The Molecular Structure of Green
Fan Yang1, Larry G. Moss2,
and George N. Phillips, Jr.1
1Department of Biochemistry and Cell Biology and the W.M. Keck Center for Computational Biology, Rice University, Houston, TX 77005-1892
of Endocrinology, Department of Medicine, Tufts University School
of Medicine and the New England Medical Center, Boston, MA 02111
Address for correspondence:
George N. Phillips, Jr. Department of Biochemistry and Cell Biology Mail Stop 140 Rice University 6100 S. Main St. Houston, TX 77005-1892 (713) 348-4910 firstname.lastname@example.org fax (713) 285-5154
The crystal structure of recombinant
wild-type green fluorescent protein (GFP) has been solved to a
resolution of 1.9 Å by multiwavelength anomalous dispersion
(MAD) phasing methods. The protein is in the shape of a cylinder,
comprising 11 strands of -sheet with an -helix inside and short
helical segments on the ends of the cylinder. This motif with
-structure on the outside and -helix on the inside, represents
a new protein fold, which we have named the
b-can. Two protomers pack
closely together to form a dimer in the crystal. The fluorophores
are protected inside the cylinders, and their structures are consistent
with the formation of aromatic systems made up of Tyr66
with reduction of its C - C bond coupled with cyclization of the
neighboring glycine and serine residues. The environment inside
the cylinder explains the effects of many existing mutants of
GFP and suggests which side chains could be modified to change
the spectral properties of GFP. Furthermore, the identification
of the dimer contacts may allow mutagenic control of the state
of assembly of the protein.
Green fluorescent protein, GFP,
is a spontaneously fluorescent protein isolated from coelenterates,
such as the Pacific jellyfish, Aequoria victoria1.
Its role is to transduce, by energy transfer, the blue chemiluminescence
of another protein, aequorin, into green fluorescent light2.
The molecular cloning of GFP cDNA3 and the demonstration
by Chalfie that GFP can be expressed as a functional transgene4
have opened exciting new avenues of investigation in cell, developmental
and molecular biology. Fluorescent GFP has been expressed in
bacteria4, yeast5, slime mold6,
plants7, 8, drosophila9, zebrafish10,
and in mammalian cells11, 12. GFP can function as
a protein tag, as it tolerates N- and C-terminal fusion to a
broad variety of proteins many of which have been shown to retain
native function.6, 13, 14 When expressed in mammalian
cells fluorescence from wild type GFP is typically distributed
throughout the cytoplasm and nucleus, but excluded from the nucleolus
and vesicular organelles (reviewed by Cubitt et al.13,
LG Moss unpublished observations). However, highly specific
intracellular localization including the nucleus, mitochondria15,
secretory pathway16, plasma membrane17 and
cytoskeleton5 can be achieved via fusions both to whole
proteins and individual targeting sequences. The enormous flexibility
as a noninvasive marker in living cells allows for numerous other
applications such as a cell lineage tracer, reporter of gene
expression and as a potential measure of protein-protein interactions18.
Green fluorescent protein is comprised
of 238 amino acids. Its wild-type absorbance/ excitation peak
is at 395 nm with a minor peak at 475 nm with extinction coefficients
of roughly 30,000 and 7,000 M-1 cm-1, respectively19.
The emission peak is at 508 nm. Interestingly, excitation at
395 nm leads to decrease over time of the 395 nm excitation peak
and a reciprocal increase in the 475 nm excitation band13.
This presumed photoisomerization effect is especially evident
with irradiation of GFP by UV light. Analysis of a hexapeptide
derived by proteolysis of purified GFP led to the prediction that
the fluorophore originates from an internal Ser-Tyr-Gly sequence
which is post-translationally modified to a 4-(p-hydroxybenzylidene)-
imidazolidin-5-one structure20. Studies of recombinant
GFP expression in E. coli led to a proposed sequential
mechanism initiated by a rapid cyclization between Ser65
and Gly67 to form a imidazolin-5-one intermediate followed
by a much slower (hours) rate-limiting oxygenation of the Tyr66
side chain by O2 21. Combinatorial mutagenesis
suggests that the Gly67 is required for formation of
the fluorophore22. While no known co-factors or enzymatic
components are required for this apparently auto-catalytic process,
it is rather thermosensitive with the yield of fluorescently active
to total GFP protein decreasing at temperatures greater than 30
C23. However, once produced GFP is quite thermostable.
