Macromolecular Structure
Determination: Comparison
of Crystallography and NMR
J Mitchell Guss, University of Sydney, New South Wales, Australia
Glenn F King, University of Connecticut Health Center, Farmington, Connecticut, USA
The two techniques used to define the three-dimensional structures of biological
macromolecules at or near to atomic resolution are X-ray crystallography and nuclear
magnetic resonance spectroscopy (NMR). These techniques are based on different
physical principles, and may be applicable to different systems, but they often yield
complementary results.
Introduction
Most biological macromolecules function correctly only
if they are folded into their proper or ‘native’ shape. To
fully understand the details of how a molecule functions,
one must first know its structure in as much detail as
possible.
The discovery of X-rays by Ro¨ ntgen at the end of
the nineteenth century was rapidly followed by their use
for exploring the structures of crystals by von Laue
and the Braggs. Experiments on diffraction from biological
fibres in the 1930s were accompanied by early experiments
on crystals of macromolecules by Dorothy Crowfoot
(Hodgkin) and J. D. Bernal. It then took more than
twenty years for the technology to be developed sufficiently
for John Kendrew to solve the first crystal structure
of a protein, namely myoglobin from sperm whale
muscle, in 1959. This was followed closely by elucidation
of the structure of haemoglobin by Max Perutz.
The assertion by Wolfgang Pauli in 1924 that
certain nuclei spin and therefore possess a magnetic
moment ultimately led to the first experimental observation
of nuclear magnetic resonance in 1945. However, it
was not until the advent of multidimensional NMR
spectroscopy in the 1970s that the technique matured
sufficiently to be applicable to macromolecular systems.
The first complete protein structure solved using NMR
methods, namely that of proteinase inhibitor IIA from bull
seminal plasma, was determinedby Kurt Wu¨ thrich’s group
in 1984.
The Protein Data Bank (see Further Reading), which is
the repository for coordinates of macromolecular structures,
now contains more than 10 000 entries representing
the structures of hundreds of different proteins that have
been elucidated using X-ray crystallography and NMR
spectroscopy.
Underlying Physics: What Sort of
Radiation Interacts with What in
Molecules?
The methods of X-ray diffraction and NMR spectroscopy
rely on fundamentally different physical processes to
generate the information needed to determine the threedimensional
structure of a macromolecule. X-ray diffraction
is essentially an imaging technique in which X-rays are
scattered by electrons in theatoms of crystal without loss of
energy (elastic scattering). The scattered X-rays generate
an interference pattern that can be recorded and subsequently
transformed to yield an image of the original
scattering object, in this case the molecules in the crystal.
The choice of X-rays, with wavelengths in the range 0.05–
0.25 nm, as the incident radiation is dictated by the need for
a radiation with a wavelength comparable to or shorter
than the spacing between the atoms. The use of longwavelength
radiation such as visible light would not allow
the visualization of small objects such as atoms or small
groups of atoms.
Structure determination by NMR is based on the
absorption of radiofrequency radiation incident on molecules
held in a strong magnetic field. Nuclei with nonzero
spin possess a magnetic moment that precesses around the
direction of the external magnetic field. Resonance can be
detected from the absorption of incident radiation
oscillating at the nuclear precession frequency. The
resonant frequency varies with the type of nucleus and
the strength of the magnetic field. More importantly, this
frequency is dependent on the chemical environment of the
nucleus and can therefore be used to distinguish nuclei of
atoms that are chemically identical but that have different
surroundings. The most commonly observed nuclei are
Article Contents
Introductory article
. Introduction
. Underlying Physics: What Sort of Radiation Interacts
with What in Molecules?
. Transforming Data into a Model (Calculated from
Distance Geometry; Built into Electron Density)
. What in the Model Has Been Inferred from Other
Information Versus What Comes Directly From the
Data?
. Judging Model Quality
. Dynamic Information
. Practical Considerations: Size, Solubility and Stability
Versus the Randomness of Crystallizability, Exchange
Rates for Complexes, etc.
. Most Common Errors and Pitfalls of Each Technique
1ENCYCLOPEDIA OF LIFE SCIENCES © 2002, John Wiley & Sons, Ltd. www.els.net
protons (1
H) and the NMR-active nuclei of carbon and
nitrogen (13
C and 15
N, respectively). The linear or onedimensional
NMR spectrum from a biological macromolecule
is too crowded to permit identification of
individual resonances. Multidimensional NMR techniques
have been developed that enable the resonances to be
spread out in two or more dimensions. These multidimensional
spectra can be interpreted to yield estimates of
the distances between hydrogen atoms that lie relatively
close together in the folded molecule.
