On Monday 26 February 2007 08:23, Richard Gillilan wrote:
> Ok, Painter and Merritt describe this situation in their Acta Cryst
> (2006) D62 439-450 article entitled "Optimal description of a protein
> structure in terms of multiple groups undergoing TLS motion." At
> least with regard to fitting L parameters from previously refined
> data, negative eigenvalues of L can happen as a result of deviations
> from the rigid body assumption (deformations). In such cases, it
> would seem that the resulting principle axes are meaningless. Painter
> and Merritt provide a means of constraining the L parameters so as to
> always yield positive eigenvalues, but it is unclear to me if Refmac5
> refinement applies any such constraint.
>
> Can anyone confirm this?

It is complicated. As you note, the discussion you quote addresses the
question of fitting a TLS model to previously determined ADPs.
The TLS formalism was developed to describe a rigid body, and if the
eigenvalues of L go negative this assumption is invalidated.
That does not, however, mean that the original ADPs are invalid
or that the bulk motion they imply is non-physical.

Analogy: Let's develop TLS models for two similar actions,
(1) swinging a baseball bat and (2) casting a fly-fishing rod.
In both cases we'll create a TLS model based on a hypothetical
snaphot of the first half of the swing. I am neither a ball player
nor a fly fisherman, so I freely admit hat my TLS models may be
unrealistic :-)

The baseball bat really is rigid, and one would expect a TLS model for
the motion of the bat to be relatively well-behaved. There is a large
angular component as you pivot your shoulders, and a smaller L component
as you shift your weight forward. The positive S and L terms tell you
that the tip of the bat moves forward (and pivots) faster than the
middle of the bat and certainly faster than the grip of the bat.

The fishing rod, on the other hand, is not so rigid. We expect to
end up with a TLS model that describes a horizontal screw axis, again
somewhere in the general region of your shoulders, and a smaller L
component as you swing the rod over your end from behind you to
in front of you. But the rod is flexible, and you are applying
force at the base. So in mid-swing the middle of the rod will lead
the tip of the rod at first, and the tip only catches up as you
complete the cast. This will manifest as negative Eigenvalues in
your TLS tensors, because the incremental motion is not continuously
increasing as you step along the rod from your grip to the tip.

So the TLS model for the fly rod "fails", because the rod is not
a rigid body. But that doesn't mean the motion of the rod is
non-physical! It just means that the rod is not rigid.

> If this is the case, then principle axes of ANISO records generated
> from TLSANL are also questionable for these particular bodies as are
> thermal ellipsoids.

The ADPs (either isotropic or anisotropic) developed directly from
a TLS model containing negative Eigenvalues can go non-positive
definite. That would be bad. But you are probably refining an
incremental Biso along with your TLS model; at least that seems
to be what most people are doing since Refmac makes it so easy.
If the incremental Biso is positive, as indeed refmac constrains
it to be, then the net ADPs may be well-behaved even though the
pure TLS component is not.

As to the axes (as opposed to the ellipsoids), I don't know how to
express a quantitative estimate for their reliability. In the
baseball/fishing examples, we expect the axes to be correctly
described notwithstanding the oddity of the fly rod Eigenvalues.
But I don't know how well that analogy holds when transferred to
protein structural analysis, which is what we really care about.

That's my off-the-cuff discourse. I hope eventually to offer
a more rigorous treatment and possible recommendations for how
to proceed with refinement or interpretation

Ethan


 
>
> Richard Gillilan
> MacCHESS
>
>
> On Feb 25, 2007, at 8:10 AM, Richard Gillilan wrote:
>
> > After TLS refinement (which seemed to be stable and produced nice
> > R_free values), I have analyzed the rigid body results with TLSANL.
> > I get negative mean-square displacements along the axes of
> > libration WRT to orthogonal axes! Am I misunderstanding something
> > here? The units are (deg^2). I see this with two different
> > structures. Here is the output from TLSANL:
> >
> > AXES OF LIBRATION WRT TO MEAN-SQUARE ANGLE
> > LIBRATION AXES MAKE TO
> > ORTHOGONAL AXES (IN ROWS) DISPLACEMENT ORTHOGONAL
> > AXES (DEG)
> >
> > ABOUT AXES (DEG^2) X Y Z
> > 0.842 0.197 0.502
> > -53.975 32.66 78.63 59.85
> > -0.494 0.657 0.570
> > 193.421 119.60 48.97 55.24
> > -0.217 -0.728
> > 0.650 -12.276 102.55 136.73 49.45
> >
> > MEAN LIBRATION (TRACE/
> > 3) 42.390
> >
> >
> > Anyone seen this happen before?
> >
> > Richard Gillilan
> > MacCHESS
>

--
Ethan A Merritt Courier Deliveries: 1959 NE Pacific
Dept of Biochemistry
Health Sciences Building
University of Washington - Seattle WA 98195-7742