J. Mol. Biol. (1975) 93, 55-62
The Molecular Symmetry of Bovine Liver Catalase WILLL~M EVENTOFF Department of Biological Scielw;es, Purdue University West Lafayette, In-d. 47907, U.S.A. AND G. V. GDRSKAYA Institute of Crystallography, Acadamy of Sciences of the U.S.S.R. Moscow B-117333, U.S.S.R. (Received 24 September 1974, and in revised form 16 December 1974) A rotation function study of bovine liver oat&se at 10 A resolution has shown the enzyme to have at least one a-fold axis, although a molecular symmetry of 222 is likely and the molecular point group 4 is possible. The orientation of the molecular axes with respect to the crystallogmphic axes has also been determined.
1. Introduction S-ray diffraction studies of bovine liver catalase have shown that the molecule possesses at least a 2-fold axis (Glauser & Rossman, 1966; Gurskaya et d., 1971). Electron microscopy studies indicate the presence of four subunits related by ap-
proximate 222 molecular symmetry (Vainshtein et a.!., 1968). In order to determine the molecular symmetry with greater precision, a rotation function study (Rossman & Blow, 1962) of the trigonal form of bovine liver catalase using 10 A resolution X-ray diffraction data was undertaken. We report here the results of that investigation.
2. Experimental Bovine liver cat&se crystallizes with 6 molecules per unit cell in the trigonal space group P3121 with lattice constants a = 173.3 A and c = 237.4 A (Longley, 1967; Rossmann & Labaw, 1967; Vainshtein et al., 1967). X-ray diffraction data were collected by oneofus (G. V. G.) as described previously (Gurskaya et al., 1971). In calculating the rotation function, only the data between 20 A snd 10 A resolution were used. The elimination of the inner reflections has the effect of sharpening the function. The original Patterson contained 1359 observed terms which were modified to remove the origin peak (Buerger, 1959). It was compared with an unmodified large term Patterson which contained those 140 terms which were greater than 2.0 times the mean intensity. Calculations were performed using both 30 A and 50 A as the radius of integration around the Patterson origin. In all cases the 27 nearest neighbors of the non-integral reciprocal lattice point were used for interpolation, which includes most terms in the first positive node of the G function (Hr < 0.725) even for the smaller radius of integration. The explorations were performed in polar co-ordinates defined in relation to the crystallographic axes as in Rossmann & Blow (1962) except that the sense of 4 is reversed: 4 is the angle the rotation axis makes with the crystallogmphic b axis, 4 is the angle the projection of the rotation axes onto the a*c plane makes with the a* axis (measured positive between +a* and +c), K 55
56
W. EVENTOFF
AND
G. V. GURSKAYA
b
b
b
(cl
FIG. 1. Stereographio projection of the rotation fun&ion for rotationa (b) K = 120°, and (0) K = 90”, and a rediue of integration of 60 A.
with
(a)
K =
180”
defines the number of degrees of rotation about the rotation axis (measured positive 8s 010&v&e looking out from the origin). The asymmetric unit was explored only for rot&ions with K = HO”, 90’ md X20”, respectively.
3. Results and Discussion The rotation function (Fig. 1) contains large peaks which correspond to a set of octahedral 432 axes. The octahedral symmetry does not disappear on reducing the radius of integration around the Patterson origin to 30 A, and therefore represents
BOVINE
LIVER
CATALASE
57
the relations between the intramolecular Patterson vectors. However, the tetrameric nature of catalase precludes the possibility that the molecular symmetry of a single molecule is 432. In fact, as shown below, these results are consistent with each molecule of catalase posessing a lower molecular symmetry, and, as in the satellite tobacco necrosis virus rotation function (Alrervall et al., 1971a), it is the coupling of the molecular and crystallographic symmetry elements which gives rise to the high symmetry found (Klug, 1971; tQkerval1 et al., 1971b) TABLE 1 Orientation of the molecukzr e-fold axes of bovine liver c&ala-se
1 2 3
90.0 46.0 136.0
36.0 126.0 126.0
t $I 8nd C$clre defined ea given in the text. $ I, wz end n 81% direotionel cosines with with a* along x, b along y, end c along z.
