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Crystallography of hemerythrin
J. Mol. Bid. (1974) 88, 125-131
Crystallography
of Hemerythrin
A. C. T. NORTH? AND G. J. STUBBS~ Laboratory of Molecular Biophykx, Department of Zoology Xouth Parks Road Oxford OX1 3PS, England (Received 6 July 1973, and in revised j’orm 16 May 1974) X-ray crystallographic studies of hemerythrin from GoZfingia gouldii show that the molecules pack in a tetragonal cell with two sets of molecules in an apparently face-centred array seen in projection along the 4-fold axis, but displaced relatively to each other by approximately c/10 in the axial direction. Both sets of molecules lie on C-fold rotation axes, so that the subunits of each octameric molecule are related in pairs by a molecular 4-fold rotation axis. The two subunits of each pair are probably related by non-crystallographic Z-fold rotation axes perpendicular to the 4-fold axes and lying at 10” and 55’ to the a and b axes. At low resolution the subunits are apparently arranged approximately in the form of a square prism. Along each 4-fold crystallographic axis there are two hemerythrin molecules, nearly equidistant and having similar but not identical orientations.
1. Introduction Hemerythrin.is a protein that occurs in several simple invertebrates, including the sipunculid worms. -It contains iron, but no haem group, and its function appears to be the transport of oxygen. Its properties have been reviewed by Klotz (1971). The work described here was carried out on the hemerytbrin of the sipunculid GolJilzgia gouldii, in the form of an azide derivative, which is extremely stable and co-ordinated in a similar way to the physiologically active oxy-derivative (Garbett et aE., 1969). The molecular weight is 108,000 and Klotz & Keresztes-Nagy (1963) have found eight subunits, each of 113 amino acid residues and containing two iron atoms. The sequence is known (Klippenstein et al., 1968) and the subunits appear to be identical, though there are minor variants involving two of the ammo acids.
2. Crystal Growth and Unit Cell Parameters Crystals were grown in 4 to 8 weeks by dialysis of 5% solutions of hemerythrin against mixtures of dipotassium hydrogen phosphate and sodium dihydrogen phosphate. Phosphate concentrations were between 2.2 and 2.4 M, pH 7, and all solutions were O-01 M in sodium azide. Crystals were needles, with dimensions up to 0.3 m x O-4 mm x 0.8 mm. From X-ray diffraction precession photographs, the Laue group of the crystals is shown by symmetry to be 4/m and, since there are no systematically absent reflections on the z-axis, the space group is P4. The unit cell dimensions are a = b = 96.9 A, c = 100.4 4. :-‘t Present address: Astbury Department of Biophysics, England. $ Present address : Abteilung Biophysik, Max-Planck D6900 Heidelberg, W. Germany. 125
University Institut
of Leeds, Leeds LS2 SJT, fur Medizinische
Forschung,
A. C. T. NORTH
126
Matthews asymmetric
AND
G. J. STUBBS
(1968) has shown that for a large number of proteins, the volume of the unit divided by the molecular weight of protein in the asymmetric unit,
Vm, lies between
1.5 and 3.5 A3/dalton.
If we assume
1 hemerythrin
molecule
of weight
108,00O/asymmetric
unit of the crystal, Vna has a value of 2.2 A3/dalton, near the centre range; Vm would lie well outside the range for either l/2 molecule or 2
of Matthews’s molecules/asymmetric‘unit. We conclude, with 1 molecule in the asymmetric unit.
therefore,
that
there
are 4 molecules/unit
cell
3. Precession Photographs In Plates I, II and III the principal projection hk0, the diagonal projection Ml, and the principal projection hOl are shown. Three features demand explanation. The first is the existence of apparently systematic absences in the hk0 projection,
only reflections
with h + k even being present.
