The **circular variance** provides a measure of the **spread** of a
set of **dihedral angles**. It is applied here to each residue's
distribution of
,
,
and
angles across all the members of the **NMR** ensemble.

So, for example, it can provide a measure of how tightly or loosely a given residue's torsion angles cluster together across the entire ensemble of models.

It is defined as

where
,
*n* being the number of members in the ensemble and
*R* is given by the expression

The value of the circular variance varies from **0** to **1**, with the
lower the value the tighter the clustering of the values about a single
mean value.

For two dimensional distributions, such as the distributions of the - values on the residue-by-residue Ramachandran plots, the expression for above is modified to

Allen, F. H. & Johnson, O. (1991) Automated conformational analysis from
crystallographic data. 4. Statistical descriptors for a distribution of
torsion angles. *Acta Cryst.*, **B47**, 62-67.

MacArthur M W & Thornton J M (1993). Conformational analysis of
protein structures derived from NMR data. *Proteins*, **17**,
232-251.