Yes, I would classify anything with I/sigmaI < 3 as "weak". And yes, of
course it is possible to get "weak" spots from small molecule crystals.
After all, there is no spot so "strong" that it cannot be defeated by a
sufficient amount of background! I just meant that, relatively
speaking, the intensities diffracted from a small molecule crystal are
orders of magnitude brighter than those from a macromolecular crystal of
the same size, and even the same quality (the 1/Vcell^2 term in Darwin's
formula).
I find it interesting that you point out the use of a 2 sigma(I)
intensity cutoff for small molecule data sets! Is this still common
practice? I am not a card-carrying "small molecule crystallographer",
so I'm not sure. However, if that is the case, then by definition there
are no "weak" intensities in the data set. And this is exactly the kind
of data you want for least-squares refinement targets and computing "%
error" quality metrics like R factors. For likelihood targets, however,
the "weak" data are actually a powerful restraint.
-James Holton
MAD Scientist
On 3/6/2011 11:22 AM, Ronald E Stenkamp wrote:
Could you please expand on your statement that "small-molecule data
has essentially no weak spots."? The small molecule data sets I've
worked with have had large numbers of "unobserved" reflections where I
used 2 sigma(I) cutoffs (maybe 15-30% of the reflections). Would you
consider those "weak" spots or not? Ron
On Sun, 6 Mar 2011, James Holton wrote:
I should probably admit that I might be indirectly responsible for
the resurgence of this I/sigma > 3 idea, but I never intended this in
the way described by the original poster's reviewer!
What I have been trying to encourage people to do is calculate R
factors using only hkls for which the signal-to-noise ratio is > 3.
Not refinement! Refinement should be done against all data. I merely
propose that weak data be excluded from R-factor calculations after
the refinement/scaling/mergeing/etc. is done.
This is because R factors are a metric of the FRACTIONAL error in
something (aka a "% difference"), but a "% error" is only meaningful
when the thing being measured is not zero. However, in
macromolecular crystallography, we tend to measure a lot of
"zeroes". There is nothing wrong with measuring zero! An excellent
example of this is confirming that a systematic absence is in fact
"absent". The "sigma" on the intensity assigned to an absent spot is
still a useful quantity, because it reflects how confident you are in
the measurement. I.E. a sigma of "10" vs "100" means you are more
sure that the intensity is zero. However, there is no "R factor" for
systematic absences. How could there be! This is because the
definition of "% error" starts to break down as the "true" spot
intensity gets weaker, and it becomes completely meaningless when the
"true" intensity reaches zero.
Historically, I believe the widespread use of R factors came about
because small-molecule data has essentially no weak spots. With the
exception of absences (which are not used in refinement), spots from
"salt crystals" are strong all the way out to edge of the detector,
(even out to the "limiting sphere", which is defined by the x-ray
wavelength). So, when all the data are strong, a "% error" is an
easy-to-calculate quantity that actually describes the "sigma"s of
the data very well. That is, sigma(I) of strong spots tends to be
dominated by things like beam flicker, spindle stability, shutter
accuracy, etc. All these usually add up to ~5% error, and indeed
even the Braggs could typically get +/-5% for the intensity of the
diffracted rays they were measuring. Things like Rsym were therefore
created to check that nothing "funny" happened in the measurement.
For similar reasons, the quality of a model refined against
all-strong data is described very well by a "% error", and this is
why the refinement R factors rapidly became popular. Most people
intuitively know what you mean if you say that your model fits the
data to "within 5%". In fact, a widely used criterion for the
correctness of a "small molecule" structure is that the refinement R
factor must be LOWER than Rsym. This is equivalent to saying that
your curve (model) fit your data "to within experimental error".
Unfortunately, this has never been the case for macromolecular
structures!
The problem with protein crystals, of course, is that we have lots of
"weak" data. And by "weak", I don't mean "bad"! Yes, it is always
nicer to have more intense spots, but there is nothing shameful about
knowing that certain intensities are actually very close to zero. In
fact, from the point of view of the refinement program, isn't
describing some high-angle spot as: "zero, plus or minus 10", better
than "I have no idea"? Indeed, several works mentioned already as
well as the "free lunch algorithm" have demonstrated that these
"zero" data can actually be useful, even if it is well beyond the
"resolution limit".
So, what do we do? I see no reason to abandon R factors, since they
have such a long history and give us continuity of criteria going
back almost a century. However, I also see no reason to punish
ourselves by including lots of zeroes in the denominator. In fact,
using weak data in an R factor calculation defeats their best
feature. R factors are a very good estimate of the fractional
component of the total error, provided they are calculated with
strong data only.
Of course, with strong and weak data, the best thing to do is compare
the model-data disagreement with the magnitude of the error. That
is, compare |Fobs-Fcalc| to sigma(Fobs), not Fobs itself. Modern
refinement programs do this! And I say the more data the merrier.
-James Holton
MAD Scientist
On 3/4/2011 5:15 AM, Marjolein Thunnissen wrote:
hi
Recently on a paper I submitted, it was the editor of the journal
who wanted exactly the same thing. I never argued with the editor
about this (should have maybe), but it could be one cause of the
epidemic that Bart Hazes saw....
best regards
Marjolein
On Mar 3, 2011, at 12:29 PM, Roberto Battistutta wrote:
Dear all,
I got a reviewer comment that indicate the "need to refine the
structures at an appropriate resolution (I/sigmaI of>3.0), and
re-submit the revised coordinate files to the PDB for validation.".
In the manuscript I present some crystal structures determined by
molecular replacement using the same protein in a different space
group as search model. Does anyone know the origin or the
theoretical basis of this "I/sigmaI>3.0" rule for an appropriate
resolution?
Thanks,
Bye,
Roberto.
Roberto Battistutta
Associate Professor
Department of Chemistry
University of Padua
via Marzolo 1, 35131 Padova - ITALY
tel. +39.049.8275265/67
fax. +39.049.8275239
roberto.battistu...@unipd.it
www.chimica.unipd.it/roberto.battistutta/
VIMM (Venetian Institute of Molecular Medicine)
via Orus 2, 35129 Padova - ITALY
tel. +39.049.7923236
fax +39.049.7923250
www.vimm.it
