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§1§ Accurate protein crystallography at ultra-high resolution: Valence
electron distribution in crambin §1§
1. [16]Christian Jelsch [17]*,
2. [18]Martha M. Teeter [19]†,
3. [20]Victor Lamzin [21]‡,
4. [22]Virginie Pichon-Pesme [23]*,
5. [24]Robert H. Blessing [25]§, and
6. [26]Claude Lecomte [27]* , [28]¶
1.
^*Laboratoire de Cristallographie et Modélisation des Matériaux
Minéraux et Biologiques, Université Henri Poincaré-Nancy 1-Centre
National de la Recherche Scientifique ESA 7036, BP 239, 54506
Vandoeuvre-lès-Nancy, France; ^†Department of Chemistry, Boston
College, Chestnut Hill, MA 02167; ^‡European Molecular Biology
Laboratory, Hamburg Outstation, c/o Deutsches Elektronen Synchrotron,
Notkestrasse 85, 22603 Hamburg, Germany; and ^§Hauptman-Woodward
Medical Research Institute, 73 High Street, Buffalo, NY 14203
1. Communicated by Herbert Hauptman, Hauptman-Woodward Medical
Research Institute, Buffalo, NY (received for review October 7,
1999)
[29]Next Section
§2§ Abstract §2§
The charge density distribution of a protein has been refined
experimentally. Diffraction data for a crambin crystal were measured to
ultra-high resolution (0.54 Å) at low temperature by using
short-wavelength synchrotron radiation. The crystal structure was
refined with a model for charged, nonspherical, multipolar atoms to
accurately describe the molecular electron density distribution. The
refined parameters agree within 25% with our transferable electron
density library derived from accurate single crystal diffraction
analyses of several amino acids and small peptides. The resulting
electron density maps of redistributed valence electrons (deformation
maps) compare quantitatively well with a high-level quantum mechanical
calculation performed on a monopeptide. This study provides validation
for experimentally derived parameters and a window into charge density
analysis of biological macromolecules.
The electronic charge density distribution of a molecule carries
information ([30]1) that determines its intermolecular interactions.
For example, the charge distribution of an enzyme complements that of
the substrate it recognizes and binds. The electrostatic potential and
electric moments derivable from the charge density ([31]1–[32]3)
provide maps that can guide the design of molecules for specified
interactions. Furthermore, powerful insights into the nature and
strength of hydrogen bonding and ionic interactions result from
analysis of the electron density gradient and Laplacian ([33]4–[34]6).
Extension of such analyses to proteins would permit a unique
understanding of the driving forces between biomolecules as well as the
subtleties of enzymatic reactions ([35]7).
Experimental electron density distributions are obtained by analysis of
single-crystal x-ray diffraction data measured to ultra-high
resolution, typically to a diffraction resolution limit d [min] ≈ 0.5 Å
([36]1, [37]8, [38]9). The crystallographic studies usually map and
analyze the deformation density, which is the difference between the
actual electron density of the molecule and the density calculated for
the promolecule, a molecular superposition of spherical, neutral, i.e.,
free, atoms. The deformation density thus reveals the redistribution of
valence electron density caused by chemical bonding and intermolecular
interactions and also is used to calibrate theoretical electron density
calculations ([39]10). However, a difficulty in crystallography is the
separation of the anisotropic atomic mean-square displacements from the
static molecular electron distribution ([40]11). Proper experimental
deconvolution requires very accurate diffraction data to ultra-high
resolution. Thus, charge density studies have so far been limited to
small-unit-cell crystals, and proteins still await study.
We have shown ([41]12, [42]13) that effective thermal displacement
deconvolution and meaningful deformation density distributions can be
achieved for larger structures at lower resolution by transferring
average experimental electron density parameters. We have built a
database of such parameters derived from ultra-high resolution crystal
structures of amino acids and small peptides that are transferable to
polypeptides and small proteins. The limits of the transferability have
been analyzed in a study of a helical octapeptide with diffraction data
to d [min] = 0.82-Å resolution ([43]13). The deformation density showed
well-defined bond peaks between atoms with small to moderate
displacement parameters (B [eq] < 4 Å^2) when the Fourier synthesis was
performed with diffraction data complete to at least 0.9-Å resolution.
