Conical Tilt Research Articles

Influence of chalcopyrite nanoplatelets on nematic phases of bend-shaped dimeric molecules: Phase diagram, birefringence, and reorientation transition

We investigated the influence of chalcopyrite (CuFeS2) nanoplatelets on the ordering of uniform and twist-bend nematic phases of achiral bend-shaped dimers, employing polarized optical microscopy, optical and electro-optical measurements. Specifically, aliphatic amine surface-functionalized hydrophobic chalcopyrite nanoplatelets were synthesized and characterized by XRD, TEM, and IR-vis-UV spectroscopy. Nanocomposites of the liquid crystal compound 1”,9”-bis(4-cyanobiphenyl-4'-yl)nonane (CB9CB) with the nanoplatelets were prepared. The study encompasses an assessment of the thermodynamic stability of the nanocomposites, constructing the corresponding phase diagram as a function of temperature and nanoplatelet mass fraction. Large phase temperature shifts were observed for minute mass fractions of NPs. Birefringence measurements were performed to investigate the orientational order parameter and the conical tilt angle's dependence on the mass fraction of the nanoplatelets and the temperature. Additionally, we measured a Fréedericksz-like reorientation transition voltage threshold and switching times as functions of the mass fraction and temperature. A huge increase of the voltage threshold was measured in the twist-bend nematic phase. The dependence of the viscoelastic coefficient ζ on NPls' mass fraction was investigated. The splay elastic constant of the helicoidal structure was estimated, using a coarse grain approximation, to be two orders of magnitude higher than in the uniform nematic phase. Finally, in the twist-bend nematic phase, the impact of temperature and nanoplatelets mass fraction on the hysteresis loop of the reorientation transition was investigated.

3D tomographic phase retrieval and unwrapping

This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii) Uniqueness for 3D phase unwrapping—General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii) Uniqueness for projection tomography—Unique determination of an object of n 3 voxels from generic n projections or n + 1 coded diffraction patterns is proved. This approach of reducing 3D phase retrieval to the problem of (phase) projection tomography has the practical implication of enabling classification and alignment, when relative orientations are unknown, to be carried out in terms of (phase) projections, instead of diffraction patterns. The applications with the measurement schemes such as single-axis tilt, conical tilt, dual-axis tilt, random conical tilt and general random tilt are discussed.

Cones and spirals: Multi-axis acquisition for scalar and vector electron tomography

Electron tomography (ET) has become an important tool for understanding the 3D nature of nanomaterials, with recent developments enabling not only scalar reconstructions of electron density, but also vector reconstructions of magnetic fields. However, whilst new signals have been incorporated into the ET toolkit, the acquisition schemes have largely kept to conventional single-axis tilt series for scalar ET, and dual-axis schemes for magnetic vector ET. In this work, we explore the potential of using multi-axis tilt schemes including conical and spiral tilt schemes to improve reconstruction fidelity in scalar and magnetic vector ET. Through a combination of systematic simulations and a proof-of-concept experiment, we show that spiral and conical tilt schemes have the potential to produce substantially improved reconstructions, laying the foundations of a new approach to electron tomography acquisition and reconstruction.

Random conical tilt reconstruction without particle picking in cryo-electron microscopy.

A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables the molecular structure to be reconstructed directly from micrographs, completely circumventing the need for particle picking. Reconstructions are demonstrated with simulated data and the effect of the missing-cone region is investigated. These results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy.

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACTThe discovery of the oblique chiral (or, the twist-bend, NTB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the NTB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the NTB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the NTB phase. Temperature dependence of the ODFs and the order parameters 〈P2(cosβ)〉, 〈P4(cosβ)〉, and 〈P6(cosβ)〉 has been measured in both phases. The parameters 〈P2(cosβ)〉 and 〈P4(cosβ)〉 increase/decrease in the N/NTB phase with decreasing temperature, while 〈P6(cosβ)〉 remains vanishingly small for all samples. The value of 〈P4(cosβ)〉 becomes negative in the NTB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.

Fast and automatic identification of particle tilt pairs based on Delaunay triangulation.

Random conical tilt (RCT) and orthogonal tilt reconstruction (OTR) are two remarkable methods for reconstructing the three-dimensional structure of macromolecules at low resolution. These techniques use two images at two different sample tilts. One of the most demanding steps in these methods at the image processing level is to identify corresponding particles on both micrographs, and manual or semiautomatic matching methods are usually used. Here we present an approach to solve this bottleneck with a fully automatic method for assigning particle tilt pairs. This new algorithm behaves correctly with a variety of samples, covering the range from small to large macromolecules and from sparse to densely populated fields of view. It is also more rapid than previous approaches. The roots of the method lie in a Delaunay triangulation of the set of independently picked coordinates on both the untilted and tilted micrographs. These triangulations are then used to search an affine transformation between the untilted and tilted triangles. The affine transformation that maximizes the number of correspondences between the two micrographs defines the coordinate matching.

