Re: [ccp4bb] Series termination effect calculation.
Yes, the constant term in the 5-Gaussian structure factor tables does become annoying when you try to plot electron density in real space, but only if you try to make the B factor zero. If the B factors are ~12 (like they are in 1m1n), then the electron density 2.0 A from an Fe atom is not -0.2 e-/A^3, it is 0.025 e-/A^3. This is only 1% of the electron density at the center of a nitrogen atom with the same B factor. But if you do set the B factor to zero, then the electron density at the center of any atom (using the 5-Gaussian model) is infinity. To put it in gnuplot-ish, the structure factor of Fe (in reciprocal space) can be plotted with this function: Fe_sf(s)=Fe_a1*exp(-Fe_b1*s*s)+Fe_a2*exp(-Fe_b2*s*s)+Fe_a3*exp(-Fe_b3*s*s)+Fe_a4*exp(-Fe_b4*s*s)+Fe_c where: Fe_c = 1.036900; Fe_a1 = 11.769500; Fe_a2 = 7.357300; Fe_a3 = 3.522200; Fe_a4 = 2.304500; Fe_b1 = 4.761100; Fe_b2 = 0.307200; Fe_b3 = 15.353500; Fe_b4 = 76.880501; and s is sin(theta)/lambda applying a B factor is then just multiplication by exp(-B*s*s) Since the terms are all Gaussians, the inverse Fourier transform can actually be done analytically, giving the real-space version, or the expression for electron density vs distance from the nucleus (r): Fe_ff(r,B) = \ +Fe_a1*(4*pi/(Fe_b1+B))**1.5*safexp(-4*pi**2/(Fe_b1+B)*r*r) \ +Fe_a2*(4*pi/(Fe_b2+B))**1.5*safexp(-4*pi**2/(Fe_b2+B)*r*r) \ +Fe_a3*(4*pi/(Fe_b3+B))**1.5*safexp(-4*pi**2/(Fe_b3+B)*r*r) \ +Fe_a4*(4*pi/(Fe_b4+B))**1.5*safexp(-4*pi**2/(Fe_b4+B)*r*r) \ +Fe_c *(4*pi/(B))**1.5*safexp(-4*pi**2/(B)*r*r); Where here applying a B factor requires folding it into each Gaussian term. Notice how the Fe_c term blows up as B-0? This is where most of the series-termination effects come from. If you want the above equations for other atoms, you can get them from here: http://bl831.als.lbl.gov/~jamesh/pickup/all_atomsf.gnuplot http://bl831.als.lbl.gov/~jamesh/pickup/all_atomff.gnuplot This infinitely sharp spike problem seems to have led some people to conclude that a zero B factor is non-physical, but nothing could be further from the truth! The scattering from mono-atomic gasses is an excellent example of how one can observe the B=0 structure factor. In fact, gas scattering is how the quantum mechanical self-consistent field calculations of electron clouds around atoms was experimentally verified. Does this mean that there really is an infinitely sharp spike in the middle of every atom? Of course not. But there is a very sharp spike. So, the problem of infinite density at the nucleus is really just an artifact of the 5-Gaussian formalism. Strictly speaking, the 5-Gaussian structure factor representation you find in ${CLIBD}/atomsf.lib (or Table 6.1.1.4 in the International Tables volume C) is nothing more than a curve fit to the true values listed in ITC volume C tables 6.1.1.1 (neutral atoms) and 6.1.1.3 (ions). These latter tables are the Fourier transform of the true electron density distribution around a particular atom/ion obtained from quantum mechanical self-consistent field calculations (like those of Cromer, Mann and many others). The important thing to realize is that the fit was done in _reciprocal_ space, and if you look carefully at tables 6.1.1.1 and 6.1.1.3, you can see that even at REALLY high angle (sin(theta)/lambda = 6, or 0.083 A resolution) there is still significant elastic scattering from the heavier atoms. The purpose of the constant term in the 5-Gaussian representation is to try and capture this high-angle tail, and for the really heavy atoms this can be more than 5 electron equivalents. In real space, this is equivalent to saying that about 5 electrons are located within at least ~0.03 A of the nucleus. That's a very short distance, but it is also not zero. This is because the first few shells of electrons around things like a Uranium nucleus actually are very small and dense. How, then, can we have any hope of modelling heavy atoms properly without using a map grid sampling of 0.01A ? Easy! The B factors are never zero. Even for a truly infinitely sharp peak (aka a single electron), it doesn't take much of a B factor to spread it out to a reasonable size. For example, applying a B factor of 9 to a point charge will give it a full-width-half max (FWHM) of 0.8 A, the same as the diameter of a carbon atom. A carbon atom with B=12 has FWHM = 1.1 A, the same as a point charge with B=16. Carbon at B=80 and a point with B=93 both have FWHM = 2.6 A. As the B factor becomes larger and larger, it tends to dominate the atomic shape (looks like a single Gaussian). This is why it is so hard to assign atom types from density alone. In fact, with B=80, a Uranium atom at 1/100th occupancy is essentially indistinguishable from a hydrogen atom. That is, even a modest B factor pretty much washes out any sharp features the atoms might have. Sometimes I wonder why we bother with form
Re: [ccp4bb] Series termination effect calculation.
