Resolution (electron density)

Resolution in terms of electron density is a measure of the resolvability in the electron density map of a molecule. In X-ray crystallography, resolution is the highest resolvable peak in the diffraction pattern. While cryo-electron microscopy is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition. Frank, 2006, p250-251]

History

Qualitative measures

In structural biology, resolution can be broken down into 4 groups:

* sub-atomic, individual elements are distinguishable and quantum effects can be studied
* atomic, individual atoms are visible and an accurate three-dimensional model can be construction
* helical, secondary structure, such as alpha helices and beta sheets
* domain, no secondary structure is resolvable

X-ray crystallography

As the crystal's repeating unit, its unit cell, becomes larger and more complex, the atomic-level picture provided by X-ray crystallography becomes less well-resolved (more "fuzzy") for a given number of observed reflections. Two limiting cases of X-ray crystallography are often discerned, "small-molecule" and "macromolecular" crystallography. "Small-molecule crystallography" typically involves crystals with fewer than 100 atoms in their asymmetric unit; such crystal structures are usually so well resolved that its atoms can be discerned as isolated "blobs" of electron density. By contrast, "macromolecular crystallography" often involves tens of thousands of atoms in the unit cell. Such crystal structures are generally less well-resolved (more "smeared out"); the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms. In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses with hundreds of thousands of atoms.

Cryo-electron microscopy

In cryo-electron microscopy, resolution is typically measured by the Fourier shell correlation (FSC)Harauz & van Heel, 1986] , a three-dimensional extension of the Fourier ring correlation (FRC)van Heel, 1982] Saxton & Baumeister, 1982] . The FSC is a comparison of two different Fourier transforms over different shells on frequency space. To measure the FSC, the data needs to be separated into two groups. Typically, the even particles form the first group and odd particles the second based on their order. This is commonly referred to as the even-odd test. Most publications quote the FSC 0.5 cutoff, which refers to the when the correlation coefficient of the Fourier shells is equal to 0.5Böttcher et al., 1997] .

Determining the resolution remains a controversial topic. Many other criteria using the FSC curve exist, including 3-σ criterion, 5-σ criterion, and the 0.143 cutoff. In 2007, a resolution criterion independent of the FSC was developed using the correlation between neighboring Fourier to distinguish signal from noise.Sousa & Grigoreiff, 2007]

Notes

References

*cite journal
last = Harauz
first = G.
coauthors = M. van Heel
title = Exact filters for general geometry three dimensional reconstruction
journal = Optik
volume = 73
pages = 146–156
year = 1986
*cite journal
last = van Heel
first = M.
title = Detection of objects in quantum-noise limited images
journal = Ultramicroscopy
volume = 8
pages = 331–342
year = 1982
*cite journal
last = Saxton
first = W.O.
coauthors = W. Baumeister
title = The correlation averaging of a regularly arranged bacterial cell envelope protein
journal = J Microscopy
volume = 127
pages = 127–138
year = 1982
*cite journal
last = Böttcher
first = B.
coauthors = Wynne, S.A.; Crowther, R.A.
title = Determination of the fold of the core protein of hepatitis B virus by electron microscopy
journal = Nature
volume = 386
pages = 88–91
doi=10.1038/386088a0
year = 1997
*cite book
last = Frank
first = Joachim
authorlink = Joachim Frank
title = Three-Dimnsional Electron Microscopy of Macromolecular Assemblies
publisher = Oxford University Press
location = New York
date = 2006
pages =
isbn = 0-19-518218-9

*cite journal
last = Sousa
first = Duncan
coauthors = Nikolaus Grigorieff
title = "Ab initio" resolution measurement for single particle structures
journal = J Struct Biol
volume = 157
pages = 201–210
doi=10.1016/j.jsb.2006.08.003
year = 2007