Real Space Refinement Difference Fourier Syntheses

REAL SPACE REFINEMENT DIFFERENCE FOURIER SYNTHESES 

The difference Fourier map calculated from this equation should be near zero in value and featureless where the model corresponds to the correct structure, as the two electron densities would essentially subtract to zero (assuming F0bs and Fcaic are scaled properly to one another). Where they differ, however, is where we would expect features to appear. At those places where the model contains atoms, and therefore electron density, but the true structure does not, then p(x, y, z)expt —p(x, y, z)modei will be negative. Negative density will appear at that location in the difference Fourier map. If the model lacks atoms, hence electron density, at places occupied by atoms in the true structure, the p(x, y, z)eXpt -p(x, y, z,)model will produce positive density. 

FIGURE 10.11 Here is a two-dimensional representation of what one would likely see in an Fo — Fc difference Fourier map, where the Fc were calculated from a model that includes an arginine side chain, shown here, which was misplaced. A region of negative difference electron density (dashed contour lines) would superimpose upon the position incorrectly occupied by the side chain, while the positive density (solid contour lines) would indicate the location to which it should be shifted. 

As noted already, most X-ray crystal structure refinement incorporates both real and reciprocal space refinement approaches, generally alternating one with the other. At the end of the refinement process, one should have both a low R factor and a featureless difference Fourier map. 

One of the most commonly employed types of difference Fourier synthesis uses as coefficients 2/ / - Fcaic, and phases calculated from the current model. This shows the investigator positive density superimposed on the model where the model is correct, with no density appearing where the model contains incorrectly placed residues or atoms and positive density appears where the model should be. There are also other higher order difference syntheses, but they are less frequently used. 

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REAL SPACE REFINEMENT DIFFERENCE FOURIER SYNTHESES... 

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