Le Lundi 17 Septembre 2012 08:32 CEST, James Holton jmhol...@lbl.gov a écrit Hello May I add a few words after the thorough comments by James. I lmay be easier to consider series termination in real space as follows. The effect of series termination in 3D on rho(r) is of convoluting the exact rho(r) with the approximation of a delta function resulting from the limit in resolution. This approximation in 3D is given exactly by the function G[X] = 3*[Sin(X) - X*Cos(X)]/X^3, where X = 2*Pi*r/d (r in Angstrom and d the resolution, also in Angstrom). This is the function appearing in the rotation function (for exactly the same reason of truncating the resolution). If you consider that the iron atom is punctual (i.e. its Fourier transform would be merely constant), then the approximation resulting from series termination is just given by G[X] (apart for a scaling factor). And if you convolute the exact and ideal rho(r) with G[X], you will obtain the exact form of rho[r] affected by series termination. Note that, considering the Gaussian approximation of the structure factors, this would amount to convolute gaussians with G[X] (see James comments). I join a figure corresponding to the simplification of a punctual iron atom. I only put on this figure the curves corresponding to the limits in resolution, 1.3, 2 an 2.5 Angstrom because at a resolution of 1 Angstrom, the iron atom is definitely not punctual. I used the same color codes as in Fig. 1 of the paper. One can see that the ripples on my approximate figure are essentially the same as in Fig. 1 of the paper. Of course, it cannot reproduce the features of rho[r] for r--0 since the iron aton is definitely not punctual. Practical comment. It is quite useful to consider the following rule of thumb: the first minimum of G[X] appears at a distance equal to 0.92*d (d = resolution) and the first maximum at 1.45*d. Therefore, if one suspects that series terminaiton effects might cause a spurious through, or peak, it may be enough to recalculate the e.d. map at different resolutions to check whether these features are moving or not. Philippe Dumas PS: it is instructive to make a comparison with the Airy function in astronomy. Airy calculated this function to take into account the distorsion brought by the limlited optical resolution of a telescope to a punctual image of a star. Nothing else than our problem, with an iron atom replacing a star... Plus ça change, plus c'est la même chose. Yes, the constant term in the 5-Gaussian structure factor tables does become annoying when you try to plot electron density in real space, but only if you try to make the B factor zero. If the B factors are ~12 (like they are in 1m1n), then the electron density 2.0 A from an Fe atom is not -0.2 e-/A^3, it is 0.025 e-/A^3. This is only 1% of the electron density at the center of a nitrogen atom with the same B factor. But if you do set the B factor to zero, then the electron density at the center of any atom (using the 5-Gaussian model) is infinity. To put it in gnuplot-ish, the structure factor of Fe (in reciprocal space) can be plotted with this function: Fe_sf(s)=Fe_a1*exp(-Fe_b1*s*s)+Fe_a2*exp(-Fe_b2*s*s)+Fe_a3*exp(-Fe_b3*s*s)+Fe_a4*exp(-Fe_b4*s*s)+Fe_c where: Fe_c = 1.036900; Fe_a1 = 11.769500; Fe_a2 = 7.357300; Fe_a3 = 3.522200; Fe_a4 = 2.304500; Fe_b1 = 4.761100; Fe_b2 = 0.307200; Fe_b3 = 15.353500; Fe_b4 = 76.880501; and s is sin(theta)/lambda applying a B factor is then just multiplication by exp(-B*s*s) Since the terms are all Gaussians, the inverse Fourier transform can actually be done analytically, giving the real-space version, or the expression for electron density vs distance from the nucleus (r): Fe_ff(r,B) = \ +Fe_a1*(4*pi/(Fe_b1+B))**1.5*safexp(-4*pi**2/(Fe_b1+B)*r*r) \ +Fe_a2*(4*pi/(Fe_b2+B))**1.5*safexp(-4*pi**2/(Fe_b2+B)*r*r) \ +Fe_a3*(4*pi/(Fe_b3+B))**1.5*safexp(-4*pi**2/(Fe_b3+B)*r*r) \ +Fe_a4*(4*pi/(Fe_b4+B))**1.5*safexp(-4*pi**2/(Fe_b4+B)*r*r) \ +Fe_c *(4*pi/(B))**1.5*safexp(-4*pi**2/(B)*r*r); Where here applying a B factor requires folding it into each Gaussian term. Notice how the Fe_c term blows up as B-0? This is where most of the