structure amplitudes and phases from a crystal model containing only one hyalmonate helix per unit cell. When these phases were combined with the observed structure amplitudes in Fourier syntheses of electron density, additional density was found corresponding to a similar second helix with its axis running centrally through each unit cell and not coincident with that of the first chain. Figure 2 shows the results of such experiments performed with observed amplitudes from the tetragonal crystal form. We obtained similar results in a similar, independent experiment with the orthorhombic crystal form. 6. Further Refinements of Tetragonal Structures In the third set of experiments we refined various models using equation (4) to optimize the fit between calculated and experimental X-ray structure amplitudes while maintaining minimum ateric compression. The stereochemically optimized model involving left-handed, coaxial helices had X-ray residuals R = O-48 and R” = O-57 before refinement and we found it impossible to reduce these substantially without producing many more unacceptable TABLE
3
Values of the refined parameters for the tetragonal structure PaSameter
Comment
value 106.9 -46.4
1 -+tlinkage s
- - 107.2 80.2
1 + 4 linkege
- 177.4
Hydroxymethyl
-79.1 -27.2 -91.4 18.1 0.04 nm=
ij ii’ u 8 m if 7 -
N-ctoetyl
Cerboxylats So&
fsQt@
Attenuation
t Relating observed and ordoulated BtNCtlllB amplitudes. $ Applied to the o&&ted amplitudes in the form exp(--B
fastor
sina e/xx) where h = 0.1642 -.
(,P, - P,). The projections are the ssme as (a) and (0). Another similar (antiparallel) single ohain with its axis at the oentrs of the unit oell is superimposed on the density. It should be noted thet the main ridges of electron density in (a) srs about 0.34 nm from the helix axis whioh ooinoides with the c-axis of the unit cell. In the difference Fourier synthesis in (b) the ridges srs only 0.17 nm from the sell edges and therefore donot indicate a similar h&x ooaxial with the tit. The ridges are, however, about 0.33 m-n from the oentre of the unit cell and it is this feat together with a shnilsr argument for (0) end (d) that oompels us to interpret this experiment as f&o favouring non-ooaxial &sins. 26
J. M. GUSS
368
TABLE
ET
AL.
4
Values of the observe@, ,I?,, and c&uhted$, F,, structure am$itudes for tetragonal sodium hyaluronate h
k
1
Jm
Pm
h
k
1
1 1 2 2 2 3 3 3 4
0 1 0 1 2 0 1 2 0
0 0 0 0 0 0 0 0 0
88 bt bt 8 17 88 29 31 18
0 12 6 61 9 0 23 18 17
1 1 2 2
0 1 0 1
4 4 4 4
9 14 40 15
9 28 24 23
1 1 2 2
0 1 0 1
5 5 5 6>
bt 8
10 6
27
33
1 1 2 2
0 1 0 1
1 1 1 1
12 24 38 49
18 20 36 66
1 1 2
0 1 0
6 6 6
18 bt 23
19 8 26
1 1 2 2
0 1 0 1
2 2 2 2
18 16 24 40
28 20 23 24
1 1 2
0 1 0
7 7 7
29 bt bt
27 6 6
1 1
0 1
3 3
17 bt
6 12
1 1 2 2 1 1
0 1 0 1 0 1
8 8 8 8 9 9
22 16 12 bt 22 27
7 17 24 8 23 17
0 1 0 1
10 10 10 10
bt bt bt 27
7 3 28 29
0 1
11 11
bt 20
4 3
88, System&o absence. bt, Intensity below observation&l threshold. Only those below-threshold within the outermost observed refleotion on any layer line are included. 8 Masked by the extended arc of (211).
.F?ll
F,
reflections
t The values of ,P,,, have been multiplied by the scale factor (Table 3). $ Atomic scattering faotors were from Intematid Tables for X-ray Crystallography
lying
(1962).
non-bonded contacts. Even when all attempts to maintain intramolecular hydrogen bonds were abandoned the residuals could not be reduced below R = 0.47 and R” = O-54. We therefore felt confident in rejecting further consideration of structures containing coaxial double helices on both stereochemical and X-ray grounds. In contrast the two remaining models with pairs of either right- or left-handed, antiparallel, non-coaxial hyaluronate helices had R = 0.33, 0.33 and R” = 0.37, O-39, respectively, even before further refinement, and R = O-31, O-30, R” = O-35, 0.36 after refinement of the polyanion conformations.