Transforming Data into a Model
(Calculated from Distance Geometry;
Built into Electron Density)
NMR is applicable to macromolecules in solution because
it can be used to measure scalar quantities that do not vary
with molecular orientation. Multidimensional spectra that
record scalar or through-bond correlations between
NMR-active nuclei are used to assign each NMR
resonance to specific nuclei in the macromolecular system.
While these spectra constitute the large majority of
experiments performed during an NMR-based macromolecular
structure determination, they yield relatively little
information about macromolecular structure. Some scalar
correlation experiments do provide useful structural
information in the form of estimates of backbone and side
chain torsion angles. However, the most useful structural
information comes from multidimensional NMR experiments
that record dipolar correlations between hydrogen
atoms.
After hydrogen nuclei have absorbed radiofrequency
radiation they can return to thermal equilibrium by
through-space dipolar interactions with neighbouring
nuclei – this process is commonly referred to as longitudinal
dipolar relaxation. The strength of the dipolar
interaction, which can be measured in nuclear Overhauser
enhancement spectroscopy (NOESY) experiments, depends
on the reciprocal of the sixth power of the
internuclear distance. Thus, NOESY experiments can be
analysed to provide semiquantitative measurements of
interhydrogen distances for hydrogen pairs separated by
less than  0.6 nm; in a 100-residue protein one might
expect to obtain several thousand interproton distance
measurements. The estimates of dihedral angles and
interproton distances are then used to reconstruct a model
of the macromolecule. There are several mathematical
procedures that can be used for this reconstruction process
– many laboratories use distance geometry techniques to
provide preliminary structures, which are then refined
using restrained molecular dynamics, while some laboratories
use only restrained molecular dynamics. In all cases,
the aim is to obtain structures that satisfy all of the
experimental data; the reconstruction procedure is
repeated many times and an ‘ensemble’ is generated
of structures (usually 10–30) that satisfy the experimental
data. The precision of the structure determination can be
obtained from an overlay of the ensemble of structures.
Regions of the structure that do not overlay well indicate
either poor-quality NMR data or flexible regions that do
not have a single well-defined structure in solution.
In contrast to NMR, the X-ray method ultimately yields
an image of the scatteringobject. SinceX-rays are scattered
by electrons, the image is of the electron density throughout
the crystal. In complete contrast with NMR spectroscopy,
where experimentally measured interhydrogen
distances are used to reconstruct the macromolecular
structure, the small hydrogen atoms generally do not
contribute significantly to the electron density map. In the
diffraction experiment only the intensities of the diffracted
waves can be recorded and all relative phase information is
lost. In order to reconstruct the image, both the phases and
the amplitudes of the diffracted waves are needed. These
missing phases are determined experimentally.
The most widely used technique for structures unrelated
to anything previously known is that of multiple isomorphous
replacement (MIR) in which heavy atoms,
which scatter X-rays more strongly, are added to
the crystal. Differences between the diffraction intensities
from native crystals and crystals with added heavy atoms
may be used to define the heavy-atom positions and then
to calculate the phases of the diffracted waves. A relatively
new method, multiple wavelength anomalous scattering,
uses the fact that X-rays from synchrotron radiation
sources can be tuned to the absorption edge of a specified
atom. This may be any atom that is present as only a
few copies in the molecule, such as a metal ion (which
may be intrinsic to the macromolecule) or selenium
atoms that have been substituted for sulfur in the
methionine residues of proteins using recombinant
DNA technology. At wavelengths near to the absorption
edge, the X-rays are scattered anomalously and large
differences in the diffraction intensities can result
from small changes in the energy of the incident X-rays.
These ‘anomalous’ atoms can then be treated in a similar
fashion to the heavy atoms in the MIR method. Another
method of determining the missing phases relies on the fact
that the unknown structure is similar to one that has
already been determined. This method, termed molecular
replacement, locates the known structure in the crystal of
the unknown and then enables an initial set of phases to be
calculated. Molecular replacement is assuming greater
importance as the database of known structures continues
to grow.
Macromolecular Structure Determination: Comparison of Crystallography and NMR
2
What in the Model Has Been Inferred
from Other Information Versus What
Comes Directly From the Data?
