Difference density map

Display

Conventionally, they are displayed as isosurfaces with positive density—electron density where there's nothing in the model, usually corresponding to some constituent of the crystal that hasn't been modelled, for example a ligand or a crystallisation adjutant -- in green, and negative density—parts of the model not backed up by electron density, indicating either that an atom has been disordered by radiation damage or that it is modelled in the wrong place—in red. The typical contouring (display threshold) is set at 3σ.

Calculation

Difference density maps are usually calculated using Fourier coefficients which are the differences between the observed structure factor amplitudes from the X-ray diffraction experiment and the calculated structure factor amplitudes from the current model, using the phase from the model for both terms (since no phases are available for the observed data). The two sets of structure factors must be on the same scale.

: C_{diffmap} = (|F_{obs}| - |F_{calc}| ) exp( 2\pi i \phi_{calc} )

It is now normal to also include maximum-likelihood weighting terms which take into account the estimated errors in the current model:

:C_{diffmap} = ( m |F_{obs}| - D |F_{calc}| ) exp( 2\pi i \phi_{calc} )

where m is a figure of merit which is an estimate of the cosine of the error in the phase, and D is a "σA" scale factor. These coefficients are derived from the gradient of the likelihood function of the observed structure factors on the basis of the current model. A difference map built with m and D is known as a mFo – DFc map.

The use of ML weighting reduces model bias (due to using the model's phase) in the 2 Fo–Fc map, which is the main estimate of the true density. However, it does not fully eliminate such bias.

References

References

1. Bank, RCSB Protein Data. "RCSB PDB: X-ray Electron Density Maps".
2. (1 October 2021). "Cryo-EM single-particle structure refinement and map calculation using Servalcat". Acta Crystallographica Section D Structural Biology.
3. (April 2015). "You are lost without a map: Navigating the sea of protein structures.". Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics.
4. (May 2008). "Iterative-build OMIT maps: map improvement by iterative model building and refinement without model bias.". Acta Crystallographica. Section D, Biological Crystallography.