The results presented in Chapter have shown that the signal to noise ratio of the anomalous scattering factors from heavy atoms in protein structures can be maximised by two different means. The narrow band approach carried out using X31 set to select out the energy of maximum and the broad band pass approach performed at a sub-optimal energy but with improved counting statistics. The factor of four larger dynamic range of the X11 detector meant measured intensities from X11 would be recorded with on average a factor of four more photon counts implying a factor of two reduction in statistical error. On the other hand X31 allowed optimisation of the signal at the white line which resulted in an increase in signal of about a factor of two. These two approaches to improving the overall signal to noise ratio were seen to be equivalent in terms of the anomalous Cullis R-factor, , calculated by MLPHARE.
The advantages of using a broad band pass approach are clear. No X-ray energy stabilisation is necessary since the anomalous scattering factors are well defined and slowly varying in such cases. This means that data acquisition is in general less susceptible to problems with the beam line optics. The approach does however rely on being able to measure sufficiently intense data so as to achieve the required increase in the signal to noise ratio.
In the MAD experiment performed here, as the sample crystals were strongly diffracting the exposure times for both the X31 and X11 experiments were several times smaller than the time required by the image plate detector to read-out and erase the image plate making the detector turn over time the rate limiting factor. The X-ray dose delivered to the sample crystal per data set was about four times larger on X11 whereas the overall experimental times per data set were similar on both beam lines. In this case no clear advantage was to be gained by using one or the other of the beam lines. However if the higher dynamic range detector had been made available on the X31 line one could have foreseen obtaining a still larger signal to noise ratio by quadrupling the X-ray dose without significantly lengthening the overall experimental time.
At the other extreme when sample crystals are very weakly diffracting the argument changes. When exposure times are significantly longer than the detector read-out and erase time, the length of the experiment is inversely proportional to the X-ray dose rate. This makes the X11 beam line favourable in terms of radiation damage. If however cryogenic cooling techniques are used then we may again favour X31 if the detector dynamic range is equivalent to that of X11. Discussion about the duration of a MAD experiment is driven mainly by the concern over radiation damage. A MAD experiment could be severely hampered if more than one sample crystal had to be used. The systematic errors from crystal absorption may introduce significant error into the anomalous difference measurements. The use of cryogenic techniques for sample preservation during data acquisition are for this reason particularly pertinent to MAD.
With the evolution of new high intensity sources such as the European Synchrotron Radiation Facility (ESRF) in Grenoble, France and the construction of intense wiggler beam lines at the EMBL outstation in Hamburg exposure times even for smaller weakly diffracting crystals may be comparable to or less than the read-out time. The rate limiting step will therefore be the detector read-out time. In these cases it would therefore seem advantageous to use very narrow bandpasses so that anomalous signals can be maximised. There are other practical considerations which concern the measurement of MAD data using the broad band pass approach. The highest intensity low resolution beam lines will in general be of the X11 design and will not offer easy tunability of the X-ray energy. Selection of the X-ray energies for data acquisition is therefore non-trivial. A beam line which offers a possibility to scan the monochromator is essential for MAD work.
For structures containing the same number and type of anomalous scatterers the anomalous diffraction ratios scale inversely as the square root of the number of non-hydrogen protein atoms as can be seen from Eqs. , and in Chapter . The observed diffraction ratios are directly proportional to the anomalous scattering factors and proportional to the square root of the number of anomalous scatterers. Since the anomalous scattering factors are mathematically equivalent to the occupancies of the heavy atoms we can conclude that it is advantageous to obtain derivatives where the occupancies of each anomalous scatterer are maximised as opposed to attempting to include a larger number of lower occupied anomalous scatterers . The case presented here was far from optimal in terms of the number of heavy atoms and their occupancies. The determination of the heavy atom positions was only made possible by the measurement of data sets (4 and 5) on the X31 beam line. In retrospect it is clear that these two data sets are essentially identical except for the differing contribution of the iridium atoms to the scattering factor. The difference in X-ray energy between the two data sets was . This meant that the contribution of normal dispersive effects () from all the protein atoms within the crystal gave a negligible change in the absorption coefficient ( at most). The largest contributors to sample crystal absorption are the iridium atoms themselves (by a factor of ). The Optical theorem relating and the atomic absorption coefficient of iridium means that within a small energy range similar values imply similar crystal absorption coefficients. This is verified for data sets 4 and 5 by the agreement in their overall scale factor which lie within of each other. In addition reflections having identical Miller indices have two factors in common between these data sets. i) they are recorded at the same position on the imaging plate detector to within a fraction of the pixel width (the average spatial displacement is and ii) assuming that the crystal orientation parameters remain constant between the data sets, they have identical path lengths through the sample crystal. This essentially means that any systematic changes introduced by the detector's response or from crystal and air absorption effects are the same for equivalent reflections measured at the two energies. Intensity differences between these reflections are therefore purely a result of the change in the real part of the anomalous scattering factor between the two energies, if radiation damage is neglected. White line permitting, the measurement of data at the equivalent of these two energies for other heavy atoms may provide one of the most systematic error free approaches to determining anomalous differences for use in either Patterson synthesis or direct methods. Systematic error is essentially removed by the experiment. These arguments are also relevant to the calculation of phases.
