Protein Structure
Determination
Part 2 -X-ray Crystallography
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Para ver esta película, debe
disponer de QuickTime™ y de
un descompresor TIFF (LZW).
The method
FT-1
FT
Crystals
X-rays
Atoms
EM versus x-ray
• electron microcope
• resolution ≈ 1nm
• de Broglie wavelength
of e- ≈ size of atom
• transmitted light
• lensing possible, 106x
mag.
• 2D image w/tilt
• measures density.
• sample is thin section
• diffractometer
• resolution up to 0.1nm
= 1Å
• wavelength ≈ size of
atom
• scattered light
• no lens possible
• 3D reconstruction
• measures relative edensity
• sample is single crystal
X-ray diffractometer
Experimental setup
X-ray source
X-ray detector
beam stop
Dimensions
X-ray detector
Beam width: ~0.20 mm
Crystal thickness: 0.10-1.00 mm
Unit cell: ~100Å = 0.00001mm
Typical protein molecule: ~30Å =
0.000003 mm
Dimensions
C-C bond distance: 1.52Å
N
C CH3
O C
Wavelength of Cu K X-rays: 1.5418Å
Dimensions
Angle of incidence= : 0-90°
N
C CH3
O C
Bragg plane separation distance (resolution): 0.7-50Å
N
Dimensions
Carbon atom
C
amount an electron
moves in one xray cycle
X-rays see e- as if they were standing still.
Electromagnetic spectrum
Wavelength of X-rays used in crystallography: 1Å - 3Å (Å
= 10-10m) most commonly 1.54Å (Cu )
Frequency = c/ =(3x108m/s) /(1.54x10-10m) ≈ 2x1018 s-1
oscillating e- scatter X-rays
…in all direction.
oscillation
e-
emission
Reflection planes
•The “amplitude” of scattering is measured.
•The amplitude is proportional to the differences of edensity in the direction of “reflection planes”
•The orientation and separation of reflection planes is
determined by the directions of the incoming and scattered
rays.
10K+ reflections
•Moving the X-rays and the detector gives a new set of
planes.
•Changing the angle of reflection changes the spacing
(resolution).
Reconstruction of e- density
The density at every point in the crystal is calculated by
summing over all of the density waves.
Topics covering in this course
•
•
•
•
•
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Crystal growth
Diffraction theory
Symmetry
Experimental methods
Interpretation of data
Software
Equations you will need to know
i
e  cos   isin 
n  2dsin 
so  s
S

x sym  Mx  v

F hkl   xyze 2 ihxky lz

Euler's theorem
Bragg's law
Reciprocol space
Symmetry
Fourier transform
xyz
xyz   F hkle2ihxky lz
hkl
Inverse Fourier transform
How to know that you know
• all terms defined
• physical/geometric interpretation
Supplementary reading
Matrix algebra
“An Introduction to Matrices, Sets and Groups for Science Students”
by G. Stephenson ($7.95)
Wave physics
“Physics for Scientists and Engineers” by Paul A. Tipler
Protein structure
“Introduction to Protein Structure”-- by Carl-Ivar
Branden and John Tooze
“Introduction to Protein Architecture : The Structural
Biology of Proteins” -- by Arthur M. Lesk
Materials
Gale Rhodes “Crystallography Made Crystal Clear”
3rd Ed. Academic Press
graph paper
straight edge
protractor
compass
calculator w/trig functions
http://www.bioinfo.rpi.edu/bystrc/courses/bcbp4870/bcbp4870.html