diffraction. Evaluating the diffraction pattern
rotation of a crystal within a monochromatic X-ray beam causes its reciprocal
lattice points to cross the surface of the so called Ewald
Whenever this happens, a diffracted beam is
originated in the center of
the Ewald sphere and passes through the reciprocal point that lies on
the Ewald spherical surface... In these circumstances the
is fulfilled. The set of all diffracted beams
constitute the so-called diffraction pattern, which is subject to
detection and evaluation. The reader should be aware that a complete
diffraction pattern can contain a highly variable number of diffraction
beams, from hundreds (simple inorganic compounds) to hundreds of
thousands (proteins or viruses).
of diffracted patterns has been carried out in different ways...
sensitive to X-rays, placed inside cameras suitable for these
experiments. Diffraction cameras most frequently used were those
of Weissenberg and precession.
Both types of cameras were designed to generate images of any
reciprocal plane. The precession diagrams (image on the left) show the
arrangement of the reciprocal points with the real geometry of the
lattice, but the diagrams obtained with the Weissenberg cameras provide
distorted images of these planes, and therefore it is necessary to know
to interpret the geometric distortion that contain the Weissenberg
diagrams for its correct interpretation.
Photographic films showing part of a
camera (left) and Weissenberg
- Using specific
detectors placed in the path of each diffracted beam, although
orienting the crystal in such a way that the diffracted beam occurs on
the equatorial plane of the Ewald sphere. This process is achieved
using four-circle goniometers.
Four-circle goniometer with a point
- Using area
that act as sensitive films and therefore can collect many diffracted
beams at the same time during a small crystal rotation. With area
detectors it is not necessary to use a four-circle goniometer.
It is enough to use a single rotating axis, the one for the crystal.
Four-circle goniometer with an area
adapted from Carleton College
Independently of the methodology used for the detection of the
diffraction pattern, its evaluation and measurement implies three well
relationship between direct and
relationship between direct and
- Measurement of the
each diffracted beam. Originally this process was carried out with a
photometer, measuring the blackening produced on photographic films, on
the spot (Tp) and on the background (Tb1, Tb2).
Later this process was carried out by scanning each diffracted
beam profile using a point detector. Nowadays area detectors are used.
They act as photographic films and generate digital images of each
measured on a photographic film with a photometer
measured by scanning beam
profiles with a point detector
measured integrating pixels on an area
and/or visual comparison of diffracted intensities is used
to look for possible
symmetry elements in reciprocal space, including systematic extinction
of certain diffracted beams. Systematic extinctions are indicative of
the type of crystal lattice and/or symmetry elements with translational
leads to the knowledge of the crystal space group.
A photographic film showing a reciprocal
plane containing the reciprocal points of type hk0.
Several possible planes of symmetry, marked with the letter m,
the end of a full evaluation of the diffraction
pattern of a crystal means having obtained a complete description of
its reciprocal lattice (geometry + intensities), and hence the
knowledge of the direct lattice: unit
cell constants (a,
type (primitive or
symmetry (space group), ie, all ingredients to
resolution of the internal structure of the crystal.
In general, what has been presented up to this point is enough to
understand what the experimental procedures to evaluate the diffraction
pattern are (considering that the diffraction pattern contains Bragg
peaks only). Therefore, the reader could now go
back to the starting
However, the advanced reader might take a look below...
many crystals are needeed and at what temperature is the diffraction
the first diffraction experiments were carried out on stable
crystalline materials, such as minerals or inorganic compounds, which
are hardly damaged by X-ray radiation, so that one or two crystals were
enough to carry out the whole diffraction experiment.
However, later on,
started dealing with much more labile and complex substances (organic
and biological samples) that, due to the rapid deterioration caused by
X-ray radiation, required the use of multiple crystals in order to
collect their diffraction pattern. As shown in a previous section, this
problem was solved through the so-called cryo-crystallography,
adaptation of a mechanism for cooling the crystals during their
exposure to X-rays, thereby achieving greater sample stability against
cryo-protected crystal in an anti-freeze matrix (left), mounted in
front of a stream of liquid nitrogen, evaporated at about 100 K (right)
procedure, still in use for most diffraction experiments in
crystallographic laboratories or in synchrotron
installations, required the development of a special technique for
mounting crystals, using small loops used to "catch" the crystal in a
liquid matrix of a cryoprotector (anti-freeze) transparent to X-rays.
