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. • Synopsis
over again “naturally” during breeding. Anew tool is
available, its potential is undeniable. Only time will tell
whether it will also bring the blessing of freeing us from
hereditary diseases. In December 2023, the rst CRISPR-Cas9 gene-editing therapy was approved. Casgevy,
launched by Vertex Pharmaceuticals, is aimed at curing
sickle cell disease. It does not correct the mutation that
causes sickle cell disease (Sect.12.13). Instead, Casgevy
is designed to compensate for the loss of adult hemoglobin by inducing fetal hemoglobin, the main oxygen
carrier in the fetus, which is normally switched off
shortly after birth. The therapy is still very complex
and expensive, but it represents apromising new treatment option.
Gene technology not only solves problems, but it
also creates new ones. The technical barrier for creating
ahomo perfectus is as low as it has ever been in human
history. The door to possible misuse is now wide open.
We can only hope that ethics and common sense will prevent this from happening. Draconian legal regulations do
more harm to the benecial use of gene technology than
to prevent its misuse. Those in positions of responsibility have recognized this and have created aframework
within which gene technology can evolve for the benet
of humanity.
12.16 Synopsis
Gene technology has developed into akey technology
-
in modern drug research because it allows the pro-
duction of pure proteins, the targeted mutagenesis to
elucidate functional and mechanistic properties of pro-
teins or to conrm and disprove binding modes, pro-
duces animal models by knocking in and out particu-
lar genes, and allows genes to be activated or silenced.
With the PROTAC method, gene technology can be
used to target proteins for cellular degradation. This
makes individualized somatic gene therapy possible.
The elucidation of the genetic code, the recombinant
-
production of genes and gene products, and the poly-
merase chain reaction were milestones in the estab-
lishment of gene technology.
The sequence analysis of the human genome revealed
-
the constitution of our genes, the number of gene
products, and many functional insights. Meanwhile,
hundreds of genomes of other species have been se-
quenced, and the analysis of the genome of individ-
uals is affordable.
The human genome contains about 25,000 genes of
-
which about 21,500 are translated into proteins. Some
sequence segments are noncoding RNAs and they ac
complish important functions in the organism (e.g., in
the ribosome or spliceosome). About 95% of the ge-
nome contains numerous sequences and signals that
control the regulation of the genome. Afunctional
classication of the gene products has been accomplished for asignicant portion of the genome.
To study the relevance of blocking the function of
-
agene product, that is, aprotein in adisease situation,
aparticular gene can be knocked out in an animal
model, mostly in mice. Genes can also be knocked
in. Such turning on and off of genes is of utmost
importance in drug research because it provides decisive information about the relevance of aplanned
therapeutic intervention.
In vitro models for drug screening could only be de-
-
veloped once proteins could be produced in pure form
and high yield. Various expression systems from bacterial up to mammalian cells can be used for the production of foreign proteins, which are brought into
cells via the corresponding coding DNA.
Genes can be silenced by RNA interference. There-
-
fore, small amounts of double-stranded RNA, usually produced by the enzyme dicer, are incorporated
into the enzyme complex RISC. RISC uses one strand
of the RNA dimer segments as atemplate to capture
mRNA molecules with acomplementary sequence
and cleaves them sequentially. By doing this, mRNAs
with particular sequences are eliminated.
To copy this principle for therapy, one needs about
-
22-base RNA molecules that have to be transported
across the membrane into cells, adifcult task with
fragile and highly polar species. Furthermore, these
molecules can cause unwanted immune responses.
Chemical modications of the RNA molecules are
aimed at improvements in the transportation, immunogenicity, and stability properties.
The PROTAC process (proteolysis-targeting chime-
-
ras) causes selective proteolytic degradation of pathogenic and, therefore, unwanted proteins into amino
acids by the cell’s own protein degradation machine.
The proteome reects the totality of all proteins in
-
acell at agiven point in time under precisely dened
conditions. Its composition changes dynamically and
differs between healthy or diseased states or under the
inuence of therapeutic treatments.
