Electron density maps: Difference between revisions

[[X-ray crystallography]] (as of July, 2021). The direct results of crystallographic experiments are electron density maps. Examining the correspondence between the electron density map and the published molecular model reveals regions of uncertainty in the model.

of the protein crystal. The amino acid (or nucleotide) sequence of the crystallized polymer(s) is known in advance. The crystallographer fits the atoms of the known molecules into the electron density map, and refines the model and map to the limits of the

of the crystal in the [[PDB]], along with the experimental diffraction data (intensities of the X-ray reflection spots, or "structure factor amplitudes"). From these combined, the electron density map can be reconstructed.  

Electron density values fill 3-dimensional space of the map (see this [http://www.bioinformatics.org/molvis/edm/ interactive visualization]). The term "map" is historical; the three-dimensional electron density was plotted on several pages, section by section, with contour lines corresponding to the value of the density at that location. These plots were called a map, in reference to topographical maps. For a paper showing several examples of maps printed in sections and overlayed, see [https://www.pnas.org/content/pnas/72/12/4866.full.pdf a paper on tRNA structure].

Electron density maps are available for most

from [https://www.ebi.ac.uk/pdbe/ PDBe]: at the page titled with the entry ID (4 characters), click on Downloads and look for "EDS map" and "EDS difference map". For some structure deposited before 2008, the diffraction data was not deposited and thus the electron density maps are not available. In 2008, the [[wwPDB]] began requiring that the data be deposited along with the model<ref name="2021berman">PMID:33963295</ref>.

2Fo-Fc is the best way to calculate an estimate of the true electron density from diffraction data and atomic model. (It is called 2Fo-Fc because the calculation involves combining the observed diffraction data, Fo, with the expected diffraction data, Fc, in a way that gives the least-biased result). It shows how well the observed density fits around the atomic model<ref name="silvaggi" />. Ideally, a feature present in the crystal but not yet included in the model will show up with half the signal strength compared to features present in the crystal and included in the model. Likewise, spurious features included in the model will show up with half signal strength. This difference between real density and 2Fo-Fc density is called model bias, and is related to using the model (and the experimental data) to judge the correctness of the model, a bit of a circular argument.

An example of an isomesh is in the figure at the upper right of this page. The isomesh is a mesh representing an  isosurface. An isosurface is a surface placed at a specific value of a continuous parameter, so that it represents the boundary between higher and lower values of that parameter. Perhaps a geographic map is a more familiar example, where each [http://wiki.gis.com/wiki/index.php/Isoline isoline] is a contour line joining positions with the same elevation. In an electron density map, an isomesh joins positions with the same electron density, for example, 1 sigma.

Fo-Fc is a "difference map". It shows where the experimental density and the atomic model disagree<ref name="silvaggi" />. If the atomic model fitted the experimental density perfectly (and there were no experimental noise), the difference map would have no densities. Typically, it has '''{{Font color|red|negative densities}}''' (atoms in the model where there is no electron density, isomesh conventionally colored '''{{Font color|red|red}}''') and '''{{Font color|blue|positive densities}}''' (electron density where there is no atom in the model, isomesh typically colored '''{{Font color|blue|blue}}''' or '''{{Font color|green|green}}'''). The isomesh typically represents the boundaries at ±3 sigma, namely, regions with a substantial level of disagreement. Because ±3 sigma is a relative measure, there will always be features in the Fo-Fc Difference Map. When the atomic model still contains glaring mistakes, these peak will correspond to real features. When the atomic model has been completed, these peaks will mostly correspond to experimental noise.

[[PyMOL]], which require considerable practice to use effectively.

[[Jmol]]

first became capable of displaying electron density maps in January, 2010. Being able to display EDM's in Jmol opens the door to examining EDMs effectively in a web browser, with a user interface (yet to be developed) that requires no specialized software knowledge.

* [[User:Karsten Theis/Electron density]] explains and illustrates how to display the electron density map for any selected portion of a crystallographic structure, at various sigma levels.