0.819 -0.406 -0.406
respeotto an orthogonal
o-o o-707 -0.707
oo-ordinate
0.673 0.679 0.679
system defined
There are four possible solutions of the rotation function although one of these can be eliminated on other grounds. In the first solution, each molecule of catalase has 222 molecular symmetry and occupies a general position in the unit cell. For this discussion, let the three orthogonal molecular axes P, &, and R of each molecule be directed along the rotation function axes I,2 or 3. The three 2-fold axes, P, Q and R, are oriented along the octrahedral 4-fold axes found in the rotation function (Table 1). In this orientation (Fig. 2(a)), the e-fold axes of the six molecules in the unit cell are interrelated by the space-group symmetry. Thus, in the Patterson, there are three equivalent orthogonal directions (along the octahedral 4-fold axes) which correspond to the superpositioning of two P, two Q and two R axes. For such a special arrangement of the three molecules relative to the crystallographic 3-fold axis, the sum of the self-Pattersons at the origin contains additional octahedral symmetry interrelating these directions (Fig. 3(a)). Since all of the axes relate vectors from the same number of molecules, they appear at approximately the same height in the rotation function (Table 2). The second possible solution is also consistent with 2.22 molecular symmetry but with one of the molecular a-fold axes being coincident with a crystallographic a-fold axis. In this packing arrangement, there are two sets of three molecules which occupy special positions a and b, respectively (Interndional Tables, 1952). In one set the molecular P axes, and in the other the molecular Q axes, are coincident with crystallo. graphic 2-fold axes. The orientation of the remaining molecular S-fold axes are along the S-fold and 4-fold octahedral axes observed in the rotation function (Fig. 2(b)). The coupling of the crystallographic and molecular symmetry elements then gives rise to octahedral symmetry (Fig. 3(b)). A similar interpretation with the molecules in general positions and having one 2-fold axis parallel to, but not coincident with, the crystallographic e-fold axes is inconsistent with the results of the rotation function. In addition, the absence of a
FIG. 2.
I”\ iI I
BOVINE
LIVER TABLE
CATALASE
69
2
Height qf the octahedrally related 4-fold, 3-fold and Z-fold peaks
180.0 180.0 ISO* 120.0 120.0 90.0 Background Origin
*
4
70.0 90.0 60.0 90.0 36.0 90.0
70.0 36.0 0.0 90.0 36.0 36.0
0.0
0.0
Height 36.7 36.6 102q 102.q 36.8 34.6 12.0s 102.8
t K, a,4and 4 (in degrees) sre def?ned as given in the text. $ These peaks represent orystallograpbio axes. § The average value of a point in the rotation funotion.
large peak in the Patterson on planes that pass through the origin and are perpendicular to the crystallographic 2-fold axes rules out this possibility. The third and fourth solutions relate to molecules with e-fold (Figs 2(c) and 3(c)) or 4-fold (Figs 2(d) and 3(d)) symmetry, rather than 222 symmetry. The presence of a single molecular 2-fold or 4-fold axis oriented along an octahedral 4-fold axis is consistent with the observed octahedral symmetry. These additional two solutions arise because the rotation function does not indicate whether the three orthogonal 2-fold axes of the first solution intersect at a point in real space. The ambiguity in the interpretation of the rotation function can be partially resolved if we take into consideration the data already published on the structure of the trigonal form of catalase. According to Vainshtein et al. (1967) and Gurskaya et al. (1971) the six molecules of catalase occupy general positions in the unit cell. This is supported by the distribution of intensity of the 001 reflections. At low resolution (d 5 30 8) catalase can be represented as a sphere (r = 42 8) of uniform density. Under these conditions, if the catalase molecules occupied special positions, the difference in the orientation of the molecules occupying the two special positions could be neglected, and the following expression would be obtained for the structure factor for the 001 reflections: F = f(cos(5nr) + cos(nr) + cos(3nr) + cos(4mr) + cos(27m) + 1) where f is the scattering factor, and 1 = 3n. Thus, only every sixth reflection, corresponding to even values of n, should be present. No such systematic absence was found, in fact Fm. 2. Projeotion of the molecular symmetry axea of bovine liver oat&se on the ab plane for the following oases. (a) The molecule is in a general position and has 222 molecular symmetry. The three $-fold axes, termed P, Q and R, are directed along the octahedral 4-fold mxes observed in the rotation function. (b) The molecule having 222 moleoular symmetry oooupies 2 different speoial $-fold positions, with the remaining moleoular 2.fold axes directed along the octahedral 4-fold and 2-fold direotions observed in the rotation function. (c) The molecule is in a general position, and hae only a single 2-fold axis, P, direoted along the octahedral I-fold axes observed in the rotation funotion. (d) The molecule is in a general position and has a single 4-fold axis, P,, direoted along the octahedral a-fold axes observed in the rotation function.
