Re: [ccp4bb]: B-factor and resolution

[Edward Berry <eaberry@lbl.gov>]

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Gerard \"CD\" Kleywegt wrote:
> well, i had a quick look at the data stored in QDB
> (gjk, acta cryst d52, 842-857) which shows that
> for 435 structures the corr coeff between resolution
> and average b is only 0.06, i.e. insignificant
> On Thu, 4 Jan 2001, Yu Wai Chen wrote:
> 
> > Dear all,
> >
> > Does any one know if there is any correlation between the overall
> > B-factor of a structure in relation to its resolution?  Are there any
> > publications on this topic?

I believe there must be very good correlation between the actual
(as opposed to reported) B-overall of a crystal and the resolution 
to which it diffracts. After all, "the crystal was well-ordered 
to 3 A" is almost synonymous with "the crystal diffracted to 3 A", 
and the B-factor is a measure of order. 

or, The B-factor is the rate at which intensity falls
off with increasing resolution, and the resolution limit is the point 
where intensity falls below the noise level.

on 27 Oct 1998 Eleanor Dodson wrote:
 > 3. What's the significance of the atomic B-factors when you have a low
 > resolution data, for example, 3.0 A; or 3.5 A.
  Very very little - common sense indicates that if the data peters out at that
 resolution the overall B must be 50 or greater..
 But depending on scaling procedure it can be seriously under-estimated - there
 are several structures in the PDB with swathes of negative Bfactors!


However there are several points along the path from data collection
to final structure at which the average B-factor can be normalize (or I
might say corrupted): 

1. When putting the data on an absolute scale, a B-factor as well as
scale factor is applied, to make the average B 0 or 20 or some ideal
value (however note the default behavior of truncate is to apply the
scale but NOT the B-factor, so some intervention is required to corrupt
the B-factor at this stage). For isomorphous phase determination a 
B-factor must be applied to bring all data sets to the same scale,
but it should be applied to the derivatives not the native.

2. When making maps to build the model, a negative B-factor (sharpening)
is often applied to enhance high-resolution details. This is well and good,
but the final model should not be refined against this "sharpened" data,
but against the original data. 

3. During refinement of low-resolution structures, the problem of fixing
scale and B-factors for protein and solvent models may be somewhat 
underdetermined, especially when the solvent model is the same as the 
protein model (Babinet-type approach used in refmac, see Kostrewa's article
in the 9/97 CCP4 newsletter and earlier work e.g. Fraser et al. 1978), and an 
arbitrary choice of some parameter can make the process more robust.
>From the refmac doc:
SCALe LSSC FIXBulk BBULk 70.0 SCBUlk -0.75  ! Fix bulk solvent parameters - often 
                                            ! ill determined for resolutions < 2.8A
(If the best-fit B-factors for solvent and protein are highly correlated, this
would bias the protein B-factor).

Thus the lack of correlation of B-factor resolution with may be related 
to the difficulty in estimating B-factor at low resolution. There may be 
a resolution below which crystallographers despair of determining the
B-overall and arbitrarily set it to e.g. 30 for refinement purposes,
which would make a big downturn in B at low resolution.

At high resolution the slope of the Wilson plot gives the B-factor.
At low resolution the fine structure in the Wilson plot due to 
secondary structure makes this impossible, however if the model is
available it predicts the fine structure and so scaling against the 
model (or rather scaling atomic B's against the data) might give
accurate values, unless the correlation with Solvent B is too great.
I have the impression that using a mask-based solvent correction as
in CNS the B-factors for solvent and protein can be well determined
at 3 or 4 A resolution. This could be tested by writing out F-part 
and F-model and scaling them against the data with ICOEFL, which 
prints some statistics about the correlation between terms.

The correlation of resolution limit with MINIMUM B-factor is 
probably better than with AVERAGE B-factor. There are many 
examples of high-resolution structures with disordered loops,
the contribution from the disordered parts would drop out at 
low resolution and the resolution limit would be determined
by the best-ordered parts of the structure.

If you try to estimate B-overall by calculating structure factors 
from the model after setting all atomic B's to 20, then scaling the
data against this set, the result is highly dependent on the
resolution range you use- presumably because the poorly-ordered
parts have greater contribution at low resolution.

I recommend a new REMARK card for deposited coordinates files which
would indicate whether the final atomic B's are refined against
original data in an attempt to determine absolute B's, or whether
the overall B is arbitrary and atomic B's should only be used to
see which parts of the structure are relatively well- or dis-ordered.

Ed