From the Department of Applied Chemistry, Faculty of Engineering, Osaka University, Suita, Osaka 565-0871, Japan, the § Department of Chemistry, Ibaraki University, Mito, Ibaraki 310-8512, Japan, and the ¶ Department of Biology, Faculty of Science, Toho University, Funabashi, Chiba 274-8510, Japan
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ABSTRACT |
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The crystal structure of plastocyanin from a
green alga, Ulva pertusa, has been determined at 1.6-Å
resolution. At its copper site, U. pertusa plastocyanin has
a distorted tetrahedral coordination geometry similar to other
plastocyanins. In comparison with structures of plastocyanins
reported formerly, a Cu(II)-S Plastocyanin is a key metalloprotein in the electron transfer
processes from photosystem II to photosystem I. Plastocyanin consists
of a polypeptide of approximate 100 amino acid residues and a type 1 copper atom (also called the "blue copper site") coordinated by the
side chains of four residues, two histidines, a cysteine, and a
methionine. Plastocyanin has 2 electron transfer paths. One is the
hydrophobic patch consisting of hydrophobic residues at the northern
end of the molecule (1) and the electron transfer occurs through
His87. Another site is called negative patch or acidic
patch located at the east end of the molecule and it has
Tyr83, called a remote site, as one of the electron paths
to the copper atom.
Crystal structure analyses of oxidized plastocyanins from poplar
(2-4), green algae Enteromorpha prolifera (5), and
Chlamydomonas reinhardtii (6), have been performed by x-ray
diffraction methods. NMR structures of reduced plastocyanins from a
green alga, Scenedesmus obliquus (7, 8), French bean (9),
parsley (10), and a blue-green alga Anabaena variabilis (11)
have been reported. Poplar plastocyanin is structurally best
characterized by x-ray crystallography; structural studies on
Hg(II)-substituted plastocyanin (12) and reduced plastocyanin at
various pH are reported (13).
At the active site, side chain atoms of the four residues, hystidinyl
nitrogens of His37 and His87, a cysteinyl
sulfur of Cys84, and a methioninyl sulfur of
Met92 coordinate to a copper atom with a distorted
tetrahedral geometry. In the oxidized condition, the bond lengths from
Cu(II) to these ligands are approximate 1.9 to 2.2 Å except the
Cu(II)-S The strong "blue" absorption band near 600 nm corresponds to the
intensed low-energy charge transfer from the S The crystal structures of Type 1 blue copper proteins indicate that the
oxidized blue copper site is similar to the reduced one. A small change
in geometry of copper site gives a small reorganization barrier, which
may be preferable to high rate electron transfer (16). The oxidized
blue copper site has been considered forced by protein matrix toward
the distorted tetrahedral structure which is preferred by Cu(I),
because typical Cu(II) inorganic compounds prefer square planar.
According to the review described by Williams (17), this idea has led
to the theory, the entatic state theory, from the published work by
Vallee and Williams (18). They regarded protein as a rigid frame and
concluded that Cu(II) ion is enforced into an unusual state by the
rigid frame to play a role of electron transfer protein. A similar
theory, the induced-rack theory, has been reported by Malmström
(19, 20). These theories are based on the idea that the copper-ligand
geometry is strained by protein conformation. The difference between
the theories is described by Williams (18): the entatic state theory
supposes that protein matrix is rigid, while the induced-rack model
requires little flexibility of protein structure.
Recently, important studies on the copper-ligand coordination were
performed by Ryde et al. (21). They calculated the optimized copper geometry on modeled blue copper proteins and concluded that the results are inconsistent with the entatic state and
induced-rack theories. Thus copper-ligand geometry is quite important
for functions and spectroscopic properties of blue copper proteins.
Here we report a novel insight into the structure of copper site of
plastocyanin from the green alga Ulva pertusa.
U. pertusa Plastocyanin--
The thalli of U. pertusa
were harvested at a beach, Futtsu, Chiba, Japan, and plastocyanin was
purified by conventional methods (22). The complete amino acid sequence
has been determined and will be reported
elsewhere.1
Crystallization--
Single crystals of U. pertusa
plastocyanin were obtained by the hanging drop vapor diffusion method.
