Root mean square deviation (bioinformatics)

The root mean square deviation (RMSD) is the measure of the average distance between the backbones of superimposed proteins. In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the RMSD of the C&alpha; atomic coordinates after optimal rigid body superposition.

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the RMSD. Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. They proved that the quaternion method is equivalent to the well-known formula due to Kabsch.

The equation
$$RMSD=\sqrt{\frac{1}{N}\sum_{i=1}^{i=N}\delta_{i}^2}$$

where δ is the distance between N pairs of equivalent atoms (usually Cα and sometimes C,N,O,Cβ).

Normally a rigid superposition which minimizes the RMSD is performed, and this minimum is returned. Given two sets of $$n$$ points $$\mathbf{v}$$ and $$\mathbf{w}$$, the RMSD is defined as follows:

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.

Uses
Typically RMSD is used to make a quantitative comparison between the structure of a partially folded protein and the structure of the native state. For example, the CASP protein structure prediction competition uses RMSD as one of its assessments of how well a submitted structure matches the native state.

Also some scientists who study protein folding simulations use RMSD as a reaction coordinate to quantify where the protein is between the folded state and the unfolded state.