Physical and chemical studies of
purified GFP have identified several important characteristics.
It is very resistant to denaturation requiring treatment with
6 M guanidine hydrochloride at 90 C or pH of <4.0 or >12.0.
Partial to near total renaturation occurs within minutes following
reversal of denaturing conditions by dialysis or neutralization24.
Circular dichroism predicts significant amounts of -sheet structure
that is subsequently lost on denaturation.24 Over
a nondenaturing range of pH, increasing pH leads to a reduction
in fluorescence by 395 nm excitation and an increased sensitivity
to 475 nm excitation25. Reduction of purified GFP
by sodium dithionite results in a rapid loss of fluorescence that
slowly recovers in the presence of room air. While insensitive
to sulfhydryl reagents such as 2-mercaptoethanol, treatment with
the sulfhydral reagent dithiobisnitrobenzoic acid (DTNB) irreversibly
The availability of E. coli
clones expressing GFP has led to extensive mutational analysis
of GFP function. Truncation of more than 7 amino acids from the
C-terminus or more than the N-terminal Met lead to total loss
of fluorescence27. All non-fluorescent mutants also
failed to exhibit absorption spectra characteristic of the intact
fluorophore, implying a possible defect in post-translational
processing. Screens of random and directed point mutations for
changes in fluorescent behavior have uncovered a number of informative
amino acid substitutions. Mutation of Tyr66 in the
fluorophore to His results in a shift of the excitation maximum
to the UV (383 nm) with emission now in the blue at 448 nm21.
A Tyr66Trp mutant is blue-shifted albeit to a lesser
degree. Both changes are associated with a severe weakening of
fluorescence intensity compared to wild type GFP. Mutation of
Ser65 to Thr, Ala, Cys or Leu causes a loss of the
395 nm excitation peak with a major increase in blue excitation22,
28. When combined with Ser65 mutants , mutations
at other sites near the fluorophore such as Val68Leu
and Ser72Ala can further enhance the intensity of green
fluorescence produced by excitation at 488 nm22, 29.
However, amino acid substitutions significantly outside this
region also affect the protein's spectral character. For example,
Ser202Phe and Thr203Ile both cause the loss
of excitation in the 475 nm region with preservation of 395 nm
excitation4, 21, 30. Ile167 Thr results
in a reversed ratio of 395 to 475 nm sensitivity13,
while Glu222Gly is associated with the elimination
of only the 395 nm excitation30. Another change, Val163Arg,
not only enhances the magnitude of the Ser65Thr mutant,
but also increases the temperature tolerance for functional GFP
expression19. Molecular evolution techniques have
been reported to improve GFP fluorescence31. Unfortunately,
a roster of substitutions associated with complete loss of function
has not been published.
Because GFP in crystallum
exhibits a nearly identical fluorescence spectrum and lifetime
to that for GFP in aqueous solution32 and fluorescence
is not an inherent property of the isolated fluorophore, the elucidation
of its three-dimensional structure will help provide an explanation
for the generation of fluorescence in the mature protein, as
well as the mechanism of autocatalytic fluorophore formation.
Furthermore, the development of fluorescent proteins with additional
emission and excitation characteristics would dramatically expand
their biological applications. Color vision is based on the fact
that spectral properties of a common fluorophore, cis-retinal,
are altered as a function of protein environment within red,
blue, or green opsins33. The GFP from the sea pansy,
Renilla reniformis, which exhibits a single major excitation
peak at 498 nm, apparently utilizes an identical core fluorophore
to that of A. victoria GFP . These findings taken together
with the spectral changes exerted by substitutions in amino acids
over 100 residues from the GFP fluorophore suggest that a rational
strategy to modify and expand the fluorescence behavior of GFP
based on protein structure may be possible. Here we report the
X-ray diffraction structure derived from a crystal of wild-type,
recombinant A. victoria green fluorescent protein.
The structure of GFP has been solved using seleniomethionyl-substituted protein and multi-wavelength anomalous dispersion (MAD) phasing methods. The electron density maps produced by the MAD phasing were very clear, revealing a dimer comprised of two quite regular -barrels with 11 strands on the outside of cylinders (Figure 1,2,3). These cylinders have a diameter of about 30 Å and a length of about 40 Å. Inspection of the density within the cylinders reveals modified tyrosine side chains as a part of an irregular -helical segment (Figure 4). Small sections of -helix also form caps on the ends of the cylinders. This motif, with a single -helix inside a very uniform cylinder of b-sheet structure, represents a new protein class, as it is not similar to any other known protein structure.
