BAYESIAN APPROACH TO THE ANALYSIS OF TIME-RESOLVED PROTEIN LAUE DIFFRACTION DATA. G.P. Bourenkov, A.N. Popov and H.D. Bartunik, Max-Planck Research Unit for Structural Molecular Biology, Protein Dynamics Group, MPG-ASMB c/o DESY, Notkestraße 85, 22603 Hamburg, Germany

A new method of deconvoluting overlapping reflections in protein Laue diffraction patterns solves the problem of the "low resolution hole" without the need for redundancy. It is therefore of particular interest for single-shot time resolved studies. For the first time, non-cyclic reactions may be investigated by Laue diffraction on short time scales. In test application to orthorhombic bovine trypsin, the new method improved the resolution from 1.7 Å to 1.4 Å as compared to standard processing methods. It provided high completeness over the whole resolution range < 7Å. The contrast in electron density maps calculated with the Laue structure factors improved dramatically; the Laue maps are of similar quality as maps that are calculated with monochromatic high-resolution data. The method follows a Bayesian statistical approach. A-priori given information about structure factor amplitudes obeying Wilson's distributions is employed. The (single or redundant) measurement of the intensity of an energetic or spatial overlap yields the normal multivariate probability density function (PDF) of the intensities of the components. This information is associated with the prior PDF through the Bayes theorem. The moments of the resulting posterior PDF give expected values for the component intensities, the structure factor amplitudes and their uncertainties. These moments are always finite and positive, even if the initial normal matrix is degenerate. Due to the nature of the wavelength normalisation curve and the dependence of the scattering power on resolution, accurate estimates are obtained for the structure factors of the components, even in the case of a single observation of an energetic overlap. Furthermore, all data can be processed to the physically relevant wavelength-dependent diffraction limit. No "soft parameters" are involved. The power of the method may be further enhanced, if a (roughly) approximate structural model is available, e.g., of an initial state of a reaction. Then, conditional prior probability density functions may be employed.