Resolution (electron density)

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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. [1]

Contents

[edit] History

[edit] Qualitative measures

Series of Resolutions for GroEL. From left to right, 4 Angstrom (A), 8 A, 16 A, and 32 A resolution. The details are smeared away as the resolution becomes lower.
Series of Resolutions for GroEL. From left to right, 4 Angstrom (A), 8 A, 16 A, and 32 A resolution. The details are smeared away as the resolution becomes lower.

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

[edit] 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.

[edit] Cryo-electron microscopy

In cryo-electron microscopy, resolution is typically measured by the Fourier shell correlation (FSC)[2], a three-dimensional extension of the Fourier ring correlation (FRC)[3][4]. 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 0.5[5][1].

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.[6]

[edit] Notes

  1. ^ a b Frank, 2006, p250-251
  2. ^ Harauz & van Heel, 1986
  3. ^ van Heel, 1982
  4. ^ Saxton & Baumeister, 1982
  5. ^ Böttcher et al., 1997
  6. ^ Sousa & Grigoreiff, 2007

[edit] References

  • Harauz, G.; M. van Heel (1986). "Exact filters for general geometry three dimensional reconstruction". Optik 73: 146-156. 
  • van Heel, M. (1982). "Detection of objects in quantum-noise limited images". Ultramicroscopy 8: 331-342. 
  • Saxton, W.O.; W. Baumeister (1982). "The correlation averaging of a regularly arranged bacterial cell envelope protein". J Microscopy 127: 127-138. 
  • Böttcher, B.; Wynne, S.A.; Crowther, R.A. (1997). "Determination of the fold of the core protein of hepatitis B virus by electron microscopy". Nature 386: 88-91. doi:10.1038/386088a0. 
  • Frank, Joachim (2006). Three-Dimnsional Electron Microscopy of Macromolecular Assemblies. New York: Oxford University Press. ISBN 0-19-518218-9. 
  • Sousa, Duncan; Nico Grigoreiff (2007). "Ab initio resolution measurement for single particle structures". J Struct Biol 157: 201-210. doi:10.1016/j.jsb.2006.08.003.