The analysis also yielded partial atomic charges that compare well with
the charges in the amber ([44]14) molecular modeling dictionary.
Here we report on the crystallographic charge density refinement of a
protein, crambin (46 residues), which is present in seeds of Crambe
abyssinica and homologous to membrane-active plant toxins ([45]15). The
structure of the protein (Fig. [46]1) at a resolution of 0.83 Å already
has been analyzed extensively to determine deviations from peptide
backbone geometry, crystallographic water structure, and disorder
correlations ([47]17–[48]19).
[49]Figure 1
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Figure 1
Ribbon diagram ([53]16) showing the general fold of crambin. The
disulfide bridges are shown in yellow. β-sheet and extended chain are
shown in green and the helices are red.
[54]Previous Section[55]Next Section
§2§ Materials and Methods §2§
§3§ Data Collection. §3§
Crambin was purified and crystallized as described ([56]17). The
crystals belong to the space group P2[1] with unit cell parameters a =
40.82; b = 18.49; c = 22.37 Å; β = 90.47°, and one molecule per
asymmetric unit. X-ray diffraction data from a single crambin crystal
at T = 100 K were measured to d [min] = 0.54 Å by using λ = 0.54 Å
synchrotron radiation and a 300-mm MarResearch imaging plate detector
at the European Molecular Biology Laboratory BW7A beamline at the DORIS
storage ring, Deutsches Elektronen Synchrotron, Hamburg. Using the
denzo ([57]20) and drear ([58]21, [59]22) program suites, the data were
reduced to a 97.6% complete data set (Table [60]1). The structure was
refined against all of the reflections, except 5% of them used to
compute the free-R crystallographic residual ([61]23).
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Table 1
X-ray diffraction data statistics
§3§ Electron Density Modeling. §3§
The electron density analysis used a simplified Hansen and Coppens
([64]24) multipolar pseudoatom model, Formula Formula The first two
terms on the right describe spherically symmetric core-plus-valence
density, and the third term describes nonspherical, multipolar
redistribution of valence-shell density caused by chemical bonding. The
valence-shell electron populations P [val] adjust for inter-atomic
charge transfer, and the multipole populations P [lm] for aspherical
intra-atomic redistribution of valence electron density. The R [l] are
Slater-type radial functions, and the Y [lm±] are real spherical
harmonic angular functions (see ref. [65]24 for more details). The
dilatation coefficients of the spherical (κ) and multipolar (κ′)
valence electron density were not considered as variables and were set
to the standard value of unity (κ = 1.16 for hydrogen atoms).
The present analysis was performed by using the mopro least-squares
computer program (C.J. and C.L., unpublished work) for multipolar
charged atom modeling, which is a version of molly ([66]24) extensively
modified for protein applications. The conjugate gradient method has
been implemented, and stereochemical restraints, analogous to those of
the shelxl-97 structure refinement program ([67]25) have been
introduced. Distance restraints were applied in the disordered parts of
the structure. To facilitate the deconvolution of the deformation
density from vibrational smearing, rigid bond ([68]11) restraints were
applied to the thermal displacement parameters. All of the hydrogen
atoms in the ordered part of crambin were located in Fourier difference
maps. For nonhydrogen atoms, the multipole expansions included the
monopolar, dipolar, quadrupolar, and octupolar terms that have
significantly nonzero P [lm] values in the amino acid and peptide
database ([69]12, [70]13). For hydrogen atoms, only the P [val]
monopole and a dipole directed along the H-X covalent bond were
included.
§3§ Crystallographic Refinement. §3§
The electron density modeling was done in three stages. In refinement
I, a conventional, spherical, neutral atom model was used. Atomic
positions, anisotropic displacement parameters, and site occupancies
for solvent molecules and disordered protein atoms were refined by
using the programs shelxl-97 ([71]25) and mopro successively.
In refinement II, the multipolar charged atom model was applied with
electron density parameters (valence population and multipoles)
transferred from the database ([72]12, [73]13) to the protein
polypeptide main chain. For the side chains, only the multipole
parameters were transferred, as the valence populations P [val] show a
lower degree of transferability in the database. Water molecules were
considered spherical and neutral. The main-chain periodic moiety
-H^αC^αCONH- was set to be globally electrically neutral; as the
protein contains a variety of side chains, their global effect on the
polypeptide main-chain charge can be expected to cancel out.
