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Lecture notes of 1 pages for the course Techniques For Biological And Chemical Sciences at QMUL
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Essential Protein Crystallography – Second Year1. X-rays are used because their wavelength is similar to the C-C bond length to be resolved
(1.5 Å).
2. Crystals are used because they orient protein molecules in space; each molecule diffracts
X-rays weakly, but the regularly arranged 1012 molecules in a crystal give appreciable
diffraction. The crystal therefore acts as an amplifier.
3. The diffraction image from a single molecule would be a continuous function (molecular
transform); the diffraction from a crystal comprises Bragg reflections (spots) i.e. the
molecular transform is sampled at the reciprocal lattice positions (or Bragg positions). In
essence, the position of the spots gives information about the crystal lattice and the
information about the structure of the protein is contained in the intensities of the Bragg
reflections.
4. The X-rays are scattered by the electrons. The scattering angle is 2θ. High resolution
reflections are towards the outer edge of the diffraction pattern, low resolution towards the
centre. (A resolution of 2 Å means atoms 2 Å apart can be resolved as separate objects).
6. X-ray structures are time and space average structures. They are averaged over the time
taken to record the image and the molecules irradiated by the X-ray beam.
7. Braggs law predicts the scattering angle (2θ) at which a reflection occurs from planes in
the crystal separated by d: λ = 2d sin θ. This can be rewritten: d = λ/2d sin θ, which
clearly shows the reciprocal nature of d and θ. The Bragg reflection corresponds to reflection
from a plane in the crystal e.g. (2,5,0) corresponds to a plane that cuts the a-axis into two, b-
axis into 5, and c-axis not at all (it is a plane parallel to the c-axis). High-resolution reflections
occur close to the outside of the image, low resolution close the centre of the image.
8. The intensity of the reflection { I(hkl) } is recorded on the image but the phase is not
recorded. This gives the phase problem in crystallography. The structure factor amplitude is
the square root of the intensity.
9. The phase can be measured experimentally by isomorphous replacement and/or
anomalous scattering.
10. At 6 Å you can see helices; 3 Å sheets; 2.3 Å water molecules; 2.0 Å or better – a really
nicely defined structure; 1.2 Å seeing individual atoms. Of course all structures have good
bits and poorer bits, i.e. parts of the structure that are less-well defined. Check out the
thermal parameters to find these areas.
11. The electron density is the Fourier Transform of the structure factor amplitudes and the
phases.
12. Crystallography can be used with molecules of any size (provided they crystallize), is fast
once you have a crystal and is great with tightly associating molecules.
13. NMR spectroscopy can yield information on protein dynamics and protein folding and on
loosely associating molecules.
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