HYALURONIC
ACID
TABLE
369
6
Cartesian w-orohztes (x, y and z) for a disaccharide residue of sodium hyaluronate in the tetragonal lattice Atom
co, C Cal C (31 C (4) C(5) co, 00, %I 0,3,
0 0 0 0
(4) (6) ma) (661
H (11 H (1) H (3) H (4) H (61
C (11 C (9) C (3) C (41 C (6) C (61 0 (11 0 (3) 0 (4) 0 (55) 0 (61
H (1) H (11 H (51 H.4,
H (5) H G%a) H @b) N
C (7) C (61 0 (71
H (cm) H (EL, H (SC) H WI N&3
x (nm x 10’)
y (mn x 10’)
z (nm x 10’)
(residue A) -2686 -3796 -4276 -3098 -2009 - 762 -2190 -4867 -6217 -3616 -1612 - 736 81 -3074 - 3422 -4780 -2692 -2388
1669 2610 3664 4381 3466 4204 814 1669 4426 6246 2623 4660 4380 1132 3002 3073 4996 2907
Gluouronate 2239 2866 1869 1364 821 399 3216 3247 2610 299 1838 -802 1306 1361 3766 1023 2171 -63 N-acetylgluoosamine 387 -990 -920 148 1472 2647 299 -2190 342 1298 3792 742 - 1369 -681 - 169 1836 2697 2238 -1932 -3286 -4126 -3760 - 3688 -4324 - 6080 - 1600 -446
(residue B) -3112 - 3246 -2962 -3814 -3671 -4692 -3616 -3216 -3416 -3997 4400 -2076 -4266 - 1889 -4867 -2636 -4396 -6638 - 2323 -2671 - 1662 -3616 - 694 - 1906 -1413 - 1676 964
6671 7207 8698 9367 8613 9161 6246 9298 10712 7226 8482 6677 7062 8862 9342 8706 10223 9011 6633 6622 6889 7231 6847 4867 6420 6060 2480
The space-group symmetry k P4,2,2 in a non-standard setting, with the origin on the 4, axis. To form the 4 residues of the up-pointing chain the symmetry operations are x, y, z; y, -2, c/4 + 3; -2, -y, c/2 + z and -y, z, 3c/4 + z. To form the residues of the down-pointing ohaiu with helix axis at a/2, b/2, the symmetry operations are a/2 + x, b/2 - y, --z; a/2 - y, b/2 - x, c/4 - z; a/2 - x, b/2 + y, c/2 - z; al2 + y, b/2 + x, 3c/4 - z.
370
J. M. CUSS
ET
AL.
On the basis of the agreement between the observed and calculated structure amplitudes alone we cannot make a choice between right and left-handed mode1s.t However, we did decide to reject further consideration of right-handed helices on steric grounds, Their conformations involve a noticeably greater degree of steric compression than for left-handed helices and do not permit extensive hydrogen bonding. In marked contrast, refinement of the model containing left-handed helices gave an elaborately hydrogen-bonded structure in which all potential hydrogenbond donors were indeed involved in hydrogen bonding.
FIG. 3. The disaeoharide of hyahwoneta showing the atom labelling. A ia gluouronate and B is IV-acetylgluooaemine. The parentheses are omitted from the atom names for olarity. Subsequent reference8 to atoms are made in a form which speoi6es the residue in addition to the etomio type oxygen atom from residue A (gluouroneta). The suband number. e.g. O&, ia a oarboxylate ecripte i and i + 1 ere used to differentiate the non-equivalent residues of the tatrasacoharide in the orthorhombio struoture.
We then sought to complete this model containing left-handed hyaluronate helices by seeking likely sites for sodium ions and water molecules using the methods described in Materials and Methods, section (e). No water sites were detected but we found a single set of sites for sodium ions in which each sodium is co-ordinated to six oxygen atoms from three hyaluronate chains. Final refinement of the complete sodium hyaluronate structure improved both the stereochemistry and the fit with the X-ray amplitudes so that R and R" became O-29 and 0.33. This retiement was followed by a three-dimensional Fourier difference synthesis. The largest peaks in this were considered as possible water molecule sites but none was found that was both stereochemically reasonable and led to an improved fit with the X-ray amplitudes. The parameters of the final structure are given in Table 3. Observed and t This ia perfectly understandable when one considers that the of anomalous scattering) cannot distinguish between a structure we have observed ia that a left-handed I-fold hyeluronate helix image of B right-handed helix in such a way that regions of power ooinoide.
