Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action. This generalizes problems of interest such as multi-reference...

In the three-dimensional (3D) structure determination of macromolecules, cryo electron microscopy (cryo-EM) is an important method for obtaining micrographs of unstained specimens for the single-particle reconstruction approach. For cryo-EM, proteins are fixed in a frozen hydrated state by quick-freezing in a thin water layer on a holey carbon film. Cryo-EM of detergent-solubilized membrane pro...

Ryanodine receptors (RyRs) form a class of intracellular calcium release channels in various excitable tissues and cells such as muscles and neurons. They are the major cellular mediators of the release of calcium ions from the sarcoplasmic reticulum, an essential step in muscle excitation-contraction coupling. Several crystal structures of skeletal muscle RyR1 peptide fragments have been solve...

In single-particle cryo-electron microscopy (cryo-EM), K-means clustering algorithm is widely used in unsupervised 2D classification of projection images of biological macromolecules. 3D ab initio reconstruction requires accurate unsupervised classification in order to separate molecular projections of distinct orientations. Due to background noise in single-particle images and uncertainty of m...

Single particle cryo-electron microscopy (cryo-EM) and 3-D reconstruction have emerged in recent years as a powerful tool for solving high-resolution 3-D structures of viruses and macromolecular complexes. However, sample preparation for single-particle cryo-EM typically relies on a dedicated purification step before EM sample grid preparation, for example, using column chromatography or gradie...

Of 14 transgenic poplar genotypes (Populus tremula × Populus alba) with antisense 4-coumarate:coenzyme A ligase that were grown in the field for 2 years, five that had substantial lignin reductions also had greatly reduced xylem-specific conductivity compared with that of control trees and those transgenic events with small reductions in lignin. For the two events with the lowest xylem lignin c...

Supplementary Note 1 (Methods) 18 1.1 General molecular dynamics setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 Models of the ribosome including tRNAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3 Refinement of the atomic models against cryo-EM maps . . . . . . . . . . . . . . . . . . . . . 19 1.4 Choice of models for simulation. . . . . . . ...

1. Abstract 2. Introduction 3. Experimental 3.1. Materials 3.2. Sample preparation 3.3. Fluorescence microscopy 3.4. Negative staining TEM 3.5. Cryo-transmission electron microscopy (cryo-TEM) 4. Results and discussion 4.1. From globule to coil: A non-first order transition 4.2. DNA interaction with CTAB and β-CD 4.3. β-CD as a decompacting agent 5. Conclusions and perspectives 6. Acknowledgeme...

This letter is meant to make scientists aware of the proper application of transmission electron microscopy (TEM) for the assessment of polymeric self-assemblies. Cryogenic (cryo)-TEM should be the method of choice. Here, we show the difference in morphologies observed in the same sample when using cryo-TEM and when using TEM with drying, demonstrating the importance of choosing the proper method.

Aligned liquid crystal elastomers (LCEs) are capable of undergoing large reversible shape change in response to thermal stimuli and may act as actuators for many potential applications such as self-assembly and deployment of micro devices. Recent advances in LCE patterning tools have demonstrated sub-millimetre control of director orientation, enabling the preparation of materials with arbitrar...