Resolution (electron density)
Encyclopedia
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.
, resolution can be broken down into 4 groups:
; 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
es with hundreds of thousands of atoms.
, resolution is typically measured by the Fourier shell correlation (FSC), a three-dimensional extension of the Fourier ring correlation (FRC). The FSC is a comparison of two different Fourier transform
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.
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. 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
criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise. In 2007, a resolution criterion independent of the FSC was developed using the correlation between neighboring Fourier to distinguish signal from noise.
X-ray crystallography
X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and causes the beam of light to spread into many specific directions. From the angles and intensities of these diffracted beams, a crystallographer can produce a...
, resolution is the highest resolvable peak in the diffraction pattern. While cryo-electron microscopy
Cryo-electron microscopy
Cryo-electron microscopy , or electron cryomicroscopy, is a form of transmission electron microscopy where the sample is studied at cryogenic temperatures...
is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition.
Qualitative measures
In structural biologyStructural biology
Structural biology is a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of biological macromolecules, especially proteins and nucleic acids, how they acquire the structures they have, and how alterations in their structures affect their function...
, 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 constructed
- helical, secondary structureSecondary structureIn biochemistry and structural biology, secondary structure is the general three-dimensional form of local segments of biopolymers such as proteins and nucleic acids...
, 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 unitCrystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
; 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
Virus
A virus is a small infectious agent that can replicate only inside the living cells of organisms. Viruses infect all types of organisms, from animals and plants to bacteria and archaea...
es with hundreds of thousands of atoms.
| Resolution (Å) | Meaning |
| >4.0 | Individual coordinates meaningless |
| 3.0 - 4.0 | Fold possibly correct, but errors are very likely. Many sidechains placed with wrong rotamer. |
| 2.5 - 3.0 | Fold likely correct except that some surface loops might be mismodelled. Several long, thin sidechains (lys, glu, gln, etc.) and small sidechains (ser, val, thr, etc.) likely to have wrong rotamers. |
| 2.0 - 2.5 | As 2.5 - 3.0, but number of sidechains in wrong rotamer is considerably less. Many small errors can normally be detected. Fold normally correct and number of errors in surface loops is small. Water molecules and small ligands become visible. |
| 1.5 - 2.0 | Few residues have wrong rotamer. Many small errors can normally be detected. Folds are extremely rarely incorrect, even in surface loops. |
| 0.5 - 1.5 | In general, structures have almost no errors at this resolution. Rotamer libraries and geometry studies are made from these structures. |
Cryo-electron microscopy
In cryo-electron microscopyCryo-electron microscopy
Cryo-electron microscopy , or electron cryomicroscopy, is a form of transmission electron microscopy where the sample is studied at cryogenic temperatures...
, resolution is typically measured by the Fourier shell correlation (FSC), a three-dimensional extension of the Fourier ring correlation (FRC). The FSC is a comparison of two different Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
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.
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. 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
Sigma is the eighteenth letter of the Greek alphabet, and carries the 'S' sound. In the system of Greek numerals it has a value of 200. When used at the end of a word, and the word is not all upper case, the final form is used, e.g...
criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise. In 2007, a resolution criterion independent of the FSC was developed using the correlation between neighboring Fourier to distinguish signal from noise.