Jose Antonio,

I've seen similar behavior few years ago with grouped B-factor
refinement in CNS.  The argument for the grouped refinement is as
follows: 

This is better than individual B-factor refinement at low resolution
because you significantly reduce the number of parameters.

There are two holes in this argument.

1.  The reduction in number of parameters is not that significant. On
average, you have some 8 atoms per residue, and thus 32 parameters with
individual B-factors (4 per atom).  With grouped B-factors you have 26,
about 20% difference.  While it sounds like a lot (hey, I just removed
2000 parameters from my 350 residue model!), it only has an effect
similar to improving resolution by ~6%, e.g. from 2.8A to 2.65A.  Worthy
goal, no doubt, but will hardly lead to dramatic improvement that would
justify these crazy jumps in B-factors.

2.  The total number of parameters is not the same as the effective
number of parameters.  Since individual B-factors are restrained, they
don't really contribute one degree of freedom per atom.  I don't know of
any reliable estimate of effective number of parameters in the
literature, but my personal guess based on several ways to estimate it
is that it may take about 5 restraints to compensate for one parameter.
B-factors are restrained by bond and by angle, thus giving 2-3
restraints per B-factor.  So, every individual B-factor only contributes
half a parameter, thus ~4 parameters per residue.  This is very much
comparable with two essentially unrestrained (as confirmed by their wild
variations) grouped B-factors.

Certainly, these are guesstimates.  For instance, at low resolution you
apply tighter restraints and thus individual B-factors may contribute
even fewer effective degrees of freedom, perhaps even ~2 per residue.
But the general point remains that you are not necessarily better off
with grouped B-factors, even at low resolution.

By the way, I always assumed (based on B-factor behavior) that grouped
B-factor refinement is unrestrained.  If it is not (in CNS and Phenix),
it is certainly not doing a good job restraining backbone-to-sidechain
and residue-to-residue variations.  One thing you could do is to
calculate average B-factors per group when you refine B-factors
individually, which can be done with baverage (Structure
analysis->Temperature factor analysis in ccp4i), and then compare it to
grouped B-factors.  Maybe it does vary a lot.

These B-factors look awfully high.  As someone who had to deal once with
the model where <B> was about 100A^2, I feel your pain :)

Cheers,

Ed. 