X-ray intensities (in the absence and its mirror image and what can be superposed on the mirror approximately equal scattering
HYALURONIC
ACID
I
(b)
(a)
4. Sohematie diagrams of the attraotive intermoleoular interactions in the tetragonel struoture. The numbers indiaete distanoes in nanometres. (a) The oontaots to the sodium ion. Helix I at (z = 0, y = 0) is anti-parallel to II at (z = -a/2, y = b/2) and III at (z = -a/2, y = -b/2). (b) The intermolecular hydrogen bonds. The helicea are the same aa in (a). The distances are between oxygen atoms. FIQ.
calculated structure amplitudes are given in Table 4. The atom labelling is shown in Figure 3 and the atomic co-ordinates are given in Table 6. The attractive noncovalent interactions (hydrogen bonds and Na . . . 0 contacts) are illustrated in Figure 4. 7. Description
of the Tetragonal Structure
(a) Polysacdaride chains The 6nal conformations at the glycosidic bridges are “fully allowed” for the 1 -+ 4 linkage and nearly “marginally allowed” (Rees, 1969) for the 1 -+ 3 linkage. (There is one short contact, 06) . . .C&, across this linkage which is O-266 nm compared to the marginally allowed value 0.270 mu.) The side-chain conformations are depicted in Figure 6. The hydroxymethyl group extends outwards to participate in inter-chain
(0)
(b) (cl showing the conformations of the side-chains and the values of the re6ned torsion angles in the tetragonel structure. (a) The wets&do group along the NE-C& bond; (b) the hydroxymethyl group along the C&-C& bond; (c) the aarboxylate group along the C&-C& bond. FICA 5. Projeotions
372
J. M.
GUSS
ET
AL.
hydrogen bonding. The acetamido group has an orientation about 30” different from that in N-acetylglucosamine (Johnson, 1966). This allows formation of an P-H---O&,] hydrogen-bond (length 0.278 nm) across the 1 -+ 4 linkage. There is a hydrogen bond (length O-253 mu) stabilizing the 1 -+ 3 linkage also-between O& of N-acetylglucosamine and O& of glucuronate. The conformation of a single chain is shown in Figure 6.
1 Fm. 6. A single hyclluronate ohain from the tetragon~l struoture. The hydrogen-bonds NEof 0.278 run, and 0$-H---0$, , of 0.253 nm, are shown. The nitrogen atoms are H---O&, shown as solid circles. This and subsequent drawings were made using oomputer program ORTEP (Johnson, 1965).
(b) CMra. packing a& cation associa;tion in the tetragonal etructzcre The left-handed helical chains are packed in the square lattice with the molecules passing through the corners antiparallel to those passing through the centres. The mutual orientation of chains corresponds to the higher symmetry of space-group P4,2,2. (No significant reduction in .Q resulted from the relaxation of the condition p1 = --pa (Fig. l(a).) Neighbouring chains along the cell edge separated by 0.989 nm and O&---H-O& hydrogen bonds (Figs 4(a) and are linked by O&-H---0$ 7(a)). In addition neighbouring antiparallel chains are linked by O&-H---O&, hydrogen bonds (Figs 4(b) and 7). The network of hydrogen bonds linking adjacent chains is supplemented by Na + . . . 0 bridges. A sodium ion bound to the two carboxyl oxygens of a residue in a corner chain is also bound to O&, OS, and O& of a centre chain and to O$, of another corner chain (Figs 4(b) and 7), completing a distorted octahedral shell (Figs 4(a) and 8).
(4
do.9l39
nm -+
:
h
(b)
I.399 nm __,
Pro. 7. Views of tho rafined tetragonal structure of sodium hyaluronate. Chains at the cell corners are shown emphasized. Hydrogen bonds are shown by dashed lines and Na+ . . . 0 contacts by dotted linea. (For clarity only some of these interactions have been shown.) (a) View along the (100) direction. The centre chain (open bonds) is translakd n/2 behind the corner chains. Only the contacts to the sodium ion NA, which binds to all 3 chains in this Figure, are shown. The a and c dimensions are indicated. (b) View along the (110) direction. The 2 corner chains are at diagonally opposit,e corners of the unit cell. The helix axes of the 3 chains shown are coplanar. Contacts to sodium ions which interact with 2 chains are shown. The 6th co-ordination positions (to chains not in this Figure) are indicated.
