Eightfold Rotational Symmetry Research Articles

Ge-Se-Te based penrose photonic quasi-crystal fiber for SCG covering 2–21 μm MIR regime

This work proposes a Penrose-based photonic quasi-crystal fiber (PQF) composed of Arsenic-free, non-toxic chalcogenide glass for Supercontinuum (SC) generation consisting of quasi-crystal lattice of air holes having eight-fold rotational symmetry. Following optimizing the structural parameters, the proposed PQF offers zero dispersion wavelength (ZDW) at around 3.8 μm, an effective mode area of 30 μm2, and a respective high nonlinearity of 824 W−1Km−1 at 2 μm wavelength. By injecting a secant hyperbolic optical pulse having a central wavelength of 4 μm with 20 kW peak power and pulse width of 50 fs, a broadband SC of 2–21 μm is generated, which mostly covers the transparency range of the proposed material as well as Mid-IR regime. To the best of our understanding, this particular type of PQF for broadband SC generation has been proposed for the first time, serving as the novelty factor. Apart from novelty, the wide-band SC assists the proposed PQF in becoming a better counterpart for applications like optical coherence tomography (OCT), frequency metrology, and other Mid-IR applications.

UBAP2L ensures homeostasis of nuclear pore complexes at the intact nuclear envelope.

Assembly of macromolecular complexes at correct cellular sites is crucial for cell function. Nuclear pore complexes (NPCs) are large cylindrical assemblies with eightfold rotational symmetry, built through hierarchical binding of nucleoporins (Nups) forming distinct subcomplexes. Here, we uncover a role of ubiquitin-associated protein 2-like (UBAP2L) in the assembly and stability of properly organized and functional NPCs at the intact nuclear envelope (NE) in human cells. UBAP2L localizes to the nuclear pores and facilitates the formation of the Y-complex, an essential scaffold component of the NPC, and its localization to the NE. UBAP2L promotes the interaction of the Y-complex with POM121 and Nup153, the critical upstream factors in a well-defined sequential order of Nups assembly onto NE during interphase. Timely localization of the cytoplasmic Nup transport factor fragile X-related protein 1 (FXR1) to the NE and its interaction with the Y-complex are likewise dependent on UBAP2L. Thus, this NPC biogenesis mechanism integrates the cytoplasmic and the nuclear NPC assembly signals and ensures efficient nuclear transport, adaptation to nutrient stress, and cellular proliferative capacity, highlighting the importance of NPC homeostasis at the intact NE.

Architecture of the linker-scaffold in the nuclear pore.

