Difference density map
Encyclopedia
In protein crystallography, a difference density map shows the spatial distribution of the difference between the measured electron density
of the crystal and the electron density explained by the current model.
Conventionally, they are displayed as isosurface
s 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.
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. It is now normal to also include weighting terms which take into account the estimated errors in the current model:
where m is a figure of merit
which is an estimate of the cosine of the error in the phase, and D is a 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.
Electron density
Electron density is the measure of the probability of an electron being present at a specific location.In molecules, regions of electron density are usually found around the atom, and its bonds...
of the crystal and the electron density explained by the current model.
Conventionally, they are displayed as isosurface
Isosurface
An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value within a volume of space; in other words, it is a level set of a continuous function whose domain is 3D-space.Isosurfaces are normally displayed using computer graphics, and are...
s 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
Ligand
In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from...
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
Radiation damage
Radiation damage is a term associated with ionizing radiation.-Causes:This radiation may take several forms:*Cosmic rays and subsequent energetic particles caused by their collision with the atmosphere and other materials....
or that it is modelled in the wrong place—in red.
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. It is now normal to also include weighting terms which take into account the estimated errors in the current model:
where m is a figure of merit
Figure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application...
which is an estimate of the cosine of the error in the phase, and D is a 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.