+-
k-f+@
374
J. M. GUSS
ET AL.
FIG. 8. Details of the sodium ion environment in the tetragonal struoture. !Cbis ia an enlargement of e se&ion of Fig. 7(a) showing the lebeh of atoms bound to the sodium ion.
8. The Orthorhombic
Structure
In developing a model for the orthorhombic structure we made the basic assumption that the structure is closely related to that of the tetragonal form. This conservation is suggested by the in@niScant change in the fibre repeat, distance (3.394 nm in the tetragonal and 3.386 nm in the orthorhombic form) and by the close similarity of the overall intensity distributions in the diffraction patterns (Plate I). In addition transitions between the two forms are accomplished easily under mild conditions of dehydration or humidification, suggesting that not only is the polyanion conformation largely preserved but so also are many of the intermolecular hydrogen bonds and Na+ . . . 0 interactions. There is no obvious explanation as to why only one of the two lateral spacings should be preserved in the transition, but, this in itself certainly means that a number of the intermolecular contacts will be maintained if there are no large changes in relative orientation and translation of the polyanions. (a) Posit&x&g the sodium ions and water moleczdEes Initially we refined a model whose starting point was the polyanion component in the same relative orientation to the a cell edge as in the tetragonal form. Retieme& of only the relative chain orientations (p) and translations (w) resulted in a model with no overshort contacts and which gave good agreement between the observed and calculated X-ray amplitudes (R = 0.36 and R” = O-42)?. The unidirectional expansion of the lattice parallel to (100) causes the separation of the helix axes of neighbouring antiparallel chains to increase from 0.699 nm to 0.769 nm and of adjacent up-pointing chains separated by a to increase from 0.989 nm to 1.153 nm. This results in the breaking of the O&---O& and O&---O& hydrogen bonds in the (100) direction and in the disruption of the previous 6-fold co-ordination about the sodium ions. Consistent with the orthorhombic symmetry, the repeating unit of the helix is now a tetrasaccharide in which the two successive disaccharides, conformationally identical in the tetragonal structure, will now be different and make d&rent intermolecular contacts. A refinement optimizing the contacts to the two sodium ions (see Materials and Methoda, section (d)) contirmed that neither disaccharide could now form the same t A model with coaxial
double helices had R = 0.49 and R" = OG at this stage.
HYALURONIC
376
ACID
six intezactions with sodium ions as in the tetragonal structure. One sodium ion, NqI), could make either of two sets of five interactions (Fig. 9(a) and the other, NaCoj, either of two sets of four interactions (F’ig. 9(b)). All the possible combinations of the sodium ion co-ordination sites were considered, and for each structure amplitudes were calculated. Possible water molecule positions were derived using the method described earlier (Materials and Methods, section (0)). I
NatI) I
I
I
I
Oh,+,OC%,+, o~)i+l I ops.,, I op,*,; I Of&,+, No (I)
(0)
Na (2)
G);
I
1
I
Of: );
OP. ), 1
I
$3, I
O&J,,+, I Na (2)
O&7,;+, J
(b) FIO. 9. Preliminary aseignmenta of binding sites for the 2 sodium ions in the orthorhombio Btruoture. (a) Nat11 may bind to either of the 2 sets of 5 oxygen &XIM from the 6 found in the tetragonal structure. In the final model 1 additional water mole&e binds to Ne(,,. (b) Na(g, may bind to 4 oqgen atoms of the polysecohsride backbone. Neither possibility inoludea O&. In the final model 3 water moleoules also bind, 1 to Nao, and 2 to Naca,.
TABLET
V&be8 of th rejined pwmeters for th orthorhombk &uc.ture P8rameter
Value
21
It
comment
120.2 - 62.2
112.3 - 60.6
-Ill*6 - 80-8
-110.1 - 76.8
- 154.6
- 167.4
- 97-7 63.3
-78.1 40.4
N-acetyl
-31.6
- 92-7
Carboxylate
66.2 0.1 nma t For disaooharide $ For disaaohaxide $ Not refined.
residue i + 1. residue i.
