Threefold Symmetry Research Articles

Magic-Angle-Pulse Driven Separation of Degenerate 1 H Transitions in Methyl Groups of Proteins: Application to Studies of Methyl Axis Dynamics.

Dynamics of protein side chains is one of the principal determinants of conformational entropy in protein structures and molecular recognition events. We describe NMR experiments that rely on the use of magic-angle pulses for efficient isolation of degenerate 1 H transitions of the I=3/2 manifold of 13 CH3 methyl groups, and serve as 'building blocks' for the measurement of transverse spin relaxation rates of the fast- and slow-relaxing 1 H transitions - the primary quantitative reporters of methyl axis dynamics in selectively {13 CH3 }-methyl-labelled, highly deuterated proteins. The magic-angle-pulse driven experiments are technically simpler and, in the absence of relaxation, predicted to be 2.3-fold more sensitive than previously developed analogous schemes. Validation of the methodology on a sample of {13 CH3 }-labeled ubiquitin demonstrates quantitative agreement between order parameters of methyl three-fold symmetry axis obtained with magic-angle-pulse driven experiments and other established NMR techniques, paving the way for studies of methyl axis dynamics in human DNAJB6b chaperone, a protein that undergoes exchange with high-molecular-weight oligomeric species.

Free energy profile of permeation of Entecavir through Hepatitis B virus capsid studied by molecular dynamics calculation

Abstract Entecavir, triphosphorylated in liver cells, is an antiviral reagent against Hepatitis B virus (HBV). The reagent inhibits reverse transcription of RNA inside the virus capsid. In the present study, free energy profile of an Entecavir triphosphate (ETVTP) molecule has been calculated when it passes through pores of the capsid along two- and three-fold rotational symmetry axes in order to investigate permeation pathway of the reagent to the inside of the capsid. The calculations have been done based on thermodynamic integration (TI) method combined with all-atomistic molecular dynamic (MD) calculations. A free energy minimum of −19 kJ/mol was found at the entrance of the pore from the outside along the three-fold symmetry axis. This stabilization is from the interaction of negatively charged ETVTP with positively charged capsid methionine residues. This excess free energy concentrates of the reagent at the entrance of the pore by a factor of about 2000. A free energy barrier of approximately 13 kJ/mol was also found near the exit of the pore to the inside of the capsid due to narrow space of the pore surrounded by hydrophobic wall made by proline residues and negatively charged wall by aspartic acid residues. There, ETVTP is partially dehydrated in order to pass through the narrow space, which causes the great free energy loss. Further, the negatively charged residues produce repulsive forces on the ETVTP molecule. In contrast, in the case of the pore along the two-fold symmetry axis, the calculated free energy profile showed shallower free energy minimum, −4 kJ/mol at the entrance in spite of the similarly high barrier, 7 kJ/mol, near the exit of the pore.

An example of the relevance of symmetry in physics: corner theorems in grids and cubic resistor networks

Equivalent resistances between various points of a resistor network are related. In this paper, we establish general relations for the corner of a planar grid and for the corner of a three-dimensional network with three-fold symmetry. In three dimensions, two demonstrations are given using Kennelly’s theorem or alternatively using van Steenwijk’s method. When three-fold symmetry is not satisfied, but when a plane of symmetry exists, then two relations can be proven relating the four corner resistances. These exact relations are useful to check detailed analytical or numerical solutions, and, when corner resistances are only partially known, to derive the values of the desired missing resistances. Examples of applications are also given in the case of regular polytopes or repeating networks such as ladders and scaffolding.

Crystallographic characterization of a tri-Asp metal-binding site at the three-fold symmetry axis of LarE

Detailed crystallographic characterization of a tri-aspartate metal-binding site previously identified on the three-fold symmetry axis of a hexameric enzyme, LarE from Lactobacillus plantarum, was conducted. By screening an array of monovalent, divalent, and trivalent metal ions, we demonstrated that this metal binding site stoichiometrically binds Ca2+, Mn2+, Fe2+/Fe3+, Co2+, Ni2+, Cu2+, Zn2+, and Cd2+, but not monovalent metal ions, Cr3+, Mg2+, Y3+, Sr2+ or Ba2+. Extensive database searches resulted in only 13 similar metal binding sites in other proteins, indicative of the rareness of tri-aspartate architectures, which allows for engineering such a selective multivalent metal ion binding site into target macromolecules for structural and biophysical characterization.

