Structural Frustration Research Articles

PDBe-KB: collaboratively defining the biological context of structural data.

The Protein Data Bank in Europe – Knowledge Base (PDBe-KB, https://pdbe-kb.org) is an open collaboration between world-leading specialist data resources contributing functional and biophysical annotations derived from or relevant to the Protein Data Bank (PDB). The goal of PDBe-KB is to place macromolecular structure data in their biological context by developing standardised data exchange formats and integrating functional annotations from the contributing partner resources into a knowledge graph that can provide valuable biological insights. Since we described PDBe-KB in 2019, there have been significant improvements in the variety of available annotation data sets and user functionality. Here, we provide an overview of the consortium, highlighting the addition of annotations such as predicted covalent binders, phosphorylation sites, effects of mutations on the protein structure and energetic local frustration. In addition, we describe a library of reusable web-based visualisation components and introduce new features such as a bulk download data service and a novel superposition service that generates clusters of superposed protein chains weekly for the whole PDB archive.

Structure Frustration Enables Thermal History-Dependent Responsive Behavior in Self-Healing Hydrogels

Biological soft tissues usually execute their functions via nonequilibrium and dynamic structural transformations. By contrast, functional hydrogels are mainly constructed by implementing static and equilibrium structures in the polymer network. Here, using polyampholyte hydrogel as a model system, we demonstrated that the nonequilibrium structure transformation in self-healing hydrogels enables the gels with many new features, including thermal history dependence, quick and asymmetric thermal response (instant transparent-to-turbid transition but slow turbid-to-transparent transition), tunable cloud point, tunable recovery time, and tiny changes in sample size and mechanical performance. These features make them distinct to conventional thermoresponsive hydrogels based on thermodynamic equilibrium and endow them with a new type of promising thermoresponsive materials. We revealed the structure change and studied the role of the thermal protocol on this thermoresponsive behavior by combining ultraviolet spectrum, small-angle X-ray scattering, rheology, and mechanical measurements. We also presented two conceptual applications of this thermoresponsive hydrogel in thermal imaging and security paper. We believe that this work will inspire future research on creating functional hydrogels via nonequilibrium structure transformations.

Paradigms of frustration in superionic solid electrolytes.

Superionic solid electrolytes have widespread use in energy devices, but the fundamental motivations for fast ion conduction are often elusive. In this Perspective, we draw upon atomistic simulations of a wide range of superionic conductors to illustrate some ways frustration can lower diffusion cation barriers in solids. Based on our studies of halides, oxides, sulfides and hydroborates and a survey of published reports, we classify three types of frustration that create competition between different local atomic preferences, thereby flattening the diffusive energy landscape. These include chemical frustration, which derives from competing factors in the anion–cation interaction; structural frustration, which arises from lattice arrangements that induce site distortion or prevent cation ordering; and dynamical frustration, which is associated with temporary fluctuations in the energy landscape due to anion reorientation or cation reconfiguration. For each class of frustration, we provide detailed simulation analyses of various materials to show how ion mobility is facilitated, resulting in stabilizing factors that are both entropic and enthalpic in origin. We propose the use of these categories as a general construct for classifying frustration in superionic conductors and discuss implications for future development of suitable descriptors and improvement strategies.This article is part of the Theo Murphy meeting issue ‘Understanding fast-ion conduction in solid electrolytes’.

Spin Frustration in Double Perovskite Oxides and Oxynitrides: Enhanced Frustration in La2MnTaO5N with a Large Octahedral Rotation.

The B-site sublattice in the double perovskite oxides A2BB'O6 (B: magnetic cation; B': nonmagnetic cation) causes spin frustration, but the relationship between the structure and spin frustration remains unclear although a number of compounds have been studied. The present study systematically investigated A2MnIIB'O6 (S = 5/2) and found that the frustration factor, defined by f = |θW|/TN (θW: Weiss temperature; TN: Néel temperature), scales linearly with the tolerance factor t, i.e., octahedral rotation. Unexpectedly, La2MnTaO5N (space group: P21/n) synthesized under high pressure is more frustrated (f = 6) than oxides with similar t values, despite the large octahedral rotation due to the small t value of 0.914. Structural analysis suggests that the enhanced frustration can be attributed to the site preference of nitride anions at the equatorial positions, which reduces the variance of neighboring Mn-Mn distances. Our findings provide a new guide to control and improve spin frustration in double perovskites with multiple anions.