The reservoir solution consists of 100 mM glycine buffer
(pH 10.0) containing 2.2 M ammonium sulfate. The actual pH
of the solution was measured to be 7.6. The protein drop was prepared
by mixing 3 µl of protein solution (10 mg/ml) with 3 µl of the
reservoir solution. Single cubic crystals appeared within 1 week.
X-ray Analyses and Data Collection--
Preliminary x-ray
experiments were performed on a Rigaku R-AXIS IIC imaging plate
detector system equipped with a Rigaku RU-300 rotating-anode x-ray
generator (fine-focused CuK
Diffraction intensity data were collected by using synchrotron
radiation (BL-6B beam line, Photon Factory, KEK, Japan). The Weissenberg camera for macromolecules (26) and large-format imaging
plates (40 × 80 cm) (27) were used for the data collection. The
crystal diffracts up to 1.6-Å resolution. Fifteen frames with a
rotation angle of 2.5° for each frame were stored. Data processing was performed by the program DENZO and SCALEPACK (28). The combined set
gave 115,971 reflections to 1.6-Å resolution in total, which were
reduced 14,759 unique reflections with an Rmerge
of 8.2% and a completeness of 91.5% (70.2% for 1.60 to 1.66 Å). The
I/ Structural Analysis and Refinement--
Structure analysis was
performed by the molecular replacement method. The crystal structure of
E. prolifera plastocyanin (5) with an 85% homology to
U. pertusa plastocyanin was used as a search model. The
amino acid sequence of U. pertusa plastocyanin (Fig. 1) is
identical to Ulva arasakii plastocyanin (22) except for
residue 12 (correspond to residue 11 of poplar plastocyanin): Ala12 in U. arasakii plastocyanin is substituted
to a serine in U. pertusa plastocyanin (Fig.
1).1 Fourteen nonidentical
residues were changed to an alanine to improve the signal to noise
ratio. Rotation and translation searches were run using the program
X-PLOR (29). The diffraction data of 15.0-4.0-Å resolution were used
for these calculations. The Patterson correlation refinement (29)
indicates that the seventh peak of the rotation function
(
Amino acid residues were replaced by using the program TURBO-FRODO
(30). A 2Fo
The structural refinement was also performed using the SHELX program
package to judge the accuracy of the final model and to prevent a
program-dependent local minimum. The resolution range and
the atoms subjected to the refinement are same as X-PLOR. No restraints
were applied at the copper site. Three refinement steps including
manual adjustment of the model were accomplished. At each step, the
coordinate shifts after 10 cycles of a conjugate-gradient least square
minimization were within 0.03 Å for the copper atom and its ligands,
and changes of each copper-ligand distance were within 0.02 Å. All
copper-ligand parameters resulted from the SHELX refinement were close
to those from X-PLOR.
Quality of the Structural Model--
The crystal structure of
U. pertusa plastocyanin was determined and refined to a
crystallographic R-factor of 0.176 and an Rfree of 0.211 at 1.6-Å resolution (Table
I). The final model has good
stereochemistry with root mean square
(r.m.s.)2 deviations of 0.012 Å from the ideal bond lengths and 5.6° from bond angles (Table I).
Except for glycines and prolines, 75 residues are found in the
energetically most favored regions and the other 5 residues are found
in additional allowed regions (31). All glycines and prolines also have
favorable dihedral angles. From the Luzzati plot (32), the upper error
limit of the atomic coordinates was estimated to be between 0.20 and
0.25 Å.
Overall Structure and Comparison with Other
Plastocyanins--
U. pertusa plastocyanin has the
eight-stranded
r.m.s. deviations of the structures between the main chain atoms of
U. pertusa plastocyanin and those of the others are as follows: poplar, 0.74 Å; C. reinhardtii, 0.62 Å; E. prolifera, 0.43 Å. Large deviations were found at four regions,
around residues 26, 55, 70, and 87 (Fig.
3). The large deviations at the second region are responsible for the two inserted residues, 58 and 60, in
poplar plastocyanin. The fourth region contains turns 6 and 7, in which
Cys84, His87, and Met92 construct a
part of the copper site (Fig. 4). The
structural difference of this site influences the structure of the
copper site and we will discuss it in the next section.
