# 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 $\displaystyle{ n }$ points $\displaystyle{ \mathbf{v} }$ and $\displaystyle{ \mathbf{w} }$, the RMSD is defined as follows:

 $\displaystyle{ \mathrm{RMSD}(\mathbf{v}, \mathbf{w}) }$ $\displaystyle{ = \sqrt{\frac{1}{n}\sum_{i=1}^{n} \|v_i - w_i\|^2} }$ $\displaystyle{ = \sqrt{\frac{1}{n}\sum_{i=1}^{n} ({v_i}_x - {w_i}_x)^2 + ({v_i}_y - {w_i}_y)^2 + ({v_i}_z - {w_i}_z)^2} }$

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$\displaystyle{ \alpha }$ 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$\displaystyle{ \alpha }$ 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

All Medline abstracts: PubMed | HubMed