These absences are maintained to the edge of a 17” precession film, that is, 2.8 A resolution. The second feature is the symmetry of the intensity distribution about axes lying at angles of about 10” and 55” with the crystal axes. The third feature is the markedly striped appearance of the diagonal projection kkl, resulting from a modulation in diffracted intensity with maxima when I w 5 x 2n and minima when 1 M 5 x (2n + 1). The ho1 projection exhibits a tendency towards a related modulation, with minima when 1 = 5 x (2n + 1) for h even and when 1 w 5 x 2n for h odd. We note also that, in the hOZprojection, rows with 1 even are considerably stronger than rows with 1 odd, at least at comparatively low angles. We consider the implications of these features
below. (a) Centring
of tlhe hk0 projection
The absences in the hk0 projection imply that the projection of the structure down c is face-centred, although the structure as a whole is not. We presume therefore that molecular features exist in pairs of similar orientation and face-centred in disposition when projected parallel to c, but with different z co-ordinates. This pseudo symmetry leads to the appearance of additional symmetry elements that apply only
FIG. 1. Projection along z of the P4 unit cell. Solid lines mark the true crystallographic asymmetric units, Broken lines mark the pseudo asymmetric units. The 2-fold and 4-fold axes of rotation are marked as solid symbols in the unit cell, and as open symbols in the pseudo unit cell. Solid and open commas mark equivalent positions in the real and pseudo cells.
PLATE I. A 17” precession procal axes am marked. The marked M.
photograph of the hk0 projection of tetragonal hemerythrin. apparent axes of symmetry at 10” to the crystallographic
Rcciaxes are
‘PLATE II. A 17” precession photograph
of the diagonal projection
kkl of tetragonal
hemerythrin.
PLATE
III.
A 17” precession
photograph
of the h0Z projection
of tetragonal
hemerythrin.
CRYSTALLOGRAPHY
OF HEMERYTHRIN
127
to the projected view of the structure. The positions of these pseudo symmetry elements are shown in Figure 1, from which it can be seen that 4-fold pseudo rotation axes are superimposed on the true Z-fold axes and that an additional set of 2-fold pseudo rotation axes appears at the intersections of the diagonals between the real and pseudo 4-fold axes. Since we have concluded that there is only one molecule per asymmetric unit iu the crystal, these additional symmetry elements can only be explained in terms of symmetry within each molecule, the molecule lying on a special position in the pseudo face-centred cell, which contains only two molecules in four equivalent positions. We consider three possible such situations, with the molecules lying, respectively : (a) on the pseudo Z-fold axes (b) on the pseudo 4-fold, true 2-fold axes (c) on the true 4-fold axes. To distinguish between these situations, we must also consider the other features of the diffraction pattern. (b) Striped appearance
of the kkl projection
The stripes are so marked and even in separation that they can arise only as the Fourier transform of two identical points, approximately c/l0 apart, convoluted with the molecular and lattice transforms. Thus, each molecular feature must be associated with a similar feature having the same orientation and separated by a distance c/IO in projection on to the x-axis but displaced in x and y. It is this difference in x co-ordinate that distinguishes the features related by the pseudo symmetry and we now make use of this information in comparing the three situations described in the preceding section. Situation (a) Each molecule lies on a pseudo Z-fold axis, the four molecules in the unit cell being related by the real $-fold axis. Thus each molecule consists of identical halves related to each other by a rotation of 180” and a translation of c/10 parallel to x. Such a translation we regard as inherently improbable, since it leads to the two halves being non-equivalent (the combination of translation and rotation leads to equivalent subunits only in the case of an infinite polymer and all the physical chemical evidence (Langerman & Klotz, 1969) points to hemerythrin being a stable octamer with equivalent subunits).