The fluorophore is highly protected,
located on the central helix within a couple of Ångstroms
of the geometric center of the cylinder. The pocket containing
the fluorophore has a surprising number of charged residues in
the immediate environment (Figure 5 and Table 1). The environment
around the fluorophore includes both apolar and polar amino acid
side chains. Phe64 and Phe46 are near the
fluorophore and separate the single tryptophan, Trp63
from direct contact with fluorophore (closest distance of 13 Å).
A table of all atoms that come in contact with the fluorophore
and their distances to the fluorophore is provided (Table 1).
The crystallographic contacts
are all rather tenuous, consisting of a few amino acids side chains
for each. The non-crystallographic symmetry is maintained by
extensive contacts and thus is likely to be the source of the
dimerization seen in solution studies (Figure 6). The dimer contacts
are fairly tight and consist of a core of hydrophobic side chains
from Ala206, Leu221, and Phe223
from each of the two monomers and a wealth of hydrophilic contacts
(Figure 5), including Tyr39, Glu142, Asn144,
Asn146, Ser147, Asn149, Tyr151,
Arg168, Asn170, Glu172, Tyr200,
Ser202, Gln204, and Ser208.
Contacts with other crystallographic molecules are not extensive,
and the salt-dependence of this dimer interface and/or the loose
contacts with neighboring molecules may explain the difficulties
with isomorphism in initial heavy atom phasing studies.
Mass spectrometry studies of the
bacterially expressed wild-type and selenio-
methionyl protein show masses of
26836.1 (±0.9) and 27069.3 (±1.4) g/mole,
respectively. The masses calculated
for the known pTu58 gene sequence, including
the original inadvertent Gln80Arg
PCR error during the cloning of the gene for GFP 4
and the cyclization and oxidation of the tyrosine are 26835.5
and 27070.0 for the seleniomethionine, respectively. The differences
of 0.6 and -0.7 g/mole are small and the results are therefore
consistent with essentially complete fluorophore formation, including
the loss of water after cyclization. The error limits do not
allow accurate determination of the degree of oxidation of the
dehydrotyrosine, however. These results indicate the starting
material for the crystallization was essentially fully formed
GFP and the lack of difference density in Fo-Fc maps in this region
shows that the crystal contains fully cyclized GFP.
The remarkable cylindrical fold
of the protein seems ideally suited for the function of the protein.
The strands of -sheet are tightly fitted to each other like staves
in a barrel, and form a regular pattern of hydrogen bonds. Together
with the short -helices and loops on the ends, the 'can' structure
forms a single compact domain and does not have obvious clefts
for easy access of diffusable ligands to the fluorophore. This
fold, taken with the observation that the fluorophore is near
the geometric center of the molecule explains the observed protection
of the fluorophore from collisional quenching by oxygen (Kbm
< 0.004 M-1s-1)34 and hence
reduction of the quantum yield. Perhaps more seriously, photochemical
damage by the formation of singlet oxygen through intersystem
crossing is reduced by the structure. The tightly constructed
-can would appear to serve this role nicely, as well as provide
overall stability and resistance to unfolding by heat and denaturants.
The location of certain amino acid
side chains in the vicinity of the fluorophore also begins to
explain the fluorescence and the behavior of certain mutants of
the protein. At least two resonant forms of the fluorophore can
be drawn, one with a partial negative charge on the benzyl oxygen
of Tyr66, and one with the charge on the carbonyl oxygen
of the imidazolidone ring. Interestingly, basic residues appear
to form hydrogen bonds with each of these oxygen atoms, His148
with Tyr66 and Gln94 and Arg96
with the imidazolidone. These bases presumably act to stabilize
and possibly further delocalize the charge on the fluorophore.
Most of the other polar residues in the pocket form an apparent
hydrogen-bonding network on the side of Tyr66 that
requires abstraction of protons in the oxidation process. It
is tempting to speculate that these residues help abstract the
protons. As for the mutants, atoms in the side chains of Thr203,
Glu222, and Ile167 are in van der Waals
contact with Tyr66, so their mutation would have direct
steric effects on the fluorophore and would also change its electrostatic
environment if the charge were changed, as suggested previously30.
