X-ray Diffraction Data analysis
Crystal symmetry, unit cell, and image scaling
The recorded series of two-dimensional diffraction patterns, each corresponding to a different crystal
orientation, is converted into a three-dimensional model of the electron density; the conversion uses the
mathematical technique of Fourier transforms. Each spot corresponds to a different type of variation in
the electron density. Data processing begins with indexing the reflections. This means identifying the
dimensions of the unit cell and which image peak corresponds to which position in reciprocal space. A
byproduct of indexing is to determine the symmetry of the crystal, i.e., its space group. Having assigned
symmetry, the data is then integrated. This converts the hundreds of images containing the thousands of
reflections into a single file, consisting of records of the Miller index of each reflection, and an intensity
for each reflection A full data set may consist of hundreds of separate images taken at different
orientations of the crystal. The first step is to merge and scale these various images, that is, 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. Optimizing the intensity scale is critical because the relative intensity of the
peaks is the key information from which the structure is determined. The repetitive technique of
crystallographic data collection and the often high symmetry of crystalline materials cause the
diffractometer to record many symmetry-equivalent reflections multiple times. This allows calculating the
symmetry-related R-factor, a reliability index based upon how similar are the measured intensities of
symmetry-equivalent reflection thus assessing the quality of the data.
Initial phasing
The data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice.
The position of each diffraction 'spot' is governed by the size and shape of the unit cell, and the
inherent symmetry within the crystal. The intensity of each diffraction 'spot' is recorded, and this intensity
is proportional to the square of the structure factor amplitude. The structure factor is a complex
number containing information relating to both the amplitude and phase of a wave. In order to obtain an
interpretable electron density map, both amplitude and phase must be known (an electron density map
allows a crystallographer to build a starting model of the molecule). The phase cannot be directly
recorded during a diffraction experiment: this is known as the phase problem. Initial phase estimates can
be obtained in a variety of ways:
Ab initio phasing or direct methods – This is usually the method of choice for small molecules
(<1000 non-hydrogen atoms), and has been used successfully to solve the phase problems for small
proteins
Crystal symmetry, unit cell, and image scaling
The recorded series of two-dimensional diffraction patterns, each corresponding to a different crystal
orientation, is converted into a three-dimensional model of the electron density; the conversion uses the
mathematical technique of Fourier transforms. Each spot corresponds to a different type of variation in
the electron density. Data processing begins with indexing the reflections. This means identifying the
dimensions of the unit cell and which image peak corresponds to which position in reciprocal space. A
byproduct of indexing is to determine the symmetry of the crystal, i.e., its space group. Having assigned
symmetry, the data is then integrated. This converts the hundreds of images containing the thousands of
reflections into a single file, consisting of records of the Miller index of each reflection, and an intensity
for each reflection A full data set may consist of hundreds of separate images taken at different
orientations of the crystal. The first step is to merge and scale these various images, that is, 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. Optimizing the intensity scale is critical because the relative intensity of the
peaks is the key information from which the structure is determined. The repetitive technique of
crystallographic data collection and the often high symmetry of crystalline materials cause the
diffractometer to record many symmetry-equivalent reflections multiple times. This allows calculating the
symmetry-related R-factor, a reliability index based upon how similar are the measured intensities of
symmetry-equivalent reflection thus assessing the quality of the data.
Initial phasing
The data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice.
The position of each diffraction 'spot' is governed by the size and shape of the unit cell, and the
inherent symmetry within the crystal. The intensity of each diffraction 'spot' is recorded, and this intensity
is proportional to the square of the structure factor amplitude. The structure factor is a complex
number containing information relating to both the amplitude and phase of a wave. In order to obtain an
interpretable electron density map, both amplitude and phase must be known (an electron density map
allows a crystallographer to build a starting model of the molecule). The phase cannot be directly
recorded during a diffraction experiment: this is known as the phase problem. Initial phase estimates can
be obtained in a variety of ways:
Ab initio phasing or direct methods – This is usually the method of choice for small molecules
(<1000 non-hydrogen atoms), and has been used successfully to solve the phase problems for small
proteins