1 +tlinkage 0
c c. Hydroxymethyl i 5
s So& factor Attenuation
fmtor§
376
J. M.
GUSS
ET
AL.
One model was clearly superior in that it possessed the following features: (i) an extensive hydrogen-bond network; (ii) the closest relationship to the tetragonal structure; (iii) direct interaction between the cations and carboxylate anions and (iv) the best X-ray agreement indices (R = O-30 and R” = O-38). In the refinement of this model the cations and water molecules were considered as independent entities additional to the linked-atom description of the hyaluronate chains but subject to the repulsive and attractive forces described previously. A fmal refinement varying backbone and side-chain conformations and packing of the TABLE
7
Value-s of the observedt, J?,, and cddatccted, I?,, structure amplitudes for orthorhombic sodiunz hyalwonate h
k
1
,Fm
Fm
h
k
1
0F In
F,
1 0 1 2 0 2 1 3 2 3 0 1 3 4
0 1 1 0 2 1 2 0 2 1 3 3 2 0
0 0 0 0 0 0> 0 0 0 0 0 0 0 0
aa S& bt bt
0 0 13 46
3 3 3 3 3 3>
6 14 21 42
62
0 1 1 0 1 2
bt 27 bt bt
49
1 0 1 2 2 0
62
69
46 sa bt 63 se 47 bt 34
44 0 14 23 0 36 26 22
1 0 1 2
0 1 1 0
4 4 4 4
bt bt 34 36
2 12 47 17
1 0 1 2
0 1 1 0
1 1 1 1
bt bt 46 36
10 4 42 26
1 0 1 2 2 0
0 1 1 0 1 2
6 6 6 6 6 6>
bt bt 31 bt
6 16 23 26
40
34
1 0 1
0 1 1
2 2 2
21 28 39
21 21 33
2
30
24
6 6 6 6 6 6>
17 9 14 21
0
0 1 1 0 1 2
bt bt 36 bt
2
1 0 1 2 2 0
34
23
2 0
1 2
2 2>
66
48
1 0
0 1
7 7>
44
49
1 0 1
0 1 1
8 8> 8
20
7
33
16
1 0
0 1
9 9>
68
37
a, System&o ebsence. bt, Intensity below observ&tionel
threshold.
t The v&~ea of ,,F,,, have been multiplied
by the scale factor
(Table 6).
HYALURONIC
ACID
377
polyanions, the cation and water positions and the X-ray scale factor resulted in a structure for which Robs is 0.29 and Rnobs is 0.33 with a value of 8 = 0.2. Final values of the parameters of this structure are given in Table 6, observed and calculated structure amplitudes in Table 7, atomic co-ordinates are given in Table 8. The attractive interactions are illustrated in Figure 10.
I - "ij,,..,
“KM,,, ,.-
“‘L33
=.0.267
“I6
0 ‘..
I
FIU. 10. Schematic diagrams of the attraotive i&era&ions in the orthorhombic structure. (a) and (b) The contacts to the sodium ions. Parallel he&es I and V are it (z = 0, y = 0) and (z = a, y = 0). The other ohains are anti-parallel to these. Helix II is at (z = -a/2, y = a/2), III at (z = -a/2, y = -a/2) and IV is at (z = a/2, y = b/2). (c) and (d) The intermoleoular hydrogen bonds. The helices are the same as in (a) and (b). In (d) the water molecule, W,,,, co-ordinated to helices I and V is the one whose co-ordinates are listed in Table 8 and which binds to the sodium ion, Na ta,, shown. The related moleoule, W,,,, is included to show the completion of the hydrogen bonds between helioes II and IV.
L-l
378
J. M. CUSS
ET
TABLE
AL.
