X-ray crystallography is a pivotal technique for determining the three-dimensional structures of crystals, particularly in biological materials, using X-ray diffraction. It involves generating diffraction patterns from single crystals, which are analyzed to create accurate atomic models, often stored in public databases. Despite its effectiveness, the method has limitations such as the need for high-quality crystals and susceptibility to radiation damage.

1. Title: X-ray Crystallography
Institute of Biotechnology
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September, 2023

2. 1. Introduction
 X-ray crystallography is a technique used for determining the
high-resolution, three-dimensional crystal structures of atom and
molecules and has been fundamental in the development of many
scientific fields.
 X-ray crystallography uses the principles of X-ray diffraction to
analyze the sample, but it is done in many different directions so that
the 3D structure can be built up.
 It is a technique that has helped to deduce the 3D crystal structure
of many materials, especially biological materials.

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 In its first decades of application, it is mainly used for determining
the size of atoms, the lengths and types of chemical bonds, the
atomic-scale differences among various materials, as well as the
crystalline integrity, grain orientation, grain size, film thickness
and interface roughness of the related materials, especially
minerals and alloys.
 It is a technique that has helped to deduce the 3D crystal structure
of many materials, especially biological materials.
 This method could also reveal the structure and function of many
biological molecules like vitamins, drugs, proteins and nucleic acids.

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 Up to date, it is still the chief method for characterizing the atomic
structure of new materials and in discerning materials that appear
similar by other experiments.
X-ray crystal structures can also explain the unusual electronic or
elastic properties of a material, shed light on chemical interactions and
processes, or function as the basis for designing pharmaceuticals
against diseases.
In particular, protein have been extensively put into structure
determination by X-ray crystallography, which is also employed
routinely in determining how a pharmaceutical drug interacts with its
protein target and what changes might improve it.

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X-ray crystallography method has advantages of no damage to
samples, free of pollution, low environmental requirements, high
performance and precision over other measuring tools.
These advantages make X-ray crystallography the most convenient
and important manner to investigate the microstructure of materials.

6. 2. Principle
In a single-crystal X-ray diffraction measurement, a crystal is mounted
on a goniometer, which is used to position the crystal at selected
orientations so that it can be analyzed from multiple angles.
In some cases where the sample is impure and the crystal structure is
not clear, the crystalline sample will need to be purified before
analysis.
X-rays are generated from an X-ray tube, and they are then filtered so
that they are monochromatic, i.e. of a single wavelength frequency.

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The atoms in the crystal refract the X-rays and the X-rays are
elastically scattered on to a detector. Because they are elastically
scattered, they have the same energy as the incident X-rays that are
fired at the sample. This generates a 2D diffraction pattern of the
crystal in a single orientation.
If the diffraction pattern is not clear, then the sample may not be pure
and will be purified at this point.
But other factors can prevent a diffraction pattern from being
generated including a too-small sample (needs to be at 0.1 nm in each
dimension), an irregular crystal structure, and the presence of any
internal imperfections—such as cracks—in the crystal.

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If the crystal is deemed to be ok, then the analysis and X-ray bombardment
towards the sample continues. The sample rotates on the goniometer so that a
series of 2D diffraction patterns are generated from various sides of the
sample.
The intensity is recorded at every orientation and the result is thousands of
2D diffraction patterns that correspond to different parts of the 3D structure.
From here, a computational approach analyses the different diffraction
phases, angles and intensities to generate an electron density map of the
sample.
The electron density map is used to generate an atomic model of the sample.
The model is constantly refined to ensure that it is accurate, and once the
final atomic model has been established, the data goes into a central database
to act as a known reference.

9. 3. Workflow
The technique of single crystal X-ray crystallography has three basic
steps.
The first and usually most difficult step is to produce an adequate
crystal of the studied material.
The crystal should be sufficiently large with all dimensions larger than
0.1 mm, pure in composition and regular in structure, and have no
significant internal imperfections such as cracks or twinning.
The crystal is subsequently placed in an intense beam of X-rays,
usually of a single wavelength, to produce regular reflection pattern.

