# Suggested problems

## Root Mean Square Deviation

Dec. 3, 2012, 10:32 p.m. by Guillaume Collet

## Protein structure superposition

Protein structure superposition is a key step in the annotation of a newly discovered protein structure. Moreover, in case of low sequence identity, it can be the only way to infer a homology relationship with other proteins.

Many methods have been developed to optimally superpose two protein structures. But to compare the quality of two different superpositions of the same proteins, the widely accepted measure of quality is the Root Mean Square Deviation

## Problem

Here, we want to evaluate the Root Mean Square Deviation of a given superposition of atoms. A superposition is a list of pairs of aligned atoms. A pair of aligned atoms is represented by the list of the 3D coordinates of each atoms x1 y1 z1 x2 y2 z2 :

43.8854 -7.1446 -13.1739 43.1437 -6.6910 -12.8891


The Root Mean Square Deviation consist in calculating the mean of the square distances and then taking the square root of this mean, like in this formula:

Given: A list of at most 50 pairs of aligned atoms (as 3D coordinates: x1 y1 z1 x2 y2 z2).

Return: The RMSD of the given superposition.

## Sample Dataset

-17.4936 46.4257 -8.9018 -18.4169 46.0578 -10.8508
43.8854 -7.1446 -13.1739 43.1437 -6.6910 -12.8891
-35.2320 -9.5141 -29.7521 -34.9683 -9.4137 -29.3649
12.3377 -27.8291 10.7187 12.3191 -28.3192 10.1106
47.3331 1.6680 -6.1179 48.1789 1.7362 -5.9315


## Sample Output

1.2015