8
Cartes&n co-ordinates for a tetrasaccharide f-es&e of sodium hyaluronate in the orthorhombic lattice Atom
z (Ml
x 104)
y (nm x 10’)
Gluouronete C (11 C (1) c (31
C (41 cm
C tea 0 (11 0 (2) 0 (31 0 (4) 0 (5) 0 (80) 0 (86) H (11 Hm, H (3) H (44 J%,
C (71 C (8) 0 (7) H (aa) Hwm, H (80) H(N)
636 -747 -671 369 1698 2744 637 - 1949 673 1617 4067 1021 -1167 -399 19 2093 2649 2696 -1668 -3021 -3828 - 3624 - 3344 -3886 -4843 - 1303
cm c (2) c (3)
Gluouronete - 2477 - 3703 -4237
c (41 C(5)
C (61 O(l) O(3) O(4)
0 (51 0 WL) H (11 H(a) H (3) H(4) Hw
H wll H (Bb) N
x 10”)
(residue A,)
2633 3166 2111 1641 1203 832 3663 3611 2668 637 2270 -380 1784 1761 4071 1263 2461 326
-2333 -3519 -3990 -2826 - 1662 -430 - 1866 -4668 -6010 -3222 -1281 -336 334 -2641 - 3226 -4417 - 2600 - 1960
IV-aoetylgluooswnine C (11 C (91 C (3)
2 (ml
1642 2442 3441 4303 3421 4219 841 1649 4272 6116 2638 4610 4486 1061 2978 2902 2828
(residue B,) -2944 -3094 -2941 -3893 -3722 -4721 -3222 -3219 -3628 -3914 - 4269 - 1934 -4084 -1906 -4930 -2713 -4890 -6672 - 2086 -2286 - 1182 -3261 -867 -326 - 1646 - 1313
(residue A‘ + 11 -2246 - 2822 - 1846
6472 7094 9181 8463 8902 6116 9181 10667 7042 8634 6673 6846 8867 9069 8641 9986 6609 6694 6967 7129 6020 6646 6740 6084
10018 10714 11762
HYALURONIC
Atom
C (4) C(6) C (6) 0 (1) 0 (3) 0 (3) O(4)
0 (6) 0 (60) 0 cab) H (1) H (1) H (3) H (4) H (6)
x (nm x 10’) Clucuronate -3126 -1917 -736 -1949 -4698 - 6298 -33574 - 1480 - 1030 386 -2769 - 3434 -4639 -2832 -2187 N-aoety&hooaamine
C (11 cm
C (3) C (4) C (6) C (6) (1) :
(3) 0 (4.) 0 (6) 0 (6) H (1) Ho, H(a) H (4) Ho,
H (30) H cab) N cm
C(a) O(7) H (80) H (3b) H (8C) H (N) N%l, %a, W(l)
w(a) W(a) W(4)
- 3400 -3486 -3446 -4612 -4394 - 6600 -3674 -3663 -4360 - 4472 -6102 -2439 -4421 -2463 - 6608
- 3433 -6770 - 6380 -2371 -2612 - 1388 -3702 -962 -1672 -647 -1607 - 1087 2161 396 4363 -3301 4133
ACID
y (mu x 10’)
(residue Al+ l)-con&wed -1430 -932 -609 -3219 -3122 - 2460 -382 - 1938 -197 -797 - 1328 - 3769 -966 -2290 -18 (residue B, + 1) -681 770 696 -396 -1690 -2676 -382 1866 -701 - 1413 - 4020 - 1069 1273 226 42 -2176 -22696 -2460 1629 2968 3722 3493 3213 4748 3766 1266 940 -603 1334 -1981 664 1777
379
2 (ml
x 104)
12706 11921 12811 9181 9743 12486 13664 10994 13963 12289 9480 11206 11246 13326 11371
14928 16626 17136 17681 16783 17099 13664 17771 18966 lb376 16839 lb168 lb339 17436 17424 17010 18163 16480 lb166 14936 14473 lb092 13600 14196 16286 16033 2449 10498 10464 10186 748 4319
Wo, to W,,, refer to the oxygen atoms of the water molecules. The crystallographioally nonequivalent residues of the tetraswcharide are labelled i and i + 1. The spaae-group symmetry is P2,2,2, in a non-standard setting. The 2l axis parallel to a passes through z = 0, y = 0 and the 2r ti parallel to z is in the a = 0 plane. To form the 2 residues of the up-pointing ohain the symmetry operations we x, y, a and -x, -y, c/2 + z. For the down-ohain the symmetq operations are a/2 + 2. b/2 - y, --z and a/2 - z, b/2 + y, c/2 - z.
J. M. GUSS
380
ET
AL.
