The Use of Partial Reflections for Scaling and Averaging X-ray Area-Detector Data

Abstract

Frozen crystals of proteins, nucleic acids or other biological macromolecules often have mosaic spreads comparable to the maximum useful oscillation angles. It is, therefore, necessary to develop scaling methods that are independent of the exclusive use of full reflections. The Hamilton, Rollett and Sparks [Acta Cryst(1965),18, 129–130] procedure for scaling frames of X-ray area-detector data has been generalized to utilize partial reflections by adding intensities of partial reflections from consecutive frames (method 1) or by correcting intensities of partial reflections, using a model to calculate the reflection partiality (method 2). Both methods have been applied to scaling and averaging of data-sets collected on crystals of biological macromolecules. The agreement factors of the scaled data are better when using method 1, although it often fails when there are rotation gaps between successive images or when the data redundancy is low. Method 2 is more stable and versatile, allowing scaling of data-sets with incompletely measured reflections and low redundancy. The major drawback of method 2 is its sensitivity to inaccuracy in calculated partiality. The actual values of the scale factors obtained with the two methods are within 5%. However, when the true value of the scale factor changes dramatically between consecutive frames (e.g.due to beam dumps and refills at a synchrotron source), the results of the two methods can differ by as much as 15% because method 1 produces physically wrong results. The scaling algorithm implemented in the commercially available programSCALEPACKis vulnerable to the same problems as method 1.