Nematic twist-bend phase under external constraints

ABSTRACTThe recently discovered twist-bend nematic phase, NTB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the NTB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the NTB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the NTB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the NTB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the NTB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the NTB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.

High resolution single particle refinement in EMAN2.1

EMAN2.1 is a complete image processing suite for quantitative analysis of grayscale images, with a primary focus on transmission electron microscopy, with complete workflows for performing high resolution single particle reconstruction, 2-D and 3-D heterogeneity analysis, random conical tilt reconstruction and subtomogram averaging, among other tasks. In this manuscript we provide the first detailed description of the high resolution single particle analysis pipeline and the philosophy behind its approach to the reconstruction problem. High resolution refinement is a fully automated process, and involves an advanced set of heuristics to select optimal algorithms for each specific refinement task. A gold standard FSC is produced automatically as part of refinement, providing a robust resolution estimate for the final map, and this is used to optimally filter the final CTF phase and amplitude corrected structure. Additional methods are in-place to reduce model bias during refinement, and to permit cross-validation using other computational methods.

Cryo-EM and the elucidation of new macromolecular structures: Random Conical Tilt revisited.

Cryo-Electron Microscopy (cryo-EM) of macromolecular complexes is a fundamental structural biology technique which is expanding at a very fast pace. Key to its success in elucidating the three-dimensional structure of a macromolecular complex, especially of small and non-symmetric ones, is the ability to start from a low resolution map, which is subsequently refined with the actual images collected at the microscope. There are several methods to produce this first structure. Among them, Random Conical Tilt (RCT) plays a prominent role due to its unbiased nature (it can create an initial model based on experimental measurements). In this article, we revise the fundamental mathematical expressions supporting RCT, providing new expressions handling all key geometrical parameters without the need of intermediate operations, leading to improved automation and overall reliability, essential for the success of cryo-EM when analyzing new complexes. We show that the here proposed RCT workflow based on the new formulation performs very well in practical cases, requiring very few image pairs (as low as 13 image pairs in one of our examples) to obtain relevant 3D maps.

A Bayesian approach for suppression of limited angular sampling artifacts in single particle 3D reconstruction.

In the single particle reconstruction, the initial 3D structure often suffers from the limited angular sampling artifact. Selecting 2D class averages of particle images generally improves the accuracy and efficiency of the reference-free 3D angle estimation, but causes an insufficient angular sampling to fill the information of the target object in the 3D frequency space. Similarly, the initial 3D structure by the random-conical tilt reconstruction has the well-known "missing cone" artifact. Here, we attempted to solve the limited angular sampling problem by sequentially applying maximum a posteriori estimate with expectation maximization algorithm (sMAP-EM). Using both simulated and experimental cryo-electron microscope images, the sMAP-EM was compared to the direct Fourier method on the basis of reconstruction error and resolution. To establish selection criteria of the final regularization weight for the sMAP-EM, the effects of noise level and sampling sparseness on the reconstructions were examined with evenly distributed sampling simulations. The frequency information filled in the missing cone of the conical tilt sampling simulations was assessed by developing new quantitative measurements. All the results of visual and numerical evaluations showed the sMAP-EM performed better than the direct Fourier method, regardless of the sampling method, noise level, and sampling sparseness. Furthermore, the frequency domain analysis demonstrated that the sMAP-EM can fill the meaningful information in the unmeasured angular space without detailed a priori knowledge of the objects. The current research demonstrated that the sMAP-EM has a high potential to facilitate the determination of 3D protein structures at near atomic-resolution.

A tilt-pair based method for assigning the projection directions of randomly oriented single-particle molecules.

In this article, we describe an improved method to assign the projection angle for averaged images using tilt-pair images for three-dimensional reconstructions from randomly oriented single-particle molecular images. Our study addressed the so-called 'initial volume problem' in the single-particle reconstruction, which involves estimation of projection angles of the particle images. The projected images of the particles in different tilt observations were mixed and averaged for the characteristic views. After the ranking of these group average images in terms of reliable tilt angle information, mutual tilt angles between images are assigned from the constituent tilt-pair information. Then, multiples of the conical tilt series are made and merged to construct a network graph of the particle images in terms of projection angles, which are optimized for the three-dimensional reconstruction. We developed the method with images of a synthetic object and applied it to a single-particle image data set of the purified deacetylase from archaea. With the introduction of low-angle tilt observations to minimize unfavorable imaging conditions due to tilting, the results demonstrated reasonable reconstruction models without imposing symmetry to the structure. This method also guides its users to discriminate particle images of different conformational state of the molecule.