Situation (b) Since there are only two pseudo 4-fold (true 2-fold) axes in the unit cell, there would have to be two molecules on each. The c/10 separation between equivalent structural units could arise in two ways. First, between the two halves of each single molecule; this we regard as improbable, since it leads to non-equivalence of subunits, as discussed under situation (a). Second, between the two molecules on each axis; each molecule would have two identical halves related by the true 2-fold axis and the translation between molecules might be pure or accompanied by a 90” rotation. If two molecules are separated along the x direction by c/10, each can be no more than c/10 thick in that direction, the pair of molecules being c/5 thick. There would then need to be a gap of 4~15 before the next pair of molecules related by the unit cell translation. The second pair of molecules in the unit cell have the same z co-ordinates as the first, being related by the true 4-fold axis, so that the crystal
12%
A. C. T. NORTH
AND
G. J. STUBBS
would contain layers of molecules roughly c/S thick, separated by mother liquor 4~15 thick. We consider this to be such an unlikely packing arrangement that it may be ruled out. Situation (c) There are two true 4-fold axes in the unit would be two molecules on each. The pair of molecules on pair on the other by the pseudo 2-fold axis. A translation pairs would account for the observed interference function limitation on the shape of the individual molecules and equivalence of subunits.
cell, so that again, there one axis is related to the of c/IO between the two without any implausible without departure from
(c) Molecdar packing in hemerythrin The vast amount of chemical information obtained by Klotz and others (Klotz, 1971) is completely in favour of equivalent subunits. Furthermore, Monod et al. (1965) have argued against the formation of stable oligomers of non-equivalent subunits, in psrticuler because of the possibility of formation of infinite helices, or at least a range of oligomers. Langerman & Klotz (1969) have demonstrated the overwhelming stability of the octamer of hemerythrin, to the exclusion of all other oligomers. For these reasons, situation (c) is the only acceptable arrangement of hemerythrin molecules in this crystal form. With the evidence considered so far, we are able to conclude that the hemerythrin molecules lie on 4-fold rotation axes, so that their eight subunits must be arranged in four identical pairs; we conclude also that there are two molecules on each such axis, those on the axis through x = y = 05 being displaced in the z direction by very close to c/10 with respeot to those on the axis through x = y = 0. There remain to be determined the relationships between the two molecules on each axis and the positions of further symmetry elements relating the subunits of each molecule.
4. Three-dimensional
Patterson Synthesis
In order to study the arrangement of subunits in more detail, we have calculated a Patterson synthesis of the protein to a resolution of 8 A using a three-dimensional set of data measured on a Hilger and Watts four-circle diffractometer. In space group P4, the only Harker section is the (z~,w,O)plane, which was found to contain two sharp peaks (in addition to the origin) at (O-48, O-42, 0) and at (0.09, 0.06, 0) of heights, respectively, 20% and 14% of the origin (Fig. 2). In this space group, a molecular feature at (x,y,x) gives rise to two Harker peaks, one at (x-y, x+y, 0), and another of half the weight at (22, 2y, 0). The observed peaks may thus be interpreted in terms of a feature at (0.45, -0.03, z). The section at w = 0.50 is very like the Harker section, and so suggests an approximate translation of half a unit cell along z. This observation corresponds with the fact that reflections with 1 odd are generally weaker than those with 1 even, as may be seen in Plates II and III. We believe, therefore, that we can say that the two molecules along each of the 4-fold axes are approximately ic apart, and have very similar orientations about, t,he $7axis. It is also possible to obtain more precise information from the Patterson synthesis about the translation between the molecules on the two sets of 4-fold axes. If there are indeed two sets of molecules having the same orientation, but translated with
CRYSTALLOGRAPHY
OF HEMERYTHRIN
a/2
b/2
0
FIG. 2. The Patterson
synthesis
of hemerythrin
at 8 A resolution.
Sections of constant
2~.
respect to each other by (4, +, z), the (4, 3, w) line of the Patterson should be predictable by taking the density on the (O,O,w) hue, halving it, translating it by +x and -x, and adding the two results. This calculation was performed for several values of x, and the result agreeing best with the observed vector density along (4, 4, w) is shown in Figure 3. From this result the z component of the molecular translation may be given more accurately as (0.090 5 0.003)~.
