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245
Situs: A package for docking crystal structures into lowresolution maps from electron microscopy
 J. Struct. Biol
, 1999
"... Threedimensional image reconstructions of largescale protein aggregates are routinely determined by electron microscopy (EM). We combine lowresolution EM data with highresolution structures of proteins determined by xray crystallography. A set of visualization and analysis procedures, termed the ..."
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Cited by 109 (7 self)
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Threedimensional image reconstructions of largescale protein aggregates are routinely determined by electron microscopy (EM). We combine lowresolution EM data with highresolution structures of proteins determined by xray crystallography. A set of visualization and analysis procedures, termed the Situs package, has been developed to provide an efficient and robust method for the localization of protein subunits in lowresolution data. Topologyrepresenting neural networks are employed to vectorquantize and to correlate features within the structural data sets. Microtubules decorated with kinesinrelated ncd motors are used as model aggregates to demonstrate the utility of this package of routines. The precision of the docking has allowed for the extraction of unique conformations of the macromolecules and is limited only by the reliability of the underlying structural data. 1999 Academic Press Key Words: topology representing neural networks; multiresolution; visualization; macromolecular
Weeds A. Cofilin changes the twist of Factin: implications for actin filament dynamics and cellular function
 J Cell Biol
, 1997
"... Abstract. Cofilin is an actin depolymerizing protein found widely distributed in animals and plants. We have used electron cryomicroscopy and helical reconstruction to identify its binding site on actin filaments. Cofilin binds filamentous (F)actin cooperatively by bridging two longitudinally assoc ..."
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Cited by 71 (1 self)
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Abstract. Cofilin is an actin depolymerizing protein found widely distributed in animals and plants. We have used electron cryomicroscopy and helical reconstruction to identify its binding site on actin filaments. Cofilin binds filamentous (F)actin cooperatively by bridging two longitudinally associated actin subunits. The binding site is centered axially at subdomain 2 of the lower actin subunit and radially at the cleft between subdomains 1 and 3 of the upper actin subunit. Our work has revealed a totally unexpected (and unique) property of cofilin, namely, its ability to change filament twist. As a consequence of this change in twist, filaments decorated with cofilin have much shorter ‘actin crossovers ’ (�75 % of those normally observed in Factin structures). Although their binding sites are distinct, cofilin and phalloidin do not bind simultaneously to Factin. This is the first demonstration of a protein that excludes another actinbinding molecule by changing filament twist. Alteration of Factin structure by cofilin/ADF appears to be a novel mechanism through which the actin cytoskeleton may be regulated or remodeled. Please address all correspondence to Dr. Amy McGough, Verna and
XMIPP: a new generation of an opensource image processing package for electron microscopy
, 2004
"... ..."
ANGULAR SYNCHRONIZATION BY EIGENVECTORS AND SEMIDEFINITE PROGRAMMING: ANALYSIS AND APPLICATION TO CLASS AVERAGING IN CRYOELECTRON MICROSCOPY
, 905
"... Abstract. The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles θ1,..., θn from m noisy measurements of their offsets θi − θj mod 2π. Of particular interest is angle recovery in the presence of many outlier measurements ..."
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Cited by 43 (17 self)
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Abstract. The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles θ1,..., θn from m noisy measurements of their offsets θi − θj mod 2π. Of particular interest is angle recovery in the presence of many outlier measurements that are uniformly distributed in [0,2π) and carry no information on the true offsets. We introduce an efficient recovery algorithm for the unknown angles from the top eigenvector of a specially designed Hermitian matrix. The eigenvector method is extremely stable and succeeds even when the number of outliers is exceedingly large. For example, we successfully estimate n = 400 angles from a full set of m = `400 ´ offset measurements of which 90 % are outliers in less than a second 2 on a commercial laptop. We use random matrix theory to prove that the eigenvector method q gives
Cryoelectron microscopy structure of an SH3 amyloid fibril and model of the molecular packing
 EMBO
, 1999
"... Amyloid fibrils are assemblies of misfolded proteins and are associated with pathological conditions such as Alzheimer’s disease and the spongiform encephalopathies. In the amyloid diseases, a diverse group of normally soluble proteins selfassemble to form insoluble fibrils. Xray fibre diffracti ..."
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Cited by 34 (0 self)
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Amyloid fibrils are assemblies of misfolded proteins and are associated with pathological conditions such as Alzheimer’s disease and the spongiform encephalopathies. In the amyloid diseases, a diverse group of normally soluble proteins selfassemble to form insoluble fibrils. Xray fibre diffraction studies have shown that the protofilament cores of fibrils formed from the various proteins all contain a crossbscaffold, with bstrands perpendicular and bsheets parallel to the fibre axis. We have determined the threedimensional structure of an amyloid fibril, formed by the SH3 domain of phosphatidylinositol39kinase, using cryoelectron microscopy and image processing at 25 Å resolution. The structure is a double helix of two protofilament pairs wound around a hollow core, with a helical crossover repeat of ~600 Å and an axial subunit repeat of ~27 Å. The native SH3 domain is too compact to fit into the fibril density, and must unfold to adopt a longer, thinner shape in the amyloid form. The 20340Å protofilaments can only accommodate one pair of flat bsheets stacked against each other, with very little interstrand twist. We propose a model for the polypeptide packing as a basis for understanding the structure of amyloid fibrils in general.