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The angles and intensities of diffracted X-rays are measured with each
compound having a unique diffraction pattern.
Previous reflections disappear and new ones appear along with the
gradual rotation of the crystal, and the intensity of every spot is
recorded at every orientation of the crystal.
Multiple data sets may have to be collected since each set covers
slightly more than half a full rotation of the crystal and typically
contains tens of thousands of reflections.

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Ultimately, these collected data are combined computationally with
complementary chemical information to obtain and refine a model
from the arrangement of atoms within the crystal.
The final refined model of the atomic arrangement is called a crystal
structure and usually stored in a public database.
Figure 1. Workflow for solving the molecular structure by X-ray
crystallography.

12. 4. Instrumentation
The instrumentation used in X-ray crystallography plays a critical role
in the process of determining the atomic structure of crystals. The
main instruments involved include:
1. X-ray Source: X-ray crystallography requires a high-intensity X-
ray source, typically an X-ray generator or a synchrotron radiation
facility. These sources emit X-rays with a specific wavelength,
usually in the range of 0.6 to 2.5 angstroms (Å), which is
appropriate for interacting with the crystal lattice
2. Monochromator: To obtain a monochromatic X-ray beam with a
specific wavelength, a monochromator is used. It filters out
unwanted X-ray wavelengths, allowing only the desired
wavelength to pass through. Monochromators can be made of
various materials, such as graphite or crystals like quartz or
silicon.

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3. Collimator: The X-ray beam emitted from the source needs to be
collimated to ensure a well-defined and focused beam. Collimators are
used to narrow down the X-ray beam, reducing its divergence and
scattering before it reaches the crystal sample.
4. Sample Mounting System: The crystal sample needs to be securely
mounted and positioned for X-ray analysis. Sample mounting systems,
such as goniometers, allow precise rotation and translation of the crystal in
order to collect diffraction data from different crystallographic orientations.
4. X-ray Detector: X-ray detectors capture the diffraction pattern
produced when X-rays interact with the crystal lattice. There are several
types of detectors used in X-ray crystallography, including photographic
films, image plates, gas detectors, and more commonly, area detectors such
as CCD (charge-coupled device) or CMOS (complementary metal-oxide-
semiconductor) detectors. These detectors record the intensities and
positions of the diffracted X-rays.

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5. Cryocooling System: Many crystallographic studies require
samples to be cooled to very low temperatures, typically around -173
degrees Celsius or lower, to reduce radiation damage and minimize
sample motion. Cryocooling systems, such as liquid nitrogen or helium
cryostats, are used to cool the crystal sample during data collection.
6. Data Acquisition System: X-ray crystallography generates a vast
amount of diffraction data that needs to be efficiently captured and
processed. Data acquisition systems, often integrated with the X-ray
detectors, enable the collection and storage of diffraction images.
7. Computational Tools: Once the diffraction data is obtained,
powerful computational tools and software packages are used for data
analysis, structure determination, and refinement. These tools employ
mathematical algorithms and techniques, such as Fourier transforms,
least-squares fitting, and phase determination methods, to extract
meaningful structural information from the diffraction data

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16. 5. Procedure
5.1 Crystallization: In most cases, the generation of a diffraction-
quality crystal is a primary barrier to solve its atomic-resolution
structure.
A pure crystal of high regularity is a general requirement in
crystallography to solve the structure of a complicated arrangement of
atoms.
There are many methods to cultivate crystal, such as gas diffusion,
liquid phase diffusion, temperature gradient, vacuum sublimation,
convection and so on, and the most widely adopted methodology is
gas phase diffusion, which can be further divided into hanging drop,
sitting drop, oil drop and microdialysis.

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The crystallography of small molecules and macromolecular differs in
the range of possible techniques applied to produce diffraction-quality
crystals.
Small molecules have few degrees of conformational freedom, and
can be crystallized by a wide range of methods.
On the contrary, macromolecules have too many degrees of freedom
to achieve a perfect crystallization so as to maintain a stable structure.

