Since small molecules are being discussed maybe I should comment. A widely used small molecule program that I don't need to advertise here refines against all measured intensities unless the user has imposed a resolution cutoff. It prints R values for all data and for I>2sig(I) [F>4sig(F)]. The user can of course improve these by cutting back the resolution but if he or she oversteps 0.84A he/she will be caught by the CIF police. This works like a radar trap so weak datasets are usually truncated to 0.84A whether or not there are significant data to that resolution. It is always instructive to compare the R-values for all data and I>2sig(I); if the former is substantially larger, a lot of noisy outer data have been included.
It is not true that small molecule datasets do not contain weak reflections. One should remember that the intensity statistics are different for centrosymmetric space groups: very weak AND very strong reflections (relative to the average in a resolution shell) are much more common! George Prof. George M. Sheldrick FRS Dept. Structural Chemistry, University of Goettingen, Tammannstr. 4, D37077 Goettingen, Germany Tel. +49-551-39-3021 or -3068 Fax. +49-551-39-22582 On Sun, 6 Mar 2011, James Holton wrote: > 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 > > > > > > > >