W.
EVENTOFF
AND
U. V. GURSKAYA
b
(a)
c-b)
Cc)
Cd)
FIU. 3. Stereographic projection representing the different solutions of the rotation funotion (oorresponding to the 08888 (e), (b), (c) snd (d) of Fig. 2); (a) when the moleoule ia in e general position and its mutuelly perpendiouhw 2-fold axes 8re equally &lined to the orystallogr8phio 3-fold 8xes 8long the direotions given by the observed 4-fold 8xes in the rotation funotion. Superscripts 1, 2, 3 refer to the molecules related by the orystallographio 3-fold 8xes. (b) When there 8re 2 sets of molecules eaoh with 8 moleouler axis &long 8 orystallogr8phio %-fold axis. The remaining moleoular 8x8s 8re then along the direotiona given by observed 4.fold 8nd Z-fold 8xes in the rotation fun&ion. Subsoripts 1, 2 refer to the two sets of molecules, reppectively. (0) When the moleoule ia in 8 general position 8nd possesses 8 single 2-fold &is, P, along the oot8hedr814-fold axis observed in the rotetion funotion. Superscripts 1, 2, 3 refer to the moleoules related by the crystallogrephio 3.fold 8x8s. (d) When the moleoule is in 8 general position end possesses 8 single 4-fold axis, Pa, elong the octahedr814-fold clxis observed in the rotation funotion. Superaoripta 1, 2, 3 refer to the moleoulea reMed by the orystallographia a-fold axes. In 8l.l 08~s the rotation function has ootahedrctl symmetry as 8 consequence of .mmming the self-Petterson of all 6 oryst8llographio8lly related molecules at the Patterson origin.
BOVINE
LIVER
CATALASE
61
(003) is very intense. The six molecules must therefore occupy general positions in the unit cell, in agreement with the position of the molecular center reported by Barynin & Vainshtein (1971) and Gurskaya et uJ. (1971). These results disprove the second solution. Although the orientations of the molecular symmetry axes have thus been determined, the exact molecular symmetry is ambiguous. As described above, molecular symmetries of 2.22,2 or 4 are all consistent with the rotation function. The equivalence of the four subunits as well as the unlikely possibility of a tetramer with 4-fold symmetry suggests that the most probable molecular symmetry is 222. However, the other possibilities cannot be ruled out on the evidence of the rotation function alone. The same X-ray data to 30 A resolution have previously been used in conjunction with electron microscopy to determine the orientation of the molecular symmetry axes (Gurskaya et al., 1971). The present results based on the higher resolution data differ by 15” to 30” in the orientation of each axis. The rotation function of catalase, like that of satellite tobacco necrosis virus (Rossmann et al., 1973), provides an example of the high symmetry that can arise through the coupling of molecular and crystallographic symmetry elements. This additional symmetry greatly complicates the interpretation of the rotation function and a general theory for the predicting of the complete symmetry of the rotation function is needed. In the present case, other methods can distinguish between the possible solutions, and the orientations of the molecular axea have been unambiguously determined. However, an ambiguity exists as to the exact molecular symmetry of catalase. The enzyme has at least a single 2-fold axis, although molecular symmetries of 222 or 4 remain possibiltiies. The authors thank Professor M. G. Rossmann and Professor B. K. Vainshtein, in whose laboratories the computational and experimental work was done, for many stimulating discussions. We also express our gratitude to Dr G. M. Lobanova for help in experimental work and to Mrs S. Wilder and Mrs 5. Hurt0 for aid in the preparation of this manuscript. This work was supported in part by the National Institutes of Health (grant no. GM10704) and the National Science Foundation (grant no. GB29696X). One author, (W. E.) would like to express appreciation to the National Institutes of Health for a postdoctoral Biophysics traineeship. REFERENCES Akervall, K., Strandberg, B., Rossmann, M. G., Bengtsson, U., Fridborg, K., Johann&en, H.. Kannan, K. K., Lovgren, S., Petef, G., Oberg, B., Eaker, D., Hjerten, S., Ryden, L. & Moring, I. (1971a). Cold Spring Harbor Symp. Quunt. Btil. 36,469-483. Akervall, K., Strandberg, B., Rossmann, M. G., Bengtsson, U., Fridborg, K., Johannisen, H., Kannan, K. K., Lovgren, S., Petef, G., Oberg, B., Eaker, D., Hjerten, S., Ryden, L. & Moring, I. (1971b). Cold Spring Harbor Symp. Quant. Bid. 36, 487-488. Barynin, V. V. & Vainshtein, B. K. (1971). Krtilografiiya, 16, 751-763. Buerger, M. J. (1959). In Ve&w Space, p, 56, John Wiley and Sons Inc., New York. Glauser, S. & Rossmann, M. G. (1966). Acta Cry&zJZogr. 21, 175-176. Gurskaya, G. V., Lobanova, 0. M. & Vainshtein, B. K. (1971). Kristullogra~ya, 16,