Comparison of the Copper Site with Other Plastocyanins and Blue
Copper Proteins--
In plastocyanins, Cu(II) is coordinated by four
atoms, N
Ryde et al. (21) calculated the energy of the copper site as
a function of Cu(II)-S
U. pertusa plastocyanin has the longest
Cu(II)-S
In addition, evidence for the longer
Cu(II)-S Structural Basis for Regulation of the Blue Copper Site by Residue
88--
The present work first provides experimental proof that the
copper geometry is sensitive to the structure of the loop between His87 and Met92 (His-Met loop) (corresponding
to turn 7 in U. pertusa plastocyanin). This means that the
copper site of the blue copper proteins is more flexible than reported
formerly (17-20). However, it should be noted that the copper site is
strained even if its effect is weak. It is impossible to control the
copper geometry by the His-Met loop, if it were rigid. Flexibility of
the copper site, especially that of Cu-S
In the case of azurin, the fifth ligand of a carbonyl oxygen
coordinates to the copper atom with a distorted trigonal bipyramidal shape (39-43). Compared with the blue copper proteins with distorted tetrahedral geometry, the Cu-S
Strength of the interaction between residues 85 and 88 is quite
important to control the Cu-S
Residue 88 which controls the structure of the His-Met loop is close to
Tyr83 which is in the negative or acidic patch and is one
of the electron transfer paths. The electron transfer reaction of
plastocyanin with cytochrome f (44) or P700 (45) should
occur when plastocyanin forms the complex with the negative patch.
Residue 88 in the His-Met loop will then change its conformation by
interacting with the pair, which will modify the geometry of the copper
site through the loop. The complex should form the most appropriate
conformation to reach the most efficient electron transfer reaction.
Consequently, the geometry of the blue copper center may transform into
the most suitable form by the conformational change of the loop.
In the Marcus theory (16), an electron transfer rate reaches its
maximum value when the nuclear factor is optimized ((Met92) bond
distance (2.69 Å) is shorter by about 0.2 Å and a
Cu(II)-S
(Cys84) distance is longer by less
than 0.1 Å in U. pertusa plastocyanin. These subtle but
significant differences are caused by the structural change at a
His-Met loop (His87-Met92) due to an absence of
a O(Asp85)-O
(Ser88) hydrogen
bond which is found in Enteromorpha prolifera plastocyanin. In addition, poplar and Chlamydomonas reinhardtii
plastocyanins with a glutamine at residue 88 have a weak cation-
interaction with Tyr83. This interaction lengthens the
Cu(II)-S
(Met92) bond of poplar and C. reinhardtii plastocyanins by 0.14 and 0.20 Å, respectively. As a
result of structural differences, U. pertusa plastocyanin
has a less distorted geometry than the other plastocyanins. Thus, the
cupric geometry is finely tuned by the interactions between residues 85 and 88 and between residues 83 and 88. This result implies that the
copper site is more flexible than reported formerly and that the rack
mechanism would be preferable to the entatic theory. The His-Met loop
may regulate the electron transfer rate within the complex between
plastocyanin and cytochrome f.
INTRODUCTION
Top
Abstract
Introduction
References
(Met92) bond of 2.8 to 2.9 Å.
Pseudoazurin, one of the blue copper proteins, has a similar
coordinational structure to plastocyanin. In pseudoazurin the bond
distances from a copper to two histidines and to a cysteine are close
to those of plastocyanin and the distance from a copper to a
methioninyl sulfur in pseudoazurin is shorter by 0.1 to 0.2 Å than
that in plastocyanin.
(cysteine)
-orbital to the copper
dx2-y2 orbital which is
the half-occupied redox-active HOMO (14). The copper
dx2-y2 orbital lies in
the NNS plane formed by the two hystidinyl N
atoms and
the cysteinyl S
atom, and the
Cu-S
(cysteine) bond bisects the lobes of the orbital
(14). Recent studies on the electronic structure of nitrite reductase
reported by Solomon and co-workers (15) indicate that the HOMO rotation relative to plastocyanin in the NNS plane decreases the intensity of
the blue band. Moreover, the geometry of the copper-thiolate bond will
strongly influence the reduction potential and the electron transfer
rates through the remote site (14, 15).
EXPERIMENTAL PROCEDURES
, operating at 40 kV and 100 mA). Laue
symmetry and cell dimensions were determined by the PROCESS program
package (23) and systematic absences were confirmed by the
pseudo-precession program HKLPLOT in the CCP4 suite (24).
