Talk:Resolution

From Proteopedia

ARTICLE REVISED JUNE 15, 2014

I incorporated most of the suggestions below into a major revision of the article. Eric Martz 02:02, 16 June 2014 (IDT)

Proposed revision V2

In structure determinations, resolution is the distance corresponding to the smallest observable feature, i.e. if two objects are closer than this distance, they appear as one combined blob rather than two separate objects. For example, because the resolution of the light microscope is limited to roughly the wave length of light (400 nm = 4000 Å), it is not possible to resolve ("see") separate atoms under a microscope (atomic distances are on the order of 1 Å). The resolution of X-ray crystallography is theoretically limited by the wave length of X-rays (also on the order of 1 Å), but in practice, the quality of the available crystals determines resolution. High numeric values of resolution, such as 4 Å, mean poor resolution, while low numeric values, such as 1.5 Å, mean good resolution. A structure determined using data to 1.5 Å would be referred to as a "1.5 Å structure". 2.05 Å is the median resolution for X-ray crystallographic results in the Protein Data Bank (88,701 on May 15, 2014).

Confusion of high vs. low resolution

High resolution is characterized by being able to distinguish smaller features, so there is an inverse relationship between the quality of a structure and the length scale given for the resolution. For example, a 1.0 Å structure resolves finer detail than a 4.0 Å structure, so the 1.0 Å structure is said to have higher resolution than the 4.0 Å structure. For non-experts, it would be less confusing if the terms were fine and rough resolution rather than high and low resolution, but high and low are the established terms in the field.

Resolution of a reflection vs resolution of a diffraction data set

Each diffraction spot (i.e. reflection) in a diffraction pattern has a nominal resolution. The higher the diffraction angle (i.e. further from the center of the diffraction image where the incoming X-ray beam would hit), the higher the resolution. In a diffraction experiment, the goal is to collect as many reflections as possible. However, reflections of high resolution are more difficult to measure because the intensity of reflections drops off at higher diffraction angles (and with that, higher resolution). In a diffraction image, you will see high intensity spots near the center, and more and more faded spots as you move away from the center. The overall resolution of a diffraction data set refers to the resolution range of reflections measured. For example, "data were collected from 20.0 Å to 2.3 Å with an overall completeness of 96.5%" means that most reflections in this range were collected, and the data set would be described in brief as "2.3 Å resolution" data set, referring to the high resolution limit of the data collection.

Resolution and crystal quality

The resolution of a diffraction pattern depends on how ordered the crystal is. If it is highly ordered (atoms are in defined positions throughout the crystal and over time), the crystal will diffract to high resolution. The more disorder there is (atoms moving over time, or the content of one unit cell different from the next), the lower the resolution of the diffraction image because the intensity of spots drops with increasing disorder. In order to still be able to measure these weak reflections, it is sometimes possible to increase the intensity of the X-rays used in the experiment, increase the exposure time or sensitivity of the detector or increase the size of the crystals.

Resolution and diffraction data quality

A well diffracting crystal will yield a high resolution diffraction data. The higher the resolution, the more reflections in the data set. The number of reflections increases with the inverse cube of the resolution, so a 1.0 Å data set has eight times the number of reflections than a 2.0 Å data set. If you compare a given reflection measured on a well diffracting crystal to one measured on a poorly diffracting crystal, the former will be measured with higher precision (lower error).

Resolution and structure quality

The higher the resolution of the diffraction data, the more measurements are present to base the model on. Also, an increase in resolution means that a given reflection is measured with less error than in a corresponding lower quality diffraction data set. As a consequence, the model can be built with fewer systematic errors (such as missing or misplaced atoms) and with less average coordinate error. The coordinate error (roughly defined as how different two models would be based on the same crystals, but independent measurement, model building and refinement) correlates with resolution, but is of a different order of magnitude. It is also influenced by completeness of the data (higher is better), the free R-factor of the refinement (lower is better), and the completeness of the model (higher is better). A typical crystallographic model based on 2.0 Å data has a coordinate error of less than 0.2 Å. (http://www.ccp4.ac.uk/newsletters/newsletter33/murshudov.html)