Self-Assembly of Polymer Grafted Nanoparticles within Spherically Confined Diblock Copolymers.

Geometric confinement plays an important role in the generation of interesting microstructures on account of structural frustration and confinement-induced entropy loss. In the present study, self-consistent field calculations have been performed to examine the self-assembly behavior of a mixture of diblock copolymers and polymer grafted nanoparticles within a spherical confinement. The analysis is aimed at obtaining the equilibrium distribution of nanoparticles with a high degree of order. The ordered mesophases of diblock copolymers provide useful templates to achieve ordering of nanoparticles in a selective domain. Self-assembly of nanoparticles within frustrated diblock copolymers is found to be very different from the bulk. A rich variety of equilibrium morphologies are observed depending on the degree of confinement and the extent of particle loading. In addition, the role of particle size and selectivity along with the length and the number of polymer chains grafted onto the surface of nanoparticles are analyzed to understand the self-assembly behavior. The specific interest is to obtain the chiral structures out of achiral block copolymers subjected to spherical confinement. The realization of various captivating microstructures, such as chiral ordering of nanoparticles, is highly essential to produce advanced nanomaterials with superior physical properties.

Structural basis for persulfide-sensing specificity in a transcriptional regulator.

Cysteine thiol-based transcriptional regulators orchestrate the coordinated regulation of redox homeostasis and other cellular processes by 'sensing' or detecting a specific redox-active molecule, which in turn activates the transcription of a specific detoxification pathway. The extent to which these sensors are truly specific in cells for a singular class of reactive small-molecule stressors, for example, reactive oxygen or sulfur species, is largely unknown. Here, we report structural and mechanistic insights into the thiol-based transcriptional repressor SqrR, which reacts exclusively with oxidized sulfur species such as persulfides, to yield a tetrasulfide bridge that inhibits DNA operator-promoter binding. Evaluation of crystallographic structures of SqrR in various derivatized states, coupled with the results of a mass spectrometry-based kinetic profiling strategy, suggest that persulfide selectivity is determined by structural frustration of the disulfide form. These findings led to the identification of an uncharacterized repressor from the bacterial pathogen Acinetobacter baumannii as a persulfide sensor.

Structural Heterogeneity, Ductility, and Glass Forming Ability of Zr-Based Metallic Glasses

We show the correlation between nanoscale structural heterogeneity, mechanical property, and glass-forming ability of Zr-Cu-Co-Al metallic glasses (MGs). Local regions with medium-range ordering (MRO) were directly visualized in electron dark-field images of (Zr 45 Cu 50 Al 5 ) 1- x (Zr 55 Co 25 Al 20 ) x MGs acquired using 4-dimensional scanning transmission electron microscopy (4D-STEM), which enables determination of the type, size, and volume fraction of MRO domains with high precision and statistical reliability. Angular correlation analysis of 4D-STEM data shows notable differences in MRO types between x = 0 and x = 1, and certain types of MRO involve structural frustration that correlates to high glass-forming ability. More importantly, the smaller and more diverse MRO at x = 0.5 correlates with a substantial increase in ductility, suggesting a potential role of MRO in the deformation of MGs. Mesoscale deformation simulation incorporating the experimentally determined MRO confirms that the diverse types and sizes of MRO can significantly influence the MGs’ mechanical behavior, which we attribute to the strain frustration mechanism due to increased heterogeneity.

THE SOCIAL AND PHYSICAL VARIABLES ASSOCIATED WITH VIOLATION OF FEMALE UNDERAGE RIGHTS AND THE ROLE OF CIVIL SOCIETY IN MEETING THEM A FIELD COMPARATIVE STUDY BETWEEN RURAL AND URBAN AREAS

This study aims at identifying relationship between social and physical environment and forms of violation to which underage female is facing in family surroundings (parents’ violence towards underage female – incest – underage marriage – females’ circumcision). Uncovering differences in the form of violation against underage female in both (rural and urban) society in family surroundings and uncovering differences in the role played by civil society institutions for confronting this phenomenon in rural and urban areas, study sample consisted of (250) cases of subjected underage females to violation in family surroundings in rural and urban areas. The researcher used (the comparative descriptive methodology) and social survey methodology) in the sample by depending on questionnaire as a main tool for collecting data using the following theories: the functional structural theory, frustration theory and social and environmental stresses theory. The research concluded some results, the most important of them are: there are difference in the forms and images of violence to which underage female confronts in the family, circumcision and underage marriage) between rural and urban areas.The researcher set a group of recommendations to limit violations of underage females’ rights in family surroundings, the most important of them is making intact and positive decisions towards the underage for protecting them from underage marriage or deforming their genitalia by performing circumcision surgery by their parents particularly in rural areas.

