Estimating unobserved reflection intensities in Laue diffraction by the maximum-entropy method

In protein crystallography, the use of low-resolution reflections is important in defining the molecular mask and polypeptide backbone. However, in Laue data collection, the loss of low-resolution reflection data (>2d_min) can be as high as 40-50%, even after the deconvolution of multiples. To estimate the reflection intensities that are not recorded in data collection, a new method is presented based on maximizing the entropy of the Patterson function subject to the constraints imposed by the intensities of the observed reflections. The method has been tested with Laue diffraction data from hen egg-white lysozyme. All unobserved reflections within 5 Å resolution were estimated, and their inclusion in the electron-density-map calculation significantly improved the connectivity. This method could also be applied to improve the completeness of monochromatic data.