The proteome can be analyzed at any given time by
-
2D gel electrophoresis. This combines aseparation by
isoelectric focusing and SDS-PAGE analysis. Differences in expression patterns indicate the involvement
of proteins in adisease situation. Back regulation
under drug administration can indicate apossible
therapeutic strategy.
Pull-down experiments with immobilized drug mol-
-
ecules on a chromatographic solid support allow
the trapping of proteins that show interaction with
-
studied drug molecules. Interaction proles for drug
molecules in the cell can be determined.
Biomolecules can be immobilized on microarray
-
chips. In particular, RNA, DNA, and their oligonucleotides are anchored on these chips to extract com-
Chapter • Gene Technology in Drug Research
12
plementary RNA or DNA sequences from large mix-
tures. Suitable uorescent labeling of the anchored
decoy sequences or of the sequences to be “shed”
makes it easy to automatically record the detection
of binding. With this, the expression patterns of cells
can be studied.
Polymorphisms, particularly single nucleotide poly-
-
morphisms (SNPs), are variations in the composition
of the genome of aspecies. These changes make indi-
viduals different, and some SNPs confer susceptibil-
ity or resistance to diseases or inuence the cellular
response to adrug.
Differences in the individual genomes might be the
-
key to atailored individual and personalized drug
therapy and can allow asusceptibility to aparticu-
lar disease pattern to be recognized. Intolerance to
agiven drug therapy could become transparent or the
classication of an individual into different metabo-
lizer classes could be achieved.
Genetic differences can be areason for the develop-
-
ment of diseases. In some cases, they are caused by
single amino acid exchanges in one gene product (e.g.,
sickle cell anemia); in other cases multifactorial genetic
causes are responsible for the disease development.
Epigenetics do not alter the sequence of DNA, but
-
regulate the transcription process by changing the
accessibility of genes. Lifestyle, experience, and en-
vironment exert their effect on the genes through the
epigenome.
Methylations, phosphorylations, and acetylations
-
transmit epigenetic information in areversible man-
ner. Either the bases of DNA are directly methylated
or the packing density of stored DNA on the histone
proteins is altered making it more or lesser accessible
to DNA reader domains. The latter process modies
the charges of positively charged Lys and Arg residues
involved in packing via the transfer of acetyl groups.
The goal of gene therapy tries to replace adefective
-
or missing gene in the cells of apatient. This would
make it possible to eliminate the genetic disease for the
individual and their offspring. Anucleic acid segment
is inserted into the genome via viral carriers, and it
codes for the protein that is to be substituted in the
patient. Gene therapy attempts to replace defective or
missing genes in apatient’s body cells. Retroviruses
are used for this purpose and anucleic acid segment
is introduced into their genome that codes for the
protein to be substituted in the patient. Retroviruses
transcribe this information into DNA and integrate
it into the DNA of the cells in the patient. With the
CRISPR-Cas9 method, highly precise gene scissors
are also available, which in the future might make it
easy to exchange diseased genes for healthy ones.
Bibliography and Further Reading
General Literature
B. R. Glick and J. J. Pasternak, Molecular Biotechnology: Principles
and Applications of Recombinant DNA, ASM Press; 6th Edition
(2022)
K. B. Mullis, F. Ferré and R. A. Gibbs, Eds., The Polymerase Chain
Reaction, Birkhäuser, Boston (1994)
N. G. Cooper, Ed., The Human Genome Project. Deciphering the
Blueprint of Heredity, University Science Books, Mill Valley, CA,
USA (1994)
T. Strachan, The Human Genome, Bios Scientic, Oxford (1992)
G. M. Monastersky and J. M. Robel, Eds., Strategies in Transgenic
Animal Science, Blackwell Science, Oxford (1995)
M. Békés, D. R. Langley, C. M. Crews, PROTAC targeted protein de-
graders: the past is prologue, Nat. Rev. Drug Discov., 21, 181–200
(2022)
J. A. Wolff, Gene Therapeutics. Methods and Applications of Direct
Gene Transfer, Birkhäuser, Boston (1994)
