Nobel Laureates of X Ray Crystallography

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Nobel Laureates of X Ray Crystallography

• Max von Laue - 1914 Nobel Prize in Physics
• Bragg(s) - 1915 Nobel Prize in Physics.
• Dorothy Hodgkin 1964 Nobel Prize in Chemistry
• Hauptman and Karle - 1985 Nobel Prize in
  Chemistry
• Roderick MacKinnon and Peter Agre 2003 Nobel
  Prize in Chemistry

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Levinthal's paradox

• How many backbone conformations of a 300 residue
  protein are possible?
• Only taking into account Phi and Psi angles,
  approximately 10³ conformations
• How is the right conformation found in our
  lifetime?
• Answer Only some angle combinations are
  energetically favorable, hence only a limited
  amount of structural conformations are possible

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Steps To Solving The Structure Of A Protein
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• When X-rays strike a macromolecular crystal, the
  atoms in the molecules produce scattered X-ray
  waves which combine to give a complex diffraction
  pattern consisting of waves of different
  amplitudes

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• What is measured experimentally are the
  amplitudes and positions of the scattered X-ray
  waves from the crystal
• X-ray crystallography provides the positions of
  all non-hydrogen atoms
• The origin of each wave must be determined so
  that they sum to give an image instead of a sea
  of noise
• Phase values must be assigned to all of the
  recorded data sometimes done computationally,
  but is usually done experimentally by labeling
  the protein with one or more heavy atoms whose
  position in the crystal can be determined
  independently

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Electron Density Calculation

• Diffraction amplitudes FTElectron density
• Take the inverse FT of the diffraction pattern to
  regenerate the electron density
• Shooting a crystal with X-rays and obtaining a
  diffraction pattern is the same as taking the
  Fourier transform of a compound. Hence, taking
  the Fourier transform again gives us the original
  structure.

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After shooting Our Protein with X-rays And
getting the FT
Taking the FT of the FT RESTORES the
original Data (mostly)
Our Protein
A very simple example of Fourier and Inverse
Fourier transforms
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• The scattered x-rays have amplitudes given by
  Fourier coefficients of electron density
• Possible to measure amplitudes
• If we could also measure phases, we could compute
  electron density by inverse Fourier transform
• We then fit a model to the density
• Phases are extremely difficult to measure

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Quick Recap

• Crystallize Protein (if humanly possible)
• Measuring diffraction amplitudes
• Using a computer to calculate electron density
• Building a model consistent w/ density

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Quality Of a Structure

• R-factors represent the percentage disagreement
  between the observed diffraction pattern and that
  calculated from the final model
• R-factors of around 20 or less are considered
  well determined structures that are expected to
  contain relatively few errors

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• Express the resolution of a structure in terms of
  a distance

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Molecular Replacement

• Use an analogous structure (similar amino acid
  sequence) and apply to the structure you are
  trying to determine
• Replacement actually means 'relocation,
  repositioning atoms.

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(Multiple) Isomorphous Replacement
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