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The range of crystallization conditions is also restricted to solution
conditions where biomacromolecules remain folded configuration.
There are several factors known to inhibit or ruin crystallization.
Crystals generally grow at a constant temperature and are protected
from shocks or vibrations that possibly disturb the crystallization.
Impurities in the molecules or crystallization solutions are also
inimical to crystallization.

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Molecules with high conformational flexibility or high tendcency to
self-assemble into regular helices are often unwilling to assemble into
crystals.
A slight change in molecular properties can even lead to large
differences in crystallization behavior.
After acquiring the initial conditions of crystal growth, it is often
necessary to optimize the crystallization conditions by adjusting
precipitant concentration, pH value, sample concentration,
temperature and ionic strength.

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Figure 2.Three methods of preparing crystals: A
Hanging drop; B Sitting drop; C Microdialysis.
Figure 2.Three methods of preparing crystals: A Hanging drop; B
Sitting drop; C Microdialysis.

21. 5.2 Data Collection
Diffraction experiments are needed after obtaining single crystal.
The X-ray irradiating to the crystal is diffracted, and the diffraction
data are recorded.
X-ray has are two main sources, one of which applied in the common
X-ray instrument produces X-rays with multiple characteristic
wavelengths by bombarding copper targets or molybdenum targets
with high energy electron flow.
Another one is the X-ray with variable wavelength generated through
synchrotron radiation. X-rays from synchrotron radiation can be
grouped into angular dispersion synchrotron radiation (ADXD) and
energy dispersive synchrotron radiation (EDXRD).

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The experimental principle of ADXD is the same as that of the normal
X-ray diffractometer, while the wavelength is lower and the energy is
higher.
The incident light of EDXRD is white light with a continuous
wavelength, and the diffraction signal is collected at a fixed angle. In
comparison with ADXD, EDXRD also has a lower resolution ratio
and technical requirement.
Diffraction data, including location and intensity of diffraction points,
are often recorded by image plates or CCD detectors.

23. 5.3 Structure Analysis and Interpretation:
Once the crystal structure is determined and validated, it is analyzed
and interpreted to gain insights into the arrangement of atoms and
their interactions within the crystal. This analysis can provide
information about chemical bonding, molecular conformations, and
other structural properties.
These steps collectively allow scientists to obtain a detailed
understanding of the atomic arrangement and three-dimensional
structure of a crystal using X-ray crystallography.

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25. 5.3.1 Crystal Symmetry, Unit Cell, and Image Scaling
Each recorded series of two-dimensional diffraction patterns
corresponding to a different crystal orientation, is converted into a
three-dimensional model of the electron density, which is completed
by the mathematical technique of Fourier transforms.
Each spot has a corresponding type of variation in the electron density
and which variation corresponds to which spot (indexing) must be
determined.
The relative strengths of the spots in different images (merging and
scaling) and how the variations should be combined to yield the total
electron density (phasing) are also necessary to be figured out.

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Data processing commences with the reflections indexation, which
means identifying the dimensions of the unit cells and which image peak
stands for which position in reciprocal space.
A byproduct of indexing is to determine the crystal symmetry. The data
is then integrated after having assigned symmetry.
The hundreds of images containing the thousands of reflections are
converted into a single file that consists of records of the miller index of
each reflection and intensity for each reflection.
These various images taken at different orientations of the crystal are
merged and scaled firstly to identify which peaks appear in two or more
images (merging) and to scale the relative images so that they have a
consistent intensity scale.

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The optimization of intensity scale is critical for the peaks intensity
since they are the key information from which the structure is
determined.
The repetitive technique of crystallographic data collection and the
high symmetry of crystalline materials lead the diffractometer to
repeatedly record many symmetry-equivalent reflections, allowing the
calculation of symmetry-related R-factor, which is a reliable index
based upon how similar are the measured intensities of symmetry-
equivalent reflections, thus evaluating the quality of the data.

