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 - 1985 Nobel Prize in Chemistry

• Roderick MacKinnon and Peter Agre – 2003 Nobel Prize in Chemistry

Cα

Cα

ψ

φ

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

Steps To Solving The Structure Of A Protein

• 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

• 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

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.

Our Protein

After shootingOur Protein with X-raysAnd getting the FT

Taking the FT of the FTRESTORES the originalData (mostly)

A very simple example of Fourier and Inverse Fourier transforms

• 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

Quick Recap

• Crystallize Protein (if humanly possible)

• Measuring diffraction amplitudes

• Using a computer to calculate electron density

• Building a model consistent w/ density

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

• Express the resolution of a structure in terms of a distance

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.

(Multiple) Isomorphous Replacement