Resolution (structural biology)

Resolution in the context of structural biology is the ability to distinguish the presence or absence of atoms or groups of atoms in a biomolecular structure. Usually, the structure originates from methods such as X-ray crystallography, electron crystallography, or cryo-electron microscopy. The resolution is measured of the "map" of the structure produced from experiment, where an atomic model would then be fit into. Due to their different natures and interactions with matter, in X-ray methods the map produced is of the electron density of the system (usually a crystal), whereas in electron methods the map is of the electrostatic potential of the system. In both cases, atomic positions are assumed similarly.

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.

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.

Cryo-electron microscopy
In cryo-electron microscopy (cryoEM), resolution is typically measured by the Fourier shell correlation (FSC), a three-dimensional extension of the Fourier ring correlation (FRC), which is also known as the spatial frequency correlation function. The FSC is a comparison of the Fourier transforms 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, 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.