Resolution in terms of

electron density In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...

is a measure of the resolvability in the electron density map of a molecule. In

X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...

, resolution is the highest resolvable peak in the

diffraction pattern Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...

, while resolution in

cryo-electron microscopy Cryogenic electron microscopy (cryo-EM) is a cryomicroscopy technique applied on samples cooled to cryogenic temperatures. For biological specimens, the structure is preserved by embedding in an environment of vitreous ice. An aqueous sample sol ...

is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition.Frank, 2006, p250-251

Qualitative measures

structural biology Structural biology is a field that is many centuries old which, and as defined by the Journal of Structural Biology, deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every le ...

, resolution can be broken down into 4 groups: (1) sub-atomic, individual elements are distinguishable 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 Protein secondary structure is the three dimensional conformational isomerism, form of ''local segments'' of proteins. The two most common Protein structure#Secondary structure, secondary structural elements are alpha helix, alpha helices and beta ...

, such as

alpha helices The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located four residues ear ...

and

beta sheets The beta sheet, (β-sheet) (also β-pleated sheet) is a common motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands) connected laterally by at least two or three backbone hydrogen bonds, forming a gen ...

; RNA helices (in ribosomes), (4) domain, no secondary structure is resolvable.

X-ray crystallography

As the crystal's repeating unit, its

unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...

, 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 In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...

; 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

virus A virus is a submicroscopic infectious agent that replicates only inside the living cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea. Since Dmitri Ivanovsky's 1 ...

es with hundreds of thousands of atoms.

Cryo-electron microscopy

, resolution is typically measured by the

Fourier shell correlation In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells i ...

(FSC),Harauz & van Heel, 1986 a three-dimensional extension of the

Fourier ring correlation In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in ...

(FRC),van Heel, 1982 which is also known as the spatial frequency correlation function.Saxton & Baumeister, 1982 The FSC is a comparison of two different

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

s 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 when the correlation coefficient of the Fourier shells is equal to 0.5.Böttcher et al., 1997 Determining the resolution threshold remains a controversial topic and many other criteria using the FSC curve exist, including 3-σ criterion, 5-σ criterion, and the 0.143 cutoff. However, fixed-value thresholds (like 0.5, or 0.143) were argued to be based on incorrect statistical assumptions.van Heel & Schatz, 2005 The new half-bit criterion indicates at which resolution one has collected enough information to reliably interpret the 3-dimensional volume, and the (modified) 3-

sigma Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as ...

criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise.van Heel & Schatz, 2005 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.Sousa & Grigoreiff, 2007 See also a 2011 review on Cyro-EM resolution measurements.

Notes

References

* * * * * * *{{cite journal , last = Sousa , first = Duncan , author2=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 , date = 2007 , pmid = 17029845 , issue = 1

External links

PDB 101 Looking at Structures: Resolution

EMstats
Trends and distributions of maps in EM Data Bank (EMDB), e.g. resolution trends Diffraction