764-773. Interraatirma Table-9 for X-ray Cry&a.%ography (1962), vol. 1, p. 257, Kynoch Birmingham, England. Klug, A. (1971). Cold Spring Harbor Symp. Quant. Bid. 36, 483-487.
Press,
62
W.
EVENTOFF
AND
Q. V. QURSKAYA
Longley, W. (1967). J. Mol. BioZ. 30, 323-327. Rossmann, M. G. & Blow, D. M. (1962). Acta Cryetdlogr. 15, 24-31. Rossmann, M. G. & Labaw, L. W. (1967). J. Mol. Biol. 29, 315-316. Rossmann, M. G., Akervall, K., Lentz, P. J., Jr & Strandberg, B. (1973). J. Mol. Biol. 79, 197-204. Vainshtein, B. K., Barynin, V. V., Gurskaya, G. V. & Nikitin, B. La. (1967). KristaZZogra$ya, 12, 860-867. Vainshtein, B. K., Barynin, V. V. & Gurskaya, Q. V. (1968). DokZ. Akad. Nauk. SSSR, 182, 569-572.
The Molecular Symmetry of Bovine Liver Catalase WILLL~M EVENTOFF Department of Biological Scielw;es, Purdue University West Lafayette, In-d. 47907, U.S.A. AND G. V. GDRSKAYA Institute of Crystallography, Acadamy of Sciences of the U.S.S.R. Moscow B-117333, U.S.S.R. (Received 24 September 1974, and in revised form 16 December 1974) A rotation function study of bovine liver oat&se at 10 A resolution has shown the enzyme to have at least one a-fold axis, although a molecular symmetry of 222 is likely and the molecular point group 4 is possible. The orientation of the molecular axes with respect to the crystallogmphic axes has also been determined.
1. Introduction S-ray diffraction studies of bovine liver catalase have shown that the molecule possesses at least a 2-fold axis (Glauser & Rossman, 1966; Gurskaya et d., 1971). Electron microscopy studies indicate the presence of four subunits related by ap-
proximate 222 molecular symmetry (Vainshtein et a.!., 1968). In order to determine the molecular symmetry with greater precision, a rotation function study (Rossman & Blow, 1962) of the trigonal form of bovine liver catalase using 10 A resolution X-ray diffraction data was undertaken. We report here the results of that investigation.
2. Experimental Bovine liver cat&se crystallizes with 6 molecules per unit cell in the trigonal space group P3121 with lattice constants a = 173.3 A and c = 237.4 A (Longley, 1967; Rossmann & Labaw, 1967; Vainshtein et al., 1967). X-ray diffraction data were collected by oneofus (G. V. G.) as described previously (Gurskaya et al., 1971). In calculating the rotation function, only the data between 20 A snd 10 A resolution were used. The elimination of the inner reflections has the effect of sharpening the function. The original Patterson contained 1359 observed terms which were modified to remove the origin peak (Buerger, 1959). It was compared with an unmodified large term Patterson which contained those 140 terms which were greater than 2.0 times the mean intensity. Calculations were performed using both 30 A and 50 A as the radius of integration around the Patterson origin. In all cases the 27 nearest neighbors of the non-integral reciprocal lattice point were used for interpolation, which includes most terms in the first positive node of the G function (Hr < 0.725) even for the smaller radius of integration. The explorations were performed in polar co-ordinates defined in relation to the crystallographic axes as in Rossmann & Blow (1962) except that the sense of 4 is reversed: 4 is the angle the rotation axis makes with the crystallogmphic b axis, 4 is the angle the projection of the rotation axes onto the a*c plane makes with the a* axis (measured positive between +a* and +c), K 55
56
W. EVENTOFF
AND
G. V. GURSKAYA
b
b
b
(cl
FIG. 1. Stereographio projection of the rotation fun&ion for rotationa (b) K = 120°, and (0) K = 90”, and a rediue of integration of 60 A.