L. E. Post, Gene Therapy: Progress, New Directions, and Issues, Ann.
Rep. Med. Chem., 30, 219–226 (1995)
J. S. Kiely, Recent Advances in Antisense Technology, Ann. Rep. Med.
Chem., 29, 297–306 (1994)
S. B. Pandit, S. Balaji and N. Srinivasan, Structural and Functional
Characterization of Gene Products Encoded in the Human Ge-
nome by Homology Detection, IUBMB Life, 56, 317–331 (2004)
P. E. Slagboom and I. Meulenbelt, Organisation of the Human Ge-
nome and our Tools for Identifying Disease Genes, Biological
Psychology, 61, 11–31 (2002)
E. S. Lander, etal., Initial Sequencing and Analysis of the Human
Genome, Nature, 409, 860–921 (2001)
J. C. Venter, etal., The Sequence of the Human Genome, Science, 291,
1304–1351 (2001)
S. L. Salzberg, Open question: How many genes do we have? BMC
Biol., 16, 94 (2018)
A. C. Lai and C. M. Crews, Induced protein degradation: An emerging
drug discovery paradigm, Nat. Rev. Drug Discov., 16, 101–114
(2017)
L. DeFrancesco, Life Technologies promises $1,000 genome. Nature
Biotech., 30, 126 (2012)
J.A. Doudna and E. Charpentier, Genome Editing. The new frontier
of genome engineering with CRISPR-Cas9, Science, 346, 1258096,
1–9 (2014)
Special Literature
K. B. Mullis, The unusual origin of the polymerase chain reaction,
Scient. American, 262(4), 56–61 (1990)
R. D. Fleischmann etal., Whole Genome Random Sequencing and As-
sembly of Haemophilus inuenzae Rd, Science, 269, 496–512 (1995)
M. D. Adams etal., Initial Assessment of Human Gene Diversity and
Expression Patterns Based Upon 83 Million Nucleotides of cDNA
Sequence, Nature, 377, Suppl., 3–174 (1995)
L. Timmons, H. Tabara, C. C. Mello and A. Z. Fire, Inducible Sys-
temic RNA Silencing in Caenorhabditis elegans, Mol Biol Cell.,
14, 2972–2983 (2003)
K. M. Sakamoto, K. B. Kim, A. Kumagai, F. Mercurio, C. M. Crews,
R. J. Deshaies, Protacs: chimeric molecules that target proteins to
the Skp1-Cullin-F box complex for ubiquitination and degrada-
tion, Proc Natl Acad Sci USA, 98, 8554–8559 (2001)
C. Arnold, PROTAC protein degraders to drug the undruggable enter
phase 3 trials, Nat Med, (2020), https://doi.org/10.1038/d41591-
024-00072-8
Bibliography and Further Reading
M. W. Chang, E. Barr, J. Seltzer, Y.-Q. Jiang, G. J. Nabel, E. G. Nabel,
M. S. Parmacek and J. M. Leiden, Cytostatic Gene Therapy for
Vascular Proliferative Disorders with a Constitutively Active Form
of the Retinoblastoma Gene Product, Science, 267, 518–522 (1995)
C. Craig, Bristol-Myers to Pay $2.7M for Transgenic Goats that Make
Human Antibodies, BioWorld Today, 6, 1 (1995)
M. S. Gadd etal., Structural basis of PROTAC cooperative recognition
for selective protein degradation, Nat. Chem. Biol., 13, 514–521
(2017)
U. Rix and G. Superti-Furga, Target proling of small molecules by
chemical proteomics, Nat. Chem. Biol., 5, 616–624 (2009)
R. K. Seide and A. Giaccio, Patenting Animals, Chemistry & Industry,
16, 656–659 (1995)
http://www.ensembl.org/Homo_sapiens/index.html (Explore the Homo
sapiens genome) (Last accessed Nov. 16, 2024)
https://www.genecards.org/ (The Human Gene Database with functional
predictions) (Last accessed Nov. 16, 2024)
https://www.proteinatlas.org/search/ (The Human Protein Altas) (Last
accessed Nov. 29, 2024)
J. Wang, S. Yazdani, A. Han, M. Schapira, Structure-based view of the
druggable genome, Drug Discov Today, 25, 561–567 (2020)
S. Adhikari etal., A high-stringency blueprint of the human proteome,
Nat Comm, 11, 5301 (2020). https://doi.org/10.1038/s41467-020-
19045-9
P. Amaral etal., The status of the human gene catalogue, Nature, 622,
