2. Nobel Laureates of X Ray Crystallography
Max von Laue Nobel Prize in Physics
Bragg(s) Nobel Prize in Physics.
Dorothy Hodgkin – 1964 Nobel Prize in Chemistry
Hauptman and Karle Nobel Prize in Chemistry
Roderick MacKinnon and Peter Agre – 2003 Nobel Prize in Chemistry

6. ψ φ Cα Cα

8. Levinthal's paradox
How many backbone conformations of a 300 residue protein are possible?
Only taking into account Phi and Psi angles, approximately 10³°° conformations
How is the right conformation found in our lifetime?
Answer: Only some angle combinations are energetically favorable, hence only a limited amount of structural conformations are possible

10. Steps To Solving The Structure Of A Protein

12. When X-rays strike a macromolecular crystal, the atoms in the molecules produce scattered X-ray waves which combine to give a complex diffraction pattern consisting of waves of different amplitudes

13. What is measured experimentally are the amplitudes and positions of the scattered X-ray waves from the crystal
X-ray crystallography provides the positions of all non-hydrogen atoms
The origin of each wave must be determined so that they sum to give an image instead of a “sea of noise”
Phase values must be assigned to all of the recorded data; sometimes done computationally, but is usually done experimentally by labeling the protein with one or more heavy atoms whose position in the crystal can be determined independently

14. Electron Density Calculation
Diffraction amplitudes = FT{Electron density}
Take the inverse FT of the diffraction pattern to regenerate the electron density
Shooting a crystal with X-rays and obtaining a diffraction pattern is the same as taking the Fourier transform of a compound. Hence, taking the Fourier transform again gives us the original structure.

15. After shooting
Our Protein with X-rays
And getting the FT
Taking the FT of the FT
RESTORES the original
Data (mostly)
Our Protein
A very simple example of Fourier and Inverse Fourier transforms

16. The scattered x-rays have amplitudes given by Fourier coefficients of electron density
Possible to measure amplitudes
If we could also measure phases, we could compute electron density by inverse Fourier transform
We then fit a model to the density
Phases are extremely difficult to measure

17. Quick Recap Crystallize Protein (if humanly possible)
Measuring diffraction amplitudes
Using a computer to calculate electron density
Building a model consistent w/ density

20. Quality Of a Structure
R-factors represent the percentage disagreement between the observed diffraction pattern and that calculated from the final model
R-factors of around 20% or less are considered well determined structures that are expected to contain relatively few errors

21. Express the resolution of a structure in terms of a distance

24. Molecular Replacement
Use an analogous structure (similar amino acid sequence) and apply to the structure you are trying to determine
“Replacement” actually means 'relocation, repositioning‘ atoms.

25. (Multiple) Isomorphous Replacement