Holographic single particle imaging for weakly scattering, heterogeneous nanoscale objects

Single particle imaging (SPI) at X-ray free electron lasers (XFELs) is a technique to determine the 3D structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random orientations. Millions of low signal-to-noise diffraction patterns with unknown orientation are collected during an X-ray SPI experiment. The patterns are then analyzed and merged using a reconstruction algorithm to retrieve the full 3D-structure of particle. The resolution of reconstruction is limited by background noise, signal-to-noise ratio in diffraction patterns and total amount of data collected. We recently introduced a reference-enhanced holographic single particle imaging methodology [Optica 7,593-601(2020)] to collect high enough signal-to-noise and background tolerant patterns and a reconstruction algorithm to recover missing parameters beyond orientation and then directly retrieve the full Fourier model of the sample of interest. Here we describe a phase retrieval algorithm based on maximum likelihood estimation using pattern search dubbed as MaxLP, with better scalability for fine sampling of latent parameters and much better performance in the low signal limit. Furthermore, we show that structural variations within the target particle are averaged in real space, significantly improving robustness to conformational heterogeneity in comparison to conventional SPI. With these computational improvements, we believe reference-enhanced SPI is capable of reaching sub-nm resolution biomolecule imaging

Understanding conformational dynamics from macromolecular crystal diffuse scattering

All macromolecular crystals contain some extent of disorder. The diffraction from such crystals contains diffuse scattering in addition to Bragg peaks and this scattering contains information about correlated displacements in the constituent molecules. While much work has been performed recently in decoding the dynamics of the crystalline ordering, the goal of understanding the internal dynamics of the molecules within a unit cell has been out-of-reach. In this article, we propose a general framework to extract the internal conformational modes of a macromolecule from diffuse scattering data. We combine insights on the distribution of diffuse scattering from short- and long-range disorder with a Bayesian global optimization algorithm to obtain the best fitting internal motion modes to the data. To illustrate the efficacy of the method, we apply it to a publicly available dataset from triclinic lysozyme. Our mostly parameter-free approach can enable the recovery of a much richer, dynamic structure from macromolecular crystallography

Ab Initio Spatial Phase Retrieval via Fluorescence Intensity Triple Correlations

A complete method for ab initio phase retrieval via spatial intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of classical incoherent emitters

An encryption-decryption framework for validating single-particle imaging

We propose an encryption–decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes’ ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design

Matrix product solution to an inhomogeneous multi-species TASEP

We study a multi-species exclusion process with inhomogeneous hopping rates. This model is equivalent to a Markov chain on the symmetric group that corresponds to a random walk in the affine braid arrangement. We find a matrix product representation for the stationary state of this model. We also show that it is equivalent to a graphical construction proposed by Ayyer and Linusson, which generalizes Ferrari and Martin's construction

Remarks on the multi-species exclusion process with reflective boundaries

We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the number of particles of each kind. We find matrices connecting the blocks in a matrix product form. The procedure (generalized matrix ansatz) to verify that a matrix intertwines blocks of the Markov matrix was introduced in the periodic boundary condition, which starts with a local relation [Arita et al, J. Phys. A 44, 335004 (2011)]. The solution to this relation for the reflective boundary condition is much simpler than that for the periodic boundary condition

Transfer matrices for the totally asymmetric exclusion process

We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L-1,L}$ and $\tilde{T}_{L-1,L}$ that intertwine the Markov matrices of consecutive system sizes: $\tilde{T}_{L-1,L}M_{L-1}=M_{L}T_{L-1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.Comment: 7 page

Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence

In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wavenumber shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimension, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the near-by shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.Comment: 10 pages, Revtex

Recovering structure from many low-information 2-D images of randomly-oriented samples

Abstract. New sources and detectors are allowing scientists to look at matter with finer spatial and temporal resolutions. These experiments can produce data that are a series of severely Poisson limited snap-shots of randomly oriented samples. An extreme case of this is destructive imaging of single particles with an x-ray free-electron laser -many frames are needed for a reconstruction, but there is no a priori information associated with the frames about particle orientation. We use Cornell's Pixel Array Detectors (PADs) to examine the practical limits of an expectation maximization (EM) algorithm designed to deal with extremely low-fluence data, having just a few photons per frame. We demonstrate image reconstruction of a high-contrast sample using hundreds of thousands of randomly oriented frames with an average x-ray photon occupancy as low as 2.5 photons per frame. Practical aspects of reducing low-fluence data, such as thresholding and noise limits, will be discussed for high-and low-contrast samples; and data collected in the presence of significant background signal