Hi Pavel

I think Ethan made my point very nicely, so I don't really have much to
add, except maybe a concrete example will help.  Let's keep it as simple
and ideal as possible: I hope you'll agree that any proposed method has
to at least work perfectly in the ideal case before you try to apply it
in the general case (at least that's how I always test my software!), so
let's construct a simple, ideal situation and see how well the
alternative methods stack up.

First let's suppose that we have 2 domains (A & B) connected by a single
bond parallel to the x axis, and the only rigid-body motion is a 1 A^2
mean-square displacement also parallel to x for both domains, so T11(A)
= T11(B) = 1 A^2 and all other TLS elements for both A & B are
identically zero.  Suppose also that the rigid-body motion describes the
actual atomic motion exactly which means of course that all the residual
Biso's will be zero, and also that the total Biso's of all atoms in both
A & B will be 8pi^2/3 (mean of the diagonal elements).  In particular
the differences between both residual Biso's and total Biso's for the 2
connecting atoms will be zero, and the rigid-bond test is satisfied.  So
obviously it won't make any difference whether we restrain residual B
difference or total B difference, the restraint will give the right
result in either case.

Now let's assume the same setup, except that now T11(B) = 0.5 A^2, but
the rigid-bond test still demands that the total Biso's (representing
the actual motion of the atoms) for the connecting atoms have zero
difference, let's suppose they are both still 8pi^2/3.  This means that
the residual Biso's for the connecting atoms in A & B are zero and
4pi^2/3 respectively.  Hence restraining the difference between residual
Biso's to zero will give a result that does not correspond to reality,
restraining the difference between total Biso's does (in fact this is
merely a direct consequence of the rigid-bond test).

I guess I'm saying the same thing as Ethan, he said it more eloquently,
I just like to see what happens when you plug in actual values.

Cheers

-- Ian


> -----Original Message-----
> From: [log in to unmask] 
> [mailto:[log in to unmask]] On Behalf Of Ethan A Merritt
> Sent: 14 November 2008 06:06
> To: Pavel Afonine
> Cc: [log in to unmask]
> Subject: Re: [ccp4bb] Choosing TLS groups.
> 
> 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
> 
> 


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