On Thursday 13 November 2008, Pavel Afonine wrote:
> Hi Ian,
> 
> > 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.
> >   
> 
> given the formula for total atomic B-factor:
> 
> Btotal = Bcryst + Btls + Blocal + ...
> 
> my naive understanding is that the B-factors describing local atomic 
> vibrations Blocal (or residual B-factors as named in Refmac) should obey 
> Hirshfeld's "rigid-bond test" (Acta Cryst. (1976). A32, 239-244), which 
> is (to some approximation) enforced by the  restraints applied to 
> "residual" B-factors (as it is Refmac or in phenix.refine).

It makes perfect sense to apply the restraints to the residual B
_within_ a TLS group.  Furthermore, the along-bond variance from the
Btls component is zero for atoms within the group anyhow (by definition).
So for two atoms in the same TLS group, applying the restraint to the
total is numerically identical to applying it to the residual B only.

But this doesn't address Ian's concern about discontinuities across
a group boundary.  If two neighboring atoms are in different TLS groups,
then the along-bond variance from the two Btls components is different.
Hence in this case the _total_ B should be restrained.

> I think given the arbitrariness (or accuracy if you like) in defining 
> TLS groups, applying similarity restraints to the total B would not be a 
> good idea. 

I do not follow you thinking on that point.  If restraining the total
B is a good idea in the usual refinement protocol, either isotropic or
anisotropic, in how would it suddenly become not a good idea in
the presence of a TLS-based protocol?

The TLS description is not "truth". It is a convenient model that allows
us to predict (or explain) the ADP for each atom. Because it is only a
model, not truth, we should restrain it to conform to our prior knowledge.
In this particular case the prior expectation is that the net ADPs
of adjacent atoms are compatible, which means that their along-bond
components should be equal.  Therefore it only makes sense to apply the
restraint to the net ADP.

Think of it like this.  The same formulae which express the "restraint"
also express the extent to which the current model deviates from our
ideal for a "good" model.  If I hand you a refined model, you can
calculate this deviation from goodness without even a hint as to
how I arrived at that model.  It might have been Biso only, it might
have been TLS, it might have been a random drawing of B values from
a large hat.  Doesn't matter.  The same is true if you apply the
restraint during refinement;  if it's a good restraint, it's good 
regardless of how your model B factors are generated.

> I faced this dilemma a few years ago when implementing TLS  
> refinement in phenix.refine. And to prove my feelings and make a 
> decision, I systematically tried both possibilities, and the best result 
> was to apply the restraints to residual B-factors. 

I hesitate to suggest it, but...
might this be pointing to a coding error rather than to a flaw in the
rationale?  

> The NCS restraints are applied to residual B-factors too
> (although I didn't test it systematically).

Applyinig NCS restraints to B factors is a whole separate area
for discussion. Let's not go there just now :-)

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