# [phenixbb] phenix and weak data

Ed Pozharski epozh001 at umaryland.edu
Tue Dec 11 22:46:29 PST 2012

```On Tue, 2012-12-11 at 11:27 -0500, Douglas Theobald wrote:

> What is the evidence, if any, that the exptl sigmas are actually negligible compared to fit beta (is it alluded to in Lunin 2002)?  Is there somewhere in phenix output I can verify this myself?

Essentially, equation 4 in Lunin (2002) is the same as equation 14 in
Murshudov (1997) or equation 1 in Cowtan (2005) or 12-79 in Rupp (2010).
The difference is that instead of combination of sigf^2 and sigma_wc you
have a single parameter, beta.  One can do that assuming that
sigf<<sqrt(beta).  Phenix log files list optimized beta parameter in
each resolution shell.  It does not list sigf though, but trust me - I
checked and it is indeed true that sqrt(beta)>sigf. I just pulled up a
random dataset refined with phenix and here is what I see

min(sigf/sqrt(beta)) = 0.012
max(sigf/sqrt(beta)) = 0.851
mean(sigf/sqrt(beta)) = 0.144
std(sigf/sqrt(beta)) = 0.118

But there are two problems.  First, in the highest resolution shell

min(sigf/sqrt(beta)) = 0.116
max(sigf/sqrt(beta)) = 0.851
mean(sigf/sqrt(beta)) = 0.339
std(sigf/sqrt(beta)) = 0.110

This is a bit more troubling.  Notice that for acentrics it's 2sigf**2
+sigma_wc, thus the actual ratio should be increased by sqrt(2), getting
uncomfortably close to 1/2.  Still, given that one adds variances, this
is at most 25% correction, and this *is* the high resolution shell.

Second, if one tries to interpret sqrt(beta) as a measure of model error
in reciprocal space, one runs into trouble.  This dataset was refined to
R~18%.  Assuming that sqrt(beta) should roughly predict discrepancy
between Fo and Fc, it corresponds to R~30%.  This suggests that for
reasons I don't yet quite understand beta overestimates model variance.
If it is simply doubled, then it becomes comparable to experimental
error, at least in higher resolution shells.

> And, in comparison, how does refmac handle the exptl sigmas?  Maybe this last question is more appropriate for ccp4bb, but contrasting with phenix would be helpful for me.  I know there's a box, checked by default, "Use exptl sigmas to weight Xray terms".

Refmac fits sigmaA to a certain resolution dependence and then adds
experimental sigmas (or not as you noticed).  I was told that the actual
formulation is different from what is described in the original
manuscript.  But what's important that if one pulls out the sigma_wc as
calculated by refmac it has all the same characteristics as sqrt(beta) -
it is generally >>sigf and suggests model error in reciprocal space that
is incompatible with (too large) observed R-values.  Kevin Cowtan's
spline approximation implemented in clipper libraries behaves much
better, meaning that R-value expectations projected from sigma_wc are
much closer to observed R-value.

Curiously, it does not make much difference in practice, i.e. refined
model is not affected as much.  For instance, with refmac there are no
significant changes whether one uses experimental errors or not.  I
could think of several reasons for this, but haven't verified any.

Cheers,

Ed.

--
"I'd jump in myself, if I weren't so good at whistling."
Julian, King of Lemurs
```