Despite the good overall agreement with the X-ray amplitudes a number of reflexions on the equator and layer line 1 = 3 that are below the threshold for observation have large calculated amplitudes. This could be due to there being water molecules in sites we have not detected (perhaps because they are not occupied in every unit cell). (b) Polysm&&de
chai?asof the orthorhombic structure
Refinement of the backbone conformation angles in the orthorhombic structure resulted in values differing on average by only 5” (maximum 14”) from those in the tetragonal structure. As a result of these changes the short contacts, O&---C&, across the 1 -+ 3 linkages were improved to 0.270 nm and 0.271 nm. The hydrogen bonds across the linkage now have lengths of O&~-H---Of’,,i+l 0.269 run; 0.257 nm; O&+,-H---O& 0.292 nm; N;-H---O&,; NfL-H---o&)d+l o-295 nm. Somewhat larger shifts occurred in the side-chain conformations (Fig. 11). This was expected since the side chains are intimately involved in the interchain packing. The orientation angles for the two non-equivalent carboxylate groups of the tetrasaccharide unit differ by about 60”.
H(N)’
(d)
HB(6b)
(e)
FIQ. 11. Projections showing the conformations Conventions are the same &s for Fig. 6. (a), (b) and (c) are for residue i. (d), (e) and (f) em for residue i -I- 1.
of the side chains in the orthorhombic
structure.
HYALURONIC
ACID
381
(c) Chain packing and cation association8 in the orthorhombic stmctwre The relationship (pl = -t+) between the polysaccharide chains implies the symmetry P2,2,2,. Relaxing the relationship again yields no significant reduction in Q. A schematic diagram of the interchain contacts involving hydrogen bonds is shown in Figure 10(b). The overall result is that the same chains are linked in essentially the same manner in both tetragonal and orthorhombic structures, with water molecules bridging the gaps caused by the extension of the lattice in the orthorhombic form. For one disaccharide of the repeating tetrasaccharide unit, the corner-to-corner hydrogen bond, O&+,-H---O&, is retained with little change in length from the tetragonal structure. Calculation of the angles C&,-O&i---O~~,+l (155”) and C&+I-O&i+l---O&i+l (121’) suggests that Ocej is the more probable interaction found in the tetragonal form is replaced donor. The O&i+l-H---O&+l by a bridge through a water molecule O&+,---W~y~---O~7),+,. This same water molecule completes the co-ordination shell about Na,,, and can also accept a hydrogen bond from O&. For the other disaccharide both the equivalent interactions are through water molecules O&, ---w(,,---o&i For and O& ---Wc2j---O&,+,. both disaccharides the hydrogen bonds between antiparallel chains are the same as in the tetragonal structure, though slightly longer. Three-dimensional Fourier difference synthesis also indicates a fourth water molecule WC*, interacting with O& and O&~~t+I of antiparallel chains. The inclusion of this water molecule caused & substantial (15%) reduction in calculated values of F(200) and P(203) : apparently these reflections are relatively sensitive to minor changes in the overall distribution of electron density. The network of hydrogen bonds is further supplemented by contacts to the sodium ions which involve a number of different polysaccharide chains (Fig 10(a)). One sodium ion, Nat,,, is involved in contacts to three hyaluronate chains and a single water molecule. The second sodium ion, Nacz,, makes only four contacts to the original six oxygen atoms but is also co-ordinated to two water molecules. One of these, Wcz,, is hydrogen-bonded to O&, so that this linkage, Na . . . O& in the tetragonal structure is restored via a water bridge, Nao, . . , W,,,----O&. The overall chain packing is shown in Figure 12.
9. Discussion and Conclusions We have described a general strategy for analysing fibrous polymer structures where the X-ray diffraction data alone (because of their characteristically small number and limited resolving power) require to be supplemented by stereochemical information. Using the linked-atom least-squares approach we maintain standard bond lengths and bond angles and (in this instance) standard pyranose ring shapes. The polymer conformation and packing are then varied to minimize steric compression (represented by overshot non-bonded contacts) or to optimize the fit with X-ray amplitudes or to do both simultaneously. Potential hydrogen bonds are recognised and can be removed from the list of repulsive interactions and even, when desired, maintained near standard lengths. Additional non-polymeric components such as cations and water molecules, detected by systematic trial of likely sites or in Fourier syntheses of electron density, can be added to the structure and their
1
t
3.39 nm 3.39
+
t
o&9
(al
nm ---*
“Ill
I
t
I.153 nm +
(b)
A
FIU. 12. Viewe of the rafined orthorhombia struoture of sodium hyaluronate. Conventiona are the game as for Fig. 7. The sodium ions are shown &B NAI and NA2. (a) View along the (100) direction; (b) view along the (010) dire&ion; (a) view along the (110) direotion.