The hydrogen atoms were moved outward along the X-H bond directions to
adjust the bond lengths to the values expected from neutron diffraction
studies ([74]26). The atomic positions and anisotropic thermal
displacement parameters were refined (alternatively) further with fixed
multipole and partial net charge parameters transferred from the
database. To ensure that the structure “forgot” the spherical atom
model, the temperature factors were annealed twice from random shifts
of up to ± 10%. As the convergence was slow, at least 400 refinement
cycles were necessary.
In refinement III, the average electron density parameters for the
polypeptide main chain were allowed to vary. All of the peptide groups
-C^a(-H^a)-C(=O)-N(-H^N)- were constrained to be electrically neutral
and equivalent. The disordered portions, accounting for 30% of the
protein atoms, were modeled with fixed electron density parameters that
were updated regularly during refinement III. The coordinates, the
thermal displacement parameters, and the charge density parameters were
refined alternatively.
§3§ Charge Refinement. §3§
Diffraction-derived atomic charges are given by q ^atom = N [val] ^atom
− P [val] ^atom, where N [val] is the number of valence electrons in
the neutral free atom and P [val] is the refined valence-shell
population in the bound pseudoatom. Charges derived from the P [val]
values might, however, be biased by effective charge transfer through
the multipoles. To compensate for this bias, the P [val] parameters
were refitted by using a spherical atom model. In this procedure
([75]27), only the valence population and dilatation coefficient were
refined while the multipole population parameters were reset to and
held fixed at P [lm] = 0, and the atomic positional and thermal
parameters were held fixed at their refined values from refinement II
or III.
§3§ Electron Density Maps. §3§
Residual maps were computed as Fourier transforms of the structure
factor differences (|F [obs]| − |F [calc]|) exp (iφ[calc]).
The experimental static deformation density was computed from the
crystallographic modeling as the atomic superposition-sum over the
molecule Δρ = Σ[atom] ρ[atom] ^multipolar − ρ[atom] ^spherical. This
density is “static” in that it is computed for atoms at rest.
A theoretical static deformation density Δρ = ρ[molecule] − Σ[atom]
ρ[free-atom] had been computed from a wavefunction for a
pseudo-monopeptide ([76]5) from an ab initio Hartree-Fock
self-consistent-field molecular orbitals calculation performed with a
triplezeta-plus-(C,N,O-d and H-p)-polarization-function Gaussian basis
set.
The dynamic experimental deformation electron density was obtained by
Fourier transformation of the difference |F [obs]|exp(iΦ[calc]
^multipolar) − |F [calc] ^spherical|exp(iΦ[calc] ^spherical). This
density is “dynamic” in that both the structure factor amplitudes and
phases are affected by atomic thermal vibrational smearing. It is
“experimental” in that the Fourier sum is truncated at the experimental
diffraction resolution limit, and the |F [obs]| coefficients
incorporate experimental error.
[77]Previous Section[78]Next Section
§2§ Results §2§
§3§ Residual Maps. §3§
An important question is whether significant deviations from the
spherical-atom approximation can be experimentally observed for
proteins. To address this issue, the crambin structure was first
refined classically, by using a spherical, neutral atom model
(refinement I). The quality of the fit to this spherical scattering
factor model was evaluated by residual electron density maps. These
maps show systematic bonding density features (Fig. [79]2 A), but also
contained a significant amount of random noise, which was not in favor
of a charge density refinement for individual atoms.
[80]Figure 2
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Figure 2
Residual electron density in the peptide bond plane. (A) For the
peptide Ala-9–Arg-10 when using a spherical neutral atom model, contour
level 0.05 e^−/Å^3. (B) Averaged over the 34 nondisordered peptides in
crambin when using a spherical neutral atom model. (C) When using a
multipolar charged atom model transferred from the database and (D)
with average valence populations and multipoles refined, contour level
0.02 e^−/Å^3. Positive: red lines; negative: blue lines.