Both NMR and X-ray structure determination methods for
macromolecules generally require prior knowledge or other
information to interpret the structural data. This stems
from the fact that in both methods the effective ‘resolution’
or ability to separate individual objects is not sufficient to
distinguish individual atoms. There are rare instances when
X-ray diffraction of macromolecules extends to better than
0.1 nm resolution and all aspects of the structure can be
determined ab initio. In most cases, however, the resolution
is in the range 0.18–0.30 nm. Resolution is not a simple
parameter in NMR structure determinations, but it may be
inferred by comparison with X-ray structures and would
typically be in the range 0.20–0.30 nm.
At a resolution of 0.2 nm, the outline of chemical groups,
such as the side-chains of proteins or the bases of nucleic
acids, can be clearly distinguished. However, to build an
atomic model, it is necessary to know the sequence of
monomers that make up the macromolecule, accurate
structures for the monomers, and the structures of the
linking groups. It is sometimes possible to assign the
sequence of a protein from a moderate-resolution electron
density map or from NMR resonance assignments, but this
would never be taken as definitive. Thus, prior information
about the sequence of monomers in the protein or nucleic
acid is generally essential for both NMR and X-ray
structure determinations.
Chemically distinct groups such as the side chains of the
amino acids aspartic acid and asparagine could never be
distinguished on thebasis of an X-ray structurealone, since
the atoms involved scatter X-rays almost equally. However,
these groups can be readily distinguished on the basis
of the differing number of NMR-active nuclei in NMR
spectroscopy. NMR spectra can also reveal the protonation
state of ionizable amino acid side-chains, whereas this
information can often only be indirectly inferred from the
pattern of hydrogen bonds and salt bridge interactions in
X-ray structures.
In addition to the covalent structural information, the
refinement or optimization of structures using either X-ray
or NMR data requires the input of restraints to prevent
convergence to an energetically unreasonable structure. In
practice this is accomplished by adding a relatively simple
molecular mechanics force field in the final stages of the
structure calculation.
Judging Model Quality
Errors associated with a macromolecular structure determination
are of quite different kinds. There are those that
yield a completely erroneous result, and the random errors
that define the precision of any experiment. The former will
be dealt with in the next section. The result of a structure
analysis is a set of three-dimensional coordinates and like
any numerical result they should be accompanied by
estimated standard deviations. This is certainly a routine
publication requirement for the crystal structure of a small
molecule. The errors are derived from the standard
deviations of the experimental intensity measurements,
which are adjusted for known systematic effects. Errors in
the atomic coordinates are then calculated from the leastsquares
structure refinement procedure. In the case of a
macromolecule, the situation is complicated by the
incorporation of restraints in the refinement procedure
and by the use of sparse matrix minimization methods,
which do not readily yield errors for the variable
parameters. The situation is compounded further for
NMR where the distances estimated from the NMR
spectra can only be assigned to ranges and not given
specific values with associated errors.
One thing that is important to note is that, whether the
technique is NMR or X-ray analysis, the errors in a
macromolecular structure determination are not uniform
throughout the structure and are different for each residue
and atom. If parts of a crystal structure are disordered, no
significant electron density may be present. If this is the
case, then the only restraint on the atomic positions of the
affected atoms is the requirement for molecular connectivity.
Parts of the structure that are disordered or undergoing
motion will be defined poorly whether the structure is
determined using NMR or X-ray diffraction. In the former
case, fewer distances will be defined for the affected region,
and the resulting structure will show large divergences for
those parts. Similarly, the X-ray structure will have high
thermal parameters for the affected regions. In the case of
X-ray analyses, these affects have been quantified by
Cruickshank, Read, Jones and others. Cruickshank’s
diffraction precision indicator is now often quoted in
publications of protein structures. The root-mean-square
deviation values for the family of structures determined by
NMR also give some estimate of the precision, although
for the case of NMR this has not been quantified and
related to standard deviations of the individual atomic
coordinates.
The best single indicator of the quality of an X-ray
structure determination is the resolution of the data. This
property is generally related directly to the quality of the
crystals and with modern instrumentation is less likely to
be limited by the equipment. The effect of increased
resolution is twofold. Firstly, higher resolution increases
the detail visible in electron density maps and reduce the
possibility of errors of interpretation. Secondly, as the
resolution increases so does the number of observations.
The increased ratio of experimental observations to
parameters effectively decreases the reliance on the
nonexperimental restraints in the refinement procedure.
