Re: [ccp4bb]: B-factor and resolution

[Edward Berry <eaberry@lbl.gov>]

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Edward Berry wrote:
> 
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> 
> Peter Burkhard wrote:
> >
> > To me this sounds a little bit too simple. The resolution limit is
> > not simply determined by the B-factor, as Ed suggests. Small crystals
> > collected at on an inhouse source might diffract only to 3.0A while
> > still being well ordered (i.e. low B-fators). From a large crystal
> > using synchrotron radiation you may be able to reach 2.0A even though
> > it has higher B-factors.
> > Actually, this is really nothing new but it may (apart from the
> > refinement-
> > program artefacts) explain the low correlation between B-fators and
> > resolution.
> 
> Agreed- the point where intensities fall below the noise level
> (resolution limit) depends not only on the rate of falloff with
> resolution (B-factor) but also on how strong the intensity is to
> begin with at low resolution (affected by size of crystal) and the
> signal/noise ratio (depends I suppose on beam intensity and
> collimation, what fraction of the beam hits the small crystal
> rather than going around it and contributing only to background).
> 
> So I wouldn't expect a correlation coefficient of 1.00. But 0.06?
> No significant correlation between B-factor and resolution limit?

To be sure, if factors like size of the crystal and synchrotron source
were far more important than B-factor in determining resolution, the CC
might be negligible. But I think the opposite is the case. First of all
I have a gut feeling that if my lousy crystal diffracts to only 3 A, 
dropping the B-overall to 10 would give a greater improvement than
making the crystal 10 x bigger or going to the hottest synchrotron 
in the world. (Unfortunately dropping the B-overall is the most
difficult approach to take, unless we find a better crystal form.)

Slightly more quantitatively, say B-overall for the structures range 
from 10-70. At 2A, and if I haven't dropped a factor of 2 somewhere, 
that makes a 1,808 x difference in intensity.

Say scattered intensity is proportional to the number of 
ordered electrons in the beam. Going from an 0.1 mm crystal to a 
1 mm crystal would give 1000 times the intensity, but I wouldn't 
expect such a dramatic improvement in resolution, partly because
much of the background is from scattering by the crystal, and 
would increase nearly in proportion. Also that intensity is spread
out over a bigger spot, so peak intensity is increased by a smaller 
factor. 

Going to a smaller unit cell makes the average spot intensity greater
because that total scattering is divided between fewer reflections.
But the variation in unit cell volume for the majority of 
protein crystals is probably less than 100-fold.

Perhaps the hottest synchrotron in the world has 1800 times the
brilliance of an x-ray tube, but I doubt if the signal/noise is 
better by that factor.

So I doubt if any of these factors is great enough to completely 
overwhelm the effect of crystal order in Gerard's statistics.
but maybe taken altogether? and with other factors I haven't
thought of?

Flip Hoedemaker points out that not all crystallographers use 
the same criterion for reporting resolution of a crystal,
which would add further jitter to the relationship.

A number of people indicated that low resolution B-overall shouldn't
be taken literally. That was actually my main point, then I wanted 
to ask "can we do better?" or should we acknowledge that fact in 
a REMARK that will warn the non-crystallographer against using the 
B-factor as a criterion of structure quality when comparing 
low-resolution structures? (OK- maybe non-crystallographers pay no
attention to B-factors and even less to REMARK statements).

Ed