Taking advantage of the repetition of the same chemical motif along the
polypeptide main chain, the signal to noise ratio of the crambin
residual map was increased by averaging over the 34 nondisordered
peptide groups (Fig. [84]2 B). The averaged map displayed significant
positive residual density in the bonds between the nonhydrogen atoms
(with a maximum Δρ = 0.12 e^−/Å^3 in the C^α-C bond), and negative
residual density was found in the H^a and H^N hydrogen regions,
indicating unmodeled electron depletion on the hydrogen atoms. These
features in the residual map clearly demonstrate that the
spherical-atom model does not provide an adequate fit to the
experimental diffraction data ([85]13, [86]28).
After transfer of the statistically significant multipoles from the
database (Table [87]2 ), the residual features were greatly reduced in
the peptide-averaged residual electron density (Fig. [88]2 C). In fact,
residual bond densities were even negative, indicating that the
deformation density transferred from the database ([89]12) needs
further adjustments (V.P.-P., C.J., C.L., and B. Guillot, unpublished
work).
View this table:
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Table 2
Average valence and multipole populations for the atoms of the
polypeptide main chain
The well-defined peaks on the covalent bonds as well as the low noise
level in the averaged residual maps (Fig. [92]2 B and C) encouraged us
to obtain chemically meaningful deformation densities for the
main-chain peptide moiety. The average statistically significant
multipole and partial net charge parameters of the peptide main-chain
atoms thus were allowed to vary in the refinement. The resultant
peptide-averaged residual density map (Fig. [93]2 D) showed
substantially less negative residual density along the peptide bonds
with |ΔΦ| < 0.06 e^−/Å^3. The progressive flattening of residual
density features through the three stages of refinement (Fig. [94]2
B–D) is convincing physical evidence of real improvement in the
modeling. The remaining global negative residual density in the peptide
bond plane (Fig. [95]2 D) may be caused by the constrains applied:
first, the peptide moiety was constrained to be neutral; second, in
this version of the database, only the multipoles that are
significantly different from zero were considered and refined, and
third, the dilatation coefficients of the valence density were fixed.
Also the scale factor had decreased by 0.3% from the spherical atom
model to the final refinement, which also might account for a global
negative residual density.
§3§ Crystallographic Statistics. §3§
Although the spherical and multipolar atom models led to significantly
different (averaged) residual densities, they yielded only slightly
different values (Table [96]1) of their crystallographic amplitude
agreement indices and their phase agreement statistics from free-R
likelihood estimates computed with the rflexpl program ([97]29). The
unweighted average phase error is 6.3° and 6.0° when using the
spherical and multipolar atom model, respectively. The effect of the
atomic model on the calculated phase also has been analyzed. The
average phase difference between the spherical and multipolar
refinements is <|ΔΦ|> = 3.8°, which is smaller than the estimated phase
error itself. This difference is presumably small because the
anisotropic thermal displacement parameters in a spherical atoms model
can accommodate much of the valence density deformation ([98]13,
[99]30) that should be properly described by a multipolar model. The
importance of model testing against residual maps also must be
emphasized.
§3§ Electron Density Parameters. §3§
The charge density refinement of the average peptide led to a realistic
static deformation density, except for the peptide oxygen atom lone
pairs. The charge density parameters of the oxygen atom therefore were
readjusted to their database values. The oxygen lone pair density had
indeed showed up less clearly than the bonding deformation density in
Fig. [100]2 B. Proper refinement of the charge density parameters
describing the oxygen lone pairs would require even higher-resolution
diffraction data and a lower thermal motion as these features are only
0.3 Å distant from the oxygen nucleus.
As expected from the residual density in Fig. [101]2 C, the multipole
populations on the peptide nonhydrogen atoms generally decreased from
their database values in refinement III (Table [102]2), whereas for the
peptide hydrogen atoms H^a and H^N the dipole populations increased by
about 25%. This electron transfer in the H→X direction was compensated
by a corresponding increase of the electronic populations P [val] on
the hydrogen atoms (Table [103]2).
§3§ Deformation Maps. §3§
The static deformation density maps after transfer and refinement of
the statistically significant multipoles (refinements II and III) are
shown in Fig. [104]3 A and B. The two densities display a correlation
coefficient of 0.89 in the peptide bond plane displayed in Fig. [105]3.
