Protein Structure Determination
Part 2 --
X-ray Crystallography
Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).
Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).
The method
Crystals X-rays Atoms
FT FT-1
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 e-
density• sample is single crystal
X-ray diffractometer
Experimental setupX-ray source X-ray detector
beam stop
Dimensions
X-ray beam
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
N
O
CH3CαC
C-C bond distance: 1.52Å
Wavelength of Cu Kα X-rays: 1.5418Å
Dimensions
N
O
CH3CαC
Angle of incidence=θ: 0-90°
Bragg plane separation distance (resolution): 0.7-50Å
Dimensions
C
N
C
Dimensions
X-rays see e- as if they were standing still.
Carbon atom
amount an electron moves in one xray cycle
Electromagnetic spectrum
Wavelength of X-rays used in crystallography: 1Å - 3Å (Å = 10-10m) most commonly 1.54Å (Cu )
Frequency = c/λ=(3x108m/s)/(1.54x10-10m) ≈ 2x1018 s-1
oscillating e- scatter X-rays
…in all direction.
e-
oscillation
emission
Reflection planes
•The “amplitude” of scattering is measured.
•The amplitude is proportional to the differences of e- density 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
• Crystal growth• Diffraction theory• Symmetry• Experimental methods • Interpretation of data• Software
Equations you will need to know
€
e iα = cosα + isinα
€
nλ = 2d sinθ
€
vS =
v s o −
v s
λ
€
vx sym = M
v x +
v v
€
F hkl( ) = ρ xyz( )xyz
∑ e2πi hx+ky +lz( )
€
ρ xyz( ) = F hkl( )hkl
∑ e−2πi hx+ky+lz( )
Bragg's law
Euler's theorem
Reciprocol space
Symmetry
Fourier transform
Inverse Fourier transform
How to know that you know
• all terms defined• physical/geometric interpretation
Supplementary reading
“An Introduction to Matrices, Sets and Groups for Science Students”by G. Stephenson ($7.95)
“Physics for Scientists and Engineers” by Paul A. Tipler
Matrix algebra
Wave physics
“Introduction to Protein Structure”-- by Carl-Ivar Branden and John Tooze
“Introduction to Protein Architecture : The Structural Biology of Proteins” -- by Arthur M. Lesk
Protein structure
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