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

Abstract

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 singleparticle 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.single-particle imaging | multitiered iterative phasing | structure determination S ingle-particle X-ray diffraction aims to determine the structures of biological molecules from an ensemble of diffraction patterns, each collected from a single particle per shot. Particles are delivered to the beam at random orientations through either a liquid medium (1) or aerosolization (2). Large-scale experimental facilities, such as the Linac Coherent Light Source (3), have been developed to perform these experiments, with initial results indicating the feasibility of single-particle diffraction as a viable technique to address challenges in the health, material, and energy sciences (4, 5).A fundamental challenge in single-particle imaging is that the orientation of each imaged particle is unknown and must be recovered to determine structural information. Additionally, many biological samples display conformational flexibility and may exist in one of many possible structural states. To account for varying structural states and avoid a loss of resolution due to averaging of states, the diffraction patterns may need to be classified to the correct state. Furthermore, single particles scatter very few photons; hence the images are heavily contaminated by shot noise, often with less than a photon per Shannon pixel at high scattering angles.Current approaches typically determine states, orientations, and structures in separate consecutive steps. Classification work includes manifold mapping (6), spectral clustering (7), principal component analysis, and support vector machines (8). Orientation methods include common curve approaches (9-12), expectation maximization (13-15), and manifold embedding (16)(17)(18)(19). Once images are classified, oriented, and assemb...

X-Ray Free-Electron Lasers for the Structure and Dynamics of Macromolecules

“…The ratio of the volume of the object of interest to background-producing solvent can be increased by increasing particle density, to illuminate several objects per snapshot pattern. The short snapshot exposures of FEL pulses, shorter than rotation times of molecules, gives coherent diffraction patterns that can be interpreted through a correlation analysis to gain the 3D structure-factor dataset of the single particle (136,137,138,139).…”

Steerable ePCA: Rotationally Invariant Exponential Family PCA

“…(22) and D (k) in eq. (25) (sePCA) 12 Recolor the covariance matrix S 13 Compute the scaling coefficientsα in Eq. (26) and keep components withα > 0 (sePCA) 14 Scale the covariance matrix…”

cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs

“…They thus have a wealth of applications in engineering and scientific computing, including image reconstruction from off-grid Fourier data (e.g. MRI gridding [1], optical coherence tomography [2], cryo electron microscopy [3]- [7], radioastronomy [8], coherent diffraction X-ray imaging [9]); wave diffraction [10]; partial differential equations [11], [12]; and long-range interactions in molecular [13] and particle dynamics [14]. For reviews, see [15]- [18].…”