The crystal belongs to cubic space group P4132 or
P4332 with the unit cell dimension of a = 88.3 Å. Supposing one molecule per an asymmetric unit, a
Vm value is calculated to be 2.73 Å3 Da
1 (solvent content 54.9%) (25).
Diffraction spots up to 2.0-Å resolution were found on the imaging plates.
(I) value is 2.3 in the highest resolution shell.
1 = 313.1°,
2 = 46.4°,
3 = 239.5°) is the correct solution. The translation
searches were performed in the both space groups P4132 and
P4332. A significant peak was obtained from the calculation
in the space group P4332 (x = 0.759, y = 0.315, z = 0.111). The height of
the top peak was T = 0.5731 for P4332 and
T = 0.2775 for P4132. An
R-factor in P4332 was 0.44 for a 15.0-4.0-Å
resolution shell.
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Fig. 1.
Amino acid sequences of plastocyanin from
U. pertusa,1 E. prolifera (52),
C. reinhardtii (53), S. obliquus (7, 8),
Chlorella fusca (54), A. variabilis (55),
Synechocystis PCC6803 (56), Silene latifolia
(57), Arabidopsis thaliana (58), Spinacia
oleracea (59), Populus nigra a (3), Pisum
sativum (60), Nicotiana tabacum a (61),
Lycopersicon esculentum (62), Phaseolus vulgaris
(63), Cucurbita pepo (64), Petroselinum crispum
(65), and Prochlorothrix hollandica (66).
Fc electron
density map clearly indicates the structures of the missing side
chains. These side chains were fitted to the 2Fo
Fc electron density map. In the first step of
structural refinement, rigid-body refinement, positional refinement,
and individual temperature factor refinement were applied, and an
Rwork decreased from 0.452 to 0.210 for an
8.0-2.3-Å resolution shell. In the third refinement step, 39 water
molecules were picked from an Fo
Fc difference Fourier map. The
Rwork was decreased to 0.173 in this step.
Gradually, the resolution range was expanded and the 10.0-1.6-Å resolution data were included at the 15th step. Three further refinement steps gave the final model. In all refinement steps, force
constants for the copper-ligands bonds were set at 50 kcal/mol Å
2 and the equilibrium bond lengths were set as follows:
Cu-N
(histidines), 2.10 Å;
Cu-S
(cysteine), 2.10 Å;
Cu-S
(methionine), 2.80 Å, where the
Cu-S
(methionine) distance is an average of plastocyanins
and pseudoazurins. The results of the refinement are summarized in
Table I.
RESULTS AND DISCUSSION
The refinement statistics
-sandwich structure (5), which is identical to the
plastocyanins from poplar, C. reinhardtii, and E. prolifera. The
-sandwich can be divided into two
-sheets,
-sheet I and
-sheet II, as described by Freeman and co-workers
(5). The
-sheet I consists of four
-strands: S1 (residues 1 to
5), S2A (14 to 16), S3 (26 to 31), and S6 (69 to 73) (Fig.
2). The
-sheet II also contains four
-strands; S2B (residues 18 to 22), S4 (39 to 43), S7 (78 to 83), S8
(93 to 99). The copper site is located at a northern end of the
molecule (Fig. 2). Seven turns, turns 1-7, were found. Turn 2 is a
type IVb turn (33) with no hydrogen bond and is bent at
cis-Pro16. Two turns, turn 3 and turn 5, are type II turns
and the others are type I turns. Turns 6 and 7 are located around the
copper site. Hydrogen bonds in the backbones of turns 6 and 7 are
essential for maintaining the structure of the copper site.
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Fig. 2.
Schematic drawing of U. pertusa
plastocyanin. The copper atom is shown in cyan at
the top of the model. The four ligands, His37,
Cys-, His87, and Met92, are represented by
ball-and-stick models. Color configuration of the ligands are similar
to that of Fig. 4. The names of the eight -strands are shown in the
figure. This figure was drawn by the program PROTEUS (System Co., Ltd.,
Japan).
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Fig. 3.
r.m.s. differences along the main chain atoms
(N, C , C, and O) between U. pertusa
plastocyanin and the others, poplar (thin solid
line), C. reinhardtii (thin broken line),
and E. prolifera (thick solid line).
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Fig. 4.