41–47 (2023)
J. M. Carlton etal., Draft Genome Sequence of the Sexually Transmit-
ted Pathogen Trichomonas vaginalis, Science, 315, 207–212 (2007)
S. Schneiker etal., Complete Genome Sequence of the Myxobacterium
Sorangium cellulosum. Nature Biotech., 25, 1281–1289 (2007)
Experimental Methods
of Structure Determination
Contents
13.1 Crystals: Aesthetic on the Outside,
Periodic on the Inside – 194
13.2 Just Like Wallpaper: Symmetries Govern
Crystal Packings – 196
13.3 Crystal Lattices Diract X-Rays – 196
13.4 Crystal Structure Analysis: Evaluating the Spatial
Arrangement and Intensity of Diraction Patterns – 197
13.5 Diraction Power and Resolution Determine
the Accuracy of aCrystal Structure – 201
13.6 Electron Microscopy: Topographic Images
Reveal Macromolecular Structures – 205
13.7 Structures in Solution: The Resonance
Experiment in NMR Spectroscopy – 208
13.8 From Spectra to Structure: Distance Maps
Evolve into Spatial Geometries – 209
13.9 How Relevant Are Structures in aCrystal or NMR Tube
to aBiological System? – 211
13.10 Synopsis – 212
Bibliography and Further Reading – 213
© The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
G. Klebe, Drug Design, https://doi.org/10.1007/978-3-662-68998-1_13
Chapter • Experimental Methods of Structure Determination
13
In this chapter, we will focus on experimental methods
used to determine the structure of ligands and proteins.
There are three main techniques that provide information about the three-dimensional structure of small organic molecules up to proteins: crystal structure analysis,
high-resolution NMR spectroscopy, and electron microscopy. The rst technique is the oldest. It goes back to an
experiment performed by Max von Laue in 1912. Just
17years earlier, Wilhelm Roentgen had discovered an
electromagnetic radiation that was later named X-rays
or “Roentgen rays” in German in his honor. Together
with his collaborators Walter Friedrich and Paul Knipping, Laue demonstrated the wave nature of X-rays using
acopper sulfate crystal. At the same time, they demonstrated the lattice structure of crystals. Just one year later,
William Lawrence Bragg and his father William Henry
Bragg reaped the rewards of these experiments. They determined the crystal structure of sodium chloride. The
technique has evolved over the years. Today, the structures of proteins and nucleic acid complexes containing
many thousands of amino acids and nucleosides have
been determined.
NMR spectroscopy is likewise arelatively new technique. In 1945, the research group of Felix Bloch and
Edward Purcell in the USA rst observed the resonance
absorption of hydrogen nuclei in amagnetic eld. From
this experiment, the technique has grown, largely due
to advances in instrumentation, to the point where the
structure of proteins with more than 800 amino acids can
be determined. However, this requires the protein to be
extensively labeled with different isotopes.
In recent years, electron microscopy has emerged as
another very powerful imaging technique, providing
direct images for structure determination of very large,
often membrane-bound protein complexes and viruses.
For this purpose, the samples must be “vitried” (sealed
in ice like aglass) in aprocess known as cryo-electron
microscopy, so that they can then be studied as individual molecules at low temperatures. On the other hand,
electron beams can also be used for crystallographic diffraction experiments to elucidate structures, similar to
classical crystallography.