HYALURONIC
ACID
343
positions and contacts optimized simultaneously with the refinement of the polymeric part of the structure. We have applied this strategy to a tetragonal form of sodium hyaluronate that contains little or no water. Various models for the polyanion have been considered. We have rejected an antiparallel double helix on three grounds: first, we have found it impossible to build any model that is free of considerable steric compression; second, even when we concede what would normally be unacceptable steric compression, the fit between the observed and model X-ray amplitudes is very poor; third, Fourier difference syntheses with single chain models providing the approximate phases indicate that the second chain in the unit cell is not coaxial with the f&t. In contrast, structures with non-coaxial chains are not sterically compressed and the fit with the X-ray amplitudes is as good as we have found for other fibrous structures. Structures with left-or right-handed helices fit the X-ray amplitudes equally well, but only left-handed helices lead to an extensively hydrogen-bonded structure in which every pot’ential donor indeed participates in hydrogen bonding. In this structure there is a unique set of sodium ion sites where sodium is octahedrally coordinated with six oxygen atoms from three hyaluronate chains. WC have also made an investigation of R more hydrated sodium hyaluronate structure that has orthorhombic symmetry but is apparently very similar in many respects to the tetragonnl form. In the orthorhombic structure we have located the sodium ions and some additional water molecules-four per tetrasaccharide. In both structures the similar molecular conformations are stabilized intramolecularly by O-H---O hydrogen bonds across the 1 -+ 3 glycosidic linkages and N-H---O hydrogen bonds across the 1 -+ 4 linkages, and intermolecularly by a network of hydrogen bonds and 0 . . . Na+ . . . 0 bridges. The dehydrated, tetragonal form contains no detectable water and the oxygen atoms in the octahedral co-ordination shells of the sodium ions are perforce part of the polyanion structures. (Three polysaccharide chains conhribute oxygen atoms to the co-ordination shell of any sodium ion.) In the high humidity, orthorhombic form at least four water molecules per tetrasaccharide appear to have been intruded. (Two are bound to one of the two sodium ions associated with each tetrasaccharide unit and one to the second sodium.) The polyanion conformations, hydrogen bondings and ionic bridges between chains are very similar to those in the tetragonal structure except that a few of the direct’ interactions between chains have been replaced by water bridges. The work at Purdue w&9 supported by grants to one of us (S. A.) from the National Science Foundation (7420505) and National Institutes of Health (GM20612). Two other authors (J. M. G. and W. T. W.) were fellows of the U.S. Arthritis Foundation and another author (D. W. L. H.) was a Jane Coffin Childs Memorial Fellow.
REFERENCES Anderson, N. S., Campbell, J. W., Harding, M. M., Rees, D. A. & Samuel, J. W. B. (1969). J. Mol. Biol. 45, 85-99. Arnott, S. & Hukins, D. W. L. (1973). J. Mol. Biol. 81, 93-106. Arnott, S. & Scott, W. E. (1972). J. Chem. Sot. Perkin Tram. II, 324-335. Arnott, S. & Wonaeott, A. J. (1966). Polymer, 7, 157-166. Arnott, S., Guss, J. M., Hukins, D. W. L. & Mathews, M. B. (1973ct). ScievLce, 180, 743-745. 26
J. M. GUSS ET
384
AL.
Arnott,
S., Guss, J. M., H&ins, D. W. L. & Mathews, M. B. (1973b). Biochem. Biophys. Res. Ccmmun. 54, 1377-1383. Arnott, S., GUSI, J. M., Hukins, D. W. L., Dea, I. C. M. & Rees, D. A. (1974a). J. Mol. Biol.
Arnott, Arnott,
88, 175-185.
S., Scott, W. E., McNab, C. G. A. & Rees, D. A. (1974b). J. Mol. Biol. 90, 253-268. S., Fulmer, A., Scott, W. E., Dea, I. C. M., Moorhouse, R. & Rees, D. A. (1974c).
J. Mol.
Atkins, Atkins, Atkins, Atkins,
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