Some strategies for MAD data collection have been discussed by Bolin et al. . One suggestion made by the authors was that in some cases it may be advantageous to measure only those data sets which require a narrow band pass, i.e at the inflection points and the white line, on the necessary beam line and dedicate the available time to improving the counting statistics of that data. If necessary an additional data set at a remote X-ray energy could then be measured either on a conventional source or on a broad band pass synchrotron beam line. This is in fact how the best solution of the lysozyme iridium structure was determined. Data sets 4 and 5 measured on X31 were used in conjunction with data set 6 measured on X11. The solution had the lowest mean phase deviation of and resulted in an electron density map which had a correlation coefficient of calculated against the electron density of the refined derivative structure. After the application of density modification techniques (SQUASH) the mean phase error dropped to and the correlation coefficient increased to . It is interesting to note that solution 3 (data sets 3, 4 and 5) and solution 11 (data sets 6, 4 and 5) are equivalent in nearly all respects except for the difference in between data set 3 and 6. Their contributions to phasing from Bijvoet differences are similar as demonstrated by their respective values of . We can therefore conclude that the increase in correlation coefficient from 0.505 to 0.544 is principally due to the increased contrast in . The inclusion of more than three data sets into the phasing analysis did not significantly improve upon the results discussed here. It may therefore be prudent in future MAD experiments to concentrate efforts on measuring three X-ray energies only and attempt to reduce statistical error in the data.
The presence of a white line feature at the absorption edge of the heavy atom in a protein has been central to many of the aspects of this thesis. It is however still true that the majority of protein derivatives prepared nowadays contain heavy atoms which have an insignificant or no white line feature such as Pt and Hg. The binding of the iridium atoms to lysozyme experienced here can by no means be considered optimal for phasing by the MAD method. Even when the MIR approach is taken multiple sites with low, variable occupancies pose a difficult problem. Indeed the uninterpretability of the anomalous Patterson maps presented earlier may well have persuaded a crystallographer searching for an isomorphous derivative to `throw away' the derivative and move on to try another compound. This non-specificity of binding may be one reason why isomorphous derivatives are rarely prepared with heavy atoms such as iridium, osmium and those with lower atomic numbers. If anomalous or isomorphous difference Patterson maps provide no clue to the presence of heavy atoms the following approach could be considered. If the sizes of the observed Bijvoet ratios lie above the level of statistical error this would suggest that heavy atoms have bound to the protein. A MAD experiment performed at the two white line inflection points and the use of direct methods with the dispersive anomalous differences may in such cases provide the most convincing evidence for the presence or absence of heavy atoms in the structure. This is costly in terms of experimental synchrotron time but may be a more realistic option as the availability of synchrotron radiation to the protein crystallography community increases.
Were the experiment performed here to be repeated the, following points would be considered. When measuring data on the rising and falling edges of the white line, great care would be taken to ensure that the values of at both energies were matched, thus ensuring that the heavy atom absorption coefficients are also matched at least to within the error margin set by the calibration apparatus, i.e. . Secondly these two data sets would be the first measured as they should provide an accurate means of checking for the presence or otherwise of heavy atoms in significant proportion as discussed above. An additional strategy would also be adopted while recording the Friedel mates for these data sets. To further reduce the effects of crystal absorption on these measurements inverse beam geometry would be used, where and its true Friedel mate are measured, i.e. slices of reciprocal space separated by are measured. Following such a strategy would ensure that each reflection and its true Friedel mate were recorded at two energies with almost identical absorption corrections. The third X-ray energy could either be chosen to be at the white line maximum or at a remote energy far above the absorption edge. It is tentatively suggested that the measurement of a third data set at the white line maximum may be advantageous since the paths travelled by the diffracted X-rays through the sample crystal will be almost identical to those for the data measured at the rising and falling edges since their Bragg angles would have barely changed. This implies that the absorption could be corrected for by the use of a single scaling factor for all diffracted rays to bring the data on to a scale which is the same as that for the other two data sets. If the radiation damage was negligible, for instance if cryogenic cooling was available and effective, one could imagine applying a single scale factor the the data set at the maximum and not performing any further scaling of the three data sets. Scaling of the individual images would however still be necessary within one data set for the reasons given earlier in Sec. .