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Tue, 13 Mar 2001 15:18:02 Refinement and Resolution Phillip Fanwick [[email protected]] Purdue University Newsgroups: sci.techniques.xtallography I am working on a problem where chemistry requires that two carbon atoms be refined as two independent sets of carbons which are about 0.45A apart. The data were collected to a resolution of 0.75A and the splitting is suggested by Shelx from the highly anisotropic adp's and by the chemistry (a totally unsaturated ring is currently nearly planar). Is it valid to refine atoms below the resolution of the experiment? If so where do you draw the line? I know the FAQ to Shelx suggest that most suggestions for splitting atoms be ignored. If one can reliably refine atomic distances below the resolution of the experiment then what does the resolution signify? Some authors suggest it is simply the resolution of the Fourier map. If this is its only meaning it would suggest one can collect low resolution data and then refine the individual atoms based on chemical knowledge using fixed geometry. The exact meaning of resolution is not discussed or well defined in most small molecule crystallography texts. Thanks for any help and clarification you can give me. Phil Fanwick [email protected]

Tue, 13 Mar 2001 19:20:41 Re: Refinement and Resolution Dr. Artem Evdokimov [[email protected]] NCI-FCRDC PSB-MCL Protein En Newsgroups: sci.techniques.xtallography Could you clarify a bit ? What kind of ring is it ? What are the numerical values for the ADP's that look suspicious ? In general, unless you're dealing with special cases, saturated carbocycles are not planar (I assume you're working with the ring larger than cyclopropane). Cyclopentane derivatives are known to have conformational disorder in crystals due to low pseudorotation barriers (CCD has at least a few examples I think). In general, though the experimental resolution does not extend to 0.45, I would try and see what happens if you split the pesky carbons and refine with disorder. If the statistics allows it, i.e. if this manipulation does not introduce a significant drop in data/parameter ratio, if the ADP's of the resulting disorder components are normal or close to normal, and if the geometry of the resulting molecule(s) makes more sense - then I'd stick to disordered carbons. Obviously, your discussion of the structure would have a caveat that this part of the molecule cannot be trusted if important conclusions have to be made on the basis of the geometry of these carbons - but then, even if you do not split them you would still have reservations about model accuracy in this area. If it is paramount to your work, can you obtain a higher resolution dataset ? Or go to lower temperature (or perhaps check if rising the temperature does not result in averaging of the disorder or elimination of one of the components)... Just a few thoughts. Artem Evdokimov -- |Dr. Artem Evdokimov Protein Engineering | | NCI-Frederick Tel. (301)846-5401 | | FAX (301)846-7148 | | [email protected] | | http://www.ncifcrf.gov/plague |

Wed, 14 Mar 2001 01:27:40 Re: Refinement and Resolution Larry M. Henling ][email protected]] California Institute of Technology, Newsgroups: sci.techniques.xtallography Ah, the vagaries of trn Phillip Fanwick wrote: > >be refined as two independent sets of carbons which are about 0.45A >The data were collected to a resolution of 0.75A and the splitting is Whether you can refine two carbon atoms (perhaps isotropically) 0.45A apart depends primarily on two factors: 1) how good your dataset is 2) more importantly, whether the two atoms are 'discretely' disordered or continuously disordered. In the first case, you should have no problem with a well-measured dataset and not a lot of really heavy atoms in the structure (we recently had a structure with disordered Cl/H2O columns where the Cl-O distance was 0.338(16)A; both the .5 Cl and .5 O refined nicely anisotropically and the two .5 H's refined acceptably (x,y,z,Uiso). In the latter case, for example a floppy tetra-n-butyl ammonium ion where the alkyl groups are all over the place, splitting the atoms usually does no good whatsoever - it is not possible to model the range of atomic positions with a few sites and ellipsoids. The resolution of the dataset pertains to whether features in the Fourier map are separated or not. However, structural results are not based on the Fourier map, but instead on a weighted least-squares fit of the model to the observed data. With proper weights, it is often possible to refine H atoms which do not even appear in the Fourier. The least squares procedure also produces estimated errors in parameters and correlations between parameters. These are the numbers used to calculate, eg, bond length sigmas, which are much less (~ thousandths of an A) than the 'resolution' of the data. [The least squares refinement should use weights based as much as possible on uncertainties in the measurements, and not chosen simply to minimize the Goodness of Fit. Use a theta cutoff in a refinement to show that high angle data gives you better results. The low angle data reflect mostly how many electrons are present and the high angle data the ADP's on heavy atoms. larry

