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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5319_Библиотеки_им_академика_М_И_Перельмана.pdf
Chapter • Experimental Methods of Structure Determination
13
. Fig. 13.8 A perforated pinhole mask can be used for adiffraction
experiment with alaser pointer. For this the displayed hole patterns
(above) must be brought to the size of the wavelength of laser light.
The diffraction patterns below were generated from these masks. The
holes in the two left masks are all of the same size, which is comparable to having only one type of atom. The hole pattern changes from
wide-meshed squares to askewed parallelogram (see red unit cells).
The diffraction patterns reect the symmetry and distance of the holes
to one another. In the third and fourth masks on the right, the distance
coordination to histidine or cysteine). These heavy at-
oms dominate the diffraction pattern so that they betray
their position in the crystal lattice. Another method takes
advantage of anomalous scattering. This effect is based
on the interaction of X-rays with the electrons of heavy
atoms. As aresult, aspherical wave propagating towards
an atom is reected with aphase shift. Simply stated, it
is returned with adelay. This effect depends on the wavelength and can be used to determine the phase. The crystal is measured on asynchroton (aparticle accelerator
that also produces electromagnetic radiation in abroad
wavelength range, including X-rays) and the diffraction
experiment is performed at several different wavelengths.
Anomalous scattering requires that aheavy atom is present in the protein structure. This is already the case for
metalloproteins. But an alternative approach can also
be taken. Proteins produced in aspecial expression system (Sect.12.6) can be generated with selenomethionine
instead of methionine. The heavier selenium acts as an
anomalous scatterer in the diffraction experiment. Especially for small molecules, there are methods that allow
asimple reconstruction of the phase information from
probability considerations in the intensity distribution
among different reections, the so-called “direct meth-
between the repeating units is identical to those of the rst masks on
the left. The composition of the motif in the repeating unit, however,
varies. It is made up as clusters of multiple holes and can be compared
to the different atoms in amolecule. The distance between the diffracted light reections (lower row) is identical for the rst, third, and fourth
masks. The intensity of the diffracted radiation, however, varies from
reection to reection. It contains information about the composition
and the geometry of the individual motifs and, thus, the “molecules”
which give rise to the diffraction patterns
ods.” Such methods are being developed also for protein structure determination. Often an already solved,
geometrically related protein structure can be used as
astarting model for astructure determination (molec-
ular replacement method). Since the structure prediction
programs such as Alphafold or Rosettafold (Sect.20.6)
have meanwhile reached aconvincing reliability, it is also
possible to generate astarting model in this way. The
model is translated and rotated in the elementary cell
by computer simulations until acalculated diffraction
pattern is obtained that matches the experimentally observed diffraction pattern of the unknown protein.
The phasing obtained at the beginning of the structural analysis with these methods is only approximate
and must be “rened.” For this purpose, the initial model
is shifted and modied step by step until an optimal
agreement with the experimental diffraction data has
been achieved. Altogether the regeneration of the phasing information is not trivial. Even in the 1960s, phasing
calculations kept one scientist busy for several years. The
methodical progress and the increased performance of
computers now allow this to be accomplished in afew
minutes. Even today, however, this step can still be very
challenging for proteins. It is becoming apparent, how-
. • Diraction Power and Resolution Determine the Accuracy of aCrystal Structure
. Fig. 13.9 View of a crystal structure of aldose reductase
(Sect.27.4). The electron density (the so-called 2F0–Fc density at the
1σ level) is displayed as ablue mesh on the predened contour level
around atryptophan residue. In(a), the diffraction data were obtained
at aresolution of 4 Å, and aFourier transform was used to calculate
the electron density. The resolution increases from(a) 4 Å to(b) 3 Å,
to(c) 2 Å, and to(d) 0.66 Å. The resolution in the last-shown contour
ever, that the structure determination of medium-sized
proteins is becoming routine. Historically, the time span
from crystallization to structure determination could be
quite long. Urease is certainly acuriosity. It was the rst
protein to be successfully crystallized. JamesB. Sumner
accomplished this back in 1926. Its 3D structure, however, was rst elucidated in 1995, that is, 70years later!
