I just stumbled on this page of movies x-ray refinement create by James Holton. X-ray crystallography is one of the reliable work-horses of protein analysis. The intrepid crystallographer turns diffraction patterns (left) into 3-dimensional electron density maps (right):
from which one can deduce the molecular structure. When the electron density maps are good, it’s almost trivial to fit a molecular structure into the density, but when it’s not, it requires black magic and a true crystallographer’s gut instinct. The following is a beautiful movie, which shows how Holton refines his molecular model to fit the electron density map:
The meshes represents differences between the real electron density and the calculated density from the model. The colors of the mesh represents different types of errors, with green and red, corresponding to large (3*sigma) errors. In the course of refinement, you want to disappear the red and green meshes.
“it’s almost trivial to fit a molecular structure into the density” : he, it’s far from being trivial ! I learnt this a few days ago.
Of course, I knew for a long time that the Hohenberg-Kohn theorem (1965) guarantees that the electron density contains enough informations to reconstruct the hamiltonian, and thus get every properties of interest. But it doesn’t tell us anything about the construction of the ultime functional (DFT).
A more physical “proof” has been proposed by Wilson in the mean time : basically, cusps indicate the presence of nucleii and the slope can be traced to the atomic number. Nevertheless, many theoretician chemists do not consider this construction as a true proof — for some molecules, electron density will no exhibit cusps where some atoms actually are. (For some crazy highly excited states, I admit).
Lucky biophysicians ! ;-)