On Thu, 2010-01-28 at 10:34 +0100, Jose Antonio Cuesta Seijo wrote:
> Dear all,
> 
> I am refining a 3.1Å structure with Phenix.refine, using two ADP
> groups per residue.
> When doing refinement in Refmac, the way to go would be to tighten the
> weights quite a bit to make up for the low resolution, resulting in
> small deviations in bond lenghts and angles from the ideal values and
> also in quite small ADP variations from atom to atom, typically in the
> range of, say, 5%.
> Now, doing the same refinement with Phenix.refine and 2 ADP groups per
> residue, the manual claims that the weights do not normally need to be
> touched. Judging by the values of R and R free (19.5% and 23.9%)
> compared to other protocols and with Refmac, it certainly does a good
> job. But the spread in ADP values in the refined model is strikingly
> high. Below is a extract from the pdb file. Note for example the jump
> from B=81.7 to B=163.8 for the main chains of ILE180 and LYS181, or
> the 163.8 to 113.5 between the main chain and the side chain of
> LYS181. Similar examples are all over the 1000+ residues in this
> structure.
> Is this normal? All global quality indicators look OK to me...
> 
> Cheers,
> 
> Jose Antonio Cuesta Seijo.
> 
> ATOM   8338  N   ARG F 178      65.398  30.884  -0.261  1.00 84.90
> N
> ATOM   8339  CA  ARG F 178      66.532  31.758  -0.521  1.00 84.90
> C
> ATOM   8340  CB  ARG F 178      67.576  31.628   0.583  1.00131.99
> C
> ATOM   8341  CG  ARG F 178      67.044  31.967   1.952  1.00131.99
> C
> ATOM   8342  CD  ARG F 178      68.084  32.695   2.778  1.00131.99
> C
> ATOM   8343  NE  ARG F 178      67.464  33.433   3.873  1.00131.99
> N
> ATOM   8344  CZ  ARG F 178      66.894  34.627   3.737  1.00131.99
> C
> ATOM   8345  NH1 ARG F 178      66.865  35.222   2.551  1.00131.99
> N
> ATOM   8346  NH2 ARG F 178      66.350  35.224   4.787  1.00131.99
> N
> ATOM   8347  C   ARG F 178      67.152  31.347  -1.839  1.00 84.90
> C
> ATOM   8348  O   ARG F 178      66.738  30.357  -2.443  1.00 84.90
> O
> ATOM   8349  N   ILE F 179      68.143  32.107  -2.287  1.00 80.99
> N
> ATOM   8350  CA  ILE F 179      68.954  31.666  -3.406  1.00 80.99
> C
> ATOM   8351  CB  ILE F 179      69.698  32.817  -4.083  1.00 53.62
> C
> ATOM   8352  CG1 ILE F 179      68.754  33.995  -4.333  1.00 53.62
> C
> ATOM   8353  CD1 ILE F 179      68.390  34.216  -5.806  1.00 53.62
> C
> ATOM   8354  CG2 ILE F 179      70.308  32.325  -5.389  1.00 53.62
> C
> ATOM   8355  C   ILE F 179      69.970  30.657  -2.884  1.00 80.99
> C
> ATOM   8356  O   ILE F 179      70.677  30.914  -1.913  1.00 80.99
> O
> ATOM   8357  N   ILE F 180      70.026  29.500  -3.528  1.00 81.67
> N
> ATOM   8358  CA  ILE F 180      70.864  28.417  -3.061  1.00 81.67
> C
> ATOM   8359  CB  ILE F 180      70.161  27.066  -3.218  1.00 71.36
> C
> ATOM   8360  CG1 ILE F 180      68.850  27.090  -2.446  1.00 71.36
> C
> ATOM   8361  CD1 ILE F 180      68.964  27.820  -1.114  1.00 71.36
> C
> ATOM   8362  CG2 ILE F 180      71.038  25.955  -2.707  1.00 71.36
> C
> ATOM   8363  C   ILE F 180      72.180  28.418  -3.811  1.00 81.67
> C
> ATOM   8364  O   ILE F 180      73.218  28.106  -3.240  1.00 81.67
> O
> ATOM   8365  N   LYS F 181      72.137  28.768  -5.092  1.00163.76
> N
> ATOM   8366  CA  LYS F 181      73.356  28.961  -5.872  1.00163.76
> C
> ATOM   8367  CB  LYS F 181      74.053  27.627  -6.155  1.00113.58
> C
> ATOM   8368  CG  LYS F 181      73.432  26.812  -7.280  1.00113.58
> C
> ATOM   8369  CD  LYS F 181      74.307  25.615  -7.656  1.00113.58
> C
> ATOM   8370  CE  LYS F 181      74.291  24.546  -6.571  1.00113.58
> C
> ATOM   8371  NZ  LYS F 181      75.015  23.306  -6.984  1.00113.58
> N
> ATOM   8372  C   LYS F 181      73.033  29.687  -7.172  1.00163.76
> C
> ATOM   8373  O   LYS F 181      71.889  29.673  -7.629  1.00163.76
> O
> ATOM   8374  N   LYS F 182      74.039  30.325  -7.760  1.00126.44
> N
> ATOM   8375  CA  LYS F 182      73.849  31.088  -8.988  1.00126.44
> C
> ATOM   8376  CB  LYS F 182      74.588  32.421  -8.897  1.00131.41
> C
> ATOM   8377  CG  LYS F 182      74.235  33.203  -7.652  1.00131.41
> C
> ATOM   8378  CD  LYS F 182      74.885  34.575  -7.634  1.00131.41
> C
> ATOM   8379  CE  LYS F 182      74.466  35.367  -6.393  1.00131.41
> C
> ATOM   8380  NZ  LYS F 182      75.076  36.730  -6.349  1.00131.41
> N
> ATOM   8381  C   LYS F 182      74.338  30.303 -10.192  1.00126.44
> C
> ATOM   8382  O   LYS F 182      75.506  29.930 -10.252  1.00126.44
> O
> ATOM   8383  N   LEU F 183      73.447  30.052 -11.146  1.00161.61
> N
> ATOM   8384  CA  LEU F 183      73.819  29.331 -12.360  1.00161.61
> C
> ATOM   8385  CB  LEU F 183      72.591  29.005 -13.214  1.00100.55
> C
> ATOM   8386  CG  LEU F 183      71.470  28.218 -12.534  1.00100.55
> C
> ATOM   8387  CD1 LEU F 183      70.602  27.516 -13.569  1.00100.55
> C
> ATOM   8388  CD2 LEU F 183      72.058  27.219 -11.558  1.00100.55
> C
> ATOM   8389  C   LEU F 183      74.810  30.141 -13.183  1.00161.61
> C
> ATOM   8390  O   LEU F 183      74.988  31.337 -12.943  1.00161.61
> O
> ATOM   8391  OXT LEU F 183      75.443  29.616 -14.103  1.00100.55
> O
> ______________________________________________________________________
> ***************************
> Jose Antonio Cuesta-Seijo
> 
> Biophysical Chemistry Group
> Department of Chemistry
> University of Copenhagen 
> Tlf: +45-35320261
> Universitetsparken 5 
> DK-2100 Copenhagen, Denmark
> ***************************


-- 
Edwin Pozharski, PhD, Assistant Professor
University of Maryland, Baltimore
----------------------------------------------
When the Way is forgotten duty and justice appear;
Then knowledge and wisdom are born along with hypocrisy.
When harmonious relationships dissolve then respect and devotion arise;
When a nation falls to chaos then loyalty and patriotism are born.
------------------------------   / Lao Tse /

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