13.5 Diffraction Power and Resolution
Determine the Accuracy of aCrystal
Structure
Apicture of the contents of the unit cell is the result of
the Fourier transform. It is portrayed in terms of the
electron density in space (. Fig.13.9). To which detail
this electron density can be determined depends on the
number of different wave fronts which are superimposed
with correct amplitude and phase. The number of wave
fronts is equivalent to the number of observed reections
density is so high that hydrogen atoms can be recognized as single density peaks in the difference density map (positive is yellow, negative is
violet of the so-called F0–Fc difference density at the 2σ level). The
electron density is so clearly structured at 2 Å(c) that it is simple to t
the indole building block in place. At 4-Å resolution(a), this assignment is problematic and can easily lead to errors
(see above). In the diffraction images with the laser beam
(. Fig.13.8), it can be seen that the intensities decrease
signicantly towards the rim. The maximum achievable
resolution is, therefore, determined by the ultimately
measurable reection still observed at the rim. It is generated by the array of planes with the smallest mutual
distance in the lattice that can still be observed in the
diffraction experiment. In . Fig.13.7a, the spacing between aset of planes is large and the occupation density
with atoms is high. Therefore, the observed reection will
be strong. In . Fig.13.7b, the planes are closer together,
the occupation density with atoms, however, is lower,
and the generated reection intensity becomes weaker.
In . Fig.13.7c, the planes of an array are very close to
one another, and the occupation with atoms is strongly
thinned out. Consequently, only avery weak reection
is expected here, possibly reaching the resolution limit.
For small organic molecules, this resolution is easily
achieved in that the atoms are visible as distinct maxima
in the electron density. If the crystal’s quality is dimin-
Chapter • Experimental Methods of Structure Determination
13
ished due to lattice defects or disorder, the resolution is
poorer. The resolution obtained from protein crystals is
usually between 1.5 and 3 Å. This means, in the best case,
aresolution is achieved that is on the order of magnitude of abond length. The upper limit is in the range
of the cross section of abenzene ring. Recently, resolutions of less than 1 Å have been increasingly achieved
(. Fig.13.9). In such cases, many details can be seen, for
example, individual hydrogen atoms or multiple spatial
arrangements of side chains.
At higher resolution, the electron density maxima are directly assigned to the atoms in the molecule
(. Fig.13.10). In the beginning this assignment is crude;
the phases used in the Fourier transform are only approximate. The position of the detected maxima must
still be optimized. This is dened as “renement of the
structure.” For this, the experimentally observed diffraction pattern is compared with the diffraction pattern that
is calculated from the atomic positions of the preliminary model. Such an initial model has to be optimized
in aleast squares renement, which is an iterative multistep process. Structural parameters such as atomic coordinates and parameters describing thermal motion are
iteratively modulated in small steps, and at each renement cycle the achieved agreement is quantied by the
so-called R-factor. It determines the agreement between
the diffraction data calculated from the obtained model
with those from the original X-ray diffraction experiment. R-values range from zero for perfect agreement
between the calculated and observed diffraction patterns
to about0.6 for aset of measured diffraction data compared to aset of random data. In protein crystallography, an R-factor in the range of0.2 is considered adesirable target for data with aresolution of about 2.5 Å.
For small organic molecules, renement typically results
in values of R < 0.05.
If the measurement is very accurate, the density of
a“pseudomolecule” with spherical atoms can be subtracted from the observed electron densities at the end of
the structure determination. What remains is the electron
distribution of the bonds between and lone pairs at the
atoms in the molecule. This is, however, only possible
with extremely high-resolution measurements. At lower
resolution, as is the case in moderately resolved protein
structure determinations, adirect assignment of the atoms of the protein to the electron density maxima cannot
be made (. Fig.13.10). More commonly, the course of
the chains is tted to the electron density. Because proteins are constructed from 20different amino acids that
prefer to take on typical geometries, the interpretation of
the electron density is simplied (. Fig.13.10e,f).
Electrons scatter X-rays. Therefore, the number of
electrons around an atom determines how well it is detectable in the resulting density. Hydrogen atoms have
only one electron in their shell. As aresult, they are often undetectable or inaccurately located in the electron
density. Hydrogen atoms can usually be identied in the
density of small molecule crystal structures, but this
will only be possible in protein structures if the resolution is less than 1 Å. This is unproblematic as long as
the hydrogen atoms are in positions that correspond to
spatially xed positions on arigid molecular scaffold,
e.g., hydrogen atoms on phenyl rings. It is more difcult
when the hydrogen atom is on aconformationally exible
group or groups that can be protonated or deprotonated.
It would be ideal to know whether acarboxyl group is
ionized or exists as afree acid and in which direction the
hydrogen atom is oriented. This information can only
be gleaned indirectly from the structure of the protein,
through an accurate analysis of the spatial orientation
and interaction geometry of the surrounding hydrogen
bonding partners.
The accuracy of structure determination depends on
the resolution of the data obtained from acrystal. Even if
the structure of the protein is displayed on the computer
screen like that of asmall organic molecule, its geometry
is determined much less accurately. The margins of error
for small molecule determinations are about 0.01 Å for
bond lengths, 0.1° for bond angles, and 1–2° for dihedral
angles (Chap.16). For protein structures, the errors are
much larger and difcult to quantify. They depend on
how the structure has been rened. Mostly the electron
density does not allow the resolution of single atoms.
