X-RAY CRYSTALLOGRAPHY 91
In the presence of ethanol, the deoxy complex was found to bind dioxygen
reversibly, noncooperatively, and with lower affi nity than when the sample was
oxygenated after solvent removal. In the latter case, dioxygen uptake was
found to be cooperative. The complex [(Fe(T piv PP)(2 - MeIm)] is a model for T
(tense) state deoxy - and oxyhemoglobin (as discussed in Sections 7.2.2 , 7.2.4,
and 7.2.6 ; also see Figures 7.7 , 7.9B, and 7.10), whereas its 1 - methylimidazole
analogue, [(Fe(T piv PP)(1 - MeIm)], is a model for the R (relaxed) state. In com-
paring these two model compounds, the sterically active 2 - methylimidazole
substituent interacts with the porphyrin ring, whereas the 1 - methylimidazole
does not interact (or behaves in a similar manner to the normal hemoglobin
ligand, histidine). If the X - ray crystallographic structures [(Fe(O 2 )(T piv PP)(2 -
MeIm)] and [(Fe(O 2 )(T piv PP)(1 - MeIm)] are compared, the total distance of
the Fe – O plus Fe – N Im bonds is > 4.00 Å for [(Fe(O 2 )(T piv PP)(2 - MeIm)] and
3.82 Å for [(Fe(O 2 )(T piv PP)(1 - MeIm)].^16 Most of the difference ( > 0.15 Å ) is in
the Fe – O bond length of [(Fe(O 2 )(T piv PP)(2 - MeIm)], leading the researchers
to conclude that the sterically active 2 - MeIm perturbs (lengthens) the Fe – O
bond more than the Fe – N Im , bond. This conclusion has signifi cance for
[(Fe(O 2 )(T piv PP)(2 - MeIm)] as a model for hemoglobin ’ s T state, which has a
smaller O 2 affi nity than the R state.
Figure 3.8 displays a so - called ORTEP view of [(Fe(O 2 )(T piv PP)(1 - MeIm)],
drawn using 30% probability ellipsoids. Note that the outer atoms show greater
uncertainty in position, as seen in their elliptical rather than spherical shape.
The fi gure illustrates a stereodiagram, which will appear three - dimensional
when the two halves of the fi gure are merged by the observer. Techniques for
visualizing stereodiagrams are found in Section 4.6.1.
For proteins, X - ray structures usually are not determined at high enough
resolution to use anisotropic temperature factors. Average values for B in
protein structures range from as low as a few Å^2 for well - ordered structures
to 30 Å^2 for structures involving fl exible surface loops. Using equation 3.8 , one
can calculate the root mean square displacement u^2 for a well - ordered
protein structure at approximately 0.25 Å (for B = 5 Å^2 ) and for a not - so - well -
ordered structure at 0.62 Å (for B = 30 Å^2 ). These seemingly small errors in
atomic positions of C, N, and O atoms derive from the fact that the bond dis-
tances and angles for individual amino acids in small compounds are well
known, and it is assumed that these do not change when the amino acids are
incorporated into large protein molecules. In fact, the limited resolution of a
protein X - ray diffraction pattern does not permit calculation of an electron
density map at atomic resolution, although amino acid residues can be distin-
guished from differences in their side chains. Usually these are displayed in
stereo diagrams such as seen in Figure 3.8.
In addition to the dynamic disorder caused by temperature - dependent
vibration of atoms, protein crystals have static disorder due to the fact that
molecules, or parts of molecules, do not occupy exactly the same position or
do not have exactly the same orientation in the crystal unit cell. However, unless
data are collected at different temperatures, one cannot distinguish between