series-termination effects come from. If you want the above equations for other atoms, you can get them from here: http://bl831.als.lbl.gov/~jamesh/pickup/all_atomsf.gnuplot http://bl831.als.lbl.gov/~jamesh/pickup/all_atomff.gnuplot This infinitely sharp spike problem seems to have led some people to conclude that a zero B factor is non-physical, but nothing could be further from the truth! The scattering from mono-atomic gasses is an excellent example of how one can observe the B=0 structure factor. In fact, gas scattering is how the quantum mechanical self-consistent field calculations of electron clouds around atoms was experimentally verified. Does this mean that there really is an infinitely sharp spike in the
[ccp4bb] mosflm and dectris pilatus
Dear all We have recently collected data at XRD1 beamline at Sincrotrone Trieste on a Dectris Pilatus detector. We are unable to integrate the images in mosflm, which keeps crashing with some error: e.g. profile_fitted_partials or b_slope or some such! (indexing seems to work ok). Any suggestions from other recent users on how to process this data in mosflm? (we have changed nullpix threshold to -1 and maximum background slope to 0.06). Thanks in advance for your replies! -Bhupesh
Re: [ccp4bb] Series termination effect calculation.
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Dear James et al., so to summarise, the answer to Niu's question is that he must add a factor of e^(-Bs^2) to the formula of Cromer/Mann and then adjust the value of B until it matches the inset. Given that you claim rho=0.025e/A^3 (I assume for 1/dmax approx. 0) for B=12 and the inset shows a value of about 0.6, a somewhat higher B-value should work. Cheers, Tim On 09/17/2012 08:32 AM, James Holton wrote: Yes, the constant term in the 5-Gaussian structure factor tables does become annoying when you try to plot electron density in real space, but only if you try to make the B factor zero. If the B factors are ~12 (like they are in 1m1n), then the electron density 2.0 A from an Fe atom is not -0.2 e-/A^3, it is 0.025 e-/A^3. This is only 1% of the electron density at the center of a nitrogen atom with the same B factor. But if you do set the B factor to zero, then the electron density at the center of any atom (using the 5-Gaussian model) is infinity. To put it in gnuplot-ish, the structure factor of Fe (in reciprocal space) can be plotted with this function: Fe_sf(s)=Fe_a1*exp(-Fe_b1*s*s)+Fe_a2*exp(-Fe_b2*s*s)+Fe_a3*exp(-Fe_b3*s*s)+Fe_a4*exp(-Fe_b4*s*s)+Fe_c where: Fe_c = 1.036900; Fe_a1 = 11.769500; Fe_a2 = 7.357300; Fe_a3 = 3.522200; Fe_a4 = 2.304500; Fe_b1 = 4.761100; Fe_b2 = 0.307200; Fe_b3 = 15.353500; Fe_b4 = 76.880501; and s is sin(theta)/lambda applying a B factor is then just multiplication by exp(-B*s*s) Since the terms are all Gaussians, the inverse Fourier transform can actually be done analytically, giving the real-space version, or the expression for electron density vs distance from the nucleus (r): Fe_ff(r,B) = \ +Fe_a1*(4*pi/(Fe_b1+B))**1.5*safexp(-4*pi**2/(Fe_b1+B)*r*r) \ +Fe_a2*(4*pi/(Fe_b2+B))**1.5*safexp(-4*pi**2/(Fe_b2+B)*r*r) \ +Fe_a3*(4*pi/(Fe_b3+B))**1.5*safexp(-4*pi**2/(Fe_b3+B)*r*r) \ +Fe_a4*(4*pi/(Fe_b4+B))**1.5*safexp(-4*pi**2/(Fe_b4+B)*r*r) \ +Fe_c *(4*pi/(B))**1.5*safexp(-4*pi**2/(B)*r*r); Where here applying a B factor requires folding it into each Gaussian term. Notice how the Fe_c term blows up as B-0? This is where most of the series-termination effects come from. If you want the above equations for other atoms, you can get them from here: http://bl831.als.lbl.gov/~jamesh/pickup/all_atomsf.gnuplot http://bl831.als.lbl.gov/~jamesh/pickup/all_atomff.gnuplot This infinitely sharp spike problem seems to have led some people to conclude that a zero B factor is non-physical, but nothing could be further from the truth! The scattering from mono-atomic gasses is an excellent example of how one can observe the B=0 structure factor. In fact, gas scattering is how the quantum mechanical self-consistent field calculations of electron clouds around atoms was experimentally verified. Does this mean that there really is an infinitely sharp spike