B-factors and coordinate error

Disorder in a crystal is reflected in lower resolution of the diffraction data, as described above. Disorder in the coordinates based on that data can be modeled by introducing B-factors for each atom. They model atomic positions being displaced (by an average distance that is related to the B-factor) from an average position (given by the coordinates). There is no direct relationship between B-factor and coordinate error. If we obtain perfect information about the electron density at atomic resolution, we can infer the average position of an atom even if it has a high B-factor (this amounts to finding the center of a fuzzy dilute cloud as opposed to a compact dense cloud). However, there is an indirect relationship: Higher disorder in a crystal results in lower resolution of the diffraction data, resulting in high coordinate errors. At the same time, the average B-factor of the model will be high, reflecting the disorder of the crystal, so overall coordinate error and overall B-factor will be correlated. For individual atoms or regions of the structure with higher disorder, there is a higher chance for systematic errors in building the model, so this correlation of high B-factors and high coordinate errors extends to separate regions of the protein as well (see [1], Figure 4 for an example of correlating B-factors with coordinate errors, given specific values for resolution, completeness and free R-factor, which influence coordinate errors as well.)

--Karsten Theis 19:12, 15 May 2014 (IDT)

Proposed revision

Proposed revision for the beginning of this article, after discussion with Keiichi Namba. Comments welcome!

The resolution of a macromolecular crystal is the smallest distance between crystal lattice planes that is resolved in the diffraction pattern. Thus high numeric values of resolution, such as 4 Å, mean poor resolution, while low numeric values, such as 1.5 Å, mean good resolution. 2.05 Å is the median resolution for X-ray crystallographic results in the Protein Data Bank (88,701 on May 15, 2014).

After an electron density map is calculated and refined with a fitted atomic model, an uncertainty of atomic position is calculated for each atom in the model. These single-atom uncertainties are called the B factors or temperature values of the atoms (see Temperature).

Determination of Resolution

The portion of the macromolecule that is best ordered in the crystal is responsible for diffraction spots that are farthest from the axis of the X-ray beam. Resolution is determined from these farthest spots based on their angle θ from the X-ray beam, using the Bragg equation solved for d:

where λ is the X-ray wavelength, and d is the smallest distance between crystal lattice planes that scatter discrete spots. The resolution is given by d.

If some portions of the macromolecule are less ordered in the crystal than others, these will have a poorer resolution. The "resolution of the crystal" represents the most ordered portions.

Cite: Explanation by Shigeta.

--Eric Martz 13:17, 15 May 2014 (IDT)

END OF PROPOSED REVISION.

Some rough notes added below for potential incorperation into the article (delete below when added ;-)

--Dan Bolser 12:08, 4 January 2009 (IST)

Post to PDB-L

Some time back I remember reading a posting to this list where some very general rules-of-thumb were given for interpreting the value of the resolution of an X-ray structure.

The rules were something like (very approximate version!)

• >4 Angstrom = Unlikely to even get backbone right (anything goes).
• >3 Angstrom = Backbone possible but side chain orientation is probably wrong.
• >2 Angstrom = Sidechain orientation is broadly correct, but 'some other problems' exist.
• >1 Angstrom = 'Some other problems' are probably gone.
• >0.5 Angstrom = Hydrogen atoms are 'visible'.

Where (if I remember correctly) the 'some other problems' were issues of sterio-chemistry, orientation of specific groups, etc.

Please note, if I remembered incorrectly the above 'rules' may be totally wrong!

Reply

I would refer you to a very nice talk Greg Warren (at Openeye) gave at the ACS meeting.

In this presentation he gave multiple examples of problematic situations many of us have seen. The bottom line is that even with apparently high resolution (<2A) many serious problems can remain due to poorly fit density, missing local density, multiple solutions to the fit, and especially ligand issues.

At least as important as resolution is Rfree, which gives you a measure of how well the model structure fits the electron density generated from structure factors (the actual experimental data).

In a general sense the table you cite is not too bad I suppose, but the problem is that there is not a general answer. A very good structure might be bad where it matters to you, and a low resolution structure, say 3A, might not be as bad as you think.

Dominic Ryan

Reply

I would also add that "quality" is not something that depends solely on resolution, but also very heavily on the environment of the residue. At 2.8A to 3A resolution, for example, it's still possible to determine the orientation of buried residues, but things may be really ugly on the surface. So, if what you want is have a measure about "what to trust" in a x-ray structure, it's a good idea to check the real-space correlation by residue (a coeficient that tells how well the modeled structure fits in the electron density), or visually check what's going on using the electron density server at http://eds.bmc.uu.se/eds/