Dynactin 3D Structure: Implications for Assembly and Dynein Binding

The multisubunit protein complex, dynactin, is an essential component of the cytoplasmic dynein motor. High-resolution structural work on dynactin and the dynein/dynactin supercomplex has been limited to small subunits and recombinant fragments that do not report fully on either ≈1MDa assembly. In the present study, we used negative-stain electron microscopy and image analysis based on random conical tilt reconstruction to obtain a three-dimensional (3D) structure of native vertebrate dynactin. The 35-nm-long dynactin molecule has a V-shaped shoulder at one end and a flattened tip at the other end, both offset relative to the long axis of the actin-related protein (Arp) backbone. The shoulder projects dramatically away from the Arp filament core in a way that cannot be appreciated in two-dimensional images, which has implications for the mechanism of dynein binding. The 3D structure allows the helical parameters of the entire Arp filament core, which includes the actin capping protein, CP, to be determined for the first time. This structure exhibits near identity to F-actin and can be well fitted into the dynactin envelope. Molecular fitting of modeled CP-Arp polymers into the envelope shows that the filament contains between 7 and 9 Arp protomers and is capped at both ends. In the 7 Arp model, which agrees best with measured Arp stoichiometry and other structural information, actin capping protein (CP) is not present at the distal tip of the structure, unlike what is seen in the other models. The 3D structure suggests a mechanism for dynactin assembly and length specification.

Automated particle correspondence and accurate tilt-axis detection in tilted-image pairs

Tilted electron microscope images are routinely collected for an ab initio structure reconstruction as a part of the Random Conical Tilt (RCT) or Orthogonal Tilt Reconstruction (OTR) methods, as well as for various applications using the "free-hand" procedure. These procedures all require identification of particle pairs in two corresponding images as well as accurate estimation of the tilt-axis used to rotate the electron microscope (EM) grid. Here we present a computational approach, PCT (particle correspondence from tilted pairs), based on tilt-invariant context and projection matching that addresses both problems. The method benefits from treating the two problems as a single optimization task. It automatically finds corresponding particle pairs and accurately computes tilt-axis direction even in the cases when EM grid is not perfectly planar.

Coordinated Rearrangements between Cytoplasmic and Periplasmic Domains of the Membrane Protein Complex ExbB-ExbD of Escherichia coli

Gram-negative bacteria rely on the ExbB-ExbD-TonB system for the import of essential nutrients. Despite decades of research, the stoichiometry, subunit organization, and mechanism of action of the membrane proteins of the Ton system remain unclear. We copurified ExbB with ExbD as an ∼240kDa protein-detergent complex, measured by light scattering and by native gels. Quantitative Coomassie staining revealed a stoichiometry of ExbB4-ExbD2. Negative stain electron microscopy and 2D analysis showed particles of ∼10nm diameter in multiple structural states. Nanogold labeling identified the position of the ExbD periplasmic domain. Random conical tilt was used to reconstruct the particles in three structural states followed by sorting of the single particles and refinement of each state. The different states are interpreted by coordinated structural rearrangements between the cytoplasmic domain and the periplasmic domain, concordant with invivo predictions.

Optimal and fast rotational alignment of volumes with missing data in Fourier space

Electron tomography of intact cells has the potential to reveal the entire cellular content at a resolution corresponding to individual macromolecular complexes. Characterization of macromolecular complexes in tomograms is nevertheless an extremely challenging task due to the high level of noise, and due to the limited tilt angle that results in missing data in Fourier space. By identifying particles of the same type and averaging their 3D volumes, it is possible to obtain a structure at a more useful resolution for biological interpretation. Currently, classification and averaging of sub-tomograms is limited by the speed of computational methods that optimize alignment between two sub-tomographic volumes. The alignment optimization is hampered by the fact that the missing data in Fourier space has to be taken into account during the rotational search. A similar problem appears in single particle electron microscopy where the random conical tilt procedure may require averaging of volumes with a missing cone in Fourier space. We present a fast implementation of a method guaranteed to find an optimal rotational alignment that maximizes the constrained cross-correlation function (cCCF) computed over the actual overlap of data in Fourier space.