Therefore, amino acids are placed in the electron density
with idealized bond lengths and angles. Their geometry is
left at the predened knowledge-based values for subsequent renement. The assignment of atom types for the
placement of side chains is partly based on assumptions.
Knowledge-based values are used or an attempt is made
to keep the hydrogen-bonding network consistent. These
aspects must be considered when evaluating the accuracy
of aprotein structure. The result of crystal structure determination is aspatially and temporally averaged image
of an “average” molecule representing the entire crystal.
It is often found that the electron density in some regions
indicates only areduced occupancy of aside chain or
part of abound ligand. In addition, alternative orientations (conformations) may be seen. Sometimes the electron density of entire regions is missing. This is indicative
of spatial “disorder” and argues for adistribution over
multiple orientations in the crystal. When describing the
diffraction phenomena, we had seen that lattice planes,
and thus the atoms arranged there, will contribute to the
diffraction pattern only if they are found periodically as
an array of planes at the same location over the whole
crystal. This is not the case with disorder. The strict periodicity is lost and with it the contribution to the diffraction pattern. Disorder in the crystal can also be dynamic,
that is, the corresponding group moves back and forth
between two or more arrangements as athermal motion.
Alternatively, the disorder can be static, meaning that
several orientations exist side by side in acrystal, but are
. • Diraction Power and Resolution Determine the Accuracy of aCrystal Structure
. Fig. 13.10 The crystal structure determination of organic mol-
ecules and proteins requires crystals with an edge length of approx.
0.01–0.3 mm. (a)In the X-ray beam, adiffraction pattern is obtained
(compare . Fig. 13.8), which in the past was registered on aphotographic plate, today with an area detector on adiffractometer. The
diffraction pattern of protein crystals shows amuch denser reection
pattern. (b)Structures of small molecules are usually measured in the
laboratory on an automated diffractometer. (c)Electron density indicates the positions of individual atoms. (d)Data from protein crystals are nowadays collected almost exclusively at synchrotron sources.
(e)With approximated phases, aFourier transform is performed and
the electron density in space is obtained, which is contoured according
to apredened electron density level. (c,f)After structure renement,
the density is interpreted and amodel of the diffracting molecule is
tted. (g)Because of the complexity of their structure, proteins are
usually represented by aribbon model that depicts the course of their
polymer chain in space. (h)The spatial blurring of the electron density
is associated with thermal motion of the atoms. It is represented for
randomly distributed. Because the structure is an aver-
aged picture, these arrangements are randomly scattered
throughout the crystal with different orientations. If part
of the molecule is completely disordered, i.e., scattered in
many orientations, the electron density is usually not visi-
ble. Today, diffraction data on protein crystals are mainly
collected at synchrotron radiation sources. Only in rare
cases are they still collected at an in-house facility using
radiation from an X-ray tube. In such atube, electrons are
emitted from alament and accelerated in ahigh-voltage
electric eld (1–100 kV). The electrons then collide with
ametal anode. As the electrons decelerate on the anode
material, X-rays are produced as characteristic brems-
strahlung. Electrons are expelled from the inner shell of
the metal atoms and electrons from an outer shell take
their place. The emitted radiation is therefore determined
by the energy difference between the shells and is specic
small molecules by ellipsoids encompassing 50% of the atomic population probability. (i)For proteins, thermal motion is indicated as socalled B-factors using acolor-coding scheme projected onto the folding pattern. Red indicates high thermal motion, while blue indicates
low thermal motion. (k)The spatial arrangement of the molecules in
the crystal lattice shows adense packing of the protein molecules (here
thrombin). However, large, at rst glance “empty” channels exist in
the crystal packing between the molecules. These channels are occupied by alarge number of water molecules. Because of their extensive
thermal motion and the resulting disorder, they are not detected in the
electron density. However, small-molecule ligands can diffuse through
these channels when the crystals are soaked with asolution of these
ligands. (7 https://sn.pub/m1wZeO)
for the metal of the anode material. In asynchrotron,
radiation is produced as electromagnetic waves when
electrons accelerated to nearly the speed of light are
forced to follow acurved path by magnetic elds. The
radiation is emitted tangentially to the trajectory of the
electrons, because physically achange in the direction
of the velocity vector on the curved trajectory means an
acceleration and thus leads to aspecial form of bremsstrahlung. In this way, abroad spectrum of wavelengths
can be produced. If desired, monochromatic radiation
can be produced using mirrors and crystals, where the
strong reection of acrystal (e.g. graphite) is used as the
primary beam. The synchrotron beam is several orders
of magnitude more intense than the beam from an X-ray
tube. Measuring times of days on an instrument in one’s
own laboratory can be reduced to seconds. However, to
minimize radiation damage to the crystal samples, it is
Chapter • Experimental Methods of Structure Determination