A quantitative explanation will require further examination.
It seems likely that other mutations of the residues identified
to be near the fluorophore would also have effects on the absorption
and/or emission spectra, and such experiments to change the electrostatic
environment around the fluorophore are in progress. By virtue
of their varied fluorophore environments and hence altered spectra,
these mutants should lead to expanded uses of green fluorescent
protein as gene markers, cell lineage markers, and encourage other
uses in biotechnology.
Mutations in regions of the sequence
adjacent to the fluorophore, i.e. in the
range of positions 65-67, have been
systematically explored22, some having significant
wavelength shifts and most suffer a loss of fluorescence intensity.
For example, mutation of the central Tyr to Phe or His shifts
the excitation bands but there is an overall loss of intensity.
Secondary mutations to compensate for the deleterious intensity
effects should also now be possible. The Ser65Thr
mutant is particularly interesting because of its reported increase
in fluorescence intensity21, 28. The mechanism for
increased fluorescence may be reduced collisional quenching,
as the additional methyl group may make for better packing in
the interior of the protein. On the other hand, the effect has
been suggested to be through improved conversion of the tyrosine
to dehydrotyrosine. However, the fact that we see significantly
altered structure relative to standard protein conformations in
the wild-type argues against a dramatic increase in cyclization
and/or oxidation. This effect is most likely produced by increased
expression and/or folding of the protein. The crystal structure
of the Ser65Thr mutant has also been solved 35,
and it will be interesting to compare the two structures for clues
about the fluorescence and other differences. The report of
improvements in GFP by DNA shuffling31, comprising
mutations Phe100Ser, Met154Thr and Val164Ala
are difficult to explain based on the structure. Positions 154
and 164 are on the surface of the protein and may exert their
effects through improved solubility and/or reduced aggregation.
The Phe-Ser mutation at first glance would appear to destabilize
the core of the protein and we have no idea how it would improve
The mechanism of activation of
the fluorophore from ordinary protein structure is consistent
with a non-enzymatic cyclization mechanism like that of Asn-Gly
deamidation 36 followed by oxidation of the tyrosine
to dehydrotyrosine, as previously suggested. The role of molecular
oxygen in this mechanism and in GFP fluorescence is paradoxical,
however. Molecular oxygen is proposed to be needed for formation
of the double bond between C and C on the tyrosine to form an
extended aromatic system, but oxygen must also be excluded from
regular interactions with the fluorophore or else collisional
quenching of the fluorescence or damaging photochemistry will
occur. The low bimolecular quenching rate suggests that the protein's
design sacrifices efficient fluorophore formation for stability
and higher quantum yields once fully formed.
The excited state dynamics of GFP
have been studied using Stark, steady state, and time-resolved
fluorescence spectroscopies37(and Youvan and Michel-Beyerle,
personal communication) . The results suggest that proton transfer
is involved in interconversions within two ground and two excited
states. The extended set of polar interactions around the flourophore
could easily accomodate proton rearrangements, with the most likely
direct effects being associated with the His148 with
the hydroxyl of Tyr66, Arg96 interactions
with the imidazolidone, or Glu222 interactions with
the hydroxyl of Ser65. Since the Ser65/Glu222
mutants have both lost their native interactions together with
their ~400 nm absorption bands, one possibility is that the 400nm
band arises from the abstraction of the Ser65 hydroxyl
proton by Glu222. This is speculation however, but
similar spectroscopic studies on mutants at these positions may
be able to differentiate the roles of these sites in excited state
The N- and C-termini truncation
studies27 and the fluorescent fusion products6,
13, 14 are now understandable, given the structure of the
protein. Since the C-terminus loops back outside the cylinder
and the last seven or so amino acids are disordered it shouldn't
be critical to have them present and further addition would seem
to be easily tolerated. These residues do not form a stave of
the barrel. The role of the N-terminus is a little less clear,
as the first strand in the barrel does not begin until amino acid
10 or 11 Thus barrel formation does not require the N-terminal
region. The N-terminal segment, is however, an integral part
of the 'cap' on one end of the protein, and may be essential in
folding events or in protecting the fluorophore. Again, extensions
at the N-terminus would not disrupt the motif structure of the
The chemical modification studies26 using sulfhydral reagents can be partially explained. Reaction of one of the cysteines near one end of the cylinder, Cys70, would appear to disrupt the packing of the cap on that end, and hence allow quenching of the fluorophore. Significant fluorescence intensity effects by the modification of Cys48 on the exterior of the protein would not be expected, a priori. The structure determination of the dithionite-reduced, non-fluorescent species has not yet been studied, but should provide additional data on the nature of the fluorophore. The pH dependence of the excitation bands at 395 nm and 475 nm25 is almost certainly due to His148, whose N atom is 3.3 Å from the Tyr66 hydroxyl oxygen atom of the fluorophore, although NMR pKa measurements or mutagenesis studies would be needed for confirmation.
