Re: poorly resolved residues

From: Ian J Tickle (i.tickle@mail.cryst.bbk.ac.uk)
Date: Fri Apr 09 1999 - 06:22:41 CDT


On Thu, 8 Apr 1999, Alexandre Alechine wrote:

> I've found that omitting  poorly resolved side-chain atoms
> from refinement often improves
> R-free (sometimes up to 0.5%). The reason is trivial:
> These side chains are on a surface of protein
> and are naturally disordered. Because the B-factors of side and main chains 
> are mutually restrained the refinement produces wrong B-factor values.
> Releasing  restrains improves R_free too, but not as well as manual omitting 
> bad side chains.

This is a problem which has been discussed by a number of people including
Dale Tronrud and myself at various CCP4 Study Weekends and Refinement
Workshops.

The basic problem is that most refinement programs (X-plor I know for sure,
but no doubt others as well) do not use a sensible weighting scheme for the
thermal parameter restraints.  I did an analysis of differences between
unrestrained isotropic thermal parameters of bonded atoms in an atomic
resolution (1A) polypeptide structure with good data, and obtained the
following relationship for the contribution to the expected error in the
Uiso's: sigma(U) =~ U^2.  If you prefer it in terms of B's it's
sigma(B) =~ B^2/8pi^2  (Formulae always seem to be simpler when you use U's!)

This error arises partly from the fact that atoms with large thermal
parameters obviously do not make a significant contribution to a large
fraction of the data at high resolution, and partly from the isotropic
approximation, i.e. atoms with large vibration amplitudes tend to be highly
anisotropic.  It is only the along-bond component of the displacement that
can be restrained, but for highly anisotropic atoms this component bears
little relationship to the spherically averaged thermal parameter.

For B = 10A^2 the formula gives sigma(B) = 1.25;  for B = 20, sigma(B) = 5;
B = 40, sigma(B) = 20;  B = 80, sigma(B) = 80.

Most people seem to use a weighting scheme corresponding to
sigma(B) = constant, where the constant is typically ~ 1 to 5A^2.  This is
tolerable for "typical" main-chain atoms with B = 10 to 20A^2, but clearly
not for side-chains.  The effect of applying thermal parameter restraints
with unrealistically high weights is obviously to drag down the large
parameter values, as you have already pointed out.

However I would maintain that the solution is not to leave them out, but to
weight them properly!  If omitting "bad" side-chains improves Rfree that must
mean you didn't have a correct model for them in the first place.

-- Ian
_______________________________________________________________________________

 Ian J. Tickle                           | Phone:  (+44) 171 631 6854
 Department of Crystallography           | Fax:    (+44) 171 631 6803
 Birkbeck College (University of London) | Email:  i.tickle@bbk.ac.uk
 Malet Street, LONDON WC1E 7HX, UK       | WWW:    http://www.cryst.bbk.ac.uk/



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