Structural, Electronic, and Magnetic Properties of Cobalt Tetrakis (Thiadiazole) Porphyrazine Molecule Films on Au(111).

We investigated the structural and electronic/spin configurations of a film of the Co tetrakis(1,2,5-thiadiazole) porphyrazine (CoTTDPz) molecule adsorbed on the Au(111) surface by a scanning tunneling microscope (STM). CoTTDPz has a structure similar to that of the Co phthalocyanine molecule, but the benzene ring of the isoindole of the phthalocyanine molecule is replaced by the pentagon moiety of 1,2,5-thiadiazoles that has an S atom at the apex. We find an ordered molecular lattice with a threefold symmetry where a nearest-neighbor distance of 1.30 nm was measured, which is significantly smaller than that observed for the metal Pc molecule. The unit cell of the lattice contains two molecules that are rotated by 60° relative to each other. With the configuration achieved by this rotation, the neighboring molecules can form a stronger interaction through bonding between the S atom at the apex of one molecule and the N atom of the other (the N atom that is bridging the thiadiazoles). The strong interaction between the molecule and the substrate appears in the spin state examined by the detection of the Kondo resonance, which is formed by the screening of an isolated spin by the conduction electron. Even though the existence of the spin was confirmed for the bulk and thick films of this molecule, no Kondo features are detected for the molecules in the first, second, and third layers of the films. However, the isolated molecule in the third layer showed an intriguing combination of the Kondo feature and an inelastic excitation feature caused by a spin-flip process.

Emitting dipole orientation and molecular orientation of homoleptic Ir(III) complexes

Origin and significance of emitting dipole orientation (EDO) of emitters in organic light-emitting diodes (OLEDs) have been studied extensively in recent years. However, EDO of homoleptic Ir(III) complexes (Homo-IrCs) have received less attention due to their three-fold molecular symmetry and resulting expectation to have random EDO. Herein, we report the EDOs of Homo-IrCs doped in various host materials. Interestingly the EDO of Homo-IrCs varies from preferred horizontal direction to rather vertical direction depending on dopant and host molecules. The variation of EDO of Homo-IrCs is correlated with the direction of the transition dipole moment (TDM) against the molecular C3 axis and the orientation of C3 axis of the dopants in films. The average orientations of the Homo-IrCs are extracted from measured the horizontal dipole ratios (Θs) and calculated TDM directions. Angle between the TDM direction and C3 axis in the Homo-IrCs under investigation are larger than 54.7° corresponding to the mutually orthogonal axes among the three transition dipole vectors so that the EDO of Homo IrCs can deviate from random orientation depending on the orientation of the C3 axis in films. Average molecular orientation of a HOMO-IrC in films varies by 10°–13° depending on host materials. In contrast, smaller variation (<5°) is observed among different Homo IrCs in a same host. The results indicate that host material is one of the dominating factors determining orientation of Homo-IrC molecules. Tris[(3,5-difluoro-4-cyanophenyl)-pyridine]iridium(III) (FCNIr) shows exceptionally high horizontal orientation, which likely originates from the dipole-dipole interaction between the dopant and hosts. FCNIr doped in diphenyl[4-(triphenylsilyl)phenyl]phosphine oxide (TSPO1) shows strong preferred horizontal EDO with the Θ of 0.78, demonstrating the possibility of large Θ value of Homo-IrCs.

Evidence of ac-Stark-shifted resonances in intense two-color circularly polarized laser fields

We report on the appearance of a structure at low energies in the photo-electron momentum distribution of the hydrogen atom exposed to two-color counter-rotating bi-circular laser fields. These structures, which arise due to AC-Stark shifted resonances, break the three-fold symmetry, typical for the $\omega-2\omega$ bi-circular fields. We discuss the physical origin of this structure in terms of partial-wave interference between direct ionization channels and a resonant pathway, that passes through the AC-Stark shifted state and show how the underlying Rydberg state population depend on the field strength and pulse duration.