5. Arrangement of the Subunits in each Molecule An octamer in which the subunits have equivalent geometries can exist either as a ring having an S-fold symmetry axis, or as a square prism having a 4-fold axis perpendicular to four Z-fold axes. (With subunits of regular shape, such as spheres, one can distinguish between a prism in which the upper set of four units is superimposed on the lower set when viewed down the 4-fold axis and an antiprism or dihedral ring in which the two sets are staggered ; no such formal distinction is possible when the subunits are irregular, as are protein subunits.) Both the &fold ring and the square prism would be compatible with the 4ufold symmetry required by the crystal cell. However, it is clear from the hk0 photograph with its strongly 4-fold transform that 9
A. C. T. NORTH
AND
G. J. STUBBS
Pm. 3. The Patterson synthesis of hemerythrin at 8 A resolution, line represents observed density. The broken line represents density (0, 0, w) on the basis of a molecular translation of (0.5, 0.5, 0.09).
line at (6, 4, w). The solid calculated from the line at
the subunits cannot be arranged around an g-fold molecular axis. The marked contrast between the strong lobes and the weak spaces between them exhibited by the hk0 transform suggests that, insofar as the subunits might appear to be spherical at low resolution, the molecule is more like a prism than an antiprism. The striking mm symmetry of the hk0 photograph about axes inclined to a and b suggests that the a-fold rotation axes that relate the subunits in the “upper” square of the prism to those in the “lower” square lie at approximately 10” and 55” to a and b. Again, this relationship would not be so clearly apparent if there were any substantial rotation between the two molecules on each 4-fold axis or between the molecules on the 0 0 x axis and those on the 4 4 z axis.
FIG. 4. The proposed molecular packing arrangement of hemerythrin. Projection along the z axis. Circles represent subunits. Broken lines represent non-crystallographic 2-fold axes of symmetry.
CRYSTALLOGRAPHY
OF HEMERYTHRIN
131
We note that the feature at (0.45, -0G3, z) suggested by the Patterson function does not appear to conform to the molecular symmetry that we have proposed, since it occurs only four times per molecule, nor does it lie along one of the non-crystallographic axes. As it lies so far from the centre of the molecule, it may well relate to the boundary regions between molecules or to contrast between protein and solvent and thus not be subject to the local 422 symmetry of an individual hemerythrin molecule. The molecular packing arrangement that we propose is illustrated in Figure 4. The feature of the packing for which we can offer no definite explanation at present is the distinction between the two molecules on each 4-fold axis. For, while the most likely explanation for the approximate halving of the cell along Gwould be for alternate molecules to be equally spaced but rotated about c so as to permit more favourable packing interactions, the Patterson function and the intensity di.stribution in the l&O zone suggests that any such rotation must be quite small. The Patterson function would be consistent with a small relative rotation, a small axial translation or a combination of the two. Further analysis of the problem must await the extension of the crystallographic studies to higher resolution. However, a somewhat analogous situation is shown by the stacked disk form of reconstituted tobacco mosaic virus protein (Klug & Durham, 1971) and the Dahlemense strain of intact tobacco mosaic virus (Caspar & Holmes, 1969), in both of which interactions between neighbouring subunits result in a small regular perturbation of the equivalence of environment that would normally be expected for chemically identical subunits. We thank Professor I. M. Klotz for the gift of the hemerythrin used throughout this work and Dr K. Garbett for discussion. We are grateful for the helpful suggestions of a referee. One of us (G. J. S.) acknowledges the support of a Commonwealth Scholarship. REFERENCES
&spar, D. L. D. & Holmes K. C. (1969). J. Mol. Biol. 46, 99. Garbett, K., Darnall, D. W., Klotz, I. M. & Williams, R. J. P. (1969). Arch. Biochem. Biophya. 135, 419-434. Klippenstein, G. L., Holleman, J. W. & Klotz, I. M. (1968). Biochemistry, 7, 3868-3878. Klotz, I. M. (1971). In Biological Macromolecules (Timasheff, S. and Fasman, G., eds), vol. 5, Dekker, New York. Klotz, I. M. & Keresztes-Nagy, 8. (1963). Biochemistry, 2, 445-452. Klug, A. & Durham, A. C. H. (1971). Cold Spring Harbor Xymp. Qua&. Biol. 36, 449. Langerman, N. R. & Klotz, I. M. (1969). Biochemistry, 8, 47464752. Matthews, B. M. (1968). J. MoZ. BioZ. 33, 491-497. Monod, J., Wyman, J. & Changeux, J. (1965). J. Mol. BioZ. 12, 88-118.