13
. Fig. 13.11 If zinc chloride is reacted with 2,4,6-tris(4-pyridyl)-
1,3,5-triazine (top center), crystals of aporous structure with cavities
are formed(a). Adrop of solvent, in which an organic test molecule
to be investigated is dissolved, is added to the crystals and the test
molecule can diffuse into the huge cavities of the crystal lattice. If
the process occurs slowly and in thermodynamic equilibrium, the test
compound will place itself in aregular fashion in the empty cavities
of the lattice(b). Its geometry can then be determined together with
the lattice of the crystalline sponge (c). Only very small amounts of
necessary to measure the structures at about 100 K in
acryogenic nitrogen gas stream. At this temperature,
many motions in the crystal are frozen and mostly static
disorder is observed. Nevertheless, it has been shown that
the structures determined correspond well to the situation at room or body temperature. These conclusions can
be drawn by comparing the results with the analogous
determination from NMR spectroscopy (Sect.13.7) and
molecular dynamics simulations (Sect.15.7). Nevertheless, detailed studies of crystal structures collected at low
and ambient temperatures have shown, as expected, that
the conformer distributions of side-chain rotamers can
differ at these different temperatures and this is reected
in the determined structures. It should be noted, however,
test substance are required for the method. For example, substances
formed during drug metabolism can be characterized after their chromatographic separation(d). The molecule shown in(c) is the glucuronidated metabolite of gembrozil. (7 https://sn.pub/aJLQMB)
that this is also where the largest differences to NMR
structures and those from molecular dynamic (MD) simulations are observed.
Crystallography of small molecules is still the most
powerful analytical method for characterizing the chemical composition and especially the stereochemistry of
organic compounds. This method allows the absolute
conguration of molecules to be determined with condence on the basis of so-called anomalous dispersion.
It requires the presence of an electron-rich atom that
exhibits such an anomalous dispersion contribution in
the molecule under investigation. For small molecules,
phosphorus or sulfur atoms may be sufcient for these
studies. For elements such as chlorine, bromine, or zinc,
. • Electron Microscopy: Topographic Images Reveal Macromolecular Structures
the effect is stronger. However, aprerequisite for all these
crystallographic determinations is the growth of asingle
crystal. Unfortunately, this is often not trivial. What can
be done if the compound under investigation will not
crystallize? In many cases, there is simply not enough
material to grow acrystal. Apromising alternative has
emerged in recent years: Diffusion in crystalline sponges!
The concept dates back to Makoto Fujita’s group at the
University of Tokyo, Japan. For example, when zinc
chloride is reacted with 2,4,6-tris(4-pyridyl)-1,3,5-triazine, crystals with aporous cavity structure are formed.
. Fig.13.11a shows asection of the crystal packing of
this structure, which contains large cavities. These crystals can be placed in adrop of organic solvent containing
asolution of the substance to be studied. The substance
can then diffuse into the cavities of this crystal lattice.
If this diffusion is slow and in thermodynamic equilibrium, the guest molecules will be taken up and arranged
regularly in the lattice. Everything else then proceeds as
in aroutine structure determination. The absolute conguration can also be determined in this sponge. The
zinc atoms help in this process. They are the necessary
anomalous scatterers in the crystal lattice. The method
requires only very small amounts of substance and the
crystallizability of the substance under investigation is
not required. The method can greatly assist medicinal
chemists in the analysis of their synthesis products.
However, this process can provide other extremely
valuable assistance in drug development. Once adrug
molecule has been developed to the stage of aclinical
candidate, it is necessary to study in detail how the substance is chemically modied in the human body. In
Sect.27.6, we will learn how enzymes, particularly in the
liver, chemically modify drugs, or “metabolize” them.
This is the process of converting adrug molecule into
aform that can be more easily eliminated from the body
via the urine. Because the metabolic process creates active
ingredients that are potentially new to the human body,
it is important to determine exactly what substances are
being formed. What is their stereochemistry and are they
toxic to the body? But before these questions can be answered, the degradation products must rst be structurally characterized. This is where the crystalline sponge
method comes into play. So-called homogenates can be
used to simulate the metabolism in the liver in the laboratory. Any metabolites formed are then separated by
chromatography. Usually, only avery small amount of
the substance is available for subsequent analysis. Mass
spectrometry would be one option for analysis. However,
this does not provide the exact topology and stereochemistry. If, on the other hand, the individual fractions are
allowed to diffuse into the crystalline sponges, the chemical structure, including stereochemistry, can be obtained
in the best case! . Fig.13.11d shows an example of the
metabolic degradation of gembrozil, alipid-lowering
drug from the class of brates (Sect.28.6). The four me-
tabolites formed could be diffused into the crystalline
sponge as guests. . Fig.13.11b,c shows the structure
of the metabolite glucuronidated at the acid function.
