Nobel Laureates of X Ray Crystallography

2. Nobel Laureates of X Ray Crystallography • Max von Laue - 1914 Nobel Prize in Physics • Bragg(s) - 1915 Nobel Prize in Physics. • Dorothy Hodgkin – 1964 Nobel Prize in Chemistry • Hauptman and Karle - 1985Nobel 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