Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase

Significance Single-particle diffraction is an emerging technique in which diffraction images are collected from individual particles, and is used to study molecular structure from multiple conformational states that may be inaccessible through other methods. However, determining structure from these experiments is challenging, since orientations and states of imaged particles are unknown and images are highly contaminated with noise. Furthermore, the number of useful images is often limited by achievable single-particle hit rates, currently around 0.1%. We introduce an iterative projection framework to simultaneously determine orientations, states, and molecular structure from limited single-particle data by leveraging structural constraints throughout the reconstruction. This framework offers a potential pathway to increasing the amount of information that can be extracted from single-particle diffraction. Free-electron lasers now have the ability to collect X-ray diffraction patterns from individual molecules; however, each sample is delivered at unknown orientation and may be in one of several conformational states, each with a different molecular structure. Hit rates are often low, typically around 0.1%, limiting the number of useful images that can be collected. Determining accurate structural information requires classifying and orienting each image, accurately assembling them into a 3D diffraction intensity function, and determining missing phase information. Additionally, single particles typically scatter very few photons, leading to high image noise levels. We develop a multitiered iterative phasing algorithm to reconstruct structural information from single-particle diffraction data by simultaneously determining the states, orientations, intensities, phases, and underlying structure in a single iterative procedure. We leverage real-space constraints on the structure to help guide optimization and reconstruct underlying structure from very few images with excellent global convergence properties. We show that this approach can determine structural resolution beyond what is suggested by standard Shannon sampling arguments for ideal images and is also robust to noise.

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