# 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^{–10}m.

## 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