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Pattersons. The “third space” of crystallography. The “phase problem”. The “phase problem”. P h a s e s. Amplitudes. The “phase problem”. P h a s e s. Amplitudes. The “spaces” of crystallography. Direct/real space Distances are in Å, Angles are in degrees Reciprocal space - PowerPoint PPT Presentation
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The “spaces” of crystallography
• Direct/real space– Distances are in Å, Angles are in degrees
• Reciprocal space– Distances in 1/Å, Angles are different
• Patterson space– Distances are in Å , Angles are in degrees– Relative distances only, origin lost– “direction” is preserved
How to make a Patterson map:
1. Set all phases to zero
2. Square all structure factors
3. Calculate Fourier transform
One atom in unit cell
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Real Space
Fraction across unit cell
Ele
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Patterson: one atom
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: one atom
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: one atom
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: two atoms
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: three atoms
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: three atoms
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Better resolution!
Patterson: five atoms
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: five atoms
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Snapshot from single virus particle
TEM
2 keV LCLS 200 fs Mimi virus single-shot.200 nm
Reconstructed image
Resolution 20nm
Seibert, et al. (2011). Nature 470, 78-81.
Patterson: five atoms + 3-fold symmetry
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Real Space
Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Patterson: five atoms + 3-fold symmetry
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Patterson
Fraction across unit cell
Ele
ctro
n de
nsity
Major Phasing techniques
• Molecular Replacement
• Multiple Isomorphous Replacement
• Anomalous Diffraction
• Direct methods
2Fo-Fc maps
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
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True density
Model
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
0.0
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
0.0
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity
2Fo-Fc maps
-0.10.00.10.20.30.40.50.60.70.80.91.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True density
Model
2Fo-Fc
Fraction across unit cell
Ele
ctro
n de
nsity