Multipolar analysis of second-harmonic generation in (111) Gallium Arsenide nanoparticles

We perform multipolar analysis of second-harmonic generation (SHG) from (111)-grown gallium arsenide (GaAs) nanoantennas and discuss its specifics. It was experimentally demonstrated that the conversion efficiency in axially-symmetric (111) GaAs nanoparticles remains constant under the polarization rotation of normally incident radiation in a wide range of particle sizes, while the SHG radiation pattern changes. We apply the analytical method based on the Lorentz lemma to explain this behaviour. The induced nonlinear current is decomposed into two rotating contributions, which are shown to generate multipoles of different parities. Thus, the total SHG intensity in the far-field is proved to be independent of the in-plane rotation of the pump polarization. Nevertheless, due to the threefold symmetry of the crystal with regard to the (111) direction, the SHG radiation pattern rotates around the polar axis repeating its shape every 60°.

Step-edge guided growth of nanowires on three-fold symmetric vicinal Si(111) surfaces

Clean vicinal surfaces exhibit a stepped pattern due to the presence of narrow terraces formed on a clean surface. Therefore, this provides a platform for the aligned growth of nanowires. Using this type of surface as a template, we have grown nanowires of iron di-silicide, which are preferentially directed along the length of the terraces and are following the step-edges. These nanowires do not follow underlying three-fold symmetry of the substrate. We have thus shown two-fold symmetric growth on a three-fold symmetric surface, where diffusion barrier energy plays an important role in determining the shape of the islands. The orientations of nanowires are governed primarily by the presence of step-edges. However, the crystallographic symmetry properties of the underlying substrate have also played its role in controlling the nanowire orientation. The system was grown by molecular beam epitaxy and analysed by scanning tunneling microscopy.

Designing sapphire surface patterns to promote AlGaN overgrowth in hydride vapor phase epitaxy

Lateral overgrowth of patterned c-plane oriented sapphire substrates (PSS) with AlGaN using hydride vapor phase epitaxy was investigated with focus on how to suppress parasitic non c-planar crystallite nucleation and propagation. To this end, trigonal PSS was fabricated with either sidewalls parallel to sapphire -facets or parallel to sapphire -facets, which are crystallographically different due to the three-fold sapphire symmetry. X-ray diffraction-based texture analysis and SEM were applied to find two types of -domains solely nucleating on PSS sidewalls close to -facets. Their occurrence effectively blocks other orientations of non c-plane AlGaN crystallites allowing for quicker coalescence of c-plane AlGaN and improving overall AlGaN material quality.

Constructing Polymorphic Nanodomains in BaTiO3 Films via Epitaxial Symmetry Engineering

AbstractFerroelectric materials owning a polymorphic nanodomain structure usually exhibit colossal susceptibilities to external mechanical, electrical, and thermal stimuli, thus holding huge potential for relevant applications. Despite the success of traditional strategies by means of complex composition design, alternative simple methods such as strain engineering have been intensively sought to achieve a polymorphic nanodomain state in lead‐free, simple‐composition ferroelectric oxides in recent years. Here, a nanodomain configuration with morphed structural phases is realized in an epitaxial BaTiO3 film grown on a (111)‐oriented SrTiO3 substrate. Using a combination of experimental and theoretical approaches, it is revealed that a threefold rotational symmetry element enforced by the epitaxial constraint along the [111] direction of BaTiO3 introduces considerable instability among intrinsic tetragonal, orthorhombic, and rhombohedral phases. Such phase degeneracy induces ultrafine ferroelectric nanodomains (1–10 nm) with low‐angle domain walls, which exhibit significantly enhanced dielectric and piezoelectric responses compared to the (001)‐oriented BaTiO3 film with uniaxial ferroelectricity. Therefore, the finding highlights the important role of epitaxial symmetry in domain engineering of oxide ferroelectrics and facilitates the development of dielectric capacitors and piezoelectric devices.

Multivalley Free Energy Landscape and the Origin of Stripe and Quasi-Stripe CDW Structures in Monolayer MX2 Compounds

