Resolution in the context of

structural biology Structural biology deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every level of organization. Early structural biologists throughout the 19th and early 20th centuries we ...

is the ability to distinguish the presence or absence of

atoms Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other ...

or groups of atoms in a biomolecular structure. Usually, the structure originates from methods such as

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

, electron crystallography, or

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

. The resolution is measured of the "map" of the structure produced from

experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...

, where an atomic model would then be fit into. Due to their different natures and interactions with matter, in

X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...

methods the map produced is of the

electron density 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 variables and is typical ...

of the system (usually a

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

), whereas in

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

methods the map is of the

electrostatic potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work needed ...

of the system. In both cases, atomic positions are assumed similarly.

Qualitative measures

, resolution can be broken down into 4 groups: (1) sub-atomic, when information about the electron density is obtained and

quantum effects Quantum mechanics is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of a ...

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 local spatial conformation of the polypeptide backbone excluding the side chains. The two most common Protein structure#Secondary structure, secondary structural elements are alpha helix, alpha helices and beta ...

, such as

alpha helices An alpha helix (or α-helix) is a sequence of amino acids in a protein that are twisted into a coil (a helix). The alpha helix is the most common structural arrangement in the secondary structure of proteins. It is also the most extreme type of l ...

and beta sheets;

RNA Ribonucleic acid (RNA) is a polymeric molecule that is essential for most biological functions, either by performing the function itself (non-coding RNA) or by forming a template for the production of proteins (messenger RNA). RNA and deoxyrib ...

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 In mathematics, a unit vector i ...

, 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

virus A virus is a submicroscopic infectious agent that replicates only inside the living Cell (biology), cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea. Viruses are ...

es with hundreds of thousands of atoms.

Cryo-electron microscopy

(cryoEM), 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 ...

(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 ...

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

Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

s of two different constructed electrostatic potential maps, each map constructed from a random half of the original dataset. Historically, there was much disagreement on which cutoff in the FSC would provide a good estimation of resolution,Böttcher et al., 1997 but the emerging gold-standard is the FSC cutoff of 0.143. This cutoff is derived from equivalencies to the X-ray crystallography standards of resolution definition.

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, though 0.143 has been shown to be strict enough so as to likely not overestimate resolution. 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. 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

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