with
(a)
K =
180”
defines the number of degrees of rotation about the rotation axis (measured positive 8s 010&v&e looking out from the origin). The asymmetric unit was explored only for rot&ions with K = HO”, 90’ md X20”, respectively.
3. Results and Discussion The rotation function (Fig. 1) contains large peaks which correspond to a set of octahedral 432 axes. The octahedral symmetry does not disappear on reducing the radius of integration around the Patterson origin to 30 A, and therefore represents
BOVINE
LIVER
CATALASE
57
the relations between the intramolecular Patterson vectors. However, the tetrameric nature of catalase precludes the possibility that the molecular symmetry of a single molecule is 432. In fact, as shown below, these results are consistent with each molecule of catalase posessing a lower molecular symmetry, and, as in the satellite tobacco necrosis virus rotation function (Alrervall et al., 1971a), it is the coupling of the molecular and crystallographic symmetry elements which gives rise to the high symmetry found (Klug, 1971; tQkerval1 et al., 1971b) TABLE 1 Orientation of the molecukzr e-fold axes of bovine liver c&ala-se
1 2 3
90.0 46.0 136.0
36.0 126.0 126.0
t $I 8nd C$clre defined ea given in the text. $ I, wz end n 81% direotionel cosines with with a* along x, b along y, end c along z.
0.819 -0.406 -0.406
respeotto an orthogonal
o-o o-707 -0.707
oo-ordinate
0.673 0.679 0.679
system defined
There are four possible solutions of the rotation function although one of these can be eliminated on other grounds. In the first solution, each molecule of catalase has 222 molecular symmetry and occupies a general position in the unit cell. For this discussion, let the three orthogonal molecular axes P, &, and R of each molecule be directed along the rotation function axes I,2 or 3. The three 2-fold axes, P, Q and R, are oriented along the octrahedral 4-fold axes found in the rotation function (Table 1). In this orientation (Fig. 2(a)), the e-fold axes of the six molecules in the unit cell are interrelated by the space-group symmetry. Thus, in the Patterson, there are three equivalent orthogonal directions (along the octahedral 4-fold axes) which correspond to the superpositioning of two P, two Q and two R axes. For such a special arrangement of the three molecules relative to the crystallographic 3-fold axis, the sum of the self-Pattersons at the origin contains additional octahedral symmetry interrelating these directions (Fig. 3(a)). Since all of the axes relate vectors from the same number of molecules, they appear at approximately the same height in the rotation function (Table 2). The second possible solution is also consistent with 2.22 molecular symmetry but with one of the molecular a-fold axes being coincident with a crystallographic a-fold axis. In this packing arrangement, there are two sets of three molecules which occupy special positions a and b, respectively (Interndional Tables, 1952). In one set the molecular P axes, and in the other the molecular Q axes, are coincident with crystallo. graphic 2-fold axes. The orientation of the remaining molecular S-fold axes are along the S-fold and 4-fold octahedral axes observed in the rotation function (Fig. 2(b)). The coupling of the crystallographic and molecular symmetry elements then gives rise to octahedral symmetry (Fig. 3(b)). A similar interpretation with the molecules in general positions and having one 2-fold axis parallel to, but not coincident with, the crystallographic e-fold axes is inconsistent with the results of the rotation function. In addition, the absence of a
FIG. 2.