This procedure is especially relevant for protein crystals. In this
type of crystals the cryoprotector matrix is dispersed through their
inner channels, replacing the water molecules, and avoiding
freezing, which would cause the crystal to break. By means of this
technique, and also thanks to the high brilliance of the synchrotron
radiation sources, the number of crystals needed to carry out a
complete diffraction experiment has been greatly reduced, especially in
the case of proteins, which usually produce crystals very sensible
against radiation and temperature.
However, with the new generations of synchrotron and/or XFEL radiation sources, the so-called serial
millisecond crystallography is being imposed (Nature
Communications (2017) 8, art. 542).The
so-called serial millisecond crystallography at a synchrotron beamline
equipped with high-viscosity injector and high frame-rate detector
allows typical crystallographic experiments to be performed at
room-temperature. Using a crystal scanning approach on microcrystals
deposited on a grid, one can collect hundreds, thousands, of partial
diffraction patterns (the crystal can rotate only few degrees) which
can be unified and scaled properly to produce a complete diffraction
pattern. Compared with serial data collected at a
laser (XFEL), the synchrotron data are of slightly lower resolution,
however fewer diffraction patterns are needed for "de novo" phasing.
Overall, the data collected by room-temperature serial crystallography
are of comparable quality to cryo-crystallographic data and can be
routinely collected at synchrotrons.
anything else besides the Bragg peaks?
The use of the very
radiation sources (synchrotron + XFEL)
has led to consider a part of the information contained in the
diffraction pattern that was not previously taken into account. We
refer to the so-called continuous diffraction, namely an intensity
distribution, poorly defined, that may appear around and between the
Bragg peaks as well as in areas of higher diffraction angle, where the
Bragg peaks have almost disappeared.
The phenomenon of
is negligible in crystals of relatively simple composition, where the
dominant aspect is the strict crystalline order and uniformity of
molecules. However, it has been shown [Nature
(2016) 530, 202-206] that
this can be very relevant in the case of biological
where the sharpness and intensity of the Bragg peaks can decrease
rapidly as a function of diffraction angle (see the diffraction pattern
shown in the figure at right).
Although the explanation of
goes beyond the scope of these pages, we considered important to add a
short explanation of this phenomenon and the importance of its
consideration in the world of biological crystallography.
The idea behind the
mentioned article is
that crystallographic resolution for some macromolecules may be limited
not by their heterogeneity, but by a deviation of strict positional
ordering of the crystalline lattice. Such molecular displacements from
the ideal lattice positions give rise to a continuous diffraction
pattern that is equal to the incoherent sum of diffraction from rigid
individual molecular complexes aligned along several discrete
crystallographic orientations and that, consequently, contains more
information than Bragg peaks alone.
still snapshot of the diffraction pattern of a biological
macromolecule. The Bragg intensity maxima disapear very quickly with
the diffaction angle. In addition, a weak speckle structure is shown
beyond the extent of Bragg peaks. Image taken from Nature
(2016) 530, 202-206.
the existence of
diffraction was already known, and it has been used to interpret
dynamic phenomena in protein crystals, the above
mentioned article provides
new important insights for determining the structure of biological
macromolecules from diffracting crystals. According to the new
considerations, the diffraction intensities contain two terms, one
representing the continuous and another one for the Bragg diffraction.
The difference is that each term is modulated by different combinations
of the asymmetric unit transform. The continuous diffraction is the sum
of the intensities of each asymmetric unit transform, whereas the Bragg
peaks depend on the coherent sum of the asymmetric unit transforms (the
unit-cell transform). See the diagram on the right showing the
ocurrence of continuous diffraction versus coherent diffraction.
considerations imply very
significant contributions for macromolecular structure determination,
but not just to increase the knowledge of the molecular details (degree
of resolution of the model), but also as a tool for assigning
showing the occurrence of
continuous diffraction versus coherent diffraction
But let's go