Wikiomics:RMSD
Definition
RMSD means Root Mean Square Deviation. It is often used in 3D geometry of molecules to compare two conformations of a given set of points, typically atoms. In other words, given a list of paired points, it gives a measure of the distance between these points.
Normally a rigid superposition which minimizes the RMSD is performed, and this minimum is returned. Given two sets of [math]\displaystyle{ n }[/math] points [math]\displaystyle{ \mathbf{v} }[/math] and [math]\displaystyle{ \mathbf{w} }[/math], the RMSD is defined as follows:
| [math]\displaystyle{ \mathrm{RMSD}(\mathbf{v}, \mathbf{w}) }[/math] | [math]\displaystyle{ = \sqrt{\frac{1}{n}\sum_{i=1}^{n} \|v_i - w_i\|^2} }[/math] |
| [math]\displaystyle{ = \sqrt{\frac{1}{n}\sum_{i=1}^{n} ({v_i}_x - {w_i}_x)^2 + ({v_i}_y - {w_i}_y)^2 + ({v_i}_z - {w_i}_z)^2} }[/math] |
An RMSD value is expressed in length units. The most commonly used unit in structural biology is the Ångström (Å) which is equal to 10–10m.
Usage
RMSD values are commonly used to measure the structural similarity between proteins structures. If the proteins are different, an alignment between amino acids is required. It can be a sequence alignment or a structural alignment, both of which can be performed in a variety of ways.
Often, the atoms for which the RMSD is given are restricted to the alignable C[math]\displaystyle{ \alpha }[/math] of a pair of proteins. This can be assumed to be the default. However, it is possible to compute the RMSD for all atoms of identical molecules. For a protein, the RMSD of all atoms is usually larger than the RMSD of C[math]\displaystyle{ \alpha }[/math] since the main chain is more constrained than the lateral chains of the amino acids.
Tools
The following tool can be used to perform a sequence alignment of protein structures and then compute the corresponding RMSD. This is not structural alignment, so it should be used with protein structures of very similar sequences:
- SuperPose [1] provides the RMSD computed on alpha carbons, backbone atoms or heavy atoms, but doesn't give the choice of which residues should be superposed.
There are also a good number of structural alignment tools, which should choose a good alignment even if the sequence conservation is very low. For aligning 2 given structures, the following online tools are available:
- DaliLite [2] uses the classic Dali heuristics.
- CE [3] is another good structure alignment method (requires Java).
Note that Dali, CE and several other algorithms of structural alignment can be used to search a database for structural homologs.
References
- Maiti R, Van Domselaar GH, Zhang H, and Wishart DS. SuperPose: a simple server for sophisticated structural superposition. Nucleic Acids Res. 2004 Jul 1;32(Web Server issue):W590-4. DOI:10.1093/nar/gkh477 |
- Holm L and Park J. DaliLite workbench for protein structure comparison. Bioinformatics. 2000 Jun;16(6):566-7. DOI:10.1093/bioinformatics/16.6.566 |
- Shindyalov IN and Bourne PE. Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Eng. 1998 Sep;11(9):739-47. DOI:10.1093/protein/11.9.739 |
Credits
- this page was initiated (definition, usage, a few links) by Martin Jambon
