Hi Phil,
The total atomic B-factor (ADP) in phenix.refine is defined as:
Utotal = Ucryst + Ugroup + Ulocal,
(of course, you can re-write it in terms of B, which is a trivial
application of proper scales: J. Appl. Cryst. (2002). 35, 477-480)
(let's stick to U in what follows below)
where:
Ucryst is determined as part of overall anisotropic scaling at bulk
solvent correction and scaling step, and it goes into total model
structure factor as following:
Fmodel = scale * exp(-h*Ucryst*ht) * (Fcalc_atoms + k_sol * exp(-B_sol*s2) * Fmask) ,
and this is always the case, regardless which refinement strategy you
choose.
The rest, Ugroup and Ulocal and their combinations, depend on
refinement strategy. Here are a few typical refinement strategies that
illustrate this:
1) If no TLS is used, but we just refine individual B-factors, then
Ugroup=0, and the total B-factor is:
Utotal = Ucryst + Ulocal, where Ulocal can be isotropic, anisotropic or
any mixture, and the ADP restraints are applied to Ulocal, and
phenix.refine has a large array of various restraints applied to
Ulocal, depending on whether Ulocal are isotropic or anisotropic.
This is the most basic ADP refinement strategy that is typically used
at 2.5-3.5A resolution and higher.
2) If we use TLS and do structure refinement at say 3.0A resolution or
higher, then
Utotal = Ucryst + Utls + Ulocal
In this case Utls = function_of(T,L,S), Ulocal are always isotropic
individual atomic B-factors. The standard restraints (including NCS, if
any) are always applied to Ulocal only. Moreover, the positive
definiteness of Utls and Ulocal is not enforced. We only enforce that
Utotal are positively definite and comply with the symmetry. Ulocal can
even be refined to a negative value, which is of course nonsensical,
but potentially can be used as an indicator of bad TLS group
separation; also, this compensate for a non-optimal choice of TLS
groups so the Utotal are still correct, even though Utls and Ulocal
taken individually may not be correct.
This is the most typical ADP refinement strategy at resolutions 3A and
higher.
3) If (for whatever reason) you ask phenix.refine to do TLS refinement
only, then:
Utotal = Ucryst + Utls.
In this case no restraints are applied. We only enforce that Utotal are
positively definite and comply with the symmetry.
I've never seen any practical use of it, unless probably at very low
resolution.
4) You can also choose simple traditional group isotropic B-factor
refinement, where you refine one isotropic B-factor per selected set of
atoms (for example one or two B-factors per residue), in this case:
Utotal = Ucryst + Ugroup.
This is what people typically do at resolutions from 3-3.5 A and lower
(if they don't want to use TLS).
5) There is also a bit weird refinement option, but I found it the most
powerful at low resolution. This is when you combine TLS refinement
with simple traditional group isotropic B-factor refinement. In this
case:
Utotal = Ucryst + Utls + Ugroup,
where Utls = function_of(T,L,S) as usual, and Ugroup is one or two
refinable isotropic B-factors per residue. You can view the Ugroup as a
work-around to compensate for coarseness or imperfectness of TLS model.
This is the best refinement strategy at resolutions from 3-3.5 A and
lower.
I guess I covered most of typical cases that people usually use,
although in phenix.refine you can mix any strategy with any.
Now, what goes into PDB ATOM and ANISOU records?
The ANISOU record receives Utotal (in Cartesian basis, see reference
above) = trace(Ucryst) + Ugroup + Ulocal, and the anisotropic part of
Ucryst (Ucryst - trace(Ucryst)) is stored in PDB file header.
The ATOM record receives Biso, which is isotropic equivalent of Utotal.
Thus defined, all you need to reproduce the R-factors is ATOM and
ANISOU records, and you do not need anything from PDB file header
(except CRYST1 record). This is why phenix.refine does it this way.
Pavel.
On 1/7/10 10:19 AM, Phil Jeffrey wrote:
Hi,
Having a discussion with a colleague yesterday on differences in Phenix
and Refmac representations of TLS B-factors in the PDB file I came
across two different definitions for what the PDB ANISOU U's correspond
to as written by Phenix:
1. From necat.chem.cornell.edu/workshops/.../WK04_PavelAfonine.pdf on
p.20
U(TOTAL)= U(ATOM) + U(TLS) + U(CRYST)
and only U(atom) + U(tls) is stored in the PDB ANISOU card.
2. From http://proteincrystallography.org/ccp4bb/message8948.html
"Utotal = Utls + Ulocal + Ucryst. So, the ANISOU records
always contain Utotal and ATOM records contain isotropic equivalent of
Utotal"
Which is not the same thing. I suspect it's #1. Am I right ?
I would think that U(cryst) is potentially a non-zero contribution to
atomic ANISOU values but is actually applied before the TLS/Anisotropic
B-factors are refined.
As a tie-breaker between #1 and #2 the program documentation suggest
that it is just U(tls)+U(atom) but the paragraph that nominally
explains it is not short of of inconsistencies, referring to the ANISOU
record as having the "the total B-factor (B_tls + B_individual)"
whereas they're not only not B's (they are U's) but it's also not the
*total* U or B by its own definitions. IMHO it would warrant a rewrite
for clarity since B and U are used interchangeably and "total" has
variable usage.
Phil Jeffrey
Princeton
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