Estimator of a change point in single index models

This paper considers the problem of change point in single index models. In order to obtain asymptotically valid confidence intervals for the estimation of the change point, the convergence rate and asymptotic distribution of the change point estimate is studied. Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.     

Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Single‐Molecule Methods to Study Membrane Receptor Oligomerization

Membrane receptors control fundamental cellular processes. Binding of a specific ligand to a receptor initiates communication through the membrane and activation of signaling cascades. This activation process often leads to a spatial rearrangement of receptors in the membrane at the molecular level. Single‐molecule techniques contributed significantly to the understanding of receptor organization and rearrangement in membranes. Here, we review four prominent single‐molecule techniques that have been applied to membrane receptors, namely, stepwise photobleaching, Förster resonance energy transfer, sub‐diffraction localization microscopy and co‐tracking. We discuss the requirements, benefits and limitations of each technique, discuss target labeling, present a selection of applications and results and compare the different methodologies.     

Dissecting Cooperative Communications in a Protein with a High‐Throughput Single‐Molecule Scalpel

Miscued communication often leads to misfolding and aggregation of the proteins involved in many diseases. Owing to the ensemble average property of conventional techniques, detailed communication diagrams are difficult to obtain. Mechanical unfolding affords an unprecedented perspective on cooperative transitions by observing a protein along a trajectory defined by two mutated cysteine residues. Nevertheless, this approach requires tedious sample preparation at the risk of altering native protein conformations. To address these issues, we applied click chemistry to tether a protein to the two dsDNA handles through primary amines in lysine residues as well as at the N terminus. As a proof of concept, we used laser tweezers to mechanically unfold and refold calmodulin along 36 trajectories, maximally allowed by this strategy in a single batch of protein preparation. Without a priori knowledge of the particular residues to which the double‐stranded DNA handles attach, we used hierarchical cluster analysis to identify 20 major trajectories, according to the size and the pattern of unfolding transitions. We dissected the cooperativity into all‐or‐none and partially cooperative events, which represent strong and weak high‐order interactions in proteins, respectively. Although the overall cooperativity is higher within the N or C lobe than that between the lobes, the all‐or‐none cooperativity is anisotropic among different the unfolding trajectories and becomes relatively more predominant when the size of the protein segments increases. The average cooperativity for all‐or‐none transitions falls within the expected range observed by ensemble techniques, which supports the hypothesis that unfolding of a free protein can be reconstituted from individual trajectories.     

Dark‐Field‐Based Observation of Single‐Nanoparticle Dynamics on a Supported Lipid Bilayer for In Situ Analysis of Interacting Molecules and Nanoparticles

Observation of single plasmonic nanoparticles in reconstituted biological systems allows us to obtain snapshots of dynamic processes between molecules and nanoparticles with unprecedented spatiotemporal resolution and single‐molecule/single‐particle‐level data acquisition. This Concept is intended to introduce nanoparticle‐tethered supported lipid bilayer platforms that allow for the dynamic confinement of nanoparticles on a two‐dimensional fluidic surface. The dark‐field‐based long‐term, stable, real‐time observation of freely diffusing plasmonic nanoparticles on a lipid bilayer enables one to extract a broad range of information about interparticle and molecular interactions throughout the entire reaction period. Herein, we highlight important developments in this context to provide ideas on how molecular interactions can be interpreted by monitoring dynamic behaviors and optical signals of laterally mobile nanoparticles.     

Rare Earth Ion Mediated Fluorescence Accumulation on a Single Microbead: An Ultrasensitive Strategy for the Detection of Protein Kinase Activity at the Single‐Cell Level

A single microbead‐based fluorescence imaging (SBFI) strategy that enables detection of protein kinase activity from single cell lysates is reported. We systematically investigated the ability of various rare earth (RE) ions, immobilized on the microbead, for specific capturing of kinase‐induced phosphopeptides, and Dy³⁺ was found to be the most prominent one. Through the efficient concentration of kinase‐induced fluorescent phosphopeptides on a Dy³⁺‐functionalized single microbead, kinase activity can be detected and quantified by reading the fluorescence on the microbead with a confocal fluorescence microscope. Owing to the extremely specific recognition of Dy³⁺ towards phosphopeptides and the highly‐concentrated fluorescence accumulation on only one microbead, ultrahigh sensitivity has been achieved for the SBFI strategy which allows direct kinase analysis at the single‐cell level.     

Construction of Nitronyl Nitroxide‐Based 3d–4f Clusters: Structure and Magnetism

Three unprecedented nitronyl nitroxide radical‐bridged 3d–4f clusters, [Ln₂Cu₂(hfac)₁₀(NIT‐3py)₂(H₂O)₂](Ln^III=Y, Gd, Dy), have been obtained from the self‐assembly of Ln(hfac)₃, Cu(hfac)₂, and the radical ligand. The Dy complex shows a slow relaxation of magnetization, representing the first nitronyl nitroxide radical‐based 3d–4f cluster with single‐molecule magnet behavior.     

The new structure type Gd3Ni7Al14

The crystal structure of Gd₃Ni₇Al₁₄ (trigadolinium heptanickel tetradecaaluminide) belongs to a family of two‐layer structures and can be described as an assembly of interpenetrating centred straight prisms. For the Ni atoms, trigonal prisms (Al₄Gd₂ and Al₆) are observed, the Al atoms are inside tetragonal (Ni₂Al₂Gd₄, Ni₂Al₄Gd₂, Al₄Gd₄, Ni₄Al₄ and Al₈) and pentagonal (Ni₄Al₆ and Al₁₀) prisms, while the Gd atoms are at the centres of pentagonal (Ni₄Al₆) and hexagonal (Ni₄Al₈) prisms. In each case, the true coordination polyhedron is a capped prism, also including atoms from the same layer. The structural features of Gd₃Ni₇Al₁₄ are similar to those of the intermetallides PrNi₂Al₃ and ZrNiAl. In all these structures, Ni‐centred trigonal prisms form infinite columns via common triangular faces. The columns share prism edges and form a three‐dimensional framework with six‐membered rings in the (001) plane in the case of the PrNi₂Al₃ and ZrNiAl types. In the case of Gd₃Ni₇Al₁₄, six‐membered rings are also observed, but only two‐thirds of the rings are interconnected via prism edges.     

Two polymorphs of 5‐cyclohexyl‐5‐ethylbarbituric acid and their packing relationships with other barbiturates

Polymorph (Ia) (m.p. 474 K) of the title compound, C₁₂H₁₈N₂O₃, displays an N—H...O=C hydrogen‐bonded layer structure which contains R₆⁶(28) rings connecting six molecules, as well as R₂²(8) rings linking two molecules. The 3‐connected hydrogen‐bonded net resulting from these interactions has the hcb topology. Form (Ib) (m.p. 471 K) displays N—H...O=C hydrogen‐bonded looped chains in which neighbouring molecules are linked to one another by two different R₂²(8) rings. Polymorph (Ia) is isostructural with the previously reported form II of 5‐(2‐bromoallyl)‐5‐isopropylbarbituric acid (noctal) and polymorph (Ib) is isostructural with the known crystal structures of four other barbiturates.