13.1 Crystals: Aesthetic on the Outside,
Periodic on the Inside
The term “crystal” causes one to immediately think
of well-formed minerals or sparkling gemstones with
amagnicent cut. The association of crystals with the
structures of the molecules that determine our lives only
occur to us as asecond thought. The crystal is typically
associated with “dead” material. When Jack Dunitz took
over his chair as professor of organic chemistry at the
ETH in Zurich at the end of the 1950s, the famous natural product chemist Leopold Ruzicka dismissively told
him that crystals are a“chemical graveyard.” Nonetheless, Dunitz and his research group showed over many
years that acrystal in no way belongs in a“graveyard,”
but rather is the key to understanding the structure, dynamics, and reactivity of molecules.
If amineral is considered, the regular construction of
the single crystals stands out. Even organic materials have
the ability to form well-shaped crystals. One must only
think of the fascinating crystals of candied sugar. Is this
external regularity arepresentation of the inner structure?
Before this question is answered, the way that crystals
are obtained should be claried. Amineralogist got it
easy. Nature has already provided well-formed crystals
over thousands or millions of years. Organic molecules
and proteins rarely occur in Nature in acrystalline state.
Conditions must be found under which they crystallize.
In general, crystals are grown from asolution. For simple organic substances, this can also be accomplished from
melted material or by sublimation. Both crystallization
methods are known from water when alake freezes over
or when beautiful hoarfrost crystals form. For crystalliza-
tion from solution, asolvent is sought in which the com-
. Fig. 13.1 Paving stones cover asurface without leaving holes (left).
This is only possible if they are derived from aparticular basic geometric pattern, for instance aparallelogram, rectangle, square, triangle, or hexagon. This basic pattern can by modulated by complementary bulges and recesses. Apath cannot be covered without holes if
equilateral pentagons or octagons are used. If an octagonal stone is
combined with asquare stone, however, the surface can be completely
covered. It is immediately clear that if asquare stone is cut along its
two diagonals, two triangles result. Adding four such pieces an octagon can be amended to asquare in this way (right)
. • Crystals: Aesthetic on the Outside, Periodic on the Inside
. Fig. 13.2 In the simplest case, amolecular packing is generated by
purely shifting the molecule in all three spatial directions. The generating unit, the elementary cell, is derived from an irregularly angled
body, aparallelepiped (right, magnied image, purple). If apoint near
the molecule is picked out and all of the molecules in the crystal pack-
pound is sufciently soluble. By changing the conditions,
the saturation point of the solution is exceeded. If this is
done slowly, small crystal nuclei will be formed which can
grow into large crystals. As arule, the solubility of the
compound decreases as the temperature is lowered. The
saturation point of the solution can be exceeded by changing the temperature. The solution can also be “thickened,”
meaning that some of the solvent is removed. Another
possibility is to add asecond solvent in which the compound is less soluble. If the ratio of the two solvents is
chosen correctly, the saturation point can be approached
slowly. For compounds with acidic or basic groups, pH
conditions can be found at which the compound exists
as asalt. Because of strong ionic interactions, salts often form better crystals. Organic compounds can also be
“salted out.” This is done by adding asalt, such as sodium
chloride, to an aqueous solution of the compound. The
salt “absorbs” the water molecules as it goes into solution.
It is surrounded by asolvation shell of water molecules.
This removes the water molecules from the surface of the
organic compound, which is also surrounded by asolvent
sphere. By this, the saturation point of the compound is
gradually exceeded and crystallization begins.
Proteins are complex entities that, as ageneral rule,
are only soluble in abuffered aqueous solution. Because
ing are connected via this point, athree-dimensional lattice will result.