Wed, 14 Mar 2001 16:07:32 Re: Refinement and Resolution Daniel Schlieper [[email protected]] Newsgroups: sci.techniques.xtallography Dear Phil, "resolution" in x-ray crystallography the length of the spacing d between the lattice planes to get a deviation angle theta of the Bragg reflection. From the famous Bragg's Law: d = lambda/(2 sin theta) with lambda the wavelength. The minimal d corresponds to the maximal theta and is named "resolution". This has nothing to do with "resolution" as used in light microscopy, stating the minimal distance of two distinguishable points. In fact, in x-ray crystallography, atoms can be distinguished even if they are much closer together than the crystallographic resolution. In protein crystallography, most structures are solved with a x-ray "resolution" d(min) = 2.0--2.5 Angstrom. The root mean square deviation of the atoms ( = "resolution" in light microscopy) in these structures are approx. 0.3 Angstrom. Do you see the difference? And yes, in the protein crystallography, we indeed collect "low" resolution data and then refine the individual atoms based on chemical knowledge. Best regards, Daniel -- Daniel Schlieper Institut fuer Biochemie Zuelpicher Strasse 47 [email protected] Universitaet zu Koeln Tel.: +49 221 470-6443, Fax: -5092 50674 Koeln, Germany

Mon, 19 Mar 2001 08:45:42 Re: Refinement and Resolution Rob Hooft [email protected] Newsgroups: sci.techniques.xtallography >>>>> "DS" == Daniel Schlieper writes: DS> Phillip Fanwick writes: >> I am working on a problem where chemistry requires that two >> carbon atoms be refined as two independent sets of carbons which >> are about 0.45A apart. The data were collected to a resolution of >> 0.75A and the splitting is suggested by Shelx from the highly >> anisotropic adp's and by the chemistry (a totally unsaturated ring >> is currently nearly planar). Is it valid to refine atoms below the >> resolution of the experiment? If so where do you draw the line? >> I know the FAQ to Shelx suggest that most suggestions for >> splitting atoms be ignored. DS> Dear Phil, "resolution" in x-ray crystallography the length of DS> the spacing d between the lattice planes to get a deviation angle DS> theta of the Bragg reflection. From the famous Bragg's Law: DS> d = lambda/(2 sin theta) DS> with lambda the wavelength. The minimal d corresponds to the DS> maximal theta and is named "resolution". DS> This has nothing to do with "resolution" as used in light DS> microscopy, stating the minimal distance of two distinguishable DS> points. In fact, in x-ray crystallography, atoms can be DS> distinguished even if they are much closer together than the DS> crystallographic resolution. These two values do have something to do with each other. In fact, if you collect data up to 0.8A resolution as is common in small molecule crystallography, you can separate two peaks in the Fourier map only if they are 0.8A or more apart; this is equivalent to the optical microscopy resolution. The difference occurs because in crystallography we have a model of spherical atoms (note: even "anisotropically" refined B factors only make a very small difference here, the resulting electron cloud is still almost spherical). Once a spherical atom of the right type is placed in a density peak, it can be seen quite clearly whether that spherical blob of density can properly explain the form of the electron density in the Fourier map. And one can even make a model where two disorder positions for the atom nicely explain the form of the density--- even if those two positions are closer together than the resolution limit. This principle makes Fo-Fc difference Fourier synthesis and structure refinement using least squares possible. It also explains bond distances that are accurate sometimes upto 0.0001 A at 0.7A resolution. Regards, Rob Hooft -- ===== [email protected] http://www.hooft.net/people/rob/ ===== ===== R&D, Nonius BV, Delft http://www.nonius.nl/ ===== ===== PGPid 0xFA19277D ========================== Use Linux! =========