X-ray crystallography and fiber diffraction

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X-ray crystallography and fiber diffraction
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Crystals
Symmetry operations
crystal asymmetric unit repeated in space
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Bravais lattices Crystallization
230 different space groups
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Wave interference
new wave ? (old waves) ? old waves
(amplitude ?wave phase)
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Diffraction

• 2 sin ? n ? / d

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von Laue conditions
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Bragg's law
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Miller indices

• Detection

rotating crystal
precession pattern
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Diffraction from a unit cell
scattered wave ? scattered waves ?
(scatterers ? relative position ? crystal
lattice)
electron density Fourier Transform (
scattered waves ? diffraction space)
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Reflections and electron density
F(h,k,l) structure factor (intensity and
phase) r(x,y,z) electron density of the unit
cell a,b,c dimensions of the unit
cell h,k,l Miller indices of the
reflections
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Phase Problem
scattered wave amplitude ? phase
intensity of reflection (amplitude)2
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Patterson function
Fourier transform (amplitudes?diffraction
space)map of the atom-to-atom distances
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Heavy atom isomorphous replacement
scattered wave (heavy atom protein) scattered
wave (protein) scattered wave (heavy atom)
Molecular replacement
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Resolution
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Model building
Refinement
Resolution
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Fiber X-ray
Helix

• DNA

Convolution
Convolution theorem
FT (A conv. B) FT(A) x FT(B)
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Diffraction from Continunuous Helix
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Diffraction from Discontinuous Helix