(7 https://sn.pub/UDQaYm)
of their amino acid composition, they carry charged
ionic groups on their surfaces. Similarly, for proteins,
it is also necessary to nd conditions under which they
associate in periodic arrays. This is achieved by slowly
changing the amount of water in which the protein is dissolved. This can be done in both directions. Hydrophobic
proteins begin to aggregate when the amount of water increases. Proteins that have stronger polar groups on their
surfaces aggregate when the water molecules are removed
from their surfaces. The adjustment of the local pH conditions to nd an optimal value, the choice of asuitable
salt for salting out, and the different temperatures are the
conditions that need to be optimized. In addition to salts,
surface-active substances (detergents) can also inuence
the solvation shell and support crystallization. Despite
this, crystallization is akind of ne art. The search for
suitable conditions requires creativity and diligence. Today, however, the crystallization methods are so elaborate
that the tedious work of setting up thousands of different
test conditions is carried out by robots.
Sometimes considerable effort is invested into structure determination. In 1995, the crystallization and structure determination of HIV integrase, one of the key enzymes in the life cycle of the virus, was accomplished
only after the 40th point mutation of the original protein.
Chapter • Experimental Methods of Structure Determination
13
These point mutations were made with the goal of altering the surface properties of the protein so that orderly
aggregation into acrystal could occur.
Let us return to the original question of whether the
orderly outwards appearance of acrystal is areection
of its inner structure. Chemically, acrystal is homogeneous. The organic molecule or the protein is the basic
building block. It is only when these building blocks are
organized in aspatially ordered fashion that aperiodic
array emerges which optimally lls space. In everyday life,
many solutions to these packing problems are easily seen,
for example, sugar cubes that will only t into the box if
they are layered in the right direction, or paving stones
that must be laid in aneat, periodic fashion to completely
cover asidewalk or astreet without gaps (. Fig.13.1).
Asingle paving stone, when correctly tted to the next,
represents arepeating unit in the lattice. Acrystallographer refers to this unit as the elementary unit cell, and the
orderly setting of one unit upon another in terms of periodic translation. In the simplest organic crystal structure,
the elementary cell contains one molecule (. Fig.13.2).
13.2 Just Like Wallpaper: Symmetries
Govern Crystal Packings
The contents of an elementary cell can also be more
complexly composed, for example, like awallpaper pattern. Abasic motif is repeated so that it lls the surface
area. Crystallographers call the basic motif the asym-
metric unit. In . Fig.13.3, this motif is aower branch.
Not all of the motifs can be generated simply by shifting
the branch; some must be additionally mirror-reected.
Apair of image and mirror-image branches represent
the elementary cell. The surface can now be lled with
this building block by simply shifting it. In addition to
reecting, basic motifs can also be rotated. By using reections and rotations, both so-called symmetry oper-
ations, the contents of the elementary cell is generated
from the asymmetric unit. This cell is layered on itself in
all three spatial directions in an orderly formed crystal
lattice. Even as athree-dimensional entity, the elementary cell must take on aparticular form to completely
ll all of the space. If the basic types of elementary cells
are combined with all of the possible symmetry operations, 230 possibilities result for the basic motif to ll
the space. The crystallographer calls them the 230 space
groups. For chiral molecules, and proteins belong to this
group, mirror reection does not occur. This reduces the
number of possible space groups signicantly. Therefore,
proteins (and nearly all of the chiral organic molecules)
crystallize in only 65space groups.
13.3 Crystal Lattices Diffract X-Rays
Max von Laue used crystals to prove the wave nature of
X-rays by diffracting them. For illustration, we shall con-
sider awater wave. When adrop of rain strikes apuddle,
circular waves propagate from the center outwards. The
drop generates aso-called elementary wave upon submersion. If two drops that are separated by aparticular
distance simultaneously strike the water’s surface, circular waves propagate outwardly from both submersion
points. It is better to observe this experiment when the
surface of the water is constantly “excited,” for exam-
. Fig. 13.3 An area can be covered not only by purely shifting an
object, the asymmetric unit. Additional symmetry operations such
as mirror reection and rotation can also be used. This way multiple
copies of the object are generated. In the presented case, the ower
branch along with its mirror image makes up the unit (the elementary
cell is outlined in red) that can be used to cover the surface simply by
shifting it regularly
. Fig. 13.4 Two raindrops strike the surface of the water and form
circular, outwardly moving water waves. These superimpose on each
other to give aband-like interference pattern. There are areas along
these bands where the water surface is quiet. In other areas, it moves
that much more strongly
. • Crystal Structure Analysis: Evaluating the Spatial Arrangement and Intensity of Diraction Patterns
ple, by aconstantly dripping tap. The circular outwardly
spreading wave fronts meet each other at some point.