Ultrathin sheets of transition metal dichalcogenides (MX2) with charge density waves (CDWs) is increasingly gaining interest as a promising candidate for graphene-like devices. Although experimental data including stripe/quasi-stripe structure and hidden states have been reported, the ground state of ultrathin MX2 compounds and, in particular, the origin of anisotropic (stripe and quasi-stripe) CDW phases is a long-standing problem. Anisotropic CDW phases have been explained by Coulomb interaction between domain walls and inter-layer interaction. However, these models assume that anisotropic domain walls can exist in the first place. Here, we report that anisotropic CDW domain walls can appear naturally without assuming anisotropic interactions: We explain the origin of these phases by topological defect theory (line defects in a two-dimensional plane) and interference between harmonics of macroscopic CDW wave functions. We revisit the McMillan-Nakanishi-Shiba model for monolayer 1T-TaS2 and 2H-TaSe2 and show that CDWs with wave vectors that are separated by 120° (i.e. the three-fold rotation symmetry of the underlying lattice) contain a free-energy landscape with many local minima. Then, we remove this 120° constraint and show that free energy local minima corresponding to the stripe and quasi-stripe phases appear. Our results imply that Coulomb interaction between domain walls and inter-layer interaction may be secondary factors for the appearance of stripe and quasi-stripe CDW phases. Furthermore, this model explains our recent experimental result (appearance of the quasi-stripe structure in monolayer 1T-TaS2) and can predict new CDW phases, hence it may become the basis to study CDW further. We anticipate our results to be a starting point for further study in two-dimensional physics, such as explanation of “Hidden CDW states”, study the interplay between supersolid symmetry and lattice symmetry, and application to other van der Waals structures.

Reorientational dynamics of trimethoxyboroxine: A molecular glass former studied by dielectric spectroscopy and 11B nuclear magnetic resonance.

In this work, trimethoxyboroxine (TMB) is identified as a small-molecule glass former. In its viscous liquid as well as glassy states, static and dynamic properties of TMB are explored using various techniques. It is found that, on average, the structure of the condensed TMB molecules deviates from threefold symmetry so that TMB's electric dipole moment is nonzero, thus rendering broadband dielectric spectroscopy applicable. This method reveals the super-Arrhenius dynamics that characterizes TMB above its glass transition, which occurs at about 204 K. To extend the temperature range in which the molecular dynamics can be studied, 11B nuclear magnetic resonance experiments are additionally carried out on rotating and stationary samples: Exploiting dynamic second-order shifts, spin-relaxation times, line shape effects, as well as stimulated-echo and two-dimensional exchange spectroscopy, a coherent picture regarding the dynamics of this glass former is gained.

Determining methyl sidechain conformations in a CS-ROSETTA model using methyl 1H-13C residual dipolar couplings.

Modelling of protein structures based on backbone chemical shifts, using programs such as CS-ROSETTA, is becoming increasingly popular, especially for systems where few restraints are available or where homologous structures are already known. While the reliability of CS-ROSETTA calculations can be improved by incorporation of some additional backbone NMR data such as those afforded by residual dipolar couplings or minimal NOE data sets involving backbone amide protons, the sidechain conformations are largely modelled by statistical energy terms. Here, we present a simple method based on methyl residual dipolar couplings that can be used to determine the rotameric state of the threefold symmetry axis of methyl groups that occupy a single rotamer, determine rotameric distributions, and identify regions of high flexibility. The method is demonstrated for methyl side chains of a deletion variant of the human chaperone DNAJB6b.

Observation of short-range Yu-Shiba-Rusinov states with threefold symmetry in layered superconductor 2H-NbSe2.

Yu-Shiba-Rusinov (YSR) states arise when magnetic impurities interact with superconductivity. The intricacy of coupling and the nature of the superconductivity determine the behavior of the YSR state, whose detailed correlations are not yet fully understood. Here, we study the YSR state of a single Fe adatom on the surface of 2H-NbSe2 with combined low temperature scanning tunneling microscopy/spectroscopy, density functional theory calculations and tight-binding modeling. It is found that the Fe adatom occupies the hollow site of the Se surface layer. A prominent YSR state close to the Fermi level is observed. The YSR state exhibits a threefold symmetry along the diagonal direction of the Se lattice. The spatial decay of the YSR state follows a behavior in three-dimensional superconductivity. This behavior contrasts with a previous study of imbedded Fe impurities, whose YSR state shows a six-fold symmetry and a two-dimensional long-range decay. According to our theoretical modeling, the coupling configurations affect the adatom-substrate hopping and the interlayer coupling of the substrate. Both factors are crucial for the consequent behavior of the YSR state.

Facile Au-assisted epitaxy of nearly strain-free GaN films on sapphire substrates.