in the middle of every atom? Of course not. But there is a very sharp spike. So, the problem of infinite density at the nucleus is really just an artifact of the 5-Gaussian formalism. Strictly speaking, the 5-Gaussian structure factor representation you find in ${CLIBD}/atomsf.lib (or Table 6.1.1.4 in the International Tables volume C) is nothing more than a curve fit to the true values listed in ITC volume C tables 6.1.1.1 (neutral atoms) and 6.1.1.3 (ions). These latter tables are the Fourier transform of the true electron density distribution around a particular atom/ion obtained from quantum mechanical self-consistent field calculations (like those of Cromer, Mann and many others). The important thing to realize is that the fit was done in _reciprocal_ space, and if you look carefully at tables 6.1.1.1 and 6.1.1.3, you can see that even at REALLY high angle (sin(theta)/lambda = 6, or 0.083 A resolution) there is still significant elastic scattering from the heavier atoms. The purpose of the constant term in the 5-Gaussian representation is to try and capture this high-angle tail, and for the really heavy atoms this can be more than 5 electron equivalents. In real space, this is equivalent to saying that about 5 electrons are located within at least ~0.03 A of the nucleus. That's a very short distance, but it is also not zero. This is because the first few shells of electrons around things like a Uranium nucleus actually are very small and dense. How, then, can we have any hope of modelling heavy atoms properly without using a map grid sampling of 0.01A ? Easy! The B factors are never zero. Even for a truly infinitely sharp peak (aka a single electron), it doesn't take much of a B factor to spread it out to a reasonable size. For example, applying a B factor of 9 to a point charge will give it a full-width-half max (FWHM) of 0.8 A, the same as the diameter of a carbon atom. A carbon atom with B=12 has FWHM = 1.1 A, the same as a point charge with B=16. Carbon at B=80
[ccp4bb] imosflm background definition
Hi all, I'm integrating data from a crystal with a fairly long axis. In iMosflm (1.0.7), the background definition is so generous that plenty of pixels from adjacent peaks are included (see attached). Can someone tell me how I redefine the background to be tighter around the spots? Thanks. Andreas -- Andreas Förster, Research Associate Paul Freemont Xiaodong Zhang Labs Department of Biochemistry, Imperial College London http://www.msf.bio.ic.ac.uk attachment: backgroundSpots.png
Re: [ccp4bb] imosflm background definition
Hi Andreas, The simple answer to this is that you do NOT attempt to redefine the background. Providing the additional spots shown in your image belong to the same lattice, mosflm will automatically exclude pixels from adjacent spots when doing the background plane fitting, so you need do nothing. It helps to have a larger box size because the background plane is better defined. To answer your question, you need to go to Settings - Processing Options - Advanced integration in imosflm, then the top 5 lines define the measurement box parameters, changing the box width and height should do what you want, although you may need to uncheck the box Optimise overall box size to stop the box being made bigger again. Best wishes, Andrew On 17 Sep 2012, at 15:03, Andreas Förster wrote: Hi all, I'm integrating data from a crystal with a fairly long axis. In iMosflm (1.0.7), the background definition is so generous that plenty of pixels from adjacent peaks are included (see attached). Can someone tell me how I redefine the background to be tighter around the spots? Thanks. Andreas -- Andreas Förster, Research Associate Paul Freemont Xiaodong Zhang Labs Department of Biochemistry, Imperial College London http://www.msf.bio.ic.ac.uk backgroundSpots.png
[ccp4bb] CCP4 Study Weekend 2012
