Rigid Spin Research Articles

Spin–orbit coupling of Europa’s ice shell and interior

Europa is an icy ocean world, differentiated into a floating ice shell and solid interior, separated by a global ocean. The classical spin–orbit coupling problem considers a satellite as a single rigid body, but in the case of Europa, the existence of the subsurface ocean enables independent motion of the ice shell and solid interior. This paper explores the spin–orbit coupling problem for Europa from a dynamical perspective, yielding illuminating analytical and numerical results. We determine that the spin behavior of Europa is influenced by processes not captured by the classical single rigid body spin–orbit coupling analysis. The tidal locking process for Europa is governed by the strength of gravity-gradient coupling between the ice shell and solid interior, with qualitatively different behavior depending on the scale of this effect. In this coupled rigid model, the shell can potentially undergo large angular displacements from the solid interior, and the coupling plays an outsize role in the dynamical evolution of the moon, even without incorporating the dissipative effects of shell non-rigidity. We additionally discuss the effects of a realistic viscoelastic shell, and catalogue other torques that we expect to be sub-dominant in Europa’s spin dynamics, or whose importance is unknown. Finally, we explore how the choice of tidal model affects the resulting equilibrium spin state.

Longitudinal fluctuations of Co spin moments and their impact on the Curie temperature of the Heusler alloy Co2FeSi

The magnetism of the full Heusler alloy Co2FeSi with its high magnetic ordering temperature is studied on a first-principles basis employing the disordered local moment approximation, the magnetic force theorem and single-site spin fluctuation theory as formulated recently in the framework of the Local Spin Density Approximation. We find that the magnetic moments of Fe and Co in Co2FeSi exhibit a quite distinctive behavior at high temperatures. The Fe moments are well localized and keep their magnitude unchanged with temperature, whereas the Co moments are itinerant and show a temperature dependence. We find that the effects of magnetic disorder strongly renormalize the Fe-Co inter-atomic exchange interactions. Our results suggest a deficiency of the classical Heisenberg model with rigid localized atomic spin moments for the description of magnetism in Co2FeSi. An accurate estimation of the Curie temperature is obtained by taking into the account the thermal longitudinal fluctuations the Co moments.

A three step recipe for designing auxetic materials on demand

Unlike regular elastic materials, when auxetic materials are compressed, they become thinner in the direction perpendicular to the applied force. Despite their outstanding mechanical properties, a systematic design of new and controlled auxetics remains underdeveloped. Here we establish a unified framework to describe bidimensional perfect auxetics with potential use in the design of new materials. Inspired by a natural connection between rotating rigid units and antiferromagnetic spin systems, we unveil the conditions for the emergence of a non-trivial floppy mode responsible for the auxetic behaviour. This model establishes three simple steps to design new auxetics. In particular, we constructed an exotic crystal, a Penrose quasi-crystal and the long-desired isotropic auxetic. The auxeticity of these designs is robust under small structural disturbances, as seen from experiments and numerical simulations. We expect that this work will allow the implementation of auxetic behaviour into advanced materials to enhance their functionalities, with a promising extension into 3D auxetics.

Frustration model and spin excitations in the helimagnet FeP

The metallic compound FeP belongs to the class of materials that feature a complex noncollinear spin order driven by magnetic frustration. While its double-helix magnetic structure with a period $\lambda_{\text{s}} \approx 5c$, where $c$ is the lattice constant, was previously well determined, the relevant spin-spin interactions that lead to that ground state remain unknown. By performing extensive inelastic neutron scattering measurements, we obtained the spin-excitation spectra in a large part of the momentum-energy space. The spectra show that the magnons are gapped with a gap energy of $\sim$5 meV. Despite the 3D crystal structure, the magnon modes display strongly anisotropic dispersions, revealing a quasi-one-dimensional character of the magnetic interactions in FeP. The physics of the material, however, is not determined by the dominating exchange, which is ferromagnetic. Instead, the weaker two-dimensional antiferromagnetic interactions between the rigid ferromagnetic spin chains drive the magnetic frustration. Using linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian with an anisotropy term capable of reproducing the observed spectra. This enabled us to quantify the exchange interactions in FeP and determine the mechanism of its magnetic frustration.

