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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 Cα atomic coordinates after optimal rigid body superposition.

When a dynamical system fluctuates about some well-defined average position the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation.






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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 Cα atomic coordinates after optimal rigid body superposition.

When a dynamical system fluctuates about some well-defined average position the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation. The size of this fluctuation can be measured, eg using Mössbauer spectroscopy or nuclear magnetic resonance
Nuclear magnetic resonance

Nuclear magnetic resonance is the name given to a physical resonance phenomenon involving the observation of specific quantum mechanics magnetism properties of an atomic atomic nucleus in the presence of an applied, external magnetic field....
, and can provide important physical information. The Lindemann index
Lindemann index

The Lindemann index is a simple measure of thermally driven disorder. The local Lindemann index is defined as:Where angle brackets indicate a time average....
 is a method of placing the RMSF in the context of the parameters of the system.

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 quaternion
Quaternion

Quaternions, in mathematics, are a non-commutative number system that extends the complex numbers. The quaternions were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space....
s, 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
Kabsch algorithm

The Kabsch algorithm is a method for calculating the optimal alignment of two sets of points. It is useful in graphics, and also in bioinformatics for calculating the RMSD between two protein structures....
.

The equation


where d is the distance between N pairs of equivalent atoms (usually Ca and sometimes C,N,O,Cß).

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:

 


An RMSD value is expressed in length units. The most commonly used unit in structural biology is the Ångström
Ångström

An ?ngstr?m or angstrom is an internationally recognized non-SI unit of length equal to 0.1 nanometre or 1 metres. It is sometimes used in expressing the sizes of atoms, lengths of chemical bonds and optical spectrum, and dimensions of parts of integrated circuits....
 (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
CASP

CASP, which stands for Critical Assessment of Techniques for Protein Structure Prediction, is a community-wide experiment for protein structure prediction taking place every two years since 1994....
 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
Reaction coordinate

In chemistry, a reaction coordinate is an abstract one-dimensional coordinate which represents progress along a reaction pathway. It is usually a geometric parameter that changes during the conversion of one or more molecular entity....
 to quantify where the protein is between the folded state and the unfolded state.

See also

  • Root mean square deviation
    Root mean square deviation

    The root mean square deviation is the measure of the average distance between the backbones of protein structural alignment proteins. In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the RMSD of the Cα atomic coordinates after optimal rigid body superposition....
  • Root mean square fluctuation
    Root mean square fluctuation

    The mean square fluctuation is a measure of the deviation between the position of particle i and some reference position.,where T is the time over which one wants to average, and is the reference position of particle i....
  • Quaternion
    Quaternion

    Quaternions, in mathematics, are a non-commutative number system that extends the complex numbers. The quaternions were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space....
    —used to optimise RMSD calculations
  • Kabsch algorithm
    Kabsch algorithm

    The Kabsch algorithm is a method for calculating the optimal alignment of two sets of points. It is useful in graphics, and also in bioinformatics for calculating the RMSD between two protein structures....
    —an algorithm used to minimize the RMSD by first finding the best rotation
  • — a tool for protein structure comparison. Uses RMSD.
  • — a protein superposition server. Uses RMSD.
  • — structural alignment based on secondary structure matching. By the CCP4 project. Uses RMSD.
  • GDT
    Global distance test

    The global distance test or GDT is a measure of similarity between two protein structures with identical amino acid sequences but different tertiary structures....
     — A different structure comparison measure
  • TM-Score
    Template Modeling Score (bioinformatics)

    The Template Modeling Score or TM-score is a measure of similarity between two protein structures with different tertiary structures. The TM-score is intended as a more accurate measure of the quality of full-length protein structures than the often used Root mean square deviation and Global distance test measures....
     — A different structure comparison measure
  • LCS — A different structure comparison measure


External links

  • —a tutorial on how to calculate RMSD
  • —another tutorial on how to calculate RMSD with example code