What happens? Alamellar pattern forms, parts of the
water’s surface remain at rest and other parts seem to
move vigorously (. Fig.13.4). In the cross section, the
water surface moves sinusoidally (. Fig.13.5). How do
two waves behave that collide and superimpose with each
other? If the wave peak and another wave peak or the
wave trough and another wave trough meet, the wave
is amplied. If, on the other hand, awave peak meets
atrough, they cancel each other out. The water surface
remains calm. The lamellar pattern of moving and still
water surface between waves that are moving outwardly
and inwardly is caused by this superimposition. It is
called interference. The band density depends on the distance between the submersion points of the drops. The
ensuing interference pattern, therefore, contains information about the relative position of the points from which
the elementary waves were generated.
If parallel water waves (e.g., awave front at the coast)
collide with abarrier that has asmall opening (e.g., aharbor entrance), semicircular waves spread outwards from
the backside. If this barrier has two neighboring openings (double slit), semicircular waves develop behind each
of the two openings. By this, the same picture as with the
two raindrops is achieved (. Fig.13.4). The two waves
interfere with each other behind the double-slit barrier,
and adiffraction pattern forms. The density of this pattern, that is, the progression of the bands, depends on the
geometry of the double slit.
Formally, the diffraction sequence on the crystal lattice is analogous. The same principles are valid, but the
superimposition is more complex. Avery simple lattice
shall be considered that has only one type of atoms. An
X-ray beam runs as aparallel wave towards this crystal. It
collides with an array of atoms and initiates an interaction
that is comparable to that between the raindrop and the
puddle. Each atom generates aspherical wave because of
the interaction between the atom’s electrons and the X-ray.
The circular wave on the water’s surface represents, therefore, the spherical wave in space. The spreading spherical
waves superimpose on one another and form awave that
leaves the crystal in achanged direction (. Fig.13.6).
Formally seen, the incoming and outgoing waves have an
angular relationship to each other that is equivalent to the
reection of the wave at aplane perpendicular to the considered array of atoms. Therefore, the diffraction of the
three-dimensional crystal lattice can be treated formally
as areection at aplane in the lattice.
Many parallel sets of such lattice planes can be inscribed on acrystal with differing relative separation
from one another and relative occupation density with
atoms (. Fig.13.7). The reected waves contain the information about the geometry (distance) and the relative
occupancy (scattering power) in this plane. To record the
diffraction properties of acrystal, each set of parallel
planes of the crystal must be oriented in the X-ray beam
so that areection is possible. This laborious work is
taken over by acomputer-controlled diffractometer.
13.4 Crystal Structure Analysis: Evaluating
the Spatial Arrangement and
Intensity of Diffraction Patterns
To demonstrate that different lattices indeed generate different diffraction patterns, asimple experiment should
be considered. For this purpose, alaser pointer and different pinhole lters are needed. The pinhole lters can
easily be made. Ablack-and-white printout of the periodic arrangements shown in . Fig.13.8 can be greatly
reduced and transferred to high-resolution photographic
lm. These perforated pinhole masks represent two-dimensional periodic lattices. When the laser beam passes
through these pinhole masks, adiffraction pattern is generated on ascreen, which is shown in . Fig.13.8. The
rst two masks change the spacing and symmetry of the
pinhole mask. This is clearly reected in the diffraction
images obtained. In the third and fourth masks, the repeating motif of three or ve differently sized holes represents amolecule with two types of atoms. These motifs
form aperiodic lattice when arranged side by side. They
have the same spacing or “dimension” as the rst image
on the left. When the diffraction images are compared,
the intensity distribution of the light spots is different in
the rst, third, and fourth images. This intensity distribution contains the information about the spatial construction of the motif that created the lattice. This information is used to determine the crystal structure and the
geometry of the molecule in the crystal.
