Root-mean-square Deviation (bioinformatics) - The Equation

The Equation

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 points and, the RMSD is defined as follows:

\begin{align} \mathrm{RMSD}(\mathbf{v}, \mathbf{w}) & = \sqrt{\frac{1}{n}\sum_{i=1}^{n} \|v_i - w_i\|^2} \\ & = \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)} \end{align}

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.

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