Only atiny amount was needed. Crystallography performed on metabolites diffusing into crystalline sponges
certainly has immense potential to massively assist in the
difcult unraveling of drug metabolism.
13.6 Electron Microscopy: Topographic
Images Reveal Macromolecular
Structures
In addition to X-rays, beams of electrons and neutrons
can also be used for diffraction experiments to determine
the structures of molecules. Electron beams have the
great advantage over X-rays and neutrons that they can
be bent by magnets. Therefore, it is possible to build converging (convex) lenses for them, comparable to alight
microscope, to show amagnied image. With X-rays, this
is practically impossible or only very inefcient to realize. This leads to the described phase problem of X-ray
crystallography. The operation that performs the task of
a“converging lens” has to be replaced by aFourier transform. Only then does the electron density of the molecules, and thus their spatial structure, become accessible
with X-rays. In the electron microscope, amagnetic lens
can be used to perform this Fourier transform directly
and then even obtain an image of individual molecules
as “shadows.” However, for along time this approach did
not provide the necessary resolution to reveal the desired
details in these structures.
In recent times, new developments—especially in
the eld of detectors for the registration of electron
beams—have enabled electron microscopy to make ade-
cisive breakthrough in the determination of the structure
of huge macromolecular complexes. The method does
not require crystallized proteins; single molecules can
be studied. Particularly in the case of larger assemblies
of huge protein complexes, crystallization is often the
bottle neck for timely structure determination.
Cryo-electron microscopy (cryo-EM) examines molecules as individual particles, similar to the way acomputer tomograph in medicine scans apatient from all
sides. The intact protein samples are exposed to an
electron beam in ahigh vacuum (. Fig.13.12). Prior
to this, they must be ash-frozen in avitreous water environment. They are then exposed to the electron beam
in many orientations at the temperature of liquid nitrogen. Thus “vitried,” thousands of projection images of
the protein are taken. The next step is the reconstruction of the 3D structure of the studied molecule from
these usually very noisy projections. This is done using
image-processing algorithms. The result is acomposite
Chapter • Experimental Methods of Structure Determination
13
. Fig. 13.12 Schematic representation of the workow during struc-
ture determination with cryo-electron microscopy. Protein molecules
are ash-frozen in avitreous water coat and deposited on agraphite
grid under high vacuum(a). An intense electron beam (sketched by
turquoise cylinder) sweeps across the grid, creating many thousands
of shadow images as projections of the molecules deposited on the
grid(b). The extremely noisy shadow projections(c) are sorted in the
spatial image of the charge density of the microscopically observed object. Since electron beams have amuch
shorter wavelength than light waves, structures down to
the 2–3 Å range can be resolved in favorable cases. By
averaging alarge number of measured shadow projections, the signal-to-noise ratio of the projections can be
signicantly improved. By iteratively evaluating individual projections, reconstructing the 3D structure, and sub
sequently improving the alignment and superposition of
the raw shadow images, the representation of the molecular complex under investigation is continuously rened.
In 2017, Jacques Dubochet, Joachim Frank, and
Richard Henderson were awarded the Nobel Prize in
Chemistry for their contributions to the development
of the cryo-EM technique. Dubochet helped the technique achieve abreakthrough by cryopreparing the pro-
tein samples in the form of avitried embedding in an
amorphously solidied water shell about 100 nm thick.
At the same time, this step allows the samples to be measured at low temperature, since the high-energy electron
computer in terms of similar orientations(d), compiled, and then averaged(d, e). As a result, the molecule under investigation emerges
more and more strongly from the background noise(e). The same procedure is followed with the many thousands of projections (f), and
an averaged spatial image of the protein molecule is generated from
these images, similar to the way in which acomputer tomograph is
generated in medicine(g)
beam would destroy the proteins very quickly at room
temperature. Joachim Frank developed the algorithms to
discover and extract the recurring patterns from the noisy
projected images of randomly distributed molecules, ultimately reconstructing amodel of the spatial structure of
the molecules under study. Richard Henderson helped
cryo-EM make an experimental breakthrough. Step by
-
step, he was able to increase the image resolution of the
bacteriorhodopsin he studied (Chap.29) until the folding
pattern of this protein was nally visible.