INTRODUCTION In eukaryotic cells, the selective bidirectional transport of macromolecules between the nucleus and cytoplasm occurs through the nuclear pore complex (NPC). Embedded in nuclear envelope pores, the ~110-MDa human NPC is an ~1200-Å-wide and ~750-Å-tall assembly of ~1000 proteins, collectively termed nucleoporins. Because of the NPC's eightfold rotational symmetry along the nucleocytoplasmic axis, each of the ~34 different nucleoporins occurs in multiples of eight. Architecturally, the NPC's symmetric core is composed of an inner ring encircling the central transport channel and two outer rings anchored on both sides of the nuclear envelope. Because of its central role in the flow of genetic information from DNA to RNA to protein, the NPC is commonly targeted in viral infections and its nucleoporin constituents are associated with a plethora of diseases. RATIONALE Although the arrangement of most scaffold nucleoporins in the NPC's symmetric core was determined by quantitative docking of crystal structures into cryo-electron tomographic (cryo-ET) maps of intact NPCs, the topology and molecular details of their cohesion by multivalent linker nucleoporins have remained elusive. Recently, in situ cryo-ET reconstructions of NPCs from various species have indicated that the NPC's inner ring is capable of reversible constriction and dilation in response to variations in nuclear envelope membrane tension, thereby modulating the diameter of the central transport channel by ~200 Å. We combined biochemical reconstitution, high-resolution crystal and single-particle cryo-electron microscopy (cryo-EM) structure determination, docking into cryo-ET maps, and physiological validation to elucidate the molecular architecture of the linker-scaffold interaction network that not only is essential for the NPC's integrity but also confers the plasticity and robustness necessary to allow and withstand such large-scale conformational changes. RESULTS By biochemically mapping scaffold-binding regions of all fungal and human linker nucleoporins and determining crystal and single-particle cryo-EM structures of linker-scaffold complexes, we completed the characterization of the biochemically tractable linker-scaffold network and established its evolutionary conservation, despite considerable sequence divergence. We determined a series of crystal and single-particle cryo-EM structures of the intact Nup188 and Nup192 scaffold hubs bound to their Nic96, Nup145N, and Nup53 linker nucleoporin binding regions, revealing that both proteins form distinct question mark-shaped keystones of two evolutionarily conserved hetero‑octameric inner ring complexes. Linkers bind to scaffold surface pockets through short defined motifs, with flanking regions commonly forming additional disperse interactions that reinforce the binding. Using a structure‑guided functional analysis in Saccharomycescerevisiae, we confirmed the robustness of linker‑scaffold interactions and established the physiological relevance of our biochemical and structural findings. The near-atomic composite structures resulting from quantitative docking of experimental structures into human and S.cerevisiae cryo-ET maps of constricted and dilated NPCs structurally disambiguated the positioning of the Nup188 and Nup192 hubs in the intact fungal and human NPC and revealed the topology of the linker-scaffold network. The linker-scaffold gives rise to eight relatively rigid inner ring spokes that are flexibly interconnected to allow for the formation of lateral channels. Unexpectedly, we uncovered that linker‑scaffold interactions play an opposing role in the outer rings by forming tight cross-link staples between the eight nuclear and cytoplasmic outer ring spokes, thereby limiting the dilatory movements to the inner ring. CONCLUSION We have substantially advanced the structural and biochemical characterization of the symmetric core of the S.cerevisiae and human NPCs and determined near-atomic composite structures. The composite structures uncover the molecular mechanism by which the evolutionarily conserved linker‑scaffold establishes the NPC's integrity while simultaneously allowing for the observed plasticity of the central transport channel. The composite structures are roadmaps for the mechanistic dissection of NPC assembly and disassembly, the etiology of NPC‑associated diseases, the role of NPC dilation in nucleocytoplasmic transport of soluble and integral membrane protein cargos, and the anchoring of asymmetric nucleoporins. [Figure: see text].

Higher-order topological insulator in a dodecagonal quasicrystal

Higher-order topological insulators (HOTIs) are a newly discovered class of topological insulators which exhibit unconventional bulk-boundary correspondence. Very recently, the concept of HOTIs has been extended to aperiodic quasicrystalline systems, where the topological band theory fails to describe topological phases. More importantly, a novel HOTI phase protected by an eightfold rotational symmetry, not found in crystalline materials, was identified in the Ammann-Beenker tiling quasicrystals. Here we report the discovery of a quasicrystalline HOTI in a dodecagonal quasicrystal. The quasicrystalline HOTI supports twelve in-gap zero-energy modes symmetrically distributed at the corners of the quasicrystal dodecagon. These zero-energy corner modes are protected by a combination of a twelvefold rotational symmetry and mirror symmetry, as well as particle-hole symmetry, which has no crystalline counterpart.

Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling

We study magnetic properties in the half-filled Hubbard model on the Ammann-Beenker tiling. First, we focus on the domain structure with locally eightfold rotational symmetry to examine the strictly localized confined states for the tightbinding model. We count the number of vertices and confined states in the larger domains generated by the deflation operations systematically. Then, the fraction of the confined states, which plays an important role for magnetic properties in the weak coupling limit, is obtained as $p=1/2\tau^2$, where $\tau(=1+\sqrt{2})$ is the silver ratio. It is also found that the wave functions for confined states are densely distributed in the system and thereby the introduction of the Coulomb interactions immediately induces the finite staggered magnetizations. Increasing the Coulomb interactions, the spatial distribution of the magnetizations continuously changes to those of the Heisenberg model. We discuss crossover behavior in the perpendicular space representation and reveal the superlattice structure in the spatial distribution of the staggered magnetizations.