ThreeDimensional Structure Determination from Common Lines in CryoEM by Eigenvectors and Semidefinite Programming ∗
"... Abstract. The cryoelectron microscopy reconstruction problem is to find the threedimensional (3D) structure of a macromolecule given noisy samples of its twodimensional projection images at unknown random directions. Present algorithms for finding an initial 3D structure model are based on the “a ..."
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Cited by 33 (15 self)
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Abstract. The cryoelectron microscopy reconstruction problem is to find the threedimensional (3D) structure of a macromolecule given noisy samples of its twodimensional projection images at unknown random directions. Present algorithms for finding an initial 3D structure model are based on the “angular reconstitution ” method in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signaltonoise ratio of the images. In this paper we describe two algorithms for finding the unknown imaging directions of all projections by minimizing global selfconsistency errors. In the first algorithm, the minimizer is obtained by computing the three largest eigenvectors of a specially designed symmetric matrix derived from the common lines, while the second algorithm is based on semidefinite programming (SDP). Compared with existing algorithms, the advantages of our algorithms are fivefold: first, they accurately estimate all orientations at very low commonline detection rates; second, they are extremely fast, as they involve only the computation of a few top eigenvectors or a sparse SDP; third, they are nonsequential and use the information in all common lines at once; fourth, they are amenable to a rigorous mathematical analysis using spectral analysis and random matrix theory; and finally, the algorithms are optimal in the sense that they reach the information theoretic Shannon bound up to a constant for an idealized probabilistic model.
Overview of methods for image reconstruction from projections in emission computed tomography
 PROC. IEEE
, 2003
"... Emission computed tomography (ECT) is a technology for medical imaging whose importance is increasing rapidly. There is a growing appreciation for the value of the functional (as opposed to anatomical) information that is provided by ECT and there are significant advancements taking place, both in t ..."
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Cited by 27 (2 self)
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Emission computed tomography (ECT) is a technology for medical imaging whose importance is increasing rapidly. There is a growing appreciation for the value of the functional (as opposed to anatomical) information that is provided by ECT and there are significant advancements taking place, both in the instrumentation for data collection, and in the computer methods for generating images from the measured data. These computer methods are designed to solve the inverse problem known as “image reconstruction from projections.” This paper uses the various models of the data collection process as the framework for presenting an overview of the wide variety of methods that have been developed for image reconstruction in the major subfields of ECT, which are positron emission tomography (PET) and singlephoton emission computed tomography (SPECT). The overall sequence of the major sections in the paper, and the presentation within each major section, both proceed from the more realistic and general models to those that are idealized and application specific. For most of the topics, the description proceeds from the threedimensional case to the twodimensional case. The paper presents a broad overview of algorithms for PET and SPECT, giving references to the literature where these algorithms and their applications are described in more detail.
Viewing Angle Classification of Cryoelectron Microscopy Images Using Eigenvectors
 SIAM J. Imaging Sci
, 2011
"... Abstract. The cryoelectron microscopy (EM) reconstruction problem is to find the threedimensional structure of a macromolecule given noisy versions of its twodimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryoEM images of nearby view ..."
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Cited by 27 (15 self)
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Abstract. The cryoelectron microscopy (EM) reconstruction problem is to find the threedimensional structure of a macromolecule given noisy versions of its twodimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryoEM images of nearby viewing angles. This identification is an important first step in threedimensional structure determination of macromolecules from cryoEM, because once identified, these images can be rotationally aligned and averaged to produce “class averages ” of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments. Key words. Cryo electronmicroscopy, class averaging, random matrices, semicircle law, angular synchronization, hairy ball theorem, parallel transport, tomography. 1. Introduction. In this paper
Sensor network localization by eigenvector synchronization over the Euclidean group
 In press
"... We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global ..."
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Cited by 25 (15 self)
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We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases, and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity and running time. While our approach is applicable to higher dimensions, in the current paper we focus on the two dimensional case.
Highresolution ab initio threedimensional xray diffraction microscopy
 Journal of the Optical Society of America A
, 2006
"... Coherent Xray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate Xray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative anal ..."
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Cited by 21 (3 self)
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Coherent Xray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate Xray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using Xray undulator radiation, and establishes the techniques to be used in atomicresolution ultrafast imaging at Xray freeelectron laser sources. OCIS codes: 340.7460, 110.1650, 110.6880, 100.5070, 100.6890, 070.2590, 180.6900 1.