The CCP4 Study Weekend (3 - 5 January 2013) East Midlands Conference Centre, University of Nottingham Thursday 3 - MX User Meeting Friday 4 / Saturday 5 - CCP4 Study Weekend Molecular Replacements We cordially invite you to participate in this year's Study Weekend at the the East Midlands Conference Centre, University of Nottingham. The annual CCP4 Study Weekend is a chance to shake off the post-New Year torpor, and work hard and play hard with your fellow crystallographers. Once again, we have put together an exciting scientific programme for Friday and Saturday, either side of the traditional conference dinner. Please also check out the satellite meetings which may be of interest. The Study Weekend is a chance to catch up with old friends, but is also a chance to meet the CCP4 staff who will be there in force to demonstrate the latest software and to answer questions - please say hello! This year, the topic for the Study Weekend is Molecular Replacements. In keeping with previous CCP4 meetings, the lectures will focus on the presentation and discussion of advanced methods and techniques developed and used by the leaders in the field. Scientific Organisers Helen Walden - Cancer Research (UK) Pietro Roversi - University of Oxford (UK) Further details of the program and the registration are at http://www.cse.scitech.ac.uk/events/CCP4_2013/ Terms and Conditions apply. Please read the cancellation policy before applying. -- Scanned by iCritical.
[ccp4bb] problem with phenix refine and non bonded interactions
I am using Phenix 1.8-1069. I am having a problem with phenix refine terminating with an error message. I added several solvent molecules, MPD and bicarbonate in Coot, and ran Phenix ReadySet to generate restraints for them and applied those restraints to all future jobs in that project. When I try to refine it, I get an error message stating that I have too many non-bonded interactions. If I generated my restraints file before running refine, this should not happen (?)
[ccp4bb] Beamline scientist position at SSRL
The Structural Molecular Biology (SMB) Group of Stanford Synchrotron Radiation Lightsource (SSRL, a Directorate of SLAC) has an opening for a Beam Line Scientist. This position will participate in a large user support team that provides expert technical methodological support for scientific experiments at seven highly-automated macromolecular crystallography beam lines. Research facilities include x-ray optics, automated crystallography instrumentation, and state-of-the-art x-ray detectors. Specific responsibilities Include (but are not limited to): 1) Beamline optimization including the alignment of beam line optics and instrumentation; 2) user training and support during experiments; 3) troubleshooting, testing, documenting optics, and instrumentation; 4) development of new instrumentation and methodologies; 5) backup Systems Manager role for Linux systems; 6) Dissemination/tours of facilities. Up to 15% time may be dedicated to scientific collaborations. All activities will be carried out in close collaboration with other scientists, engineers, software developers and technicians. Applicants must be willing to provide user support outside of regular hours. To obtain more information about this position and apply please see: https://ch.tbe.taleo.net/CH12/ats/careers/requisition.jsp?org=SLACcws=1rid=905 Ana -- --- Ana Gonzalez a...@slac.stanford.edu Staff Scientist Stanford Synchrotron Radiation Lightsource 2575 Sand Hill Road, MS 99 Menlo Park CA 94025 Phone: (650) 926 8682 Fax: (650) 926 3292 ---
[ccp4bb] B-iso vs. B-aniso
Dear community, The protein model I am refining has 400 amino acids (3320 atoms). Some real quick calculations tell me that to properly refine it anisotropically, I would need 119,520 observations. Given my unit-cell dimension and space-group it is equivalent to about a 1.24 A complete data set. However, I have had a couple of cases where anisotropic B-factor refinement significantly improved R-work and R-free, while maintaining a reasonable gap for lower resolution models (1.4-1.5 A, around 70,000 reflections). What is the proper way of modelling the B-factors? Any thoughts and/or opinions from the community are welcome. Cheers,
Re: [ccp4bb] B-iso vs. B-aniso