Crystallography
of Hemerythrin
A. C. T. NORTH? AND G. J. STUBBS~ Laboratory of Molecular Biophykx, Department of Zoology Xouth Parks Road Oxford OX1 3PS, England (Received 6 July 1973, and in revised j’orm 16 May 1974) X-ray crystallographic studies of hemerythrin from GoZfingia gouldii show that the molecules pack in a tetragonal cell with two sets of molecules in an apparently face-centred array seen in projection along the 4-fold axis, but displaced relatively to each other by approximately c/10 in the axial direction. Both sets of molecules lie on C-fold rotation axes, so that the subunits of each octameric molecule are related in pairs by a molecular 4-fold rotation axis. The two subunits of each pair are probably related by non-crystallographic Z-fold rotation axes perpendicular to the 4-fold axes and lying at 10” and 55’ to the a and b axes. At low resolution the subunits are apparently arranged approximately in the form of a square prism. Along each 4-fold crystallographic axis there are two hemerythrin molecules, nearly equidistant and having similar but not identical orientations.
1. Introduction Hemerythrin.is a protein that occurs in several simple invertebrates, including the sipunculid worms. -It contains iron, but no haem group, and its function appears to be the transport of oxygen. Its properties have been reviewed by Klotz (1971). The work described here was carried out on the hemerytbrin of the sipunculid GolJilzgia gouldii, in the form of an azide derivative, which is extremely stable and co-ordinated in a similar way to the physiologically active oxy-derivative (Garbett et aE., 1969). The molecular weight is 108,000 and Klotz & Keresztes-Nagy (1963) have found eight subunits, each of 113 amino acid residues and containing two iron atoms. The sequence is known (Klippenstein et al., 1968) and the subunits appear to be identical, though there are minor variants involving two of the ammo acids.
2. Crystal Growth and Unit Cell Parameters Crystals were grown in 4 to 8 weeks by dialysis of 5% solutions of hemerythrin against mixtures of dipotassium hydrogen phosphate and sodium dihydrogen phosphate. Phosphate concentrations were between 2.2 and 2.4 M, pH 7, and all solutions were O-01 M in sodium azide. Crystals were needles, with dimensions up to 0.3 m x O-4 mm x 0.8 mm. From X-ray diffraction precession photographs, the Laue group of the crystals is shown by symmetry to be 4/m and, since there are no systematically absent reflections on the z-axis, the space group is P4. The unit cell dimensions are a = b = 96.9 A, c = 100.4 4. :-‘t Present address: Astbury Department of Biophysics, England. $ Present address : Abteilung Biophysik, Max-Planck D6900 Heidelberg, W. Germany. 125
University Institut
of Leeds, Leeds LS2 SJT, fur Medizinische
Forschung,
A. C. T. NORTH
126
Matthews asymmetric
AND
G. J. STUBBS
(1968) has shown that for a large number of proteins, the volume of the unit divided by the molecular weight of protein in the asymmetric unit,
Vm, lies between
1.5 and 3.5 A3/dalton.
If we assume
1 hemerythrin
molecule
of weight
108,00O/asymmetric
unit of the crystal, Vna has a value of 2.2 A3/dalton, near the centre range; Vm would lie well outside the range for either l/2 molecule or 2
of Matthews’s molecules/asymmetric‘unit. We conclude, with 1 molecule in the asymmetric unit.
therefore,
that
there
are 4 molecules/unit
cell
3. Precession Photographs In Plates I, II and III the principal projection hk0, the diagonal projection Ml, and the principal projection hOl are shown. Three features demand explanation. The first is the existence of apparently systematic absences in the hk0 projection,
only reflections
with h + k even being present.
