Scaling of data from different wavelengths.



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Scaling of data from different wavelengths.

The image scaling procedure described above should only be applied to sets of oscillation images collected at one wavelength. This is because reflections which are redundant by symmetry are only strictly equivalent when they have all been measured at the same X-ray wavelength whereas symmetry equivalent reflection at several wavelengths should not necessarily be equal due to the changes in scattering power of any heavy atoms in the structure. Scaling between data sets which have been measured at several wavelengths cannot therefore use scale factors based upon the comparison of redundant reflections.

Even so most methods which are currently used for inter-wavelength scaling can only be seen as approximate procedures for the same reason. That is, at different wavelengths, particularly around a heavy atom absorption edge the resultant atomic scattering factor of the heavy atom changes. This in turn has the effect of changing the average intensity of the protein diffraction pattern, [117], albeit by a small amount (typically a few percent). Without precise knowledge of the positions and occupancies of the heavy atoms in the structure it is not possible at this stage of the analysis to do any better than simply scale the data sets measured at different wavelengths according to their average intensities and ignore the changes in the overall scattering power of the constituent atoms. Refinement of the approximate scale factors is usually done at a later stage when some information about the heavy atom partial structure is available.

The program used during this work for inter wavelength scaling is SCALEIT [31] from the CCP4 program suite [22]. Again one data set is chosen as a reference to which the other sets will be scaled using the multiplicative factor [23]

where l denotes the data set number. The temperature factor is given here in its anisotropic form where are the elements of the symmetric temperature factor matrix accounting for any anisotropic dependence of the average intensity as a function of resolution. is an overall scale factor.

Before refinement of and for the th data set an approximate scale factor is calculated and applied for the derivative set of structure factors using

where are the set of reference structure factors. The procedure followed for the refinement is similar to that devised by Fox and Holmes [34] where the function to be minimised is defined as

where is the inverse scale factor, is the error attached to and the sums are taken over all reflections, and all data sets . is defined by



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Gwyndaf Evans
Fri Oct 7 15:42:16 MET 1994