Radius of Gyration Restraints

A pseudopotential for the radius of gyration allows a restraint for the overall size of a group of atoms. The radius of gyration is defined as

$$\ensuremath{R_{\mbox{\scriptsize {gyr}}}}= \left[ <(r-<r>)^2> \right]^{1/2},$$ (26.1)

where $r$ is atom position, and $<\cdot>$ denotes average over all atoms.

The expected value for this quantity has been emprically determined to be

$$\ensuremath{R_{\mbox{\scriptsize {gyr}}}}= 2.2 \ensuremath{N_{\mbox{\scriptsize {res}}}}^{0.38},$$ (26.2)

where is the number of residues in a compact globular region. In the case of elongated structures, residues can be selected in regional groupings for this restraint. The reference is Kuszewski, Gronenborn, and Clore (1999).