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Dear, 1.24A resolution is reasonable for anisotropic refinement - including restraints you have more observations than the number of reflections, so just doing the calculation does not give a concise answer! You should try and see if the refinement is stable and makes sense (e.g. check the number of npd-atoms etc.) You may also try the RIGU command in the beta-version of shelxl (Acta Cryst. (2012). A68, 448-451)! Regards, Tim On 09/17/2012 08:31 PM, Yuri Pompeu wrote: Dear community, The protein model I am refining has 400 amino acids (3320 atoms). Some real quick calculations tell me that to properly refine it anisotropically, I would need 119,520 observations. Given my unit-cell dimension and space-group it is equivalent to about a 1.24 A complete data set. However, I have had a couple of cases where anisotropic B-factor refinement significantly improved R-work and R-free, while maintaining a reasonable gap for lower resolution models (1.4-1.5 A, around 70,000 reflections). What is the proper way of modelling the B-factors? Any thoughts and/or opinions from the community are welcome. Cheers, - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iD8DBQFQV284UxlJ7aRr7hoRAh5FAJ43TevZbbQLYGeE1yM2cqKjZ5KMFACg5bCs Ijn4owVvuuHldNSnK4Iax1E= =4Jdg -END PGP SIGNATURE-
Re: [ccp4bb] B-iso vs. B-aniso
On Monday, September 17, 2012 11:31:53 am Yuri Pompeu wrote: Dear community, The protein model I am refining has 400 amino acids (3320 atoms). Some real quick calculations tell me that to properly refine it anisotropically, I would need 119,520 observations. Given my unit-cell dimension and space-group it is equivalent to about a 1.24 A complete data set. However, I have had a couple of cases where anisotropic B-factor refinement significantly improved R-work and R-free, while maintaining a reasonable gap for lower resolution models (1.4-1.5 A, around 70,000 reflections). What is the proper way of modelling the B-factors? I laid out my thoughts on this topic at last year's CCP4 Study Weekend. The print version of it may be found here: To B or not to B: a question of resolution? Acta Cryst. D68, 468-477. http://dx.doi.org/10.1107/S0907444911028320 One lesson is that lower R-work and R-free does not necessarily indicate that anisotropic refinement is justified. In other words, it is not so easy to determine how much improvement is significant improvement. Any thoughts and/or opinions from the community are welcome. Cheers, -- Ethan A Merritt Biomolecular Structure Center, K-428 Health Sciences Bldg University of Washington, Seattle 98195-7742
Re: [ccp4bb] B-iso vs. B-aniso
Dear Yuri, Why do you think you need 36 reflections per atom when atoms with anisotropic B-factors only have 9 parameters? You can get away with much fewer in many cases especially if you have good restraints. As Ethan points out, a drop in R-free after adding many parameters may be misleading. Proper testing will give you a clearer example. The Hamilton test in Ethan's paper is implemented in PDB_REDO (http://scripts.iucr.org/cgi-bin/paper?ba5174) and I had a quick look at some refinement statistics for structures with ~21 reflections/atom (like your case): according to PDB_REDO's strict criteria anisotropic B-factors are acceptable in two thirds of the cases. This was tested with Refmac on 285 PDB entries; ShelX's new restraints may well increase the success rate. HTH, Robbie Joosten Netherlands Cancer Institute www.cmbi.ru.nl/pdb_redo -Original Message- From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Yuri Pompeu Sent: Monday, September 17, 2012 20:32 To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] B-iso vs. B-aniso Dear community, The protein model I am refining has 400 amino acids (3320 atoms). Some real quick calculations tell me that to properly refine it anisotropically, I would need 119,520 observations. Given my unit-cell dimension and space- group it is equivalent to about a 1.24 A complete data set. However, I have had a couple of cases where anisotropic B-factor refinement significantly improved R-work and R-free, while maintaining a reasonable gap for lower resolution models (1.4-1.5 A, around 70,000 reflections). What is the proper way of modelling the B-factors? Any thoughts and/or opinions from the community are welcome. Cheers,