Dear Bernhard, dear John, On 11/20/12 6:10 AM, Bernhard Rupp wrote:
As already mentioned by jrh, I again want to impress that B-factor and occupancy are in principle two entirely different parameters. They may appear as achieving the same thing upon refinement at the resolution we deal with in most macromolecular structures. The fact is that reduced occupancy just **scales down** the entire scattering function at a given B, while an increased B-factor **changes the shape** of the scattering curve, i.e. makes it narrower in reciprocal space and thus in direct space gives a broader electron density. Reduced occupancy just reduces electron density levels. Those are physically distinctly different although not easily separable effects. I have an applet that can be used to see the point http://www.ruppweb.org/cgi-bin/webscat.exe?E1=O&B=50.0&Occupation_factor=0.5&B1=Submit On 11/20/12 12:05 AM, Jrh wrote: Dear Pavel, Also worth mentioning the obvious that the mathematical functional form of an occupancy and a B factor in its -ve exponential is very different BUT at lower resolutions they behave similarly. Thus higher resolution refinement allows an 'easier' determination of each parameter. I surely agree about occupancy and B-factor having distinct and different mathematical meaning and effects. It's obvious from the structure factor formula being proportional to q*exp(-B*s**2). No plots needed to see it! -;) Unless we are going into subatomic resolution world with their deformation density maps (most kinds of which are in fact model calculated maps!), at typical macro-molecular resolutions we don't deal with electron density distribution, but its Fourier image. Needless to say that such image may be as far away from the true electron density as your set of Fobs is far away from being fully complete. Whether the differences between "scaling" and "changing the shape" are visible, significant or reliably distinguishable in this context isn't very obvious to me. As John pointed out, at lower resolution the effect of q or B is similar, while it is less true as resolution becomes higher. Perhaps the line where a) effects of q and B become (in)distinguishable and b) one should be used instead of the other, is subtle. I guess the original poster found the answer empirically by trying to do both, and judging the trial success by flatness of residual map it produced, which is probably the most robust way to figure this out (as long as what you try makes sense). PS: Partial occupancy is not the same as disorder. You can have well-ordered different occupancies that manifest themselves then in superstructure patterns. Common in small molecule/materials. Put nomenclature rigor aside (bad idea?), my (rather simplistic!) understanding is that both are disorder but of different kind and nature, thus two different and simple parameters to model it, q and B. While occupancy is to reflect the fraction of unit cells having that atom there, the B-factor describes small (within harmonic approximation) vibration of it. Larger-scale vibrations are accounted for by more complex models, such as anharmonic approximations: Gram-Charier expansion or "bananas and pears" of Reilly et al (Acta Cryst. A67, 346-356) (was a nice talk about it at ECM27!). All the best, Pavel
