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 resolution in cryo-electron microscopy is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition.^[1]

Qualitative measures

In structural biology, resolution can be broken down into 4 groups: (1) sub-atomic, when information about the electron density is obtained and quantum effects can be studied, (2) atomic, individual atoms are visible and an accurate three-dimensional model can be constructed, (3) helical, secondary structure, such as alpha helices and beta sheets; RNA helices (in ribosomes), (4) domain, no secondary structure is resolvable.^{[clarification needed]}

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.^[4]

Cryo-electron microscopy

In cryo-electron microscopy (cryoEM), resolution is typically measured by the Fourier shell correlation (FSC),^[5] a three-dimensional extension of the Fourier ring correlation (FRC),^[6] which is also known as the spatial frequency correlation function.^[7] The FSC is a comparison of the Fourier transforms of two different constructed charge density maps, each map constructed from half of the orginal dataset.

Historically, there was much disagreement on which cutoff in the FSC would provide a good estimation of resolution^[1][8], but the emerging gold-standard is the FSC cutoff of 0.143.^[9] This cutoff is derived from equivalencies to the X-ray crystallography standards of resolution definition.^[10]

Historical measurements

Many other criteria for determining resolution using the FSC curve exist, including the 3-σ criterion, 5-σ criterion, and 0.5 threshold. However, fixed-value thresholds (like 0.5, or 0.143) were argued to be based on incorrect statistical assumptions,^[11] though 0.143 has been shown to be strict enough so as to likely not overestimate resolution.^[9] The half-bit criterion indicates at which resolution there exists enough information to reliably interpret the volume, and the (modified) 3-σ criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise.^[11]

In 2007, a resolution criterion independent of the FSC, Fourier Neighbor Correlation (FNC), was developed using the correlation between neighboring Fourier voxels to distinguish signal from noise. The FNC can be used to predict a less-biased FSC.^[12]

See also

• Structural biology
• X-ray crystallography
• Cryogenic electron microscopy

Notes

References

• Harauz, G.; M. van Heel (1986). "Exact filters for general geometry three dimensional reconstruction". Optik. 73: 146–156.
• van Heel, M.; Keegstra, W.; Schutter, W.; van Bruggen E.F.J. (1982). Arthropod hemocyanin studies by image analysis, in: Structure and Function of Invertebrate Respiratory Proteins, EMBO Workshop 1982, E.J. Wood. Life Sciences Reports. Vol. Suppl. 1. pp. 69–73. ISBN 9783718601554.
• Saxton, W.O.; W. Baumeister (1982). "The correlation averaging of a regularly arranged bacterial cell envelope protein". Journal of Microscopy. 127 (2): 127–138. doi:10.1111/j.1365-2818.1982.tb00405.x. PMID 7120365. S2CID 27206060.
• 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 (6620): 88–91. Bibcode:1997Natur.386...88B. doi:10.1038/386088a0. PMID 9052786. S2CID 275192.
• van Heel, M.; Schatz, M. (2005). "Fourier shell correlation threshold criteria". Journal of Structural Biology. 151 (3): 250–262. doi:10.1016/j.jsb.2005.05.009. PMID 16125414.
• Frank, Joachim (2006). Three-Dimnsional Electron Microscopy of Macromolecular Assemblies. New York: Oxford University Press. ISBN 0-19-518218-9.
• Sousa, Duncan; Nikolaus Grigorieff (2007). "Ab initio resolution measurement for single particle structures". J Struct Biol. 157 (1): 201–210. doi:10.1016/j.jsb.2006.08.003. PMID 17029845.

External links

• PDB 101 Looking at Structures: Resolution
• EMstats Trends and distributions of maps in EM Data Bank (EMDB), e.g. resolution trends
• Structural resolution and electron density

This page was last edited on 5 January 2024, at 01:50