I”\ iI I
BOVINE
LIVER TABLE
CATALASE
69
2
Height qf the octahedrally related 4-fold, 3-fold and Z-fold peaks
180.0 180.0 ISO* 120.0 120.0 90.0 Background Origin
*
4
70.0 90.0 60.0 90.0 36.0 90.0
70.0 36.0 0.0 90.0 36.0 36.0
0.0
0.0
Height 36.7 36.6 102q 102.q 36.8 34.6 12.0s 102.8
t K, a,4and 4 (in degrees) sre def?ned as given in the text. $ These peaks represent orystallograpbio axes. § The average value of a point in the rotation funotion.
large peak in the Patterson on planes that pass through the origin and are perpendicular to the crystallographic 2-fold axes rules out this possibility. The third and fourth solutions relate to molecules with e-fold (Figs 2(c) and 3(c)) or 4-fold (Figs 2(d) and 3(d)) symmetry, rather than 222 symmetry. The presence of a single molecular 2-fold or 4-fold axis oriented along an octahedral 4-fold axis is consistent with the observed octahedral symmetry. These additional two solutions arise because the rotation function does not indicate whether the three orthogonal 2-fold axes of the first solution intersect at a point in real space. The ambiguity in the interpretation of the rotation function can be partially resolved if we take into consideration the data already published on the structure of the trigonal form of catalase. According to Vainshtein et al. (1967) and Gurskaya et al. (1971) the six molecules of catalase occupy general positions in the unit cell. This is supported by the distribution of intensity of the 001 reflections. At low resolution (d 5 30 8) catalase can be represented as a sphere (r = 42 8) of uniform density. Under these conditions, if the catalase molecules occupied special positions, the difference in the orientation of the molecules occupying the two special positions could be neglected, and the following expression would be obtained for the structure factor for the 001 reflections: F = f(cos(5nr) + cos(nr) + cos(3nr) + cos(4mr) + cos(27m) + 1) where f is the scattering factor, and 1 = 3n. Thus, only every sixth reflection, corresponding to even values of n, should be present. No such systematic absence was found, in fact Fm. 2. Projeotion of the molecular symmetry axea of bovine liver oat&se on the ab plane for the following oases. (a) The molecule is in a general position and has 222 molecular symmetry. The three $-fold axes, termed P, Q and R, are directed along the octahedral 4-fold mxes observed in the rotation function. (b) The molecule having 222 moleoular symmetry oooupies 2 different speoial $-fold positions, with the remaining moleoular 2.fold axes directed along the octahedral 4-fold and 2-fold direotions observed in the rotation function. (c) The molecule is in a general position, and hae only a single 2-fold axis, P, direoted along the octahedral I-fold axes observed in the rotation funotion. (d) The molecule is in a general position and has a single 4-fold axis, P,, direoted along the octahedral a-fold axes observed in the rotation function.
W.
EVENTOFF
AND
U. V. GURSKAYA
b
(a)
c-b)
Cc)
Cd)
FIU. 3. Stereographic projection representing the different solutions of the rotation funotion (oorresponding to the 08888 (e), (b), (c) snd (d) of Fig. 2); (a) when the moleoule ia in e general position and its mutuelly perpendiouhw 2-fold axes 8re equally &lined to the orystallogr8phio 3-fold 8xes 8long the direotions given by the observed 4-fold 8xes in the rotation funotion. Superscripts 1, 2, 3 refer to the molecules related by the orystallographio 3-fold 8xes. (b) When there 8re 2 sets of molecules eaoh with 8 moleouler axis &long 8 orystallogr8phio %-fold axis. The remaining moleoular 8x8s 8re then along the direotiona given by observed 4.fold 8nd Z-fold 8xes in the rotation fun&ion. Subsoripts 1, 2 refer to the two sets of molecules, reppectively. (0) When the moleoule ia in 8 general position 8nd possesses 8 single 2-fold &is, P, along the oot8hedr814-fold axis observed in the rotetion funotion. Superscripts 1, 2, 3 refer to the moleoules related by the crystallogrephio 3.fold 8x8s. (d) When the moleoule is in 8 general position end possesses 8 single 4-fold axis, Pa, elong the octahedr814-fold clxis observed in the rotation funotion. Superaoripta 1, 2, 3 refer to the moleoulea reMed by the orystallographia a-fold axes. In 8l.l 08~s the rotation function has ootahedrctl symmetry as 8 consequence of .mmming the self-Petterson of all 6 oryst8llographio8lly related molecules at the Patterson origin.
