Hi Frank,

- I tend to call it "isotropic atomic displacement parameters" and "anisotropic atomic displacement parameters", correspondingly "isotropic ADP" and "anisotropic ADP", which is also consistent with:
J. Appl. Cryst. (2002). 35, 477-480
On the handling of atomic anisotropic displacement parameters
R. W. Grosse-Kunstleve and P. D. Adams

- What you wrote below can be boiled down to the question: "Are very tight restraints equivalent to constraints?". A few years ago I tried to see if refinement of individual coordinates with very tight restraints can approach rigid body refinement. The answer I got was "no". Of course one needs to keep in mind that it might all be dependent on particular implementation, minimizers, and other technicalities. I don't know what mathematics says here.

- I would just take whole PDB and re-refine it alternative options at appropriate resolutions (for example, use iso- or anisotropic ADP for model at resolution between 1.2 and 2.0A) and see how the best choice correlates with model/data characteristics. I'm sure there will be dependencies allowing you to get some empirical rules. However, I'm sure there will be a number of exceptions, where only trying appropriate options will bring you the definitive answer.

- Using TLS is another branch of this story. The total atomic B-factors can be presented at least as a sum of three contributions:

Utotal = Ulocal + Utls + Ucryst

where
    - Utotal is the total ADP,
    - Ulocal reflects the local atomic vibration (also named as residual B) and should obey Hirshfeld's rigid bond criteria (F.L. Hirshfeld. Acta Cryst. (1976). A32, 239-244. "Can X-ray data distinguish bonding effects from vibrational smearing?");
    - Ucryst reflects global lattice vibrations (Ucryst is determined and refined at anisotropic scaling),
- Utls reflects global motion (which can be further subdivided into the motion of the molecule as a whole and into the motion of its domains).

Obviously, the presence of global motion is not the function of data resolution (in sense that a molecule does not "know" about your crystallographic experiment and its resolution), so ideally you need always model it (= you need always use TLS). However this faces a number of technical problems currently making it impossible:
- robust and reliable choice of TLS groups;
- robust and reliable separation of Utls and *anisotropic* Ulocal. A first attempt is described here: P. Afonine & A. Urzhumtsev. (2007). CCP4 Newsletter on Protein Crystallography. 45. Contribution 6. "On determination of T matrix in TLS modeling";
- not to mention a strong correlations of parameters which potentially may lead to troubles in optimization flow;
- ... and many other...

Phenix.refine has a pretty sophisticated algorithm of combined TLS refinement which is outlined at slides #28-32:
http://cci.lbl.gov/~afonine/aca2008_knoxville_neutron/

Pavel.

On 12/11/2008 9:08 AM, Frank von Delft wrote:

Question at large:  do any formalisms exist, or are any envisioned, that 
deal with this question more rigorously?  E.g. in principle everything 
is always ADP, but as resolution decreases, the restraints are tightened 
accordingly, so that there is an appropriately refined continuum from 
fully ADP @ 1A to isotropic @ 2A to TLS only @ 3A?

I know for a fact I've heard about this somewhere, but can't remember where.

phx.


that in principle always refine ADP for everything, but tighten the 
restraints automatically,


Pavel Afonine wrote:

Hi Gerwald,

from what I recall is if you refine anisotropic ADP at "too low" 
resolution in other refinement programs, they were often stopping 
complaining about non-positive definite U or unstable refinement. This 
seemed to me the main technical limit.

In phenix.refine this does not happen but it doesn't mean that refining 
anisotropic ADP at "too low" resolution will yield meaningful results.

I'm not sure that there is an exact resolution borderline for doing (or 
not doing) individual anisotropic ADP refinement. From my experience, 
I've never seen a case at ~1.5A and higher where switching from iso- to 
anisotropic model was not good. Then this question transforms into "at 
which resolution you start refining waters as anisotropic?"... A very 
rough number I would say is 1.2-1.1A and higher.

In-between 1.5 and 1.7 (1.8A) is a "gray zone", where it is very likely 
that anisotropic ADP refinement will result in over-fitting, however 
there is a chance that it might still be valid.

Summarizing, if I have a data at resolution between between 1.5 and 1.8A 
resolution, I just try two refinements: in one refining isotropic and in 
another refining anisotropic ADPs. Rfree is your best friend here (and 
Rfree-Rwork). In my opinion, this is the most robust and cheep way to 
get the answer.

Cheers,
Pavel.


On 12/11/2008 7:48 AM, gerwald jogl wrote:

Hi All,

I was wondering if there is information/recommendations out there for 
the resolution required to refine individual anisotropic adps. I think 
the recommendation for shelx is at least 1.5 A resolution.
In addition, is phenix set up and would it make sense to combine tls 
with individiual anisotropic adps?

All comments welcome,
Gerwald
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