Local frustration determines loop opening during the catalytic cycle of an oxidoreductase.

Local structural frustration, the existence of mutually exclusive competing interactions, may explain why some proteins are dynamic while others are rigid. Frustration is thought to underpin biomolecular recognition and the flexibility of protein-binding sites. Here, we show how a small chemical modification, the oxidation of two cysteine thiols to a disulfide bond, during the catalytic cycle of the N-terminal domain of the key bacterial oxidoreductase DsbD (nDsbD), introduces frustration ultimately influencing protein function. In oxidized nDsbD, local frustration disrupts the packing of the protective cap-loop region against the active site allowing loop opening. By contrast, in reduced nDsbD the cap loop is rigid, always protecting the active-site thiols from the oxidizing environment of the periplasm. Our results point toward an intricate coupling between the dynamics of the active-site cysteines and of the cap loop which modulates the association reactions of nDsbD with its partners resulting in optimized protein function.

Confinement-induced ordering of grafted nanoparticles aided by diblock copolymers

Self-assembly behavior of polymer grafted nanoparticles in ordered phases of geometrically confined diblock copolymers is studied using self-consistent field theory. Entropy loss and structural frustration introduced by physical confinement significantly alter the morphology of ordered phases from the bulk behavior. In particular, a rich variety of three-dimensional microstructures, for example, helical structures, are obtained under confinement. In the present study, we demonstrate that ordered microstructures of diblock copolymers can be employed as promising structural scaffolds to host and self-assemble nanoparticles within the selective domain. Templated self-assembly of nanoparticles offers a potential route to fabricate advanced nanomaterials with superior properties. Analysis reveals various stable equilibrium phases of block copolymers embedded with nanoparticles with a high degree of nanoscale ordering. The arrangement of nanoparticles is controlled by tuning various parameters such as block fraction in diblock copolymers, particle loading, size and number of grafted chains, and degree of confinement. At a low volume fraction, nanoparticles self-organize into chiral microstructures, such as single and double helices, even though the system contains only achiral species. Upon enhancing particle loading, the helical structure becomes less favorable and various other three-dimensional phases such as ring and disk morphologies are obtained. The regions of helical, ring, disk, and concentric lamellar phases are identified in terms of parameters related to grafted particles. Understanding the factors affecting localization of nanoparticles enables us to control the particulate self-assembly behavior of nanoparticles to design novel and advanced nanocomposites with desirable properties.

Phase behavior of disk-coil block copolymers under cylindrical confinement: Curvature-induced structural frustrations.

In this paper, we explore the self-assembly behavior of disk-coil block copolymers (BCPs) confined within a cylinder using molecular dynamics simulations. As functions of the diameter of the confining cylinder and the number of coil beads, concentric lamellar structures are obtained with a different number of alternating disk-rich and coil-rich bilayers. Our paper focuses on the curvature-induced structural behavior in the disk-rich domain of a self-assembled structure, which is investigated by calculating the local density distribution P(r) and the orientational distribution G(r,θ). In the inner layers of cylinder-confined disk-coil BCPs, both P(r) and G(r,θ) show characteristic asymmetry within a bilayer which is directly contrasted with the bulk and slab-confined disk-coil BCPs. We successfully explain the structural frustration of disks arising from the curved structure due to packing frustration of disks and asymmetric stretching of coils to the regions with different curvatures in a bilayer. Our results are important to understand the self-assembly behavior of BCPs containing a rigid motif in a confined structure, such as a self-assembled structure of bacteriochlorophyll molecules confined by a lipid layer to form a chlorosome, the photosynthetic antennae complex found in nature.