BOVINE
LIVER
CATALASE
61
(003) is very intense. The six molecules must therefore occupy general positions in the unit cell, in agreement with the position of the molecular center reported by Barynin & Vainshtein (1971) and Gurskaya et uJ. (1971). These results disprove the second solution. Although the orientations of the molecular symmetry axes have thus been determined, the exact molecular symmetry is ambiguous. As described above, molecular symmetries of 2.22,2 or 4 are all consistent with the rotation function. The equivalence of the four subunits as well as the unlikely possibility of a tetramer with 4-fold symmetry suggests that the most probable molecular symmetry is 222. However, the other possibilities cannot be ruled out on the evidence of the rotation function alone. The same X-ray data to 30 A resolution have previously been used in conjunction with electron microscopy to determine the orientation of the molecular symmetry axes (Gurskaya et al., 1971). The present results based on the higher resolution data differ by 15” to 30” in the orientation of each axis. The rotation function of catalase, like that of satellite tobacco necrosis virus (Rossmann et al., 1973), provides an example of the high symmetry that can arise through the coupling of molecular and crystallographic symmetry elements. This additional symmetry greatly complicates the interpretation of the rotation function and a general theory for the predicting of the complete symmetry of the rotation function is needed. In the present case, other methods can distinguish between the possible solutions, and the orientations of the molecular axea have been unambiguously determined. However, an ambiguity exists as to the exact molecular symmetry of catalase. The enzyme has at least a single 2-fold axis, although molecular symmetries of 222 or 4 remain possibiltiies. The authors thank Professor M. G. Rossmann and Professor B. K. Vainshtein, in whose laboratories the computational and experimental work was done, for many stimulating discussions. We also express our gratitude to Dr G. M. Lobanova for help in experimental work and to Mrs S. Wilder and Mrs 5. Hurt0 for aid in the preparation of this manuscript. This work was supported in part by the National Institutes of Health (grant no. GM10704) and the National Science Foundation (grant no. GB29696X). One author, (W. E.) would like to express appreciation to the National Institutes of Health for a postdoctoral Biophysics traineeship. REFERENCES Akervall, K., Strandberg, B., Rossmann, M. G., Bengtsson, U., Fridborg, K., Johann&en, H.. Kannan, K. K., Lovgren, S., Petef, G., Oberg, B., Eaker, D., Hjerten, S., Ryden, L. & Moring, I. (1971a). Cold Spring Harbor Symp. Quunt. Btil. 36,469-483. Akervall, K., Strandberg, B., Rossmann, M. G., Bengtsson, U., Fridborg, K., Johannisen, H., Kannan, K. K., Lovgren, S., Petef, G., Oberg, B., Eaker, D., Hjerten, S., Ryden, L. & Moring, I. (1971b). Cold Spring Harbor Symp. Quant. Bid. 36, 487-488. Barynin, V. V. & Vainshtein, B. K. (1971). Krtilografiiya, 16, 751-763. Buerger, M. J. (1959). In Ve&w Space, p, 56, John Wiley and Sons Inc., New York. Glauser, S. & Rossmann, M. G. (1966). Acta Cry&zJZogr. 21, 175-176. Gurskaya, G. V., Lobanova, 0. M. & Vainshtein, B. K. (1971). Kristullogra~ya, 16,
764-773. Interraatirma Table-9 for X-ray Cry&a.%ography (1962), vol. 1, p. 257, Kynoch Birmingham, England. Klug, A. (1971). Cold Spring Harbor Symp. Quant. Bid. 36, 483-487.
Press,
62
W.
EVENTOFF
AND
Q. V. QURSKAYA
Longley, W. (1967). J. Mol. BioZ. 30, 323-327. Rossmann, M. G. & Blow, D. M. (1962). Acta Cryetdlogr. 15, 24-31. Rossmann, M. G. & Labaw, L. W. (1967). J. Mol. Biol. 29, 315-316. Rossmann, M. G., Akervall, K., Lentz, P. J., Jr & Strandberg, B. (1973). J. Mol. Biol. 79, 197-204. Vainshtein, B. K., Barynin, V. V., Gurskaya, G. V. & Nikitin, B. La. (1967). KristaZZogra$ya, 12, 860-867. Vainshtein, B. K., Barynin, V. V. & Gurskaya, Q. V. (1968). DokZ. Akad. Nauk. SSSR, 182, 569-572.