A Carbazole-Derived Nitroxide That Is an Analogue of Cytidine: A Rigid Spin Label for DNA and RNA.

A variety of semirigid and rigid spin labels comprise a valuable arsenal for measurements of biomolecular structures and dynamics by electron paramagnetic resonance (EPR) spectroscopy. Here, we report the synthesis and characterization of rigid spin labels Ċ and Ċm for DNA and RNA, respectively, that are carbazole-derived nitroxides and analogues of cytidine. Ċ and Ċm were converted to their phosphoramidites and used for their incorporation into oligonucleotides by solid-phase synthesis. Analysis of Ċ and Ċm by single-crystal X-ray crystallography verified their identity and showed little deviation from planarity of the nucleobase. Analysis of the continuous-wave (CW) EPR spectra of the spin-labeled DNA and RNA duplexes confirmed their incorporation into the nucleic acids and the line-shape was characteristic of rigid spin labels. Circular dichroism (CD) and thermal denaturation studies of the Ċ-labeled DNAs and Ċm-labeled RNAs indicated that the labels are nonperturbing of duplex structure.

TB2J: A python package for computing magnetic interaction parameters

We present TB2J, a Python package for the automatic computation of magnetic interactions, including exchange and Dzyaloshinskii–Moriya, between atoms of magnetic crystals from the results of density functional calculations. The program is based on the Green’s function method with the local rigid spin rotation treated as a perturbation. As input, the package uses the output of either Wannier90, which is interfaced with many density functional theory packages, or of codes based on localized orbitals. One of the main interests of the code is that it requires only one first-principles electronic structure calculation in the non-relativistic case (or three in the relativistic case) and from the primitive cell only to obtain the magnetic interactions up to long distances, instead of first-principles calculations of many different magnetic configurations and large supercells. The output of TB2J can be used directly for the adiabatic magnon band structure and spin dynamics calculations. A minimal user input is needed, which allows for easy integration into high-throughput workflows. Program summaryProgram Title: TB2JCPC Library link to program files:https://doi.org/10.17632/dm45fcn69d.1Developer’s repository link:https://github.com/mailhexu/TB2JCode Ocean capsule:https://codeocean.com/capsule/6486145Licensing provisions: BSD 2-clauseProgramming language: PythonNature of problem: TB2J is a package for the computing of parameters in the extended Heisenberg model of the magnetic interaction, including the isotropic exchange, anisotropic exchange and Dzyaloshinskii–Moriya interactions from first principles result. It can make use of the Wannier function Hamiltonian, which can be constructed from many first principles codes, or localized orbital based codes.Solution method: It uses the magnetic force theorem and takes the rigid spin rotation as a perturbation to the electronic structure. The energy variation is calculated from the Green’s functions from tight-binding like Hamiltonian based on Wannier functions or localized orbitals.Additional comments including restrictions and unusual features: Isotropic exchange, anisotropic exchange, and Dzyaloshinskii–Moriya interactions can all be computed with the input of many DFT codes through the interface of Wannier90, or directly from localized orbital codes. The magnetic interaction parameters up to any distance can be computed from one DFT calculation. A minimum user-input is required which provides a black-box like experience. It generates output for several spin dynamics codes and thus bridges the first principles electronic structure simulation with the large scale spin dynamics simulation.

The ‘hidden side’ of spin labelled oligonucleotides: Molecular dynamics study focusing on the EPR-silent components of base pairing

Nitroxide labels are combined with nucleic acid structures and are studied using electron paramagnetic resonance experiments (EPR). As X-ray/NMR structures are unavailable with the nitroxide labels, detailed residue level information, down to atomic resolution, about the effect of these nitroxide labels on local RNA structures is currently lacking. This information is critical to evaluate the choice of spin label. In this study, we compare and contrast the effect of TEMPO-based (NT) and rigid spin (Ç) labels (in both 2′-O methylated and not-methylated forms) on RNA duplexes. We also investigate sequence- dependent effects of NT label on RNA duplex along with the more complex G-quadruplex RNA. Distances measured from molecular dynamics simulations between the two spin labels are in agreement with the EPR experimental data. To understand the effect of labelled oligonucleotides on the structure, we studied the local base pair geometries and global structure in comparison with the unlabelled structures. Based on the structural analysis, we can conclude that TEMPO-based and Ç labels do not significantly perturb the base pair arrangements of the native oligonucleotide. When experimental structures for the spin labelled DNA/RNA molecules are not available, general framework offered by the current study can be used to provide information critical to the choice of spin labels to facilitate future EPR studies.