Nowadays, under optimal conditions, complexes can
be determined down to atomic details of their spatial
structure. Only recently did Holger Stark’s group at the
MPI in Göttingen succeed in determining acryo-EM
structure of apoferritin with aresolution of 1.25 Å! This
is certainly still the exception. When comparing the reso-
lution limits of diffraction methods and cryo-EM, some
caution is required because the resolutions are dened
and calculated differently. Referring to the closest lattice plane distance, as in diffraction techniques, does not
. • Electron Microscopy: CT on Single Molecules and Diraction on Two-dimensional Crystals
work in the cryo-EM technique. In order to reliably evaluate the quality of the data collected at the many projections in athree-dimensional volume, an evaluation in
Fourier space is performed. This is done by dividing the
dataset into two equal parts and calculating the Fourier
shell correlation. From the inside to the outside, the data
are processed in individual shells and it is determined
how well the Fourier components of the transformed
data correlate in both parts of the dataset. The shell in
which the correlation falls below apredetermined threshold is specied as the resolution limit. The analysis is,
therefore, more of ameasure of the internal consistency
of the two splitted datasets.
Cryo-EM is already the method of choice for studying multiprotein complexes, such as the spliceosome, and
for addressing mechanistic questions about the function
of individual proteins in acomplex. Conventional structure determination in drug design typically requires resolutions of 2 Å or better. Structures must be able to be
determined without signicant effort on ligand series. In
contrast, each additional EM structure virtually means
acompletely new structure determination. For these reasons, classical X-ray crystallography is likely to remain
the workhorse for many years to come. One advantage
of cryo-EM is certainly that the molecules are in afrozen
water environment. This is certainly closer to physiological conditions than acrystalline assembly. In addition,
the method is better at capturing different states of aprotein. For example, if the protein exists as amonomer and
adimer side by side, this will be recorded. However, the
computational cost of structure determination increases
dramatically with increasing resolution.
An alternative, which was initially pursued intensively, is to use crystalline material for the electron microscopic electron microscopic studies. Since the averaged image of several aligned molecules is examined in
aperiodic crystalline array, astronger signal is observed.
The converging lens step (Fourier transform) is omitted
and the reections in the diffraction space are measured
on the crystalline sample as in X-ray diffraction. Electrons penetrate only slightly into the crystalline sample
material, but are scattered much more strongly by the
molecules in the crystal. Therefore, much smaller crystals can be used, and even crystals that are wafer-thin in
one direction and consist of only one or afew molecular
layers are sufcient.
Despite the lower radiation exposure, the electrons
still result in considerable destruction of the samples. It
is important to remember that the crystals used are only
about abillionth of the sample quantity of acrystal used
for X-ray diffraction. The data for an X-ray structure can
often be measured on one single crystal. The electron microscope, on the other hand, requires many hundreds of
the tiny crystals, often only 5 µm in size. They are also
ash-frozen under high vacuum and exposed directly to
the electron beam. The images are also very noisy and
have to be averaged over many images. To obtain detailed
resolution perpendicular to the two-dimensional crystal
plane, crystals must be measured in many orientations.
AFourier transform is used to obtain acharge density
distribution of the molecules, similar to X-ray diffraction.
Its interpretation or renement is done in the same way as
in X-ray experiments. The phases required for the Fourier
transform can be determined in the electron microscope
by direct imaging in the “converging lens mode.” In the
group of Tamir Gonen at the University of California,
Los Angeles, USA, the idea was developed to minimize
radiation damage by reducing the intensity of the electron beam. Thus, agreater number of reections can be
collected on individual crystals. In this way, the micro-ED
method was successfully applied to aresolution range of
about 1 Å by electron diffraction. The method can also be
extended to the structure determination of small organic
molecules. Since only very small crystals are required, the
method works even with materials that look almost like
an amorphous powder to the naked eye. To demonstrate
its applicability, the Gonen group took nished drugs
and crushed the tablets. The resulting powder was still
crystalline enough to be used in an electron microscope
to determine the structure of the drug molecules in the
sample. It was also possible to nd sufciently large crystallites of the precipitant that remained in aask after
asubstance was recovered following evaporation of the
solvent. They still allowed the structure to be determined
using the micro-ED method. This method may represent
a breakthrough in crystallographic structure analysis,
since in many cases the supposed bottleneck of single
crystal growth may prove to be irrelevant.
Another type of radiation that can be used for diffraction experiments on biomolecules is abeam of neutrons.
