XRay

• Why use X-ray crsytallography?

  to determine 3D structure of molecules at atomic resolution

  to determine where the protein is located and what the function will be
• Workflow: 1. Protein crystallisation 2. X-ray diffusion 3. Electron density maps 4. Atomic model
• Protein crystallisation = Pure protein (>95%) solutions produced recombinantly, using bacterial expression. Can produce proteins in bacteria, mammalian cells, insect cells
• Xray crystallography needs crystals
• Protein + specific solution = crystals
• Crystal

  Ordered 3D array of molecules
• Asymmetric unit


  smallest repeating object within crystal
• Unit cell


  smallest volume element completely representative of the whole crystal
• repetition of unit cell

  crystal
• Lattice

  Array of unit cell vertices
• Crystal motif * Crystal lattice = crystal structure
• Not all diffractions are useful, multiple ways in which they can bounce = many planes. Only consider the ones that go through the two vertices
• how x-rays are diffracted = diffraction pattern of isolated protein
• Constructive interference: Intensifies reflection, occurs when two or more waves combine to produce a resultant wave with an amplitude that is greater than the sum of the individual waves
• Destructive interference


  waves cancel each other out
• Braggs law (n(lambda) = 2s sin theta) predicts when there is constructive interference
• the greater the angle the higher the resolution

  3A is low res, 1A is high res
• Extract theta/angles of refraction: distance between two atoms
• Reflections allowed by Braggs law, planes that intersect the sphere, on detector you will only those planes

  
• How X-rays are formed: when an electron transitions to a lower level, it loses energy corresponding to the energy levels between shells, energy is emitted as X-ray photons

  
• Mathematical relationship between an object and its diffraction pattern.

  Fourier transform
• To convert the diffraction pattern to an ELECTRON DENSITY mapneed to know the POSITION, INTENSITY and PHASE of as many reflections as possible
• 3 ways to derive phases

  Multiple isomorphous replacement

  multiple wavelength anomalous dispersion

  molecular replacement
• Heavy atoms absorb x-rays, solve heavy atom structure, estimate phase of protein reflection made
• Isomorphous replacement: Position of heavy atom in the unit cell determined directly from intensity differences. Only possible for one or two heavy atoms per asymmetric unit.
• Multiwavelength Anomalous Dispersion: heavy atom already in protein, soak in metal or manipulate using molecular biology tools: replace methionine with selenomethionine, can use more than one wavelength to obtain diffraction pattern
• In MAD 3 data sets are measured at dif wavelengths from one crystal. Intensity dif used to calculate the positions of the anomalous atoms in the unit cell: effect of anomalous atoms can be used to calculate phases
• Molecular replacement uses structure of similar protein as a structural model, known structure can be superimposed in the unit cell in the same orientation as the unknown proteins. If a proteins sequence is >30% identical: high probability of the same fold.
• R factor: measure of the agreement between the observed and calculated structure factors in X-ray crystallography. A lower R-factor indicates a better fit between the observed and calculated data, suggesting a more accurate atomic model.
• R-free factor

  • The R-free factor is an additional measure used to validate crystallographic models.
  • In the refinement process, a subset of the data (usually 5-10%) is randomly selected and excluded from the refinement. This excluded subset is referred to as the "test set."
• A large discrepancy between the R-factor and R-free factor may indicate overfitting, and it is desirable to have both values similar.
• Difference in map shows where atoms are ‘missing’ (maxima; positive electron density; green)
• Also shows if the atom was modelled in the wrong place/not where it should be (minima; negative electron density)
• $6\AA$: can define secondary structure
• $3\AA$:can define main chain of polypeptide
• $2.5\AA$: can identify sidechains
• $1.5\AA$: can resolve individual atoms
• $<1.0\AA$: some hydrogen atoms visible
• Assess quality of model: is structural model is compliant of the quality checks from diffraction data?
• Validate model: is the structure right in the context of the cell and it’s function?