These absences are maintained to the edge of a 17” precession film, that is, 2.8 A resolution. The second feature is the symmetry of the intensity distribution about axes lying at angles of about 10” and 55” with the crystal axes. The third feature is the markedly striped appearance of the diagonal projection kkl, resulting from a modulation in diffracted intensity with maxima when I w 5 x 2n and minima when 1 M 5 x (2n + 1). The ho1 projection exhibits a tendency towards a related modulation, with minima when 1 = 5 x (2n + 1) for h even and when 1 w 5 x 2n for h odd. We note also that, in the hOZprojection, rows with 1 even are considerably stronger than rows with 1 odd, at least at comparatively low angles. We consider the implications of these features
below. (a) Centring
of tlhe hk0 projection
The absences in the hk0 projection imply that the projection of the structure down c is face-centred, although the structure as a whole is not. We presume therefore that molecular features exist in pairs of similar orientation and face-centred in disposition when projected parallel to c, but with different z co-ordinates. This pseudo symmetry leads to the appearance of additional symmetry elements that apply only
FIG. 1. Projection along z of the P4 unit cell. Solid lines mark the true crystallographic asymmetric units, Broken lines mark the pseudo asymmetric units. The 2-fold and 4-fold axes of rotation are marked as solid symbols in the unit cell, and as open symbols in the pseudo unit cell. Solid and open commas mark equivalent positions in the real and pseudo cells.
PLATE I. A 17” precession procal axes am marked. The marked M.
photograph of the hk0 projection of tetragonal hemerythrin. apparent axes of symmetry at 10” to the crystallographic
Rcciaxes are
‘PLATE II. A 17” precession photograph
of the diagonal projection
kkl of tetragonal
hemerythrin.
PLATE
III.
A 17” precession
photograph
of the h0Z projection
of tetragonal
hemerythrin.
CRYSTALLOGRAPHY
OF HEMERYTHRIN
127
to the projected view of the structure. The positions of these pseudo symmetry elements are shown in Figure 1, from which it can be seen that 4-fold pseudo rotation axes are superimposed on the true Z-fold axes and that an additional set of 2-fold pseudo rotation axes appears at the intersections of the diagonals between the real and pseudo 4-fold axes. Since we have concluded that there is only one molecule per asymmetric unit iu the crystal, these additional symmetry elements can only be explained in terms of symmetry within each molecule, the molecule lying on a special position in the pseudo face-centred cell, which contains only two molecules in four equivalent positions. We consider three possible such situations, with the molecules lying, respectively : (a) on the pseudo Z-fold axes (b) on the pseudo 4-fold, true 2-fold axes (c) on the true 4-fold axes. To distinguish between these situations, we must also consider the other features of the diffraction pattern. (b) Striped appearance
of the kkl projection
The stripes are so marked and even in separation that they can arise only as the Fourier transform of two identical points, approximately c/l0 apart, convoluted with the molecular and lattice transforms. Thus, each molecular feature must be associated with a similar feature having the same orientation and separated by a distance c/IO in projection on to the x-axis but displaced in x and y. It is this difference in x co-ordinate that distinguishes the features related by the pseudo symmetry and we now make use of this information in comparing the three situations described in the preceding section. Situation (a) Each molecule lies on a pseudo Z-fold axis, the four molecules in the unit cell being related by the real $-fold axis. Thus each molecule consists of identical halves related to each other by a rotation of 180” and a translation of c/10 parallel to x. Such a translation we regard as inherently improbable, since it leads to the two halves being non-equivalent (the combination of translation and rotation leads to equivalent subunits only in the case of an infinite polymer and all the physical chemical evidence (Langerman & Klotz, 1969) points to hemerythrin being a stable octamer with equivalent subunits).