As expected from Fig. [106]2 C, there is a decrease of the rms
deformation density from 0.24 to 0.18 e^−/Å^3 in the peptide bond
plane. The database deformation density is clearly overestimated, as
the rms value computed on a sample of 13 experimental deformation maps
of peptide bonds present in the database is 0.194 ± 0.005. A
preliminary analysis of the current version of the database seems to
indicate that the overestimation of the deformation density is caused
by the dilatation coefficients κ and κ′, which were fixed to unity for
the non-H atoms. When average contraction/expansion coefficients are
used, the database deformation density has a rms value of 0.18, and the
correlation coefficient with the crambin-derived map reaches 92%.
[107]Figure 3
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Figure 3
Deformation map in peptide bond plane. (A) Static map obtained from the
database parameters. (B) Experimental static map obtained by using
atomic charges and multipole parameters refined against the crambin
diffraction data. (C) Theoretical static map computed for the
pseudo-monopeptide (Z)-N-acetyl-α,β-dehydrophenylalanine methylamide
([111]5). (D) Experimental dynamic map for the peptide Ala-9–Arg-10 of
crambin. The contour level is 0.05 e^−/Å^3. Positive: red lines;
negative: blue lines.
To further validate the results, the crambin experimental deformation
density maps were compared with corresponding theoretical maps obtained
from quantum mechanical calculations on the monopeptide (Z)-N-acetyl-α,
β-dehydrophenylalanine methylamide ([112]5) (Fig. [113]3 C). The bond
peak heights display an almost quantitative agreement in the two static
maps (Fig. [114]3 B and C). The experimental and theoretical
deformation densities have rms values of 0.18 and 0.20 e^−/Å^3,
respectively and give a correlation coefficient of 0.88 (if the regions
within 0.15-Å radius around the atomic nuclei are ignored). The
excellent consistency between the experimental results of this charge
density analysis of a protein and theoretical results for a high-level
calculation on a small peptide is remarkable.
According to the rms deformation densities, the 6–311G++ calculations
on the monopeptide do not agree with the database transferred map,
which again seems overestimated. The theoretical map has a rms
deformation density (0.20) that is in good agreement with the
experimental values found on 13 peptide bonds (0.194 ± 0.005) present
in the database; it is, however, slightly higher than the crambin
refined value (0.18).
The slightly lower deformation density features of the crambin refined
map might be caused by the less than small molecule quality of the
diffraction data and by the higher thermal motion. This attenuation
effect has been observed even more dramatically in the refinement of
atomic charges (see next paragraph).
A usual X-X refinement ([115]24), where the deformation density is in
principle deconvoluted from the thermal motion, was not attempted, as
the electron density residual in Fig. [116]2 B was weaker than what is
usually observed for small molecules. Also, such a refinement is
possible only for atoms with a sufficiently low thermal motion that
have thus a contribution to the diffraction that extends to the
subatomic resolution level (0.5 Å). The charge density parameters
refinement turned out to have a slow convergence; it was thus performed
only after the database transfer, which is a point close to the real
structure and therefore yields the best coordinates and thermal
displacement parameters ([117]12).
To see the charge density on individual atoms, the (unaveraged) dynamic
deformation map after refinement III has been computed. This density
incorporates the thermal motion of the atoms and the errors of the
diffraction data. The dynamic deformation density is shown in Fig.
[118]3 D for the peptide bond Ala-9–Arg-10. The density peaks are
generally visible on the covalent bonds; however, they are strongly
affected by the vibrationnal smearing and presumably also by the noise
in the diffraction data. As expected, lone-pair peaks on the oxygen
atom are attenuated because of thermal-motion smearing.
§3§ Atomic Charges Refinement. §3§
An important longer-range aim of our studies is to determine
experimental electrostatic parameters for biological macromolecules and
to calibrate the theoretically derived electrostatic parameters used in
biomolecular modeling calculations ([119]31). Net atomic charges can,
for instance, be derived experimentally from x-ray diffraction data via
pseudoatom modeling ([120]3, [121]27, [122]31). In analyses of
small-molecule structures, spherical-atom charges refitted after
multipolar refinements have been shown to yield molecular electric
moments that agree well with independently measured experimental values
([123]3, [124]27).
The refitted charges of the crambin peptide atoms after refinement II
were: C^a +0.06, C +0.32, O −0.18, N −0.44, H^a +0.08, and H^N +0.16
electrons. These are charges for volume-occupying spherical atoms, and
they are chemically sensible, although generally smaller than the
nuclear-centered effective point-charges in the amber molecular
modeling dictionary ([125]14). The refitted charges after refinement
III were further attenuated to unrealistically small values, despite
the apparent reasonableness of the refined bonding deformation density.