Neutrons are produced either in areactor by nuclear ssion of uranium isotopes or from aspallation source. In
the latter case, heavy metals such as mercury emit out
neutrons after they have been bombarded with high-energy electrons in anuclear conversion reaction. Aneutron
beam behaves much like an X-ray beam in adiffraction experiment. However, the strength with which the chemical
elements contribute to the scattering power in areection
is completely different to X-rays. For example, hydrogen
is astrong scatterer and the Hisotope can be easily distinguished from the Disotope (deuterium). An element
like sulfur is aweak scatterer, and the metal vanadium is
practically invisible to neutrons. Therefore, this metal is
often used as amaterial for sample containers for neutron
diffraction experiments. For biological samples, neutrons
have the incredible advantage of being very powerful at
visualizing geometries involving hydrogen atoms. This is
especially true for the study of hydrogen bonds and protonation states of acidic and basic groups. But also the
orientation of water molecules and their dynamic behavior are visualized (. Fig.4.10). Why not do all structure
determinations with neutrons? Unfortunately, the inten-
13
Chapter • Experimental Methods of Structure Determination
sity of aneutron beam is much, much weaker than that
of an X-ray beam, which means that the crystals required
for neutron diffraction must be much larger, with edge
lengths of several millimeters. Crystals of this size can be
successfully grown from very few proteins.
13.7 Structures in Solution: The Resonance
Experiment in NMR Spectroscopy
Many atomic nuclei have an angular momentum, or spin.
The nuclei that occur in biological systems that have
anuclear spin are the hydrogen isotope 1H, the carbon
isotope 13C, the nitrogen isotope 15N, the uorine isotope
19
F (in biology rarely found), and the phosphorus isotope
31
P (for the sake of simplicity, only nuclei with aspin of
½ will be considered here). Just as atop would, these
nuclei rotate about their axes. As long as no magnetic
eld is applied, the tops orient in all possible spatial directions. In amagnetic eld, they are forced into alignment (. Fig.13.13). If atoy top is spun, it will move in
the gravitation eld. This eld has, as the magnetic eld,
one preferred direction. If the alignment of the rotation
axis of the top and the direction of the gravitation eld,
which is oriented towards the center of the Earth, are
not exactly the same, the top will wobble. The end of
the rotation axis performs acircular movement, an arc,
with avery precise rotational velocity. It depends on the
mass and geometry of the top. In physics this movement
is known as precession.
Atomic nuclei with aspin behave in avery similar
way. In contrast to the macroscopic top, they obey the
laws of quantum mechanics. This means that the rotation axes that their precession movement takes on can
only adopt very specic angles with respect to the applied
eld direction. The result for the 1H, 13C, 15N, 19F, and
31
P nuclei is that the rotation axis for the precession arc
can only be parallel or antiparallel to the direction of
the eld (so-called spin ±½ particles). The orientation in
the direction of the eld is energetically somewhat more
favorable than the rotation antiparallel to the direction
of the eld. Statistically, therefore, more nuclear spins
in the substance sample will align with the direction of
the eld. If an additional magnetic eld is applied to the
outer magnetic eld and its frequency corresponds to the
precession frequency of the nuclear spin, the occupancy
of “parallel” to “antiparallel” spinning nuclei can be reversed and aresonance absorption for the sample can
be registered. After aparticular time span, the original
situation is restored (relaxation) for entropic reasons.
The rotational velocity of the top’s axis for precession
movements is characteristic for each type of nucleus. It
further depends on, and is additionally modulated by,
the composition of the chemical environment in which
the nucleus resides. Acarbon atom of aphenyl ring has
adifferent resonance frequency than that of an aliphatic
. Fig. 13.13 Atomic nuclei with a rotational momentum behave
like aspinning top. In the absence of an external magnetic eld, they
orient in all possible directions randomly (left). Upon application of
amagnetic eld, they orient their rotation axes parallel or antiparallel to the direction of the eld (right). The precession movement is
oriented in an arc around the applied eld direction. The two orientations, parallel or antiparallel, with respect to the direction of the eld
are energetically different. Because of this, there is asmall difference
in occupancy between the two states. By applying an electromagnetic
eld with afrequency corresponding to the rotational movement of
the precession of the axis of the top, the occupation can be inverted.
This resonance absorption, the exact frequency of which depends on
the type of nucleus and its immediate chemical environment, is registered with aspectrometer
chain. The relative position of the resonance absorption
in relation to astandard reference is also called the chem-
ical shift. Furthermore, the individual nuclei can perceive
the spin orientation of the neighboring nuclei. An alignment in the same direction as aneighboring nucleus is
energetically different from that of an antiparallel orientation. This inuence also modulates the rotational speed
of the spin on the observed nucleus. The information
transfer regarding the orientation or the magnetic state
of the nuclei in the vicinity can be transmitted over several bonds. This transfer can even occur through space
without any direct covalent connection.