Macromolecular Structure Determination: Comparison of Crystallography and NMR
3
The equivalent quantity for resolution for an NMR
structure determination would be the number of experimentally
derived restraints used in the refinement procedure
(interproton distances, dihedral angles and
orientational restraints). In the NMR experiment this
parameter is directly related to individual residues and
atoms and therefore varies throughout the structure, while
resolution in the X-ray experiment is a single global
parameter.
Dynamic Information
One of the principal differences in the outcomes of
structure determinations based on NMR and X-ray
diffraction data is the availability of information relating
to dynamics or macromolecular motion. In the NMR
experiment, measurements are made over a time scale of
nanoseconds to seconds, which encompasses many of the
important motions of biological macromolecules. It is
possible using NMR to directly measure the motions of
molecular groups or entire domains.
The scattering event, at the heart of the X-ray diffraction
experiment, is fast compared with atomic or molecular
motion. However, to record a measurable signal, experiments
generally lasting minutes if not hours are required.
Furthermore, the diffraction pattern arises from the entire
crystal, which may not be uniform throughout. If the
molecules exist in randomly different conformers throughout
the crystal then the analysis will result in an average.
Thus the X-ray diffraction experiment provides both a
spatial and a temporal average. One of the parameters used
in the refinement of the structure gives some indication of
molecular motion. This exponential factor accounts for
both real atomic motion that may be occurring in the
crystal and the ‘disorder’ that results from having different
conformations in the crystal. This conformational disorder
may itself indicate parts of the molecule that would be
flexible in solution. In theory, at least, making measurements
at different temperatures can separate the two
components, but this may be difficult in practice.
Practical Considerations: Size,
Solubility and Stability Versus the
Randomness of Crystallizability,
Exchange Rates for Complexes, etc.
X-ray diffraction is practically limited only by the ability to
grow crystals. Structures of large molecular assemblies,
such as proteosomes, the ATP synthase complex, the
photoreaction centre and viruses, have been solved using
X-ray diffraction. Essentially the same methods are
applicable to large structures as to small ones. With
present technology, the practical limit for a complete
protein structure determination using NMR is around 30–
40 kDa; however, this size limit includes numerous small
proteins as well as many autonomously folded protein
domains. Recent NMR developments that take advantage
of anisotropic magnetic interactions promise to significantly
increase this size limit in future years by narrowing
spectral lines at high magnetic field strengths and by
allowing the extraction of orientational restraints in
addition to traditional dihedral angle and interproton
distance restraints.
The upper size limit for determination of nucleic acid
structures using NMR is typically lower than for proteins
because of their intrinsically more limited spectral dispersion.
However, protein–RNA structures as large as 38 kDa
in size have been solved using NMR.
Somewhat surprisingly, given that the most often
claimed difference of X-ray and NMR methods is that
one is applicable to molecules in the crystal or solid state
and the other to molecules in solution, the requirements for
obtaining suitable experimental samples are in fact very
similar. In both cases the sample should be very pure. This
is especially important for X-ray crystallography, where
even small amounts of impurities, especially those similar
to the target molecule, may prevent crystallization or give
crystals that diffract poorly. Recording multidimensional
NMR spectra or growing crystals requires considerable
time, ranging from hours to weeks or even longer. The
samples must therefore be stable for long periods.
For NMR, the sample should be 4 95% pure,
monodisperse, and concentrated enough to give a measurable
signal. NMR is a relatively insensitive spectroscopic
technique and therefore the biomolecule or biomolecular
complex needs to be in solution at a concentration of about
1 mmol L2 1
, which corresponds to around 5–10 mg for a
20 kDaprotein, depending onthe sample size (usually 250–
500 mL). The oligomeric state of the protein should be
ascertained for proper interpretation of the NMR data;
this can be achieved using methods such as analytical
ultracentrifugation, dynamic light scattering, gel filtration
chromatography, and pulsed-field-gradient NMR. Specialized
NMR experiments are required for the extraction
of intermolecular interproton distances in oligomers or
biomolecular complexes.
Predicting whether or not a particular sample will
crystallize and thus be amenable to X-ray diffraction is
notoriously difficult. Extensive experiments with dynamic
light scattering have shown that the best starting point is a
monodisperse solution, just the requirement for NMR.