Situation (b) Since there are only two pseudo 4-fold (true 2-fold) axes in the unit cell, there would have to be two molecules on each. The c/10 separation between equivalent structural units could arise in two ways. First, between the two halves of each single molecule; this we regard as improbable, since it leads to non-equivalence of subunits, as discussed under situation (a). Second, between the two molecules on each axis; each molecule would have two identical halves related by the true 2-fold axis and the translation between molecules might be pure or accompanied by a 90” rotation. If two molecules are separated along the x direction by c/10, each can be no more than c/10 thick in that direction, the pair of molecules being c/5 thick. There would then need to be a gap of 4~15 before the next pair of molecules related by the unit cell translation. The second pair of molecules in the unit cell have the same z co-ordinates as the first, being related by the true 4-fold axis, so that the crystal
12%
A. C. T. NORTH
AND
G. J. STUBBS
would contain layers of molecules roughly c/S thick, separated by mother liquor 4~15 thick. We consider this to be such an unlikely packing arrangement that it may be ruled out. Situation (c) There are two true 4-fold axes in the unit would be two molecules on each. The pair of molecules on pair on the other by the pseudo 2-fold axis. A translation pairs would account for the observed interference function limitation on the shape of the individual molecules and equivalence of subunits.
cell, so that again, there one axis is related to the of c/IO between the two without any implausible without departure from
(c) Molecdar packing in hemerythrin The vast amount of chemical information obtained by Klotz and others (Klotz, 1971) is completely in favour of equivalent subunits. Furthermore, Monod et al. (1965) have argued against the formation of stable oligomers of non-equivalent subunits, in psrticuler because of the possibility of formation of infinite helices, or at least a range of oligomers. Langerman & Klotz (1969) have demonstrated the overwhelming stability of the octamer of hemerythrin, to the exclusion of all other oligomers. For these reasons, situation (c) is the only acceptable arrangement of hemerythrin molecules in this crystal form. With the evidence considered so far, we are able to conclude that the hemerythrin molecules lie on 4-fold rotation axes, so that their eight subunits must be arranged in four identical pairs; we conclude also that there are two molecules on each such axis, those on the axis through x = y = 05 being displaced in the z direction by very close to c/10 with respeot to those on the axis through x = y = 0. There remain to be determined the relationships between the two molecules on each axis and the positions of further symmetry elements relating the subunits of each molecule.
4. Three-dimensional
Patterson Synthesis
In order to study the arrangement of subunits in more detail, we have calculated a Patterson synthesis of the protein to a resolution of 8 A using a three-dimensional set of data measured on a Hilger and Watts four-circle diffractometer. In space group P4, the only Harker section is the (z~,w,O)plane, which was found to contain two sharp peaks (in addition to the origin) at (O-48, O-42, 0) and at (0.09, 0.06, 0) of heights, respectively, 20% and 14% of the origin (Fig. 2). In this space group, a molecular feature at (x,y,x) gives rise to two Harker peaks, one at (x-y, x+y, 0), and another of half the weight at (22, 2y, 0). The observed peaks may thus be interpreted in terms of a feature at (0.45, -0.03, z). The section at w = 0.50 is very like the Harker section, and so suggests an approximate translation of half a unit cell along z. This observation corresponds with the fact that reflections with 1 odd are generally weaker than those with 1 even, as may be seen in Plates II and III. We believe, therefore, that we can say that the two molecules along each of the 4-fold axes are approximately ic apart, and have very similar orientations about, t,he $7axis. It is also possible to obtain more precise information from the Patterson synthesis about the translation between the molecules on the two sets of 4-fold axes. If there are indeed two sets of molecules having the same orientation, but translated with
CRYSTALLOGRAPHY
OF HEMERYTHRIN
a/2
b/2
0
FIG. 2. The Patterson
synthesis
of hemerythrin
at 8 A resolution.
