Methods: X-ray Crystallography. Biochemistry 4000 Dr. Ute Kothe. Why X-rays?. Optics: Limit of resolution ~ l /2 Distance between atoms: 0.1 – 0.3 nm Wavelenght of X-rays: 0.1 – 10 nm Allows structure determination at atomic resolution Problem: No lenses available for X-rays
Dr. Ute Kothe
at atomic resolution
No lenses available for X-rays
(as for visible light in microscope)
Wavelength, Amplitude, Phase
Growing a Crystal
Collecting X-ray diffraction pattern
Solving of Phase Problem
Calculate Electron Density Map
Constructing a Structural Model
Refining the Structural Model
Why? Diffraction pattern of single molecule too weak for detection
=> sum of several diffraction patterns of identically oriented
molecules with identical conformation
Supersaturated Solution: Concentration higher than intrinsic solubility S0
Hanging Drop Method:
Alternative: Sitting Drop
bDescription of Crystals
characterized by edge length and angles
can contain several molecules
is repeated multiple times along the axis of the crystal
Assymetric Unit: minimal part of the unit cell which is related to other parts by defined symmetry operations
Huygen’s principle of diffraction:
Each point in front of a wavefront acts as a point of progapation for a new wavelet.
b) Constructive interference of scattered waves
=> Amplitude = 2E
c) Destructive interference of scattered waves
=> Amplitude = 0 (wave 180° out of phase)
Simplification: reflection at planes (one dimension: distance d of planes)!
Van Laue Conditions replace Bragg’s Law
(too much to explain in Bchm 4000)
Instead of “n”, three Miller Indices (h, k, l) define the integer number of wavelenght that result in an observed reflection froma 3D crystal.
Example: 2 points in space
Each diffraction spot corresponds to one set of Miller indices (h, k, l).
I(h,k,l) = I(-h,-k,-l)
X-ray diffraction photograph
of Sperm Whale Myoglobin crystal
Missing Information to get electron density!
What about hydrogen atoms?
5Å - a helices roughly visible
3Å - peptide chain visible, side chains if sequence known
2Å - conformations of side chains visible
Rasmussen et al., Science 2007