Paradigms of Structural, Chemical, and Dynamical Frustration in Superionic Conductors

Rationally motivated computational discovery and optimization of solid electrolytes require the development of reliable descriptors for fast ionic conductivity. However, many of the fundamental motivations for superionic behavior in solids remain enigmatic, which has generally slowed progress in screening electrolyte candidates, as well as in tuning existing materials to maximize ionic conductivity. I will discuss our efforts using first-principles molecular dynamics simulations to unravel various mechanisms of ionic conductivity in model classes of solid electrolytes. Using computational “experiments”, our simulations systematically isolate factors such as stoichiometry, strain, composition, and crystal structure in the determination of ionic conductivity. Collectively, the results point to the importance of a frustrated energy landscape in promoting ultrafast diffusion. Different types of frustration in model superionic conductors will be discussed, arising from factors such as off-stoichiometry, competition between interstitial site occupancies, symmetry incompatibilities between local bonding character and lattice geometry, and dynamical frustration coupled to anharmonic processes. Physicochemical origins of the relevance of these factors for cation mobility will be explored, with a view towards developing design rules for engineering faster ionic conductors. Our findings suggest that the relative contributions of the different frustration paradigms depend chiefly on the fundamental nature of the lattice-forming ions, suggesting there may be no single universal descriptor for ionic conductivity, but rather classes of superionic conductors with similar underlying motivations. Specific examples will be drawn from our recent results on superionic materials based on oxides, halides, and polyatomic anions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Magnetolattice coupling, magnetic frustration, and magnetoelectric effect in the Cr-doped FeVO4 multiferroic material and their correlation with structural phase transitions

A detailed account of magnetolattice coupling, magnetic frustration, and magnetoelectric effects in ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{VO}}_{4}$ ($x=0\ensuremath{-}1.0$) studied by temperature-dependent synchrotron x ray diffraction (SXRD), temperature- and magnetic-field-dependent dielectric permittivity $\ensuremath{\varepsilon}$, and magnetization measurements are presented in this paper where progressive Cr doping leads to structural transitions from triclinic (T)---monoclinic (M)---orthorhombic (O) symmetries. SXRD data shows an intricate relationship between magnetic, ferroelectric, and lattice degrees of freedom in these systems. ${\mathrm{FeVO}}_{4}$ reaches a magnetically ordered state with two successive antiferromagnetic orderings at ${\mathrm{T}}_{N1}$ (21.85 K) and ${\mathrm{T}}_{N2}$ (15.65 K), having collinear and noncollinear natures, respectively, as evidenced in DC magnetization measurements. Progressive ${\mathrm{Cr}}^{3+}$ incorporation at the ${\mathrm{Fe}}^{3+}$ site in ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{VO}}_{4}$ shifts these transitions to higher temperatures in T phase ($x=0.0$ and 0.10). At $x=0.175$ [in (T $+$ M) phase], these transitions become closer to each other. Beyond this concentration, a single broad antriferromagnetic transition is observed in M $(x=0.20\ensuremath{-}0.30$) and O ($x=0.90\ensuremath{-}1.0$) phases. A nonlinear behavior in isotherm M-H curves below ${\mathrm{T}}_{N2}$ indicates field-induced spin-reorientation transitions at higher magnetic field. In dielectric permittivity $\ensuremath{\varepsilon}$ a sharp peak at ${\mathrm{T}}_{N2}$ in T and near M regions with a minimal suppression because of applied magnetic field is found and no such peak is observed in far M phase. A discontinuity evidenced in electromagnetic susceptibility indicates magnetoelectric effect at the polar to nonpolar transition regions. The structural incongruence in progressive transformation from T to M to O symmetries plays a vital role in controlling the nature of magnetic interactions. Our results indicate a strong correlation between structural transitions, magnetolattice coupling, magnetic frustrations, and magnetoelectric effect in ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{VO}}_{4}$.

Structural and optical diversity in copper halide-based ferromagnetic inorganic-organic layered hybrids

Self-assembled two-dimensional lead-free inorganic-organic hybrids, (C12H25NH3)2Cu(Cl1-xBrx)4 and (C6H9C2H4NH3)2Cu(Cl1-xBrx)4 have been investigated for various compositions 0 ≤ x ≤ 1. Uniformly crystalline single phase (C12H25NH3)2Cu(Cl1-xBrx)4 systems are grown layer by layer along the c-axis. In the case of (C6H9C2H4NH3)2Cu(Cl1-xBrx)4, we find binary crystalline phase for the composition 0 < x ≤ 1 and structural frustration is indicated through the observation of split in the (00l) diffraction peaks. For both the systems, Raman vibrational modes in the range of 70–400 cm−1 are related to buckling of distorted octahedra of CuX6 (X = Cl and Br) in the inorganic planes. The Raman frequencies compositional red-shift is due to the reduced bonding strength of the Cu-X vibrations by the replacement of higher electronegative Cl atoms with lower electronegative Br atoms. In the infrared spectrum also, symmetric (∼1491 cm−1) and asymmetric (∼1582 cm−1) deformations of NH3-X bonds show a redshift in the frequency with the increasing Br-content in both types of systems. The optical absorption spectra, typical d-d transitions in Cu2+ and consistent band-edge related redshift features have been discussed in detail.

