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International Conference on Image and Vision Computing New Zealand (IVCNZ)

作者： Millane, Rick P. Taylor, Joshua T. Arnal, Romain D. Wojtas, David H. Clare, Richard M. Univ Canterbury Computat Imaging Grp Dept Elect & Comp Engn Christchurch New Zealand

ISBN: (纸本)9781728141879

Many inverse problems in imaging involve solving an optimization problem. In many cases, the problem is high-dimensional and non-convex, requiring the solution of a difficult, non-convex, global optimization problem. Such problems can be made tractable by enforcing hard constraints and treating the problem as a constraint satisfaction problem to locate a global solution, which can be refined using soft constraints if necessary. iterative projection algorithms are an effective way of solving non-convex constraint satisfaction problems. The difficulty of solution, and the performance of these algorithms, depends on the degree of non-convexity of the constraints. Here we use simulations of a phase retrieval problem to study the performance of an iterative projection algorithm, the difference map algorithm, to study performance as a function of non-convexity.

关键词： iterative projection algorithms constraint satisfaction phase retrieval inverse problems optimization

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iterative projection algorithms in protein crystallography. II. Application

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2015年第4期71卷 451-459页

作者： Lo, Victor L. Kingston, Richard L. Millane, Rick P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch 1 New Zealand Univ Auckland Sch Biol Sci Auckland 1 New Zealand

iterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.

关键词： iterative projection algorithms phasing density modification phase determination

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iterative projection algorithms in protein crystallography. I. Theory

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2013年第5期69卷 517-527页

作者： Millane, Rick P. Lo, Victor L. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch 1 New Zealand

A general class of iterative projection algorithms is described and proposed as a tool for phasing in protein crystallography in order to improve the radius of convergence over that of conventional density-modification algorithms. Their relationship to conventional density modification is described. The common iterative projection algorithms, their convergence properties and their application to protein crystallography are described. These algorithms offer the possibility of protein structure determination starting with only information on the molecular envelope and low-order non-crystallographic symmetry.

关键词： iterative projection algorithms phasing density modification phase determination

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Crystal structure via fluctuation scattering

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IUCRJ 2024年第4期11卷 538-555页

作者： Adams, Patrick Greaves, Tamar L. Martin, Andrew V. RMIT Univ Melbourne Vic 3000 Australia

Crystallography is a quintessential method for determining the atomic structure of crystals. The most common implementation of crystallography uses single crystals that must be of sufficient size, typically tens of micrometres or larger, depending on the complexity of the crystal structure. The emergence of serial data-collection methods in crystallography, particularly for time-resolved experiments, opens up opportunities to develop new routes to structure determination for nanocrystals and ensembles of crystals. Fluctuation X-ray scattering is a correlation-based approach for single-particle imaging from ensembles of identical particles, but has yet to be applied to crystal structure determination. Here, an iterative algorithm is presented that recovers crystal structure-factor intensities from fluctuation X-ray scattering correlations. The capabilities of this algorithm are demonstrated by recovering the structure of three small-molecule crystals and a protein crystal from simulated fluctuation X-ray scattering correlations. This method could facilitate the recovery of structure-factor intensities from crystals in serial crystallography experiments and relax sample requirements for crystallography experiments.

关键词： serial crystallography correlated fluctuations molecular crystals fluctuation X-ray scattering iterative projection algorithms X-ray cross-correlation analysis structure-factor intensities Bragg peak intensity.

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Direct phasing algorithm for protein crystals with high solvent content using low-resolution diffraction data

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ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2023年第7期79卷 610-623页

作者： Jiang, Yu-Meng Miao, Han Pan, Xin-Yu Wang, Qi Dong, Zheng Geng, Zhi Dong, Yu-Hui Chinese Acad Sci Beijing Synchrotron Radiat Facil Inst High Energy Phys Beijing 100049 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

Over the past decade, iterative projection algorithms, an effective approach to recovering phases from a single intensity measurement, have found application in protein crystallography to directly surmount the 'phase problem'. However, previous studies have always assumed that some prior knowledge constraints (i.e. a low-resolution envelope about the protein structure in the crystal cell or histogram matching requiring a similar density distribution to the target crystal) must be known for successful phase retrieval, thus hindering its widespread application. In this study, a novel phase-retrieval workflow is proposed that eliminates the need for a reference density distribution by utilizing low-resolution diffraction data in phasing algorithms. The approach involves randomly assigning one out of 12 possible phases at 30 degrees intervals (or two for centric reflections) to produce an initial envelope, which is then refined through density modification after each run of phase retrieval. To evaluate the success of the phase-retrieval procedure, information entropy is introduced as a new metric. This approach was validated using ten protein structures with high solvent content, demonstrating its effectiveness and robustness.