Bose–Einstein condensates in an eightfold symmetric optical lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11434011, 11522436, and 11774425), the National Key R&D Program of China (Grants No. 2018YFA0306501), the Beijing Natural Science Foundation, China (Grant No. Z180013), and the Research Funds of Renmin University of China (Grants Nos. 16XNLQ03 and 18XNLQ15).

We investigate the properties of Bose–Einstein condensates (BECs) in a two-dimensional quasi-periodic optical lattice (OL) with eightfold rotational symmetry by numerically solving the Gross–Pitaevskii equation. In a stationary external harmonic trapping potential, we first analyze the evolution of matter-wave interference pattern from periodic to quasi-periodic as the OL is changed continuously from four-fold periodic to eight-fold quasi-periodic. We also investigate the transport properties during this evolution for different interatomic interaction and lattice depth, and find that the BEC crosses over from ballistic diffusion to localization. Finally, we focus on the case of eightfold symmetric lattice and consider a global rotation imposed by the external trapping potential. The BEC shows vortex pattern with eightfold symmetry for slow rotation, becomes unstable for intermediate rotation, and exhibits annular solitons with approximate axial symmetry for fast rotation. These results can be readily demonstrated in experiments using the same configuration as in Phys. Rev. Lett. 122 110404 (2019).

Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions

The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we theoretically study a nonequilibrium cavity-QED setup realizing a zero-temperature quantum phase transition from a homogeneous Bose-Einstein condensate to a quasicrystalline phase via collective superradiant light scattering. Across the superradiant phase transition, collective light scattering creates a dynamical, quasicrystalline optical potential for the atoms. Remarkably, the quasicrystalline potential is "emergent" as its eightfold rotational symmetry is not present in the Hamiltonian of the system, rather appears solely in the low-energy states. For sufficiently strong two-body contact interactions between atoms, a quasicrystalline order is stabilized in the system, while for weakly interacting atoms the condensate is localized in one or few of the deepest minima of the quasicrystalline potential.

Coordination shells and coordination numbers of the vertex graph of the Ammann-Beenker tiling.

The vertex graph of the Ammann-Beenker tiling is a well-known quasiperiodic graph with an eightfold rotational symmetry. The coordination sequence and coordination shells of this graph are studied. It is proved that there exists a limit growth form for the vertex graph of the Ammann-Beenker tiling. This growth form is an explicitly calculated regular octagon. Moreover, an asymptotic formula for the coordination numbers of the vertex graph of the Ammann-Beenker tiling is also proved.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]4 ('Ni4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.

Nuclear Pore-Like Structures in a Compartmentalized Bacterium.

Planctomycetes are distinguished from other Bacteria by compartmentalization of cells via internal membranes, interpretation of which has been subject to recent debate regarding potential relations to Gram-negative cell structure. In our interpretation of the available data, the planctomycete Gemmata obscuriglobus contains a nuclear body compartment, and thus possesses a type of cell organization with parallels to the eukaryote nucleus. Here we show that pore-like structures occur in internal membranes of G.obscuriglobus and that they have elements structurally similar to eukaryote nuclear pores, including a basket, ring-spoke structure, and eight-fold rotational symmetry. Bioinformatic analysis of proteomic data reveals that some of the G. obscuriglobus proteins associated with pore-containing membranes possess structural domains found in eukaryote nuclear pore complexes. Moreover, immunogold labelling demonstrates localization of one such protein, containing a β-propeller domain, specifically to the G. obscuriglobus pore-like structures. Finding bacterial pores within internal cell membranes and with structural similarities to eukaryote nuclear pore complexes raises the dual possibilities of either hitherto undetected homology or stunning evolutionary convergence.

