In
bioinformatics, the root-mean-square deviation of atomic positions, or simply root-mean-square deviation (RMSD), is the measure of the average distance between the atoms (usually the backbone atoms) of
superimposed proteins. Note that RMSD calculation can be applied to other, non-protein molecules, such as small organic molecules.
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
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
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, for example using
Mössbauer spectroscopy
Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer (sometimes written "Moessbauer", German: "Mößbauer") in 1958, consists of the nearly recoil-free emission and abs ...
or
nuclear magnetic resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
, and can provide important physical information. The
Lindemann index 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
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
Kabsch algorithm.
The solution given by Kabsch is an instance of the solution of the ''d''-dimensional problem, introduced by Hurley and Cattell.
The
quaternion solution to compute the optimal rotation was published in the appendix of a paper of Petitjean.
This
quaternion solution and the calculation of the optimal isometry in the ''d''-dimensional case were both extended to infinite sets and to the continuous case in the appendix A of another paper of Petitjean.
The equation
:
where ''δ
i'' is the distance between atom ''i'' and either a reference structure or the mean position of the ''N'' equivalent atoms. This is often calculated for the backbone heavy atoms ''C'', ''N'', ''O'', and ''C
α'' or sometimes just the ''C
α'' atoms.
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:
:
A RMSD value is expressed in length units. The most commonly used unit in
structural biology
Structural biology is a field that is many centuries old which, and as defined by the Journal of Structural Biology, deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every le ...
is the
Ångström
The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
(Å) which is equal to 10
−10 m.
Uses
Typically RMSD is used as a quantitative measure of similarity between two or more protein structures. For example, the
CASP
Critical Assessment of Structure Prediction (CASP), sometimes called Critical Assessment of Protein Structure Prediction, is a community-wide, worldwide experiment for protein structure prediction taking place every two years since 1994. CASP prov ...
protein structure prediction
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different ...
competition uses RMSD as one of its assessments of how well a submitted structure matches the known, target structure. Thus the lower RMSD, the better the model is in comparison to the target structure.
Also some scientists who study
protein folding
Protein folding is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproduc ...
by computer simulations use RMSD as a
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 entities. In molecu ...
to quantify where the protein is between the folded state and the unfolded state.
The study of RMSD for small organic molecules (commonly called
ligands when they're binding to macromolecules, such as proteins, is studied) is common in the context of
docking,
as well as in other methods to study the
configuration of ligands when bound to macromolecules. Note that, for the case of ligands (contrary to proteins, as described above), their structures are most commonly not superimposed prior to the calculation of the RMSD.
RMSD is also one of several metrics that have been proposed for quantifying evolutionary similarity between proteins, as well as the quality of sequence alignments.
See also
*
Root mean square deviation
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents ...
*
Root mean square fluctuation
*
Quaternion – used to optimise RMSD calculations
*
Kabsch algorithm – an algorithm used to minimize the RMSD by first finding the best rotation
*
GDT – a different structure comparison measure
*
TM-score – a different structure comparison measure
*
Longest continuous segment (LCS) — A different structure comparison measure
*
Global distance calculation (GDC_sc, GDC_all) — Structure comparison measures that use full-model information (not just α-carbon) to assess similarity
*
Local global alignment (LGA) — Protein structure alignment program and structure comparison measure
References
Further reading
* Shibuya T (2009). "Searching Protein 3-D Structures in Linear Time." Proc. 13th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2009), ''LNCS'' 5541:1–15.
*
*
*
* {{cite journal , vauthors=Maiorov VN, Crippen GM , year=1994 , title=Significance of root-mean-square deviation in comparing three-dimensional structures of globular proteins , journal=J Mol Biol , volume=235 , issue=2 , pages=625–634 , doi=10.1006/jmbi.1994.1017 , pmid=8289285, hdl=2027.42/31835 , url=https://deepblue.lib.umich.edu/bitstream/2027.42/31835/1/0000782.pdf , hdl-access=free
External links
Molecular Distance Measuresmdash;a tutorial on how to calculate RMSD
RMSDmdash;another tutorial on how to calculate RMSD with example code
Secondary Structure Matching (SSM)— a tool for protein structure comparison. Uses RMSD.
— different structure comparison measures. Description and services.
SuperPose— a protein superposition server. Uses RMSD.
— structural alignment based on secondary structure matching. By the CCP4 project. Uses RMSD.
*A
Python
Python may refer to:
Snakes
* Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia
** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia
* Python (mythology), a mythical serpent
Computing
* Python (pro ...
script is available at https://github.com/charnley/rmsd
*An alternate
Python
Python may refer to:
Snakes
* Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia
** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia
* Python (mythology), a mythical serpent
Computing
* Python (pro ...
script is available at https://github.com/jewettaij/superpose3d
Statistical deviation and dispersion
Protein methods
Bioinformatics