The dimer we see as the asymmetric
unit in the crystal is likely to be the same one formed in solution,
since the ionic strength of the crystallization buffer is low,
and we see dimers at low (<100 mM) ionic strengths in solution.
Thus, it is not surprising to us to see the large number of hydrophilic
dimer contacts. The smaller hydrophobic patch could conceivably
be involved in physiological interactions with aequorin, as there
would be a natural advantage to close proximity for efficient
energy transfer. It is not known at present whether dimers form
in physiological circumstances, or what the effect of dimerization
is on energy transfer, aside from the circumstantial inferences
on the excitation spectra previously reported on the native protein25.
The dimer contacts should now be able to be modified in such
a way to disrupt the formation of dimers without affecting stability
and folding. Other nearby residues could also be converted to
hydrophobic residues to enhance dimer stability if desired. Control
of the dimerization will be important for fluorescence resonance
energy transfer (FRET) studies of protein-protein interactions
using GFP, as one would not want to induce association and hence
resonance energy transfer between the differently colored GFP
proteins by mechanisms other that of the target protein interactions.
Mutants may also be developed for reduction of aggregation
during expression and hence fewer problems with inclusion bodies.
Thus the three-dimensional structure
of GFP has provided a physico-chemical
basis of many observed features
of the protein, including its stability, protection of it
fluorophore, behavior of mutants,
and dimerization properties. The structure will also
allow directed mutation studies
to complement random and combinatorial approaches.
Green fluorescent protein was
purified from E. coli strain BL21(DE3)pLysS (Novagen) containing
plasmid pTu58, bearing the wild-type Aequorea victoria
green fluorescent protein4. For the seleniomethionine
protein, the plasmid was moved to E. coli methionine auxotroph
strain B834(DE3)pLysS (Novagen). The purification involved cell
lysis, centrifugation of cell debris, and four column chromatography
steps: DEAE anion exchange column (Sigma, CL-6B) with a zero to
1M NaCl gradient in 10mM phosphate, 2mM EDTA, 2mM DTT, pH 7; a
hydrophobic interaction column (Sigma, CL-4B) with a 0.1 to zero
M phosphate gradient in 2mM EDTA, 2mM DTT, pH 7; an HPLC anion
exchange column (Bio-Rad, Bio-Gel DEAE-5PW) with a zero to 1M
NaCl gradient in 10 mM phosphate, 2 mM EDTA, 2mM DTT, pH 7; and
an HPLC gel filtration column (Bio-Rad, Bio-Gel SEC-125) with
0.1 M phosphate, 2mM EDTA, 2mM DTT, pH 7. Gel filtration columns
run at 10mM phosphate showed predominately a 2-fold higher molecular
weight species. Matrix-assisted laser desorption ionization mass
spectrometry was performed by the University of Texas Health Sciences
Center analytical chemistry service.
The protein was crystallized in
sitting drop vapor diffusion wells (Hampton Research) at room
temperature using 58% 2-methyl-2,4-pentanediol (Aldrich), 50mM
morpholino ethane sulfonic acid, 0.1% sodium azide at pH 6.8.
The protein concentration varied, but was typically 20-30 mg/ml.
Crystals grew as green fluorescent square bipyramids up to 0.5
mm on a side. The space group was determined to be P41212
or its enantiomorph, with a=b=87.15 Å and c=119.85 Å
at cryogenic temperatures, and a=b= 89.23 Å and c= 119.78
Å at room temperature. The unit cell also varies with changes
in ionic strength, and this effect thwarted solution by multiple
isomorphous replacement. Packing density calculations suggested
that there were probably two molecules per asymmetric unit.
Multi-wavelength anomalous dispersion
(MAD) data were taken at Brookhaven beam line X4A at four wavelengths.
