On Wednesday 12 November 2008 02:54:54 Ian Tickle wrote:
> 
> All - I was just in a discussion about TLS and one thing that came out
> that I hadn't been aware of is that for the Biso restraints Refmac
> restrains the difference between the 'residual' Bs, i.e. with the TLS
> contributions subtracted, not the 'total' Bs.  Now it seems to me that
> this isn't quite correct, because it's the total motion of the atoms
> that matters, i.e. the total mean square along-bond displacements for
> bonded atoms should be equal.  However, I can see that in practical
> terms it won't make any significant difference provided appropriate
> precautions are taken with the choice of TLS groups.
> 
> What I mean by this is that at least for domain-sized groups the
> difference between the TLS contributions to the Bs for bonded atoms
> within the *same* TLS group will be very small (but maybe not so small
> for secondary-structure element or residue-sized groups), so in that
> case the difference between the residual Bs for bonded atoms will be
> essentially equal to the difference between total Bs and it won't matter
> which you restrain.  However for bonded atoms in *different* TLS groups
> this won't necessarily be true.

My opinion is that the requirement for consistency between adjacent TLS
groups is best met by restraints applied to the anisotropic expansion
of the net (TLS + Biso) model.  That is, in order to refine the TLS
parameters, they are first used to create a 6-parameter U^{ij} description
for each atom.  At this point the usual restraints for anisotropic
refinement (BFAC and RBON in refmac terminology) should be applied to
all atoms.  This has the effect of insuring that the U^{ij} terms for
adjacent atoms, even adjacent atoms in different TLS groups, are similar.

As I understand the flow through refmac, this is a bit problematic if
you consider only one "macro-cycle" of refinement.  Refmac performs the
TLS refinement first, and then in a separate step refines the residual 
Biso along with xyz coordinates.  That means the contribution of the new
residual Biso was not accounted for in any anisotropic restraints 
applied during the prior TLS refinement.

However, I believe that if you cycle again through the
TLS-followed-by-Biso macro-cycle, then the affect of the residual Biso
from the previous cycle will be properly accounted for.
So long as successive macro-cycles converge, the consistency of 
adjacent TLS groups should end up properly constrained by RBON.

I am uncertain whether this is in fact what happens when people use
the default refmac scripts and control flow through ccp4i.
It would indeed be a very good idea to pin this down.

I started to write a validation tool to check exactly this point
- whether the equivalent U^{ij} values of atoms at the boundary
between adjacent TLS groups were consistent.  But I'm afraid I never
around to polishing it up and contributing it.
Thanks for bringing it back to mind!

> So it seems to me that the safe option is to choose TLS groups for
> domains, SSE's etc, such that there are flexible 'linkers' separating
> them that are not assigned to a TLS group, so that the domains can move
> essentially independently.  One can still test whether linked domains do
> actually behave as though the motion occurs by libration or torsion at a
> single bond (i.e. a rigid linker) connecting the domains by comparing
> the TLS results for the flexible and rigid linker cases.
> 
> Of course in many cases Nature already provides flexible linkers
> connecting domains, and presumably the very reason they're there is to
> allow some independent, but tethered, motion (this is no doubt a
> much-simplified view of what's happening since non-bonded contacts will
> also affect the motion and the purpose of the linker may well be to
> constrain the motion in some specific way).
> 
> So I was wondering whether people do generally choose TLS groups with
> this in mind, and indeed 


> does the TLSMD server take this into account 
> when selecting TLS groups?

Sort of.  Implicitly.  The usual starting point for TLSMD analysis is
a model that was refined with a conventional Biso model for the ADPs.
That means the usual isotropic restraints should have insured that 
adjacent atoms have consistent isotropic B values.  TLSMD then finds
an optimal assignment of TLS segments that describe/predict the 
input distribution of Biso values.  So assuming that the input model
had no discontinuities, the output description as TLS segments +
residual Biso should also have no discontinuities.  

But it's a case of garbage in => garbage out.
If you feed a discontinuous isotropic model into TLSMD, it will do its
best to find a multi-segment TLS description of that same discontinuous
model.  That was the context in which I was working on a validation test;
I figured to have the TLSMD server issue a warning if it found such a
discontinuity.  It wouldn't necessarily be more than a mild warning,
however, as the discontinuity might still be smoothed out by subsequent 
crystallographic refinement. 

There is a further wrinkle that I have not thought about as much as
I probably should have in the context of the TLSMD algorithm.
As outlined above, if the input model is correctly constructed then there
should be no discontinuities in Biso across TLS segment boundaries in the
output multi-segment model.  But there is no test for discontinuity in
the eigenvalues of the U^{ij} description across a segment boundary,
equivalent to the refmac RBON or shelxl DELU restraint.  Again this may be
corrected later by subsequent crystallographic refinement using anisotropic
restraints, but perhaps some consideration of this issue should factor into
the definition of "optimal" when choosing segment boundaries.

	Ethan

-- 
Ethan A Merritt
Biomolecular Structure Center
University of Washington, Seattle 98195-7742