Reconstruction methods In free electron laser X-ray diffraction

One of the most important issues in femtosecond free electron laser X-ray diraction is to reconstruct the 3D charge density of molecule from a mass of diraction snapshots. In order to determine the orientation of single molecule from diraction patterns, we rst determine the moments and products of inertia of this from 2D experiment data (diraction patterns or EM images to obtain the elements of the inertia tensor. If diraction patterns from uniformly random orientations or some preferred orientations are collected, the principal axes of the molecule can be extracted, together with the Euler angles which relate the principal axes of the molecule to the laboratory frame axes. This is achieved by nding the maximum and minimum values for the measured moments from many single-molecule patterns. Simulations for GroEL protein indicates that the calculation of the autocorrelation help eliminate the Poisson noise in Cryo- EM images and can make correct orientation determination. The eect of water jacket surrounding the protein molecule is studied based on molecular dynamics simulation result. The intensities from water and interference is found to suppress those from protein itself. A method is proposed and applied to the simulation data to show the possibility for it to overcome the water background problem. The scattering between Bragg re ections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if suciently nely-sampled diraction data are available from many nanocrystals of dierent sizes lying in the same orientations without knowledge of the distribution of particle size or requiring atomic-resolution data. Triple correlation of the diraction patterns are made use of to reconiii