Ball-and-stick models at the copper site with
a 2Fo Fc electron density
map. The map was contoured at a level of 1.5
.
atoms of His37 and
His87, the S
atom of Cys84, and
the S
atom of Met92, in a distorted
tetrahedral geometry (Fig. 4). The bond distances and the bond angles
of the copper site are summarized in Table II. In U. pertusa
plastocyanin, the bond distance between Cu(II) and
S
(Met92) is shorter by 0.13 to 0.23 Å than
the other plastocyanins and is rather close to that of pseudoazurin and
nitrite reductase (Table II). This short
Cu(II)-S
(Met92) distance can be explained by
the structural differences at turn 7 (residues 88 to 91). The large
deviation is found at turn 7 located near the copper site (Figs. 3 and
5). At turn 7, the amino acid difference
is found at only residue 88 (Fig. 1): U. pertusa has an
alanine; E. prolifera has a serine; poplar and C. reinhardtii have a glutamine. E. prolifera plastocyanin
has a hydrogen bond between O(Asp85) and
O
(Ser88) (Fig. 5A), which
withdraws turn 7 toward Asp85. The Gln88
residue of poplar and C. reinhardtii plastocyanins do not
have the hydrogen bond but a cation-
interaction (34, 35) with Tyr83 by stacking on its an aromatic ring (Fig.
5B), which is the "remote site" residue. The
O(Asp85)-O
(Ser88) hydrogen bond
found in E. prolifera plastocyanin pulls the
C
(Met92) atom toward Asp85
through the backbone of the turn 7 (Fig. 5A). Compared with
U. pertusa plastocyanin, Met92 of E. prolifera plastocyanin rotates 12° around its C
atom, and C
(Met92) atom translates by 0.4 Å. This effect lengthens the Cu(II)-S
(Met92) distance
in E. prolifera plastocyanin. Corresponding regions of
poplar and C. reinhardtii plastocyanins, with the cation-
interaction between Tyr83 and Gln88, have an
intermediate structure between U. pertusa and E. prolifera. In conclusion, the
Cu(II)-S
(Met92) distance is strongly
influenced by the structure of turn 7: U. pertusa
plastocyanin with the little restraint has the shortest distance of
2.69 Å, E. prolifera plastocyanin with the strong restraint
has the longest distance of 2.92 Å, and poplar and C. reinhardtii plastocyanins with the weak restraint have
intermediate distances of 2.82 and 2.89 Å, respectively.
Bond lengths and bond angles of copper site
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Fig. 5.
Comparison of the structures of plastocyanins
around the turn 7 and the copper site. U. pertusa
plastocyanin (yellow) is superimposed against E. prolifera (red) in A and poplar plastocyanin
(orange) in B. Green dots mean the
O (Ser88)-O(Asp85) hydrogen bond
in E. prolifera plastocyanin. The models are translated
after the r.m.s. fitting so that the copper atoms of all models occupy
the same position. To clarify the view, the following atoms are
omitted: side chain atoms of residues 85, 86, 89, and 90; carbonyl
oxygen atoms of residues 83, 84, and 86-92. This drawing was prepared
by the program MIDASPLUS (67, 68).
(methionine) distance (21).
According to their results, energies of the copper sites of U. pertusa and E. prolifera plastocyanins are higher by
approximately 1 and 5 kJ/mol, respectively, than the minimum energy
point. An energy of the copper site of E. prolifera plastocyanin is then higher by approximately 4 kJ/mol than that of
U. pertusa plastocyanin, taking account of only the
Cu(II)-S
(Met92) distance. This energy
difference fits surprisingly well to the binding energy of the
O(Asp85)-O
(Ser88) hydrogen bond
in E. prolifera plastocyanin if we suppose that the effect
of the hydrogen bond is 0.5 to 1.5 kcal/mol (correspond to 2.2 to 6.5 kJ/mol) as reported by Fersht et al. (36). In the case of
poplar and C. reinhardtii plastocyanins, cation-
interaction between Tyr83 and Gln88 are
estimated at about 2 and 4 kJ/mol, respectively. These agree with the
binding energy (~10 kJ/mol) of the benzene-ammonia system (37) which
is a model of cation-
interaction with a neutral nitrogen. Thus, the
shorter Cu(II)-S
(Met92) distance of U. pertusa plastocyanin due to the absence of the O(Asp85)-O
(Ser88) hydrogen bond
is consistent with the results of the energy analysis on the
Cu(II)-S
(methionine) coordination. In conclusion,
U. pertusa plastocyanin, free from restraint by the hydrogen
bond between residues 85 and 88, is close to the minimum energy state,
whereas E. prolifera plastocyanin, with the elongated
Cu(II)-S
(Met92) bond by the
O(Asp85)-O
(Ser88) hydrogen bond,
has the higher energy state. Consequently, our crystal structure
suggests that the Cu(II)-S
(Met92) bond of
E. prolifera plastocyanin is slightly "racked" by the O(Asp85)-O
(Ser88) hydrogen bond.