To measure an NMR spectrum (nuclear magnetic resonance), asolution of the substance has to be placed in
astrong magnetic eld. In addition, avariable electromagnetic eld is applied to the sample. The frequencies at
which the nuclei in the sample have resonance, meaning
when they ip from parallel to antiparallel, are recorded.
The resulting spectrum discloses information about the
composition and the chemical environment around the
studied nuclei. It contains information about the spatial
structure of the molecules under investigation. Based on
the work of Richard Ernst, who received the Nobel Prize
in Chemistry in 1991, multidimensional NMR techniques
have been developed over the last 30years. By applying
suitable measurement conditions and selective electromagnetic elds, information about the mutual inuence
of resonance frequencies between individual nuclei is
separated and analyzed. This bidirectional transfer of information about the magnetic state of neighboring nuclei
. • From Spectra to Structure: Distance Maps Evolve into Spatial Geometries
is evident from the signal form in the multidimensional
spectra, and it is registered in the form of cross peaks.
In 1965, Anet and Bourn performed decoupling experiments in which they saturated aparticular hydrogen atom in the spectrum by irradiating it separately at
the corresponding resonance frequency. They observed
that the resonance intensity of aneighboring hydrogen
atom, which was not covalently bonded to the saturated
Hatom, increased by 45%. This, of course, provides important information about the spatial proximity of the
atoms. This so-called nuclear Overhauser effect (NOE) is
often used in NMR experiments to elucidate the structure
and conformation of biomolecules and their interactions.
Only the hydrogen isotope 1H occurs in nearly 100%
natural abundance. Therefore, it can be assumed that for
statistical reasons, two 1H nuclei will always be adjacent
to each other in amolecule. In contrast, the 13C and 15N
isotopes are scarce. As aresult, statistically they are only
very rarely found in the direct vicinity of one another.
Data on the mutual inuence of the magnetization of
these nuclei are required for the spectra. Therefore, it is
necessary to enrich the proteins with the appropriate isotopes. For this, bacteria are fed with isotopically labeled
substrates such as glucose or ammonium chloride and
will then produce proteins that are isotopically enriched.
It is even necessary to produce deuterated proteins for
the structural investigation of very large proteins. Today, by using numerous spectroscopic techniques, spectra
from proteins of more than 800 amino acids have been
successfully interpreted. The following questions can be
addressed by NMR analysis:
Which atomic nuclei occur in which chemical environ-
-
ment?
What is in the immediate, covalently connected neigh-
-
borhood of these nuclei? Information about the spa-
tial orientation of atoms in the vicinity is also con-
tained within these spectral parameters.
Which geometric relationships are given between dif-
-
ferent segments of the polypeptide chain? This results
from information transfer about magnetic states of
nuclei that are not directly connected by covalent
bonds.
13.8 From Spectra to Structure: Distance
Maps Evolve into Spatial Geometries
This last-mentioned observation, which results from
the nuclear Overhauser effect (NOE), yields intramolecular distances of spatially neighboring but not directly
covalently bound atoms. The entire connectivity, that
is, alist of all covalent bonds within amolecule, and
alist of the recorded intramolecular noncovalent NOE
distances are applied to generate the structure for the
molecule (. Fig.13.14). For this purpose, so-called dis-
tance–geometry calculations are used to create the spatial
coordinates of the atoms.
Often, distance geometry produces several equally
good structural models that satisfy the experimentally
NMR studies are usually performed in solution. In this
way, dynamic processes can be observed by changes in
the spectra. Fluorine atoms are isotopically pure as 19F
nuclei and they are rarely used by Nature. As anucleus,
it can be observed very well in the NMR spectrometer.
Therefore, it is auseful probe to study the properties of
biomolecules. Fluorine-containing amino acids can be
introduced into proteins under special expression conditions. The 19F resonances can then be used to study
the structural and dynamic properties of proteins. An
example is given in Sect.21.14.
. Fig. 13.14 A multidimensional NMR spectrum contains informa-
tion about the spatial vicinity of atomic nuclei in amolecule (here, the
trypsin inhibitor from bovine pancreas). It is expressed in cross peaks.
This provides information about the distance between noncovalently bonded atoms in amolecule. The individual signals of the spectra
are assigned to atoms in the molecule (e.g.,A and B). The positions
that these atoms have in the polypeptide chain are known from the
sequence of the protein (above left). The intensity of the cross peak
indicates which spatial distance is found between nucleiA andB in the
folded polypeptide chain (above right). Just as was done forA andB,
the many other cross peaks are evaluated and translated into distance
conditions. With the totality of this distance information, it is possible
to fold the polypeptide chain in space