Precise Distance Measurements in DNA G-Quadruplex Dimers and Sandwich Complexes by Pulsed Dipolar EPR Spectroscopy.

DNA G‐quadruplexes show a pronounced tendency to form higher‐order structures, such as π‐stacked dimers and aggregates with aromatic binding partners. Reliable methods for determining the structure of these non‐covalent adducts are scarce. Here, we use artificial square‐planar Cu(pyridine)4 complexes, covalently incorporated into tetramolecular G‐quadruplexes, as rigid spin labels for detecting dimeric structures and measuring intermolecular Cu2+–Cu2+ distances via pulsed dipolar EPR spectroscopy. A series of G‐quadruplex dimers of different spatial dimensions, formed in tail‐to‐tail or head‐to‐head stacking mode, were unambiguously distinguished. Measured distances are in full agreement with results of molecular dynamics simulations. Furthermore, intercalation of two well‐known G‐quadruplex binders, PIPER and telomestatin, into G‐quadruplex dimers resulting in sandwich complexes was investigated, and previously unknown binding modes were discovered. Additionally, we present evidence that free G‐tetrads also intercalate into dimers. Our transition metal labeling approach, combined with pulsed EPR spectroscopy, opens new possibilities for examining structures of non‐covalent DNA aggregates.

Benzoyl‐Protected Hydroxylamines for Improved Chemical Synthesis of Oligonucleotides Containing Nitroxide Spin Labels

Oligonucleotides containing nitroxide spin labels, used in biophysical studies of nucleic acids, are frequently prepared by chemical synthesis. However, during the synthesis of spin‐labeled oligonucleotides, the nitroxides are partially reduced to the corresponding amines. Here we report that a benzoylated hydroxylamine can be used as a protected form of the nitroxide to avoid this reduction. The benzoyl group is stable through the oligonucleotide synthesis and is readily removed under standard oligonucleotide deprotection conditions, yielding a hydroxylamine that is oxidized in situ to the nitroxide. This method was used to incorporate the rigid spin labels Ç and Çm into DNA and RNA oligonucleotides, respectively, including a doubly labeled 36‐nucleotide long DNAzyme. Enzymatic digestion of the spin‐labeled oligonucleotides and subsequent HPLC analysis showed that the nitroxides were intact. This protecting group strategy facilitates the high‐yielding synthesis of spin‐labeled DNA and RNA oligonucleotides using the phosphoramidite method.

Influence of Mg2+ on the conformational flexibility of a tetracycline aptamer.

The tetracycline-binding RNA aptamer (TC-aptamer) is a synthetic riboswitch that binds the antibiotic tetracycline (TC) with exceptionally high affinity. Although a crystal structure exists of the TC-bound state, little is known about the conformational dynamics and changes upon ligand binding. In this study, pulsed electron paramagnetic resonance techniques for measuring distances (PELDOR) in combination with rigid nitroxide spin labels (Çm spin label) were used to investigate the conformational flexibility of the TC-aptamer in the presence and absence of TC at different Mg2+ concentrations. TC was found to be the essential factor for stabilizing the tertiary structure at intermediate Mg2+ concentrations. At higher Mg2+ concentrations, Mg2+ alone is sufficient to stabilize the tertiary structure. In addition, the orientation of the two spin-labeled RNA helices with respect to each other was analyzed with orientation-selective PELDOR and compared to the crystal structure. These results demonstrate for the first time the unique value of the Çm spin label in combination with PELDOR to provide information about conformational flexibilities and orientations of secondary structure elements of biologically relevant RNAs.

Highly Efficient Tuning of Ferromagnetic Spin Interactions in High-Spin Arylamine Structures by Incorporation of Spin Bearing Carbazole Units.