Wide-angle, polarization-insensitive and broadband absorber based on eight-fold symmetric SRRs metamaterial

In this paper, we propose a novel three dimensional metamaterial design with eight-fold rotational symmetry that shows a polarization-insensitive, wide-angle and broadband perfect absorption in the microwave band. By simulation, the polarization-insensitive absorption is over 90% between 26.9GHz to 32.9GHz, and the broadband absorption remains a good absorption performance to a wide incident angles for both TE and TM polarizations. The magnetic field distribution are investigated to interpret the physical mechanism of broadband absorption. The broadband absorption is based on overlapping the multiple magnetic resonances at the neighboring frequencies by coupling effects of multiple metallic split-ring resonators (SRRs). Moreover, it is demonstrate that the designed structure can be extended to other frequencies by scale down the size of the unit cell, such as the visible frequencies. The simulated results show that the absorption of the smaller absorber is above 90% in the frequency range from 467THz to 765THz(392–642nm), which include orange to purple light in visible region(400–760nm). The wide-angle and polarization-insensitive stabilities of the smaller absorber is also demonstrated at visible region. The proposed work provides a new design of realization of a polarization-insensitive, wide-angle and broadband absorber ranging different frequency bands, and such a structure has potential application in the fields of solar cell, imaging and detection.

Course of dislocation lines in templated three-dimensional colloidal quasicrystals

We present an approach based on colloidal epitaxy to obtain three-dimensional colloidal quasicrystals, i.e., structures with long-range order but no periodicity. In contrast to other attempts to obtain soft-matter quasicrystals by design, no fine tuning of the colloid-colloid interactions is required. By using Monte Carlo simulations, we explore the development of multiple layers with the desired quasicrystalline symmetry when the colloidal particles sediment onto suitable quasicrystalline substrates. In addition, well-defined defect lines can be induced in the grown colloidal quasicrystal by constructing substrates with well-chosen defects that lead to induced defect lines. We present a study of the three-dimensional course of such dislocation lines by inducing and analyzing stable lines that bend, unstable ones that split up, or defect lines that merge with other defects. Dislocations are characterized by Burgers vectors that are composed of a phononic part as in a periodic crystal and an additional phasonic part that is unique to quasicrystals. As in a periodic crystal, the sum of all Burgers vectors is conserved along defect lines and at all forks. However, unlike in a periodic crystal, the course of a dislocation line in a quasicrystal depends on its position. Furthermore, although in a quasicrystal all Burgers vectors can always be written as sum of Burgers vectors with a smaller phononic part, we find dislocations that do not decompose into dislocations with smaller phononic Burgers vectors. For quasicrystals with eightfold and twelvefold rotational symmetry, we identify basis Burgers vectors that denote stable dislocations. Our results can be verified in experiments and are important for applications of colloidal quasicrystals, e.g., for the development of photonic quasicrystals.

Ferromagnetic resonance study of eightfold artificial ferromagnetic quasicrystals

We have performed broadband (10 MHz–18 GHz) and narrowband (9.7 GHz) ferromagnetic resonance (FMR) measurements on permalloy thin films patterned with quasiperiodic Ammann tilings having eightfold rotational symmetry. We observed highly reproducible mode structures in the low-frequency, hysteretic regime in which domain walls and unsaturated magnetization textures exist. A minimum of 10 robust modes were observed in patterned samples, compared to the single uniform mode observed in unpatterned permalloy films. The field dependence and approximate eightfold rotational symmetry of the FMR spectra are in good agreement with micromagnetic simulations that confirm the importance of patterning for controlling static and dynamic magnetic response.

Bi-stiffness property of motion structures transformed into square cells

Cellular solids with internal microstructures enable the reduction in some environmental loads because of their lightweight bodies, and deliver unique elastic, electromagnetic and thermal properties. In particular, their large deformability without topological change is one of their most interesting solid properties. In this study, we propose a bar-and-joint framework assembled with a basic unit of motion structure, which has eightfold rotational symmetry (MS-8). The MS-8 is made of tetragons, arranged in a concentric fashion, which are transformed into either one of two different aligned patterns of square cells according to the coordinated rotations of the inside squares. Square cells are extremely anisotropic, which is why the stiffness of the MS-8 changes dramatically in the transformation process. Thus, the MS-8 exhibits bi-stiffness according to the two different motions. Taking advantage of the bi-stiffness property, the possibilities of deformation behaviours for repetitive structures of MS-8s are discussed.

