A Bayesian Approach to Laue Diffraction Analysis and its Potential for Time-Resolved Protein Crystallography

A solution to the energy-overlap problem in Lane diffraction is described that does not require redundancy in the measurements. The new method follows a Bayesian approach with multidimensional probability density functions. The only assumption made is the validity of Wilson statistics. The intensity components of reflection multiplets are deconvoluted and estimates of their precision are obtained. The Laue patterns are processed to their physically relevant wavelength-dependent resolution limit; no `soft parameters' are involved. The Bayesian method may also be applied to deconvoluting spatial overlaps. The power of the method is demonstrated by a test application to bovine trypsin. The completeness at low and medium resolution as well as at very high resolution (1.4 Å) is enhanced very substantially as compared with standard procedures; the `low-resolution hole' problem is solved. As a consequence, the contrast in electron-density maps improves so far that they become comparable in quality with maps from monochromatic data at high resolution. The new method is Of interest for all types of Laue diffraction experiments, in particular for single-shot time-resolved studies on short time scales. Simulation calculations for single-shot Laue conditions and for the disorder-order transition in trypsinogen as a model system demonstrate the potential power of applications in protein crystallography that combine high resolution and Bayesian processing.