The wavelengths to be used were determined by reference and crystal
absorption scans. The data were taken at liquid nitrogen temperature
using inverse-beam geometry in wedges of four degrees and processed
using DENZO38. Native and selenio-methionine data
sets were also taken in the laboratory on an R-AXIS IIC detector
with CuK radiation. The native data set used in the refinement
had a Rmerge of 7.7% to 1.9 Å resolution (99+%
complete in all shells with 5-fold average redundancy). Selenium
atoms were located initially by standard difference Patterson
maps between selenium-substituted and native protein using SHELX9639
and HEAVY40 and confirmed by Patterson maps using the
MAD data. MADSYS software41 was used to give the anomalous
diffraction differences shown in Table 2. and to extract Fa, Ft,
and phase information.
The resulting MAD-phased map was solvent flattened and two-fold averaged based on the selenium sites using CCP442, skeletonized using the program O43, and immediately revealed two 11-stranded cylindrical -barrels. The polypeptide chain was traced for one of the barrels beginning from the seleniomethionines and extending the structure in each direction, helped by the recognition of the modified tyrosine in the middle of the barrel as Tyr66, the nucleus of the fluorophore. The correct enantiomorph is space group P41212, as confirmed by the handedness of the b-barrel and the a-helices. Refinement has been started using the program X-Plor44 using the native data collected at room temperature; the current R-factor at 1.9 Å is 0.21 with an R-free of 0.26, with good geometry (rms bond and angle deviations from ideality of 0.013 Å and 1.8, respectively) and tight restraint of the non-crystallographic symmetry. All measured data were included in the refinement. Coordinates and structure factors have been deposited at the Brookhaven Protein Data Bank under accession numbers 1GFL and R1GFLSF, respectively.
We would like to thank J. Sobelewski
and L. Moitoso-deVargas for initial purification of GFP, Prof.
Dan Leahy for procedures for growing the seleniomethionine auxotroph
and helpful suggestions, Drs. Mike Berry, Frank Whitby, Mike Soltis,
Henry Bellamy, Michael Stowell, Craig Ogata for help with MAD
data collection, Prof. Frank Prendergast for suggesting the name
the Howard Hughes Medical Institute and Brookhaven National Laboratory
(beamline X4A) and Stanford's SSRL (beamline X1-5) for synchrotron
time, and the W. M. Keck Foundation, Robert A. Welch Foundation,
and NIH AR40252 (GNP), GRASP Center (DK34928) and DK34447 (LGM)
for financial support.
Table 1. List of amino acid side
chains with close contacts (less than 5 Å) to the fluorophore.
The fluorophore is defined as the 7 atoms of the phenol of Tyr66,
the 6 atoms of the imidazolidone, and the bridging methylene between
the rings. The following amino acid side chains would be expected
to have the most direct effects on fluorescence and perhaps fluorophore
formation. The atom names are taken from the Brookhaven Protein
Data Bank nomenclature.
|Arg 96||NH2||Tyr 66||O||2.7|
|Gln 94||NE2||Tyr 66||O||3.0|
|His 148||ND1||Tyr 66||OH||3.3|
|Gln 69||CD||Tyr 66||O||3.4|
|Glu 222||OE2||Tyr 66||CE2||3.5|
|Val 150||CG2||Tyr 66||CE1||3.6|
|Phe 165||CE1||Tyr 66||CD1||3.6|
|Thr 203||CG2||Tyr 66||CE2||3.6|
|Ile 167||CD1||Tyr 66||OH||3.7|
|Thr 62||CG2||Tyr 66||CG||3.7|
|Tyr 145||CE2||Tyr 66||OH||3.7|
|Ser 205||OG||Tyr 66||CE2||4.0|
|Val 61||CG1||Tyr 66||CE2||4.4|
|Gln 183||NE2||Tyr 66||O||4.8|
|Val 68||CG2||Ser 65||C||4.9|
Table 2. Anomalous diffraction differences
and scattering factors for seleniomethionyl GFP at the four wavelengths
used. Following the format used by Yang et al.41,
Bijvoet differences ratios are given in diagonal elements with
centric values in parentheses, and dispersive differences are
given in off-diagonal elements. Scattering factors were chosen
to minimize the cumulative errors in Bijvoet and dispersive terms.
|30 > d > 3.4 (Å)||3.4 > d > 2.7 (Å)||2.7 > d > 2.2 (Å)||scattering
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