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 [1]
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 [59]
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 [59]. 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.