28. 5.3.2 Initial Phasing
The data collected from a diffraction experiment represents a reciprocal
space of the crystal lattice.
The size and shape of the unit cell, and the inherent symmetry within the
crystal govern the position of each diffraction 'spot', whose intensity is
recorded and proportional to the square of the structure factor amplitude.
The structure factor contains information involving both amplitude and
phase of a wave, both of which must be known to obtain an interpretable
electron density map that enables a crystallographer to build a starting model
of the molecule.
During a diffraction experiment, the phase cannot be directly recorded, which
is known as the phase problem. The estimates of initial phase can be finished
in a variety of ways such as Ab initio phasing, direct methods, molecular
replacement, anomalous X-ray scattering and heavy atom methods.

29. 5.3.3 Model Building and Phase Refinement
An initial model can be established after obtaining initial phases.
This model can be applied to refine the phases, atomic positions and
respective Debye-Waller factors with the aim of fitting the observed
diffraction data, thus getting an improved model and ideally yielding a
better set of phases.
A new model can then be fit to a novel electron density map and a
further round of refinement is performed, which continuously
proceeds until the correlation between the diffraction data and the
model is maximized. The agreement is measured by an R-factor
defined as

30. Con”t…
where F is the structural factor. A similar quality criterion Rfree is
calculated from a subset of reflections that are not included in the
structure refinement.
Model qualities including chemical bonding features of stereochemistry,
hydrogen bonding and the distribution of bond lengths and angles are
complementarily measured. Phase bias is a serious problem in such
iterative model building, but can be checked by a common technique of
omit maps. In many cases, crystallographic disorder smears the electron
density map and weakly scattering atoms are routinely invisible.
It is also likely that a single atom appears multiple times in an electron
density map. In still other cases, the covalent structure deduced for the
molecule is detected to be incorrect or changed.

31. 5.4 Deposition of the Structure
Once the model of a molecular structure is finalized, it would be often
deposited in crystallographic databases such as the Cambridge
Structural Database for small molecules, the Inorganic Crystal
Structure Database for inorganic compounds or the Protein Data Bank
for protein structures.

32. 6. Applications of X-ray Crystallography
1. Structural Biology: Reveals protein and nucleic acid structures
for drug discovery.
2. Drug Discovery and Design: Optimizes drug candidates and
understands binding modes.
3. Material Science: Analyzes crystal structures for developing new
materials.
4. Chemical Crystallography: Determines molecular structures and
studies reaction mechanisms.
5. Geological Studies: Identifies minerals and studies geological
processes.
6. Pharmaceutical Industry: Characterizes drug properties for
formulation stability.
7. Nanotechnology: Designs nanomaterials with specific
functionalities.

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8. Protein Engineering and Enzyme Catalysis: Enhances
understanding of enzyme structures.
9. Physical and Solid-State Chemistry: Investigates solid-state
materials’ properties.

34. 7. Limitations of X-ray Crystallography
1. Requires high-quality single crystals.
2. Relies on large sample sizes.
3. Time-consuming process.
4. Radiation damage can alter crystal structure.
5. Limited to crystalline materials.
6. The phase problem requires additional approaches.
7. Assumes perfect order and static structure.
8. Some samples may be sensitive to X-ray radiation.

35. 8. References
1. Rupp, B. (2010). “An Introduction to X-ray Crystallography.” In
Protein Crystallography: Methods and Protocols (2nd ed., pp. 1-38).
Humana Press. DOI: 10.1007/978-1-60761-795-2_1.
2. Rhodes, G. (2017). “Principles of X-ray Crystallography.” In
Crystallography Made Crystal Clear: A Guide for Users of
Macromolecular Models (3rd ed., pp. 1-34). Academic Press. DOI:
10.1016/B978-0-12-802950-2.00001-9.
3. Cullity, B. D., & Stock, S. R. (2001). “Diffraction: The Study of
Crystalline Materials through X-rays, Electrons, and Neutrons.” In
Elements of X-ray Diffraction (3rd ed., pp. 1-56). Prentice Hall.
4. Prince, E. (2004). “X-ray Diffraction.” In Mathematical Techniques
in Crystallography and Materials Science (2nd ed., pp. 173-232).
Springer. DOI: 10.1007/0-306-48555-7_5.
5. Helliwell, J. R. (2012). “X-ray Crystallography: An Introduction to
the Techniques.” Oxford University Press. ISBN: 978-0199659845.