Presumably the refinement of atomic charges is more sensitive to the
quality of the diffraction data, the scale factor calculation, and the
level of thermal motion, and it requires more accurate data to even
higher resolution.
[126]Previous Section[127]Next Section
§2§ Discussion §2§
The resolution (0.54 Å) and the quality of the crambin diffraction data
presented in this study permit the refinement of the average multipole
parameters for the polypeptide backbone, but not of the individual
atoms as suggested by the noise level in the nonaveraged maps (Figs.
[128]2 A and [129]3 D). With the availability of intense
third-generation synchrotron sources, crystallographic data could be
collected with high signal/noise ratios to even higher resolution for
the current crambin crystals. This experiment might allow meaningful,
nonaveraged, individual-atom charge density analysis for the inner
region of the protein that has a low thermal motion. The high
diffraction power of the crambin crystals with respect to protein
crystallography is correlated with the low thermal displacement
parameters of the protein atoms ([130]13); the median value is only B
[eq] = 2.5 Å^2.
This moderate thermal motion may be attributed to the three disulfide
bridges present in the crambin structure, the small unit cell, and the
tight crystal packing with only 30% (vol/vol) solvent, nearly all of
which is ordered. Low thermal vibration (B [eq] < 4 Å^2) of the
molecular structure is a prerequisite for measuring diffraction
intensities to ultra-high resolution ([131]13). The thermal motion
level in crambin is, however, high compared with usual values found in
small molecules crystallography (B ≈1–2 Å^2).
The work described here opens the way to numerous electron density
studies for proteins, because atomic-resolution protein diffraction is
becoming more and more accessible and accurate ([132]32). Depositions
at the Protein Data Bank of crystal structures of small and even medium
size proteins at resolutions better than 1.2 Å are becoming more
frequent ([133]33). For instance, from crystals of human aldose
reductase ([134]34), a 36-kDa protein, a diffraction data set to 0.65-Å
resolution recently has been collected and the multipolar refinement is
underway.
Further enhancements in protein crystal diffraction to the ultra-high
resolution level will extend the number of proteins that can be studied
with electron density methods. Research in the manipulation of crystal
growth conditions and the use of cryo-crystallography will be crucial.
These techniques can reduce the crystal mosaicity and/or lower the
attenuating contribution of the atomic displacement parameters to
diffraction intensities. This study shows that, at least for small
proteins, the collection of diffraction data to the subatomic level has
become feasible because of the remarkable technological advances in
synchrotron beamline facilities and area detectors.
The determination of the charges and the electronic distribution for
the atoms in the active site of enzymes will provide new information
and enable a better understanding of their function ([135]7). Another
important application of charge density to structural biology would be
the determination of electronic properties and oxidation states of
reactive metallic centers in redox and electron transfer
metalloproteins. Ultra-high resolution crystallographic studies
performed in parallel on metalloproteins and biomimetic compounds
([136]35, [137]36) in combination with quantum mechanical calculations
will yield new insights into redox processes in biology. With the
enhancement of charge density modeling, the development of the database
of transferable parameters and the continued technological advances of
experimental crystallography, analyzing the electronic structure of
macrobiomolecules has considerable unexplored potential ([138]8).
[139]Previous Section[140]Next Section
§2§ Acknowledgments §2§
We thank Dr. Marie-Madeleine Rohmer (Strasbourg) for her help in the
computation of Fig. [141]3 C, the two referees for their comments on
the database parameters, and the European Union for financial support
for part of this work through Framework IV Biotechnology Contract
BIO4-CT96–1809. R.H.B. is grateful for research support from National
Institutes of Health Grant GM56829.
[142]Previous Section[143]Next Section
§2§ Footnotes §2§
* [144]↵ ¶ To whom reprint requests should be addressed. E-mail:
lecomte{at}lcm3b.u-nancy.fr.
* Data deposition: The atomic coordinates have been deposited in the
Protein Data Bank, [145]www.rcsb.org (PDB ID code [146]1ejg).
* Copyright © 2000, The National Academy of Sciences
[147]Previous Section
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