# Root mean square fluctuation

- Root mean square fluctuation
The **mean square fluctuation** (**MSF**) is a measure of the deviation between the position of particle i and some reference position.

$MSF=frac\{1\}\{T\}sum\_\{t\_j=1\}^\{T\}(x\_i(t\_j)\; -\; ilde\{x\}\_i)^2$,

where T is the time over which one wants to average, and $ilde\{x\}\_i$ is the reference position of particle i. Typically this reference position will be the time-averaged position of the same particle i, ie. $overline\{x\}\_i$

Note that where the difference between RMSD and MSF is that with the later the average is taken over time, giving a value for each particle i. With RMSD the average is taken over the particles, giving time specific values.

** See also **

*Quadratic mean

*Root mean square deviation (bioinformatics)

* Root Mean Square Fluctuation calculated by GROMACS [*http://www.gromacs.org/documentation/reference/online/g_rmsf.html*]

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