关键词： low-resolution envelopes iterative projection algorithms phasing phase determination

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Ab initio reconstruction from one-dimensional crystal diffraction data

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2022年第3期78卷 249-261页

作者： Arnal, Romain D. Millane, Rick P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch New Zealand

Filamentary and rod-like assemblies are ubiquitous in biological systems, and single such assemblies can form one-dimensional (1D) crystals. New, intense X-ray sources, such as X-ray free-electron lasers, make it feasible to measure diffraction data from single 1D crystals. Such experiments would present some advantages, since cylindrical averaging of the diffraction data in conventional fiber diffraction analysis is avoided, there is coherent signal amplification relative to single-particle imaging, and the diffraction data are oversampled compared with those from a 3D crystal so that the phase problem is better determined than for a 3D crystal [Millane (2017). Acta Cryst. A73, 140-150]. Phasing of 1D crystal diffraction data is examined, by simulation, using an iterative projection algorithm. Ab initio phasing is feasible with realistic noise levels and little envelope information is required if a shrink-wrap algorithm is also incorporated. Some practical aspects of the proposed experiments are explored.

关键词： 1D crystals phase problem iterative projection algorithms shrink-wrap algorithm filaments

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Macromolecular phasing using diffraction from multiple crystal forms

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2021年第1期77卷 19-35页

作者： Metz, Markus Arnal, Romain D. Brehm, Wolfgang Chapman, Henry N. Morgan, Andrew J. Millane, Rick P. Univ Hamburg Dept Phys D-22761 Hamburg Germany Deutsch Elektronen Synchrotron DESY Ctr Free Electron Laser Sci D-22607 Hamburg Germany Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch New Zealand Hamburg Ctr Ultrafast Imaging Hamburg Germany Univ Melbourne ARC Ctr Excellence Adv Mol Imaging Parkville Vic Australia

A phasing algorithm for macromolecular crystallography is proposed that utilizes diffraction data from multiple crystal forms - crystals of the same molecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the molecular envelope and positional relationships between the molecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing.

关键词： multiple crystal forms ab initio phasing iterative projection algorithms X-ray free-electron lasers XFELs

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Inter-Bragg crystallographic phase retrieval from shape transforms, stacking faults and substitutional disorder

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ULTRAMICROSCOPY 2023年第1期249卷 113728页

作者： Chen, J. P. J. Pande, K. Donatelli, J. J. Martin, A. V. Ayyer, K. Chapman, H. N. Bean, R. Schmidt, K. E. Kirian, R. A. Arizona State Univ Dept Phys Tempe AZ 85287 USA Univ Canterbury Dept Elect & Comp Engn Christchurch 8041 New Zealand Lawrence Berkeley Natl Lab Ctr Adv Math Energy Res Applicat Berkeley CA 94720 USA RMIT Univ Sch Sci Melbourne Vic 3000 Australia Max Planck Inst Struct & Dynam Matter D-22761 Hamburg Germany Ctr Free Electron Laser Sci D-22761 Hamburg Germany European XFEL D-22869 Schenefeld Germany

One of the brilliant ideas of John Spence when he saw the first diffraction patterns from the Linac Coherent Light Source was that one could solve the crystallographic phase problem by utilising the intensities between Bragg peaks. Because these intensities are due to the Fourier transform of the shape of the crystal, the approach came to be known as "shape-transform phasing."Shape-transform phasing was developed over the next ten years and formed the basis for many other interesting ideas and pursuits. Here we describe the current best implementation of the original idea using a lattice occupancy formalism and show that certain types of crystal defects can also be modelled via this approach, allowing the molecular structure to be recovered from the additional information offered by the inter-Bragg intensities from these crystal defects.

关键词： Shape transform phasing Lattice occupancy model Crystal disorder Phase retrieval iterative projection algorithms

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Progress towards imaging biological filaments using X-ray free-electron lasers 35

Progress towards imaging biological filaments using X-ray fr...

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35th International Conference on Image and Vision Computing New Zealand (IVCNZ)

作者： Arnal, Romain D. Wojtas, David H. Millane, Rick P. Univ Canterbury Computat Imaging Grp Dept Elect & Comp Engn PB 4800 Christchurch 8140 New Zealand

ISBN: (纸本)9781728185798

X-ray free-electron lasers (XFELs) are opening new frontiers in structural biology. The extreme brilliance of these highly coherent X-ray sources allows for ever smaller crystals to be used while still being able to diffract enough photons to provide sufficient data for structure determination. Biomolecules arranged into filaments are an important class of targets that are expected to greatly benefit from the continuous improvements in XFEL capabilities. Here we first review some of the state-of-the-art research in using XFELs for the imaging of biological filaments. Extrapolating current trends towards single particle imaging, we consider an intermediate case where diffraction patterns from single filaments can be measured and oriented to form a 3D dataset. Prospects for using iterative projection algorithms (IPAs) for ab initio phase retrieval with such data collected from single filaments are illustrated by the reconstruction of the electron density of a B-DNA structure from simulated, noisy XFEL data.

关键词： X-ray free electron laser fibrils filaments 1D crystal phase problem phase retrieval iterative projection algorithms structural biology

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Characteristics of iterative projection algorithms

Characteristics of iterative projection algorithms

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Conference on Image Reconstruction from Incomplete Data VII

作者： Lo, Victor Millane, Rick P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch 1 New Zealand

A brief description of various iterative projection algorithms and the relationships between them is given, along with some possible reasons for their ability to solve non-convex problems. An empirical model of their ... 详细信息

ISBN: (纸本)9780819492173

关键词： iterative projection algorithms

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