Molecular assembly of botulinum neurotoxin progenitor complexes

Botulinum neurotoxin (BoNT) is produced by Clostridium botulinum and associates with nontoxic neurotoxin-associated proteins to form high-molecular weight progenitor complexes (PCs). The PCs are required for the oral toxicity of BoNT in the context of food-borne botulism and are thought to protect BoNT from destruction in the gastrointestinal tract and aid in absorption from the gut lumen. The PC can differ in size and protein content depending on the C. botulinum strain. The oral toxicity of the BoNT PC increases as the size of the PC increases, but the molecular architecture of these large complexes and how they contribute to BoNT toxicity have not been elucidated. We have generated 2D images of PCs from strains producing BoNT serotypes A1, B, and E using negative stain electron microscopy and single-particle averaging. The BoNT/A1 and BoNT/B PCs were observed as ovoid-shaped bodies with three appendages, whereas the BoNT/E PC was observed as an ovoid body. Both the BoNT/A1 and BoNT/B PCs showed significant flexibility, and the BoNT/B PC was documented as a heterogeneous population of assembly/disassembly intermediates. We have also determined 3D structures for each serotype using the random conical tilt approach. Crystal structures of the individual proteins were placed into the BoNT/A1 and BoNT/B PC electron density maps to generate unique detailed models of the BoNT PCs. The structures highlight an effective platform that can be engineered for the development of mucosal vaccines and the intestinal absorption of oral biologics.

Projection-based volume alignment

When heterogeneous samples of macromolecular assemblies are being examined by 3D electron microscopy (3DEM), often multiple reconstructions are obtained. For example, subtomograms of individual particles can be acquired from tomography, or volumes of multiple 2D classes can be obtained by random conical tilt reconstruction. Of these, similar volumes can be averaged to achieve higher resolution. Volume alignment is an essential step before 3D classification and averaging. Here we present a projection-based volume alignment (PBVA) algorithm. We select a set of projections to represent the reference volume and align them to a second volume. Projection alignment is achieved by maximizing the cross-correlation function with respect to rotation and translation parameters. If data are missing, the cross-correlation functions are normalized accordingly. Accurate alignments are obtained by averaging and quadratic interpolation of the cross-correlation maximum. Comparisons of the computation time between PBVA and traditional 3D cross-correlation methods demonstrate that PBVA outperforms the traditional methods. Performance tests were carried out with different signal-to-noise ratios using modeled noise and with different percentages of missing data using a cryo-EM dataset. All tests show that the algorithm is robust and highly accurate. PBVA was applied to align the reconstructions of a subcomplex of the NADH: ubiquinone oxidoreductase (Complex I) from the yeast Yarrowia lipolytica, followed by classification and averaging.

Structural Characterization of the Helicobacter Pylori VacA Toxin by Single Particle Em and X-Ray Crystallography

Helicobacter pylori is a Gram-negative bacterium that infects the human stomach and contributes to the pathogenesis of peptic ulceration, gastric adenocarcinoma and gastric lymphoma. H. pylori secretes an exotoxin called vacuolating toxin (VacA), known for its ability to induce vacuolation in the cytoplasm of mammalian cells. VacA can cause depolarization of membrane potential, alteration of mitochondrial membrane permeability, apoptosis, activation of mitogen-activated protein kinases, inhibition of T cell activation and proliferation, and autophagy. The mechanisms by which these processes occur are not yet fully understood but many of these toxic effects depend on the capacity of VacA to form anion-selective membrane channels. VacA is an 88 kDa protein that contains two distinct domains, p55 and p33. The 88 kDa monomers can assemble into large water-soluble oligomeric “flower”-shaped structures. Using single particle electron microscopy and the random conical tilt approach, we have determined three-dimensional (3D) structures of six distinct VacA oligomeric conformations at ∼15 A resolution. This analysis shows that VacA can organize into a number oligomeric conformations that include both single and double layer hexamers and heptamers. The structures, regardless of oligomeric type, contain two prominent features: extended straight “legs” with a slight kink at the distal end and a central “spoke-like” density that contains two distinct globular domains separated by a thin connecting density. We have also generated structures of three VacA mutant proteins that all form oligomers but differ in activity. Overall, these studies provide the most detailed analysis of p33 structure to date and also provide a more thorough understanding of how VacA forms oligomers.