Arylamine moieties oxidized to radical cations are considered promising spin bearing units in high-spin-type compounds. Here, we report the first use of carbazole-3,6-diamine units as efficient, rigid spin containing units. The use of rigid spin bearing units enhances significantly spin exchange interactions. The design using density functional theory calculations shows the progressive increase of the exchange coupling constant dependent on the considered model molecules. Two of the most representative molecules containing flexible (dimer 1) and rigid spin coupling unit (dimer 2) were synthesized. Electrochemical and pulsed-electron paramagnetic resonance nutation studies showed that both dimers can be oxidized to yield a majority of dicationic diradicals exhibiting S = 1 ground states. The high values of the dimer 2 exchange coupling constant obtained both computationally ( J/ kB = 145 K; HHeis. = - JS1 S2) and experimentally ( J/ kB = 90-100 K) indicate the beneficial role of the carbazole moiety incorporated into spin bearing units.

Structural dynamics of calmodulin-ryanodine receptor interactions: electron paramagnetic resonance using stereospecific spin labels

We have used electron paramagnetic resonance, with rigid and stereospecific spin labels, to resolve structural states in calmodulin (CaM), as affected by binding of Ca and a CaM-binding peptide (RyRp) derived from the ryanodine receptor (RyR), the Ca channel that triggers muscle contraction. CaM mutants containing a pair of cysteines in the N-lobe and/or C-lobe were engineered and labeled with a stereospecifically bound bifunctional spin label (BSL). RyRp was synthesized with and without TOAC (a stereospecifically attached spin-labeled amino acid) substituted for a single amino acid near the N-terminus. Intramolecular DEER distance measurements of doubly-labeled BSL-CaM revealed that CaM exists in dynamic equilibrium among multiple states, consistent with open, closed, and compact structural models. Addition of RyRp shifted the equilibrium partially toward the compact state in the absence of Ca, and completely toward the compact state in the presence of Ca, supporting a conformational selection model. Inter-protein distance measurements show that Ca stabilizes the compact state primarily by inducing ordered binding of the CaM N-lobe to RyRp, while only slightly affecting the C-lobe. The results provide insight into the structural mechanism of CaM-mediated RyR regulation, while demonstrating the power of using two types of rigidly and stereospecifically bound spin labels.

Dynamics of Nucleic Acids at Room Temperature Revealed by Pulsed EPR Spectroscopy

AbstractThe investigation of the structure and conformational dynamics of biomolecules under physiological conditions is challenging for structural biology. Although pulsed electron paramagnetic resonance (like PELDOR) techniques provide long‐range distance and orientation information with high accuracy, such studies are usually performed at cryogenic temperatures. At room temperature (RT) PELDOR studies are seemingly impossible due to short electronic relaxation times and loss of dipolar interactions through rotational averaging. We incorporated the rigid nitroxide spin label Ç into a DNA duplex and immobilized the sample on a solid support to overcome this limitation. This enabled orientation‐selective PELDOR measurements at RT. A comparison with data recorded at 50 K revealed averaging of internal dynamics, which occur on the ns time range at RT. Thus, our approach adds a new method to study structural and dynamical processes at physiological temperature in the <10 μs time range with atomistic resolution.

Dynamics of Nucleic Acids at Room Temperature Revealed by Pulsed EPR Spectroscopy

The investigation of the structure and conformational dynamics of biomolecules under physiological conditions is challenging for structural biology. Although pulsed electron paramagnetic resonance (like PELDOR) techniques provide long-range distance and orientation information with high accuracy, such studies are usually performed at cryogenic temperatures. At room temperature (RT) PELDOR studies are seemingly impossible due to short electronic relaxation times and loss of dipolar interactions through rotational averaging. We incorporated the rigid nitroxide spin label Ç into a DNA duplex and immobilized the sample on a solid support to overcome this limitation. This enabled orientation-selective PELDOR measurements at RT. A comparison with data recorded at 50 K revealed averaging of internal dynamics, which occur on the ns time range at RT. Thus, our approach adds a new method to study structural and dynamical processes at physiological temperature in the <10 μs time range with atomistic resolution.

