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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
ψ
φ
Cα
Cα
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
Steps To Solving The Structure Of A Protein
• 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
• 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 nonhydrogen 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
Electron Density Calculation
• Diffraction amplitudes = FT{Electron 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.
Our Protein
After shooting
Our Protein with X-rays
And getting the FT
Taking the FT of the FT
RESTORES the original
Data (mostly)
A very simple example of Fourier and Inverse Fourier transforms
• 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
Quick Recap
• Crystallize Protein (if humanly possible)
• Measuring diffraction amplitudes
• Using a computer to calculate electron
density
• Building a model consistent w/ density
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
• Express the resolution of a
structure in terms of a distance
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.
(Multiple) Isomorphous
Replacement