(Cys84) distance in all reported
crystal structures of plastocyanins (Table II). This value is rather
close to that of pseudoazurin and nitrite reductase compared with those
of plastocyanins. The optimized Cu(II)-S
(cysteine)
distance (Table II) calculated by the quantum chemical theories is in
good agreement with U. pertusa plastocyanin, pseudoazurin, and nitrite reductase, whereas the other plastocyanins deviate significantly from the optimized distance as follows: poplar, shorter
in 0.11 Å; E. prolifera, shorter in 0.06 Å; C. reinhardtii, shorter in 0.07 Å (Table II). The shorter
Cu(II)-S
(cysteine) distance is compensated by the longer
Cu(II)-S
(methionine) distance (15). Therefore, the
longer Cu(II)-S
(Cys84) distance of U. pertusa plastocyanin may be responsible for the shorter
Cu(II)-S
(Met92) distance.
(Cys84) distance of U. pertusa plastocyanin was found by the resonance Raman spectrum (38). The Raman band corresponding to
Cu(II)-S
(Cys84) bond of U. pertusa plastocyanin is observed at lower frequency than the
others. This result strongly supports the present results.
(methionine)
bond, should be required for the structure of plastocyanin. Consequently, the present results indicate that the rack model (19,
20), which agrees with the softness of the blue copper site, is more
plausible for the blue copper proteins rather than the entatic theory
(17, 18).
(methionine) distance of
azurin is long by approximately 0.3 to 0.5 Å. In azurin, the weak Cu-O bond attracts the copper ion to the ligated oxygen and causes the
lengthening of Cu-S
(methionine) bond. This is consistent
with the soft interaction of the methioninyl sulfur with the copper ion
and suggests that the Cu-O bond is well balanced against the soft
Cu-S
(methionine) bond in azurin.
(methionine) geometry,
because the copper geometry is crucial for the electron transfer
ability. In the His-Met loop, the discrepancy of primary structures is
only found at residue 88 (Fig. 1) in various sources. This implies that
the conserved residues in the loop are essential to maintain its
structure, whereas residue 88 probably characterizes the properties of
plastocyanin. The structural diverseness of the His-Met loop caused by
the difference of residue 88 may vary the electron transfer rate in
plastocyanin and other blue copper proteins.
G° =
, where
G° and
are the driving force and the
reorganization energy, respectively). Moreover, the conformational
change is an important factor for the reorganization energy in a
protein (46). Within the complexes between plastocyanin and its pair, the most important conformational change may occur probably at the
His-Met loop and the copper site. That is to say, to reach the
optimized condition of the nuclear factor, the conformational change of
the His-Met loop occurs when the complex is formed, and then it may
optimize the structure of the copper site.
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ACKNOWLEDGEMENTS |
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We thank Professor N. Sakabe, Dr. N. Watanabe, and Dr. M. Suzuki for support in data collection at KEK, Japan.
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FOOTNOTES |
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* This work was supported in part by the Tsukuba Advanced Research Alliance (TARA) Sakabe project.The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
The coordinates and the structure factors (code 1IUZ) have been deposited in the Protein Data Bank, Brookhaven National Laboratory, Upton, NY.
Present address: Dept. of Life Science, Faculty of Science, Himeji
Institute of Technology, Kamigori, Ako-gun, Hyogo 678-1297, Japan.
To whom correspondence should be addressed. Tel.:
81-6-6879-7408; Fax: 81-6-6879-7409; E-mail:
kai{at}chem.eng.osaka-u.ac.jp.
The abbreviation used is: r.m.s., root mean square.
1 T. Fukazawa, unpublished results.
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REFERENCES |
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