Assessing topology and surface orientation of an antimicrobial peptide magainin 2 using mechanically aligned bilayers and electron paramagnetic resonance spectroscopy

Aligned CW-EPR membrane protein samples provide additional topology interactions that are absent from conventional randomly dispersed samples. These samples are aptly suited to studying antimicrobial peptides because of their dynamic peripheral topology. In this study, four consecutive substitutions of the model antimicrobial peptide magainin 2 were synthesized and labeled with the rigid TOAC spin label. The results revealed the helical tilts to be 66° ± 5°, 76° ± 5°, 70° ± 5°, and 72° ± 5° for the TOAC substitutions H7, S8, A9, and K10 respectively. These results are consistent with previously published literature. Using the EPR (electron paramagnetic resonance) mechanical alignment technique, these substitutions were used to critically assess the topology and surface orientation of the peptide with respect to the membrane. This methodology offers a rapid and simple approach to investigate the structural topology of antimicrobial peptides.

Resolving the Conformational Dynamics of DNA with Ångstrom Resolution by Pulsed Electron-Electron Double Resonance and Molecular Dynamics.

Pulsed electron-electron double resonance (PELDOR/DEER) experiments of nucleic acids with rigid spin labels provide highly accurate distance and orientation information. Here we combine PELDOR experiments with molecular dynamics (MD) simulations to arrive at an atomistic view of the conformational dynamics of DNA. The MD simulations closely reproduce the PELDOR time traces, and demonstrate that bending, in addition to twist-stretch motions, underpin the sub-μs dynamics of DNA. PELDOR experiments correctly rank DNA force fields and resolve subtle differences in the conformational ensembles of nucleic acids, on the order of 1-2 Å. Long-range distance and angle measurements with rigid spin labels provide critical input for the refinement of computer models and the elucidation of the structure and dynamics of complex biomolecules.

Probing topology and dynamics of the second transmembrane domain (M2δ) of the acetyl choline receptor using magnetically aligned lipid bilayers (bicelles) and EPR spectroscopy

Characterizing membrane protein structure and dynamics in the lipid bilayer membrane is very important but experimentally challenging. EPR spectroscopy offers a unique set of techniques to investigate a membrane protein structure, dynamics, topology, and distance constraints in lipid bilayers. Previously our lab demonstrated the use of magnetically aligned phospholipid bilayers (bicelles) for probing topology and dynamics of the membrane peptide M2δ of the acetyl choline receptor (AchR) as a proof of concept. In this study, magnetically aligned phospholipid bilayers and rigid spin labels were further utilized to provide improved dynamic information and topology of M2δ peptide. Seven TOAC-labeled AchR M2δ peptides were synthesized to demonstrate the utility of a multi-labeling amino acid substitution alignment strategy. Our data revealed the helical tilts to be 11°, 17°, 9°, 17°, 16°, 11°, 9°±4° for residues I7TOAC, Q13TOAC, A14TOAC, V15TOAC, C16TOAC, L17TOAC, and L18TOAC, respectively. The average helical tilt of the M2δ peptide was determined to be ∼13°. This study also revealed that the TOAC labels were attached to the M2δ peptide with different dynamics suggesting that the sites towards the C-terminal end are more rigid when compared to the sites towards the N-terminus. The dynamics of the TOAC labeled sites were more resolved in the aligned samples when compared to the randomly disordered samples. This study highlights the use of magnetically aligned lipid bilayer EPR technique to determine a more accurate helical tilt and more resolved local dynamics of AchR M2δ peptide.

Impact of spin label rigidity on extent and accuracy of distance information from PRE data.

Paramagnetic relaxation enhancement (PRE) is a versatile tool for NMR spectroscopic structural and kinetic studies in biological macromolecules. Here, we compare the quality of PRE data derived from two spin labels with markedly different dynamic properties for large RNAs using the I-A riboswitch aptamer domain (78 nt) from Mesoplamsa florum as model system. We designed two I-A aptamer constructs that were spin-labeled by noncovalent hybridization of short spin-labeled oligomer fragments. As an example of a flexible spin label, UreidoU-TEMPO was incorporated into the 3' terminal end of helix P1 while, the recently developed rigid spin-label Çm was incorporated in the 5' terminal end of helix P1. We determined PRE rates obtained from aromatic 13C bound proton intensities and compared these rates to PREs derived from imino proton intensities in this sizeable RNA (~78 nt). PRE restraints derived from both imino and aromatic protons yielded similar data quality, and hence can both be reliably used for PRE determination. For NMR, the data quality derived from the rigid spin label Çm is slightly better than the data quality for the flexible UreidoTEMPO as judged by comparison of the structural agreement with the I-A aptamer crystal structure (3SKI).

