Page History

Abstract: The development of X-ray free-electron lasers has enabled new experiments to study uncrystallized biomolecules that were previously infeasible with traditional X-ray sources. One such emerging experimental technique is fluctuation X-ray scattering (FXS), where one collects a series of diffraction patterns, each from multiple particles in solution, using ultrashort X-ray pulses that allow snapshots to be taken below rotational diffusion times of the particles. The resulting images contain angularly varying information from which angular correlations can be computed, yielding several orders of magnitude more information than traditional solution scattering methods. However, determining molecular structure from FXS data introduces several challenges, since, in addition to the classical phase problem, one must also solve a hyper-phase problem to determine the 3D intensity function from the correlation data. In another technique known as single-particle diffraction (SPD), several diffraction patterns are collected, each from an individual particle. However, the samples are delivered to the beam at unknown orientations and may also be present in several different conformational states. In order to reconstruct structural information from SPD, one must determine the orientation and state for each image, extract an accurate 3D model of the intensity function from the images, and solve for the missing complex phases, which are not measured in diffraction images.

In this talk, we present the multi-tiered iterative phasing (M-TIP) algorithm for determining molecular structure from both FXS and SPD data. This algorithm breaks up the associated reconstruction problems into a set of simpler subproblems that can be efficiently solved by applying a series of projection operators. These operators are combined in a modular iterative framework which is able to simultaneously determine missing parameters, the 3D intensity function, the complex phases, and the underlying structure from the data. In particular, this approach is able to leverage prior knowledge about the structural model, such as shape or symmetry, to obtain a reconstruction from very limited data with excellent global convergence properties and high computational efficiency. We show results from applying M-TIP to determine molecular structure from both simulated data and experimental data collected at the Linac Coherent Light Source (LCLS).