The starting concentration for crystallization may range
from a few to as much as 100 mg ml2 1
. While the basic
principles of crystallization are well understood, controlling
the rate of reaching supersaturation and the formation
of nuclei is not predictable. Most macromolecules are
therefore crystallized by a random factorial approach in
Macromolecular Structure Determination: Comparison of Crystallography and NMR
4
which selected variables, including precipitant, pH, and
added ions, are systematically varied and the most
promising combinations are followed up by fine screening.
Complexes, such as an enzyme with bound substrate or
inhibitor, need to be sufficiently stable in solution and be in
sufficient concentration that crystals can be grown. Most
complexes that have been crystallized have micromolar or
lower binding affinities. NMR, on the other hand, is able to
observe even transient complex formation in solution
provided that there is time for the transfer of magnetization.
This can provide a very powerful tool for studying the
formation of weak complexes. NMR experiments such as
saturation and inversion transfer can often be used to
measure exchange rates. One particularly convenient
feature of NMR spectroscopy is that binding surfaces,
such as between a protein and a ligand, can be elucidated
without the need to determine the structure of the protein–
ligand complex. The biomolecule of interest is simply
titrated with the ligand; the resonance frequencies of atoms
involved in ligand binding are generally perturbed during
the titration, thus revealing the nature of the interaction.
This interface mapping technique can be applied to drug
screening.
Most Common Errors and Pitfalls of
Each Technique
It is possible to make a catastrophic error at an early stage
of a crystal structure analysis, for example to assign the
wrong space-group symmetry, and then to derive both a
molecular and crystal structure that are completely
incorrect. Fortunately, this type of error is very rare and
can usually be prevented by careful attention to detail and
by using the various aids that have been developed for
monitoring the course of the progress of a crystal structure
analysis. The best known of these tools is the free R factor,
which monitors the agreement of the calculated and
observed diffraction amplitudes but omits any bias from
the model. Careful attention to this parameter prevents
over-parametrization of the refinement procedure. In a
relatively low-resolution X-ray analysis, the entire chain of
the macromolecule may not be visible and breaks in the
experimental electron density may lead to an incorrect
connectivity in the model. The use of unbiased electron
density maps with combined experimental and calculated
phases can help overcome some of these problems.
It is difficult to make a catastrophic error in NMR
structure determinations without several critical resonance
assignment errors. A single incorrectly assigned interproton
distance should not cause serious problems, since it
should reveal itself as irreconcilable with the many
hundreds to thousands of other experimentally derived
restraints. However, several key resonance assignment
errors with unfortunate structural consequences have been
documented in recent years. A more common and easily
avoided problem is incorrectly analysing the spectra of a
homooligomeric macromolecule as though it were a
monomer; this leads to the designation of what should be
intermonomer interproton distance measurements as
intramonomer distances, often with disastrous consequences.
It should be borne in mind that molecules that
are monomeric in vivo can often polymerize at the high
concentrations necessary for NMR spectroscopy.
Further Reading
Berman HM, Westbrook J, Feng Z et al. (2000) The Protein Data Bank.
Nucleic Acids Research, 28: 235–242. [http://www.rcsb.org/pdb/]
Carter WC Jr and Sweet RM (eds) (1997) Macromolecular Crystallography.
Methods in Enzymology, vols 276 and 277. New York:
Academic Press.
Cavanagh J, Fairbrother WJ, Palmer AG III and Skelton NJ (1996)
Protein NMR Spectroscopy: Principles and Practice. San Diego:
Academic Press.
Clore GM and Gronenborn AM (1998) New methods of structure
refinement for macromolecular structure determination by NMR.
Proceedings of the National Academy of Sciences of the USA 95: 5891–
5898.
Drenth J (1999) Principles of Protein X-ray Crystallography, 2nd edn.
New York: Springer-Verlag.
Evans JNS (1995) Biomolecular NMR Spectroscopy. Oxford: Oxford
University Press.
Glusker JP and Trueblood KN (1985) Crystal Structure Analysis: A
Primer, 2nd edn. Oxford: Oxford University Press.
McRee DE (1993) Practical Protein Crystallography. San Diego:
Academic Press.
Prestegard JH (1998) New techniques in structural NMR – anisotropic
interactions. Nature Structural Biology 5: 517–522.
Rhodes R (1993) Crystallography Made Crystal Clear. San Diego:
Academic Press.
Wu¨ thrich K (1986) NMR of Proteins and Nucleic Acids. New York:
Wiley.
Macromolecular Structure Determination: Comparison of Crystallography and NMR
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