Sections of constant
2~.
respect to each other by (4, +, z), the (4, 3, w) line of the Patterson should be predictable by taking the density on the (O,O,w) hue, halving it, translating it by +x and -x, and adding the two results. This calculation was performed for several values of x, and the result agreeing best with the observed vector density along (4, 4, w) is shown in Figure 3. From this result the z component of the molecular translation may be given more accurately as (0.090 5 0.003)~.
5. Arrangement of the Subunits in each Molecule An octamer in which the subunits have equivalent geometries can exist either as a ring having an S-fold symmetry axis, or as a square prism having a 4-fold axis perpendicular to four Z-fold axes. (With subunits of regular shape, such as spheres, one can distinguish between a prism in which the upper set of four units is superimposed on the lower set when viewed down the 4-fold axis and an antiprism or dihedral ring in which the two sets are staggered ; no such formal distinction is possible when the subunits are irregular, as are protein subunits.) Both the &fold ring and the square prism would be compatible with the 4ufold symmetry required by the crystal cell. However, it is clear from the hk0 photograph with its strongly 4-fold transform that 9
A. C. T. NORTH
AND
G. J. STUBBS
Pm. 3. The Patterson synthesis of hemerythrin at 8 A resolution, line represents observed density. The broken line represents density (0, 0, w) on the basis of a molecular translation of (0.5, 0.5, 0.09).
line at (6, 4, w). The solid calculated from the line at
the subunits cannot be arranged around an g-fold molecular axis. The marked contrast between the strong lobes and the weak spaces between them exhibited by the hk0 transform suggests that, insofar as the subunits might appear to be spherical at low resolution, the molecule is more like a prism than an antiprism. The striking mm symmetry of the hk0 photograph about axes inclined to a and b suggests that the a-fold rotation axes that relate the subunits in the “upper” square of the prism to those in the “lower” square lie at approximately 10” and 55” to a and b. Again, this relationship would not be so clearly apparent if there were any substantial rotation between the two molecules on each 4-fold axis or between the molecules on the 0 0 x axis and those on the 4 4 z axis.
FIG. 4. The proposed molecular packing arrangement of hemerythrin. Projection along the z axis. Circles represent subunits. Broken lines represent non-crystallographic 2-fold axes of symmetry.
CRYSTALLOGRAPHY
OF HEMERYTHRIN
131
We note that the feature at (0.45, -0G3, z) suggested by the Patterson function does not appear to conform to the molecular symmetry that we have proposed, since it occurs only four times per molecule, nor does it lie along one of the non-crystallographic axes. As it lies so far from the centre of the molecule, it may well relate to the boundary regions between molecules or to contrast between protein and solvent and thus not be subject to the local 422 symmetry of an individual hemerythrin molecule. The molecular packing arrangement that we propose is illustrated in Figure 4. The feature of the packing for which we can offer no definite explanation at present is the distinction between the two molecules on each 4-fold axis. For, while the most likely explanation for the approximate halving of the cell along Gwould be for alternate molecules to be equally spaced but rotated about c so as to permit more favourable packing interactions, the Patterson function and the intensity di.stribution in the l&O zone suggests that any such rotation must be quite small. The Patterson function would be consistent with a small relative rotation, a small axial translation or a combination of the two. Further analysis of the problem must await the extension of the crystallographic studies to higher resolution. However, a somewhat analogous situation is shown by the stacked disk form of reconstituted tobacco mosaic virus protein (Klug & Durham, 1971) and the Dahlemense strain of intact tobacco mosaic virus (Caspar & Holmes, 1969), in both of which interactions between neighbouring subunits result in a small regular perturbation of the equivalence of environment that would normally be expected for chemically identical subunits. We thank Professor I. M. Klotz for the gift of the hemerythrin used throughout this work and Dr K. Garbett for discussion. We are grateful for the helpful suggestions of a referee. One of us (G. J. S.) acknowledges the support of a Commonwealth Scholarship. REFERENCES
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