Rigid Spin Labels for Improved Distance and Dynamics in Intrinsically Disordered Proteins and Peptides

Spin-labeling and Electron Paramagnetic Resonance spectroscopy (EPR) have become powerful tools for structure determination in proteins and biomacromolecules. Usual spin labels, such as the disulfide-linked MTSL labels are flexible, owing to multiple single bonds separating the nitroxide from the protein backbone. We investigate spin labels rigidly linked to the backbone in a series of peptides derived from the KVKVLGDVIEV peptide[1], with the 4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid (TOAC). These peptides mimic amyloid-aggregation proteins. They were found to form stable oligomers that are cell-toxic, and enabled X-ray crystallography to determine their structures[1].We synthesized and characterized three TOAC-peptides (TOAC1 -3) and one reference peptide (EZ). We show that the EPR rotation correlation times differ depending on TOAC position. Only one of the TOAC variants (peptide TOAC2) showed aggregation by CD signatures similar to[1], same as the non-TOAC containing EZ peptide. Changes in room temperature EPR spectra suggestive of amyloid aggregation were found in TOAC2, but not in the other TOAC variants.Peptide sequences:Peptides: TOAC1: KVKVT∗GDVIEV; TOAC2: T∗KVKVLGDVIEVG; TOAC3: KVKVLGDVIEVT∗G; EZ: KVKVLGDVIEVGG, where T∗ stands for TOAC.ResultsTOAC2 and EZ acquire β sheet character under aggregation conditions (in H2O, shaking at 1000 rpm at 310 K). Rotation correlation times (τr) by continuous wave EPR at 9 GHz are: TOAC1: 0.398 ± 0.018 ns; TOAC2: 0.122 ± 0.005 ns; TOAC3: 0.316 ± 0.028 ns. For TOAC2 τr increases to 0.162 ± 0.007 ns upon aggregation.Conclusions:We propose that for rigid spin labels such as TOAC, the spin label position and the peptide host are crucial and that the TOAC label may interfere with peptide properties. The results are essential to design spin-labeled constructs for the investigation of intrinsically disordered proteins.[1] Laganowsky et al., Science 335 (2012) 1228.

Determination of helix orientations in a flexible DNA by multi-frequency EPR spectroscopy

Distance measurements are performed between a pair of spin labels attached to nucleic acids using Pulsed Electron-Electron Double Resonance (PELDOR, also called DEER) spectroscopy which is a complementary tool to other structure determination methods in structural biology. The rigid spin label Ç, when incorporated pairwise into two helical parts of a nucleic acid molecule, allows the determination of both the mutual orientation and the distance between those labels, since Ç moves rigidly with the helix to which it is attached. We have developed a two-step protocol to investigate the conformational flexibility of flexible nucleic acid molecules by multi-frequency PELDOR. In the first step, a library with a broad collection of conformers, which are in agreement with topological constraints, NMR restraints and distances derived from PELDOR, was created. In the second step, a weighted structural ensemble of these conformers was chosen, such that it fits the multi-frequency PELDOR time traces of all doubly Ç-labelled samples simultaneously. This ensemble reflects the global structure and the conformational flexibility of the two-way DNA junction. We demonstrate this approach on a flexible bent DNA molecule, consisting of two short helical parts with a five adenine bulge at the center. The kink and twist motions between both helical parts were quantitatively determined and showed high flexibility, in agreement with a Förster Resonance Energy Transfer (FRET) study on a similar bent DNA motif. The approach presented here should be useful to describe the relative orientation of helical motifs and the conformational flexibility of nucleic acid structures, both alone and in complexes with proteins and other molecules.