Once a set of native phases were available the positions of the iridium atoms in the unit cell were determined using the difference Fourier method. Fig. and Fig. show difference density maps calculated using the isomorphous differences between native and derivative and the anomalous differences from data set 3 respectively. The anomalous difference map contains six strong peaks, only four of which are clearly present in the isomorphous difference map.
Sites 1 and 5 are located near to the Arg 14 side chain. The sites are Å apart suggesting that they represent two conformations of the side chain with an iridium atom bound to the NE1 or NE2 nitrogen. Similarly, sites 2 and 4 are bound to Asn 65 and sit Å apart in a double conformation. Site 3, the strongest, is located near to the NE1 nitrogen of Trp 62. The last site, IR6 is Å away from IR3 but is not obviously bound to any nearby side chains. In fact the closest protein atom is Å away. Given also that this site is very weak in the isomorphous difference density it was not included in the refinement of the derivative structure. It is interesting to note however that this site is clearly visible in the anomalous difference Fourier.
Figure: Isomorphous difference Fourier density map projected along the z axis through of the cell. Four iridium sites are clearly visible in the map along with several weaker peaks. Iridium 5 is the next weakest site. Iridium 1 and 2 appear twice since they sit on the border between neighbouring asymmetric units related by the four-fold screw axis along the z direction.
Figure: Anomalous difference Fourier density map showing exactly the same projection as in figure . The same four sites are still present but two weaker sites become visible.
Iridium sites 1 to 5 were added to the native model and refined in exactly the same way as with the native set. The model was refined against the best available data which had been collected on X11 (data set 6). During the refinement however it was observed that the B-factors of all the iridium atoms were highly unstable and refined to values in excess of 100Å if the occupancy was assumed to be 1.0. The reason for this was thought to be due to lack of modelling of disordered ligands which may have been bound to the iridium centres. The presence of such ligands, whether they be disordered chlorine ions or water molecules is effectively to expand the electron density around the metal atom and make it cover a larger volume of space. This is equivalent to regarding the metal atom as having an increased atomic number and having a larger isotropic mean displacement from its atomic centre and is therefore equivalent to a metal atom with a higher B-value. In fact B-values of Å correspond to mean displacements of Å which are comparable to typical bond lengths for such atoms. A second possible explanation for this is anisotropy of the iridium atoms either from static disorder or through anisotropic thermal motion.
During the refinement this was dealt with simply by resetting the iridium B-values to 40Å after every 20 ARP cycles. A value of 40Å was chosen since this was the average B-value of the neighbouring side chain atoms to which the iridium ions were bound. During these 20 cycles the B-values had on average increased to about 60Å. The occupancies of the iridium sites were also adjusted manually every 20 cycles so that the electron density at the atomic centre agreed with that determined from theory. Agarwal  obtained an expression for the electron density for one atom in terms of a two Gaussian approximation for the atoms scattering factors in reciprocal space  given a particular value of temperature factor. Assuming that the data are complete over the range from then for the two Gaussian approximation for the th atom in the structure the expression for the model electron density at a position in real space is
An updated expression has more recently been obtained to take into account series termination in the Fourier transform and also incorporate a five Gaussian approximation . Thus theoretical values of the electron density at the atomic centre of a fully occupied iridium site for data to a resolution of 2.5Å were calculated and compared with those values in the map. The occupancy of each of the iridium sites was then adjusted over the course of sixty cycles until the theoretical and experimental densities agreed to within .
After 190 cycles of ARP the final R-factor was for all reflections and for reflections with compared with a starting R-factor of . A total of 132 water molecules were added and 118 of these had B-values less than 70Å. Table shows the coordinates, occupancies and refined B-values of the five iridium sites.
Table: The final fractional coordinates, occupancies and temperature factors of the five refined iridium sites in the derivative structure of Lysozyme.
The correlation coefficient between the refined native and derivative electron density maps was 0.92. The average phase deviation for reflections lying between 10 and 2.5Å was and was constant as a function of resolution to within . This suggested that the native and derivative structures were isomorphous up to Å.