Pavel Afonine wrote:
Dear Ed,
Tightly restrained refinement will be equivalent to
torsion angle parametrization, since bonds and angles are essentially
fixed (but dihedrals are not).
Simply not true. Think why -:) Hint: in restrained refinement the weight
applies to all terms - bonds, angles, torsions, etc... So if you choose
tight weight in such refinement the torsions will be restrained as
tightly as other terms (at least as it would be in CNS or
phenix.refine). In torsion angle refinement (which is, in fact, a
constrained rigid-body refinement) you still have weights, and you can
make your torsion angle refinement as tight as you like.
However, many refinement programs allow you to adjust the weights of
different terms differently. So, if you were to make the bond length and
angle terms sufficiently tight, but leave the torsion restraints loose,
you can indeed end up with something very similar to torsion angle
refinement.
So why use torsion angle refinement? Because in the scheme I've outlined
above the target function can have vastly different curvatures along
different directions in parameter space. This presents a problem for the
minimiser - without a good deal of second order information the
refinement steps have to be incredibly small (step size related to the
sharpest curvature) and minimisation process becomes impossibly slow.
However, it is seems possible to me that a sufficiently good minimiser
with a carefully constructed sparse curvature matrix may be able to
deliver the same benefits as torsion refinement while working in
Cartesian space.
Kevin