Electronic properties of a two-dimensional quasicrystal model based on octagonal covering structure

A two-dimensional quasilattice with eight-fold rotational symmetry is formed by covering of identical octagonal clusters; a tight-binding Hamiltonian is presented based on it. We study the electronic properties by analyzing the energy spectrum and wave functions. The main energy levels are obtained and the gaps are labeled. The wave functions with different localization features are found and the self-similar distribution is shown.

Structural and Functional Studies of Nup107/Nup133 Interaction and Its Implications for the Architecture of the Nuclear Pore Complex

Nuclear pore complexes (NPCs) are 40-60 MDa protein assemblies embedded in the nuclear envelope of eukaryotic cells. NPCs exclusively mediate all transport between cytoplasm and nucleus. The nucleoporins that build the NPC are arranged in a stable core of module-like subcomplexes with eight-fold rotational symmetry. To gain insight into the intricate assembly of the NPC, we have solved the crystal structure of a protein complex between two nucleoporins, human Nup107 and Nup133. Both proteins form elongated structures that interact tightly via a compact interface in tail-to-tail fashion. Additional experiments using structure-guided mutants show that Nup107 is the critical anchor for Nup133 to the NPC, positioning Nup133 at the periphery of the NPC. The significant topological differences between Nup107 and Nup133 suggest that *-helical nucleoporin domains of the NPC scaffold fall in different classes and fulfill largely nonredundant functions.

Eightfold quasipatterns in an optical pattern-forming system.

Quasipatterns with an eightfold rotational symmetry and irregular two- and three-mode patterns are found in an experiment on optical pattern formation. The patterns exist in the transverse cross section of a laser beam that traverses a system built from a sodium vapor cell and a plane feedback mirror with a quarter-wave plate placed into the feedback loop. The occurrence of the quasipatterns is reproduced by numerical simulations and explained by amplitude equations that contain only odd-order terms and are derived from the microscopic model. The selection process is governed by the angle dependence of the cubic cross coupling coefficients in the amplitude equations. Up to our knowledge it provides the first experimental example for a stabilization mechanism proposed earlier that is based on an oscillatory dependence of the cubic cross coupling coefficient on the angle between the interacting wave vectors. The relationship to the prediction of quasipatterns in a similar setup without additional wave plate [Phys. Rev. A 53, 1072 (1996)] is discussed.

Exact solution of an octagonal random tiling model.

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.

Primary structure of the thermosome from Thermoplasma acidophilum.

The thermosome, a chaperonin from the archaebacterium Thermoplasma acidophilum, consists of two subunits (M(r) 58,000 and 60,000) which assemble into a cylindrical complex of pseudo eight-fold rotational symmetry. The sequences of the two subunits are approximately 60% identical to each other and to TF55 from Sulfolobus shibatae, and are 30-40% identical to the subunits of the TCP1 containing ring complex (TRiC) from the eukaryotic cytosol. A dendrogram of this family of chaperonins contains eight eukaryotic branches of TRiC subunits and one archaebacterial branch of thermosome subunits. Alignment of thermosome/TRiC sequences with eubacterial and eukaryotic Hsp60 sequences reveals a statistically significant similarity in two large N- and C-terminal blocks of sequence. Based on this alignment and on the recently published crystal structure of GroEL, we propose that subunits of the thermosome/TRiC family of chaperonins have a similar equatorial domain and overall domain topology as GroEL but differ in the structure of the apical domain.

Organization of the nuclear pore complex in Saccharomyces cerevisiae

Fractions enriched for nuclear pore complexes (NPCs) have been isolated from Saccharomyces cerevisiae. The sequential extraction of nuclei with detergent, nucleases, and salt reveals an organization of the yeast NPC similar to other eukaryotes. Yeast NPCs contain a 30-nm “ring” structure not previously described in other organisms. This structure appears to organize 10-nm filaments into an assembly which exhibits an eight-fold rotational symmetry. Some proteins in the NPC fraction are capable of forming intermediate-sized filaments. These studies suggest that some component of the nuclear pore complex organizes an interaction between nuclear and cytoplasmic networks of intermediate filaments.