[phenixbb] Stereochemistry statistics

Ralf W. Grosse-Kunstleve rwgk at yahoo.com
Thu Jan 20 09:49:22 PST 2011

Hi Mike,

> When phenix calculates the stereochemistry statistics for a model,
> two of the statistics given are RMS(chirality) and RMS(planarity).

It is best to think of these as "RMSD" - root mean square differences.

We have tables with "ideal" values that are compared with "model" values,
e.g. angle_ideal and angled_model. The RMSD are

sqrt( mean( (model_value-ideal_value)**2 ) )

Therefore the units of the RMSD values are the same as those of the
individual values, as you suggest...

> What specific measurements are being calculated to produce these
> statistics, and what are the units for the numbers given? For example,
> is RMS(planarity) telling me the average distance out of plane for
> an atom that should be in plane? If this is the case I imagine the
> units are angstroms?

Yes, that's right. (We compute a plane that minimizes the RMSD.)

The chiral differences are computed as differences of volumes;
the units are Angstrom**3. Four atoms are involved, labeled as
"centre", "1", "2", "3". These are used to compute three vectors:
a = 1 - centre
b = 2 - centre
c = 3 - centre
The chiral volume is a.dot(b.cross(c)), using the vector dot product
and cross product. Note that this is the same formula as used for
computing unit cell volumes.