Structural Analysis of the Oligomeric States of Helicobacter pylori VacA Toxin

Helicobacter pylori is a Gram-negative bacterium that colonizes the human stomach and contributes to peptic ulceration and gastric adenocarcinoma. H. pylori secretes a pore-forming exotoxin known as vacuolating toxin (VacA). VacA contains two distinct domains, designated p33 and p55, and assembles into large “snowflake”-shaped oligomers. Thus far, no structural data are available for the p33 domain, which is essential for membrane channel formation. Using single-particle electron microscopy and the random conical tilt approach, we have determined the three-dimensional structures of six VacA oligomeric conformations at ~15-Å resolution. The p55 domain, composed primarily of β-helical structures, localizes to the peripheral arms, while the p33 domain consists of two globular densities that localize within the center of the complexes. By fitting the VacA p55 crystal structure into the electron microscopy densities, we have mapped inter-VacA interactions that support oligomerization. In addition, we have examined VacA variants/mutants that differ from wild-type (WT) VacA in toxin activity and/or oligomeric structural features. Oligomers formed by VacA∆6–27, a mutant that fails to form membrane channels, lack an organized p33 central core. Mixed oligomers containing both WT and VacA∆6–27 subunits also lack an organized core. Oligomers formed by a VacA s2m1 chimera (which lacks cell-vacuolating activity) and VacAΔ301–328 (which retains vacuolating activity) each contain p33 central cores similar to those of WT oligomers. By providing the most detailed view of the VacA structure to date, these data offer new insights into the toxin's channel-forming component and the intermolecular interactions that underlie oligomeric assembly.

Three-Dimensional Reconstruction of Intact Human Integrin αIIbβ3 in a Phospholipid Bilayer Nanodisc

Abstract 92Integrin αIIbβ3 is a heterodimeric transmembrane signaling receptor that plays a central role in hemostasis and thrombosis. Both two-dimensional (2D) electron microscopic (EM) images of detergent-solubilized intact αIIbβ3 and the x-ray crystallographic structure of the unliganded αIIbβ3 ectodomain show a bent, compact conformation, but these do not provide information about the orientation of the ectodomain relative to the membrane. 2D EM of intact αIIbβ3 inserted into a lipid nanodisc was interpreted as consistent with the crystal structure, with the head region pointing toward the membrane. Three-dimensional (3D) reconstructions of detergent-solubilized αIIbβ3 by transmission cryo-electron microscopy (cryo-EM), small angle neutron scattering (SANS), and small angle x-ray scattering (SAXS) have been interpreted, however, as showing the head region either pointing toward (SANS, SAXS) or away (cryo-EM) from the membrane. Moreover, it has been difficult to fit the crystallographic structure of the receptor with the 3D data from these other methods. To obtain a 3D reconstruction of intact αIIbβ3 in a phospholipid bilayer in the absence of detergent, we inserted purified, intact single αIIbβ3 molecules into nanodiscs, and after removing αIIbβ3 molecules in the active and extended conformations, studied them by negative stain EM, using the random conical tilt method and additional refinements to create a 3D electron density map with a resolution by Fourier shell correlation of 20.5 Å. We employed mAbs to the αIIb cap domain (10E5), β3 βI domain (7E3), and β3 PSI domain (7H2), to establish landmarks in the EM map. The 3D reconstruction indicates that inactive αIIbβ3 adopts a bent, compact conformation, but the head domain containing the αIIb β-propeller and β3 βI domains is on the top of ectodomain, pointing away from the lipid bilayer. Moreover, unlike in the crystal structure of the ectodomain, the lower leg domains in the 3D reconstruction are not straight, parallel, and adjacent throughout their length, but rather have complex shapes, move in different directions, and only join as they near the lipid bilayer and transmembrane domains. Our reconstruction is consistent with mAb kinetic binding data using mAbs 10E5 and 7E3 and appears to be able to reconcile the SANS and cryo-EM data. Instead of the jackknife-like dive conformation of the crystal structure, with a single bend at the waist, our 3D reconstruction suggests more of a deep knee bend conformation, with bends at both the waist and knees. The deadbolt hypothesis of integrin activation postulates an interaction between the β3 β tail domain and the β3 βI domain in the inactive receptor. In our reconstruction, however, the β3 β tail domain and the β3 βI domain are not juxtaposed. The jackknife hypothesis of activation postulates that the headpiece faces toward the membrane in the inactive, bent conformation, limiting ligand access to the binding site, and that activation results in extension of the headpiece away from the membrane to the top of the integrin, providing greater access to the binding site. Our data suggest that despite the head region pointing away from the membrane, its proximity to the membrane may still limit access of ligand. [Display omitted] Disclosures:No relevant conflicts of interest to declare.