An excerpt from the Shelx manual (which I think is a good reference for proper handling of atoms on special positions in refinement of small or large molecules):
4.3 Special position constraints Constraints for the coordinates and anisotropic displacement parameters for atoms on special positions are generated automatically by the program for ALL special positions in ALL space groups, in conventional settings or otherwise. For upwards compatibility with SHELX-76, free variables may still be used for this, but it is better to leave it to the program. If the occupancy is not input, the program will fix it at the appropriate value for a special position. If the user applies (correct or incorrect) special position constraints using free variables etc., the program assumes this has been done with intent and reports but does not apply the correct constraints; accidental application of wrong special position constraints is one of the easiest ways to cause a refinement to 'blow up' ! Also, please check the book of Shmueli and Weiss, "Introduction to crystallographic statistics" p. 5, last paragraph and the next page where a rigorous treatment of of contribution to the structure factor of atoms in general and special positions in the unit cell is given (eq. 1.2.10). Thus, occupancy of an atom on a 3-fold would be 1/3, 1/2 on a 2-fold, 1/4 on a 4-fold and so forth. Cheers, Boaz ----- Original Message ----- From: Ian Tickle <ianj...@gmail.com> Date: Saturday, December 11, 2010 0:41 Subject: Re: [ccp4bb] Fwd: [ccp4bb] Wyckoff positions and protein atoms To: CCP4BB@JISCMAIL.AC.UK > No that surely can't be right. Application of a symmetry > operator to > a point on a special position which is unchanged by the operator > doesn't generate a symmetry copy of the point, because there is no > symmetry copy of such a point! For general Wyckoff > positions it does, > for sure. If you look at the entry for R3 (hexagonal or > rhombohedralsetting, it doesn't matter which) on the Wyckoff > position website I > indicated earlier, you'll see a column labelled 'multiplicity' which > is 3 for the general position and 1 for the special > position. This > means that the symmetry operator generates 3 symmetry copies of a > general position (including the original), but only 1 copy (i.e. only > the original) of the special positions on the 3-fold. > > That's precisely why such points are called "special positions" - > i.e. > you have to treat them specially! If what you describe is > what the > refinement program or whatever is doing then it would imply > there's a > programming error, i.e. the program is not treating special positions > as special, it's treating them instead as general > positions. As I > said whenever you see fractional occupancy reported it should imply > some kind of disorder, i.e. the atom exists on that site in only the > indicated fraction of the unit cells in the lattice. > > -- Ian > > On Fri, Dec 10, 2010 at 10:02 PM, Sue Roberts > <s...@email.arizona.edu> wrote: > > Hi Ian > > > > No disorder is involved. > > > > The occupancy of an (fully occupied) atom on an n-fold > rotation axis is 1/n > > If a two-fold, 1/2 > > If a three-fold, 1/3 > > > > When you sum over all the atoms in the unit cell, application > of the symmetry operations to atoms lying on the rotation axis > generates atoms with unchanged coordinates. Hence to generate a > fully occupied atom on a n-fold symmetry axis, the original > occupancy has to be 1/n. > > > > Sue > > > > On Dec 10, 2010, at 2:53 PM, Ian Tickle wrote: > > > >> Good point Colin! 2-Zn insulin is of course a classic > example of > >> this, where the two independent Zn2+ ions both sit on the > >> crystallographic 3-fold in R3. It doesn't matter whether you count > >> the metal ion as part of the protein or not: if I understand > Gloria's>> original question correctly, all that matters is that > the atom/ion is > >> present in the crystal structure. > >> > >> In fact here are some extracts from the PDB entry (4INS): > >> > >> REMARK 375 ZN ZN B 31 LIES ON A SPECIAL POSITION. > >> REMARK 375 ZN ZN D 31 LIES ON A SPECIAL POSITION. > >> REMARK 375 HOH B 251 LIES ON A SPECIAL POSITION. > >> REMARK 375 HOH D 44 LIES ON A SPECIAL POSITION. > >> REMARK 375 HOH D 134 LIES ON A SPECIAL POSITION. > >> REMARK 375 HOH D 215 LIES ON A SPECIAL POSITION. > >> REMARK 375 HOH D 269 LIES ON A SPECIAL POSITION. > >> > >> HETATM 835 ZN ZN B 31 -0.002 -0.004 7.891 0.33 > 10.40 ZN > >> HETATM 836 ZN ZN D 31 0.000 0.000 -8.039 0.33 > 11.00 ZN > >> HETATM 885 O HOH B 251 -0.023 -0.033 11.206 0.33 > 21.05 O > >> etc > >> > >> Hmmm - but shouldn't the occupancy of the Zn be 1.00 if it's > on the > >> special position (assuming it's not disordered), though the > first Zn > >> above and the water do appear to be disordered since they're not > >> actually on the special position. Fractional occupancy > always implies > >> some kind of disorder: occupancy = 1/3 of an atom on a special > >> position would imply occupancy disorder, i.e. it's randomly > present in > >> only 1/3 of the unit cells. > >> > >> -- Ian > >> > >> > >> On Fri, Dec 10, 2010 at 1:11 PM, Colin Nave > <colin.n...@diamond.ac.uk> wrote: > >>> Does one regard the metal atom in a metalloprotein as being > part of the protein? > >>> > >>> If so, a shared metal could occupy a special position in a > dimer for example. > >>> > >>> In Acta Cryst. (2008). D64, 257-263 "Metals in proteins: > correlation between the metal-ion type, coordination number and > the amino-acid residues involved in the coordination" I. > Dokmanic, M. Sikic and S. Tomic ( http://scripts.iucr.org/cgi- > bin/paper?S090744490706595X ) it says there are 25 cases of > metal atoms in special positions. > >>> > >>> Also Acta Cryst. (2002). D58, 29-38 "The 2.6 Å resolution > structure of Rhodobacter capsulatus bacterioferritin with metal- > free dinuclear site and heme iron in a crystallographic `special > position' "D. Cobessi, L.-S. Huang, M. Ban, N. G. Pon, F. Daldal > and E. A. Berry ( http://scripts.iucr.org/cgi- > bin/paper?S0907444901017267 ) though the 'special position' is > justifiably in quotation marks in this example as disorder is present. > >>> > >>> Colin > >>> > >> > > > > Dr. Sue A. Roberts > > Dept. of Chemistry and Biochemistry > > University of Arizona > > 1041 E. Lowell St., Tucson, AZ 85721 > > Phone: 520 621 8171 > > s...@email.arizona.edu > > http://www.biochem.arizona.edu/xray > > > > > > > > > > > > > > > > > > > > > Boaz Shaanan, Ph.D. Dept. of Life Sciences Ben-Gurion University of the Negev Beer-Sheva 84105 Israel Phone: 972-8-647-2220 ; Fax: 646-1710 Skype: boaz.shaanan
