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iterative projection algorithms in protein crystallography. II. Application

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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iterative projection algorithms for reconstructing compact binary images

Iterative projection algorithms for reconstructing compact b...

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Conference on Image Reconstruction from Incomplete Data V

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

ISBN: (纸本)9780819472960

An algorithm is described for reconstructing compact binary images from limited Fourier amplitude data. This problem arises in macromolecular crystallography where one wishes to reconstruct the molecular envelope from crystal x-ray diffraction amplitudes using a solvent contrast series. Such data are the amplitude of the Fourier transform of all object that has a constant electron density within the boundary of the molecule and zero outside. The image is thus binary and compact, but, the data are available only within a limited resolution range in Fourier space and are undersampled. The problem is solved Using all iterative projection algorithm;a class of algorithm used to solve inverse problems for which the solution is subject to a, number of constraints that, represent a priori information and the data. Unfortunately, these algorithms experience convergence difficulties if one or more of the constraints are non-convex, which is the case for all the constraint's in this problem. We solve the problem by constructing appropriate projection operators and implementing the difference map projection algorithm. Simulations axe used to study convergence behaviour of the algorithm.

关键词： Phase retrieval Image reconstruction iterative projection algorithms X-ray crystallography

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iterative projection algorithms for solving constraint satisfaction problems: Effect of constraint convexity

Iterative projection algorithms for solving constraint satis...

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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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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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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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Shape transform phasing of edgy nanocrystals

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2019年第2期75卷 239-259页

作者： Chen, J. P. J. Donatelli, J. J. Schmidt, K. E. Kirian, R. A. Arizona State Univ Dept Phys Tempe AZ 85287 USA Lawrence Berkeley Natl Lab Ctr Adv Math Energy Res Applicat Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Dept Appl Math Berkeley CA 94720 USA

Diffraction patterns from small protein crystals illuminated by highly coherent X-rays often contain measurable interference signals between Bragg peaks. This coherent 'shape transform' signal introduces enough additional information to allow the molecular densities to be determined from the diffracted intensities directly, without prior information or resolution restrictions. However, the various correlations amongst molecular occupancies/vacancies at the crystal surface result in a subtle yet critical problem in shape transform phasing whereby the sublattices of symmetry-related molecules exhibit a form of partial coherence amongst lattice sites when an average is taken over many crystal patterns. Here an iterative phase retrieval algorithm is developed which is capable of treating this problem;it is demonstrated on simulated data.

关键词： iterative projection algorithms shape transforms shape transform phasing phase retrieval nanocrystals serial femtosecond crystallography X-ray free-electron lasers

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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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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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The phase problem for two-dimensional crystals. II. Simulations

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2018年第5期74卷 537-544页

作者： Arnal, Romain D. Zhao, Yun Mitra, Alok K. Spence, John C. H. Millane, Rick P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch New Zealand Arizona State Univ Dept Phys Tempe AZ 85287 USA Univ Auckland Sch Biol Sci Auckland New Zealand

Phasing of diffraction data from two-dimensional crystals using only minimal molecular envelope information is investigated by simulation. Two-dimensional crystals are an attractive target for studying membrane proteins using X-ray free-electron lasers, particularly for dynamic studies at room temperature. Simulations using an iterative projection algorithm show that phasing is feasible with fairly minimal molecular envelope information, supporting recent uniqueness results for this problem [Arnal & Millane (2017). Acta Cryst. A73, 438-448]. The effects of noise and likely requirements for structure determination using X-ray free-electron laser sources are investigated.

关键词： phase problem phase retrieval two-dimensional crystals XFELs ab initio phasing iterative projection algorithms membrane proteins

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