Determination of mean and standard deviation of dihedral angles

Backbone torsional angles are a characteristic and useful parameter for the description and characterisation of protein structures determined by x-ray crystallography or NMR spectroscopy. For the comparison of an ensemble of three-dimensional structures the calculation of the statistical parameters mean and standard deviation would be very useful. However, they are not defined unambiguously for periodic quantities such as the dihedral angles. In this paper a plausible and unique definition of these parameters is introduced and a straightforward method for their calculation is given. (C) 1999 Academic Press.