The nearly strain-free GaN films were epitaxially grown successfully on the Au-coated c-plane sapphire substrate by a convenient chemical vapor deposition approach. The growth of GaN single crystalline epitaxial films is a self-patterned process. The morphology, structure, compositions and optical properties of as-synthesized GaN materials were characterized through field-emission scanning electron microscopy, atomic force microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, energy dispersive spectroscopy mapping, Raman spectroscopy and photoluminescence spectroscopy. The characterization results confirm that the epitaxial GaN films grown on Au-coated c-plane sapphire substrates have a single-crystalline and nearly strain-free structure, and exhibit strong UV emission. A possible growth mechanism of the GaN film is proposed: Au-assisted vapor deposition initiates the nucleation of the GaN seeds, and then these seeds grow into inclined inverted hexagonal GaN pyramids with a threefold azimuthal symmetry and vertical inverted hexagonal pyramids; and subsequently, the vertical inverted hexagonal pyramids expand laterally and annihilate the inclined inverted hexagonal pyramids; eventually these vertical pyramids coalesced to form nearly strain-free GaN films. This synthesis strategy provides a new idea for the simple self-patterned growth of nearly strain-free GaN epitaxial films on Au-coated sapphire substrates, and will promote broader applications in GaN-based electronic and optoelectronic devices.

Nickel(ii)-methyl complexes adopting unusual seesaw geometries.

We report four-coordinate nickel(ii)-methyl complexes of tris-carbene borate ligands which adopt rare seesaw geometries. Experimental and computational results suggest the structural distortion from threefold symmetry results from a combination of electronic stabilization of the singlet state, strong field donors, and constrained angles from the chelating ligand.

Rotational quenching of an interstellar gas thermometer: CH3CNHe collisions.

Among all the molecular species found in the interstellar medium, molecules with threefold symmetry axes play a special role, as their rotational spectroscopy allows them to act as practical gas thermometers. Methyl-cyanide (CH3CN) is the second most abundant of those (after ammonia). We compute in this paper the collisional dynamics of methyl-cyanide in collision with helium, for both the A- and the E-symmetries of CH3CN. The potential energy surface is determined using the CCSD(T)-F12b formalism and fit with convenient analytic functions. We compute the rotationally inelastic cross sections for all levels up to 510 cm-1 of collision energy, employing at low energy exact Coupled Channels methods, and at higher energies, approximate Coupled States methods. For temperatures from 7 K up to 300 K, rates of quenching are computed and most are found to differ from those reported earlier (up to a factor of a thousand), calling for a possible reexamination of the temperatures assigned to low density gasses.

De novo design of a homo-trimeric amantadine-binding protein.

The computational design of a symmetric protein homo-oligomer that binds a symmetry-matched small molecule larger than a metal ion has not yet been achieved. We used de novo protein design to create a homo-trimeric protein that binds the C3 symmetric small molecule drug amantadine with each protein monomer making identical interactions with each face of the small molecule. Solution NMR data show that the protein has regular three-fold symmetry and undergoes localized structural changes upon ligand binding. A high-resolution X-ray structure reveals a close overall match to the design model with the exception of water molecules in the amantadine binding site not included in the Rosetta design calculations, and a neutron structure provides experimental validation of the computationally designed hydrogen-bond networks. Exploration of approaches to generate a small molecule inducible homo-trimerization system based on the design highlight challenges that must be overcome to computationally design such systems.

Periodic System of Fullerenes: the Column of Three-Fold Symmetry

We have studied possible ways of growing the fullerenes having initial three-fold symmetry. Beginning with the basic fullerenes C8, C14 and C20, which belong to the Δn = 4,6 and 8 series of the periodic table of fullerenes, we obtained intermediate fullerenes are C10, C12, C16 and C18; which fill up the gaps between the basic ones. The intermediate fullerenes are imperfect or semi-perfect. The imperfection is connected either with extra 'interstitial' or 'vacancy' carbon dimers, both types of dimers playing the role of defects. Only the basic fullerenes have the symmetry of the corresponding column, the intermediate fullerenes having no such symmetry. Considering these fullerenes as imperfect due to defects, one can define them as the fullerenes conserving three-fold topological symmetry. These features are also inherent to other more massive fullerenes which create different families and incorporate fullerenes from C8 to C56. We have calculated their energies and discussed possible reasons of their dependence on a fullerene size and shape.