The reections, that is, the intensity of the individual
light spots in the diffraction pattern, contain information about the spatial geometry of the molecule. There
is amathematical technique, the Fourier transform, that
can be used to translate the diffraction pattern back to
the generating motif expressed as a density in space.
AFourier transform is the superposition of many sine
and cosine functions to describe the periodicity in space.
The intensity of the diffracted reections determines the
contribution of the superimposed sine and cosine functions, as well as their relative phase. The importance of
these aspects for the superposition of waves has already
been emphasized in the explanation of interference
(. Fig.13.5). Unfortunately, this relative phasing information is lost in the diffraction experiment. The diffractometer records only the intensity of the reections.
This lack of information is known as the phase problem
in crystal structure determination. The relative phases
must be reconstructed for the individual reections using computational methods and appropriate measurement conditions. Often large electron-rich elements (e.g.,
heavy metal ions) are embedded in the protein (e.g., by
a
b
c
Chapter • Experimental Methods of Structure Determination
. Fig. 13.5 The waves are sinusoidal
in cross-section. The distance between
two wave peaks is called the wavelength. The height of the water wave
at the summit is called the amplitude.
The position at which the wave crosses
the resting position determines the
phase. (a)If two wave trains with the
same phase meet, they will add to
each other and the amplitude doubles.
This situation is found in the places in
. Fig.13.4 where the water’s surface
moves more strongly. (b)If there is
aphase difference of exactly one half
of awavelength, the wave peaks will
meet with the troughs. Both waves cancel each other out. This represents the
parts of . Fig.13.4 where the water
surface is very still. (c)Any other superimposed phase shift causes awave,
the amplitude of which is somewhere
between the extremes in(a) and(b)
13
. Fig. 13.6 If awave front (blue) in one plane meets with arow of
atoms (black points on the dotted lines), each atom in this row will
become the starting point for athree-dimensional circular wave. This
is analogous to those created when the raindrop hits the surface of
apuddle. The circular waves that formed from the back row of atoms
superimpose upon one another just as in the case with the water waves
. Fig.13.4). All circular waves are generated with the same phase in
(
the indicated direction of the incoming wave (left). As aresult of this
superimposition, anew wave front forms (red) that leaves the crystal
in an altered direction. Relative to the direction of the incoming wave,
they have an angle that is formally areection of the incoming wave
front on the atom row that is marked with the green line. If adifferent
incoming direction is taken (blue), the circular waves will not be generated from the same place (right), that is, there is aphase difference between them. Their superimposition does not lead to anew wave front
leaving the crystal
. • Crystal Lattices Diract X-Rays
. Fig. 13.7 A cluster of parallel planes can be laid through the at-
oms of acrystal lattice(a,b,c). In the rst three images, one sort of
atoms is present. The relative distance of the inscribed planes from
one another and their atomic occupation density varies. Each of these
planes can give rise to “reections” in an X-ray diffraction experiment.
For this, the crystal must be brought into the correct orientation for
the incoming beam each time. The X-ray counter must be positioned
in away so that it captures the out-going X-ray beam. It is from this
geometry that the spatial orientation of the cluster of planes in the
crystal is determined. The occupation density of the atoms decides
how “well” aparticular array of planes reects the incoming X-ray
beam. This information is contained in the intensity (amplitude) of
the outgoing wave. (d)Three different types of atoms in amolecular
crystal have different spatial relationships to one another. A parallel cluster of planes can be placed through each type of atom in the
molecule (here atriatomic molecule). The amplitude of the outgoing
beam results as a superposition of three sets of waves reected at
these planes. Therefore, the observed intensity contains information
about the relative distance of the atoms on the mutually parallel lattice
planes and, therefore, their arrangement in the molecule