Sites of high local frustration in DNA origami

The self-assembly of a DNA origami structure, although mostly feasible, represents indeed a rather complex folding problem. Entropy-driven folding and nucleation seeds formation may provide possible solutions; however, until now, a unified view of the energetic factors in play is missing. Here, by analyzing the self-assembly of origami domains with identical structure but different nucleobase composition, in function of variable design and experimental parameters, we identify the role played by sequence-dependent forces at the edges of the structure, where topological constraint is higher. Our data show that the degree of mechanical stress experienced by these regions during initial folding reshapes the energy landscape profile, defining the ratio between two possible global conformations. We thus propose a dynamic model of DNA origami assembly that relies on the capability of the system to escape high structural frustration at nucleation sites, eventually resulting in the emergence of a more favorable but previously hidden state.

Enhanced thermal stability of dielectric, energy storage, and discharge efficiency in a structurally frustrated piezoelectric system: Erbium modified Na0.5Bi0.5TiO3-BaTiO3

We have systematically investigated the effect of rare earth erbium (Er3+) substitution on the structural, ferroelectric, piezoelectric, and dielectric behaviour of the morphotropic phase boundary lead-free piezoelectric 0.94Na0.5Bi0.5TiO3-0.06BaTiO3 (NBT-6BT). We found that the system shows very good thermal stability of energy density, discharge efficiency, and dielectric permittivity. Detailed structural studies confirmed that Er modification induces a great deal of structural frustration which causes the system to thermally evolve towards the paraelectric state in a very sluggish manner. Our results seem to suggest that, among other factors, this sluggish temperature variation of the structural distortion is an important factor which imparts thermal stability to the energy storage and dielectric properties.

Implications of heterostructural alloying for enhanced piezoelectric performance of (Al,Sc)N

An understanding of the heterostructural implications on alloying in the aluminum nitride-scandium nitride system (${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$) can highlight opportunities and design principles for enhancing desired material properties by leveraging nonequilibrium states. The fundamental thermodynamics, and therefore composition- and structure-dependent mechanisms, underlying property evolution in this system have not been fully described, despite significant recent efforts driven by interest in enhanced piezoelectric performance. Practical realization of these enhanced properties, however, is hindered by the strong driving thermodynamic driving force for phase separation in the system, highlighting the need for increased study into the role of heterostructural alloying on the thermodynamics and composition-structure-property relationships in this system. With this need in mind, ab initio computed alloy thermodynamics and properties are compared to combinatorial thin-film synthesis and characterization to develop a more complete picture of the structure and property evolution across the ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ composition space. The combination of structural frustration and a flattened free-energy landscape lead to substantial increases in electromechanical response. The energy scale of alloy metastability is found to be much larger than previously reported, helping to explain difficulties in achieving homogeneous materials with high scandium concentration. Scandium substitution for aluminum softens the wurtzite crystal lattice, and energetic proximity to the competing hexagonal boron-nitride structure enhances the piezoelectric stress coefficient. Overall, this work provides insight into the understanding of the structure-processing-property relationships in the ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ system, suggests material design strategies for even greater property enhancements, and demonstrates the increased property tunability and underexplored nature of nonequilibrium heterostructural alloys.

Structural, Chemical, and Dynamical Frustration: Origins of Superionic Conductivity in closo-Borate Solid Electrolytes

Li2B12H12, Na2B12H12, and their closo-borate relatives exhibit unusually high ionic conductivity, making them attractive as a new class of candidate electrolytes in solid-state Li- and Na-ion batteries. However, further optimization of these materials requires a deeper understanding of the fundamental mechanisms underlying ultrafast ion conduction. To this end, we use ab initio molecular dynamics simulations and density-functional calculations to explore the motivations for cation diffusion. We find that superionic behavior in Li2B12H12 and Na2B12H12 results from a combination of key structural, chemical, and dynamical factors that introduce intrinsic frustration and disorder. A statistical metric is used to show that the structures exhibit a high density of accessible interstitial sites and site types, which correlates with the flatness of the energy landscape and the observed cation mobility. Furthermore, cations are found to dock to specific anion sites, leading to a competition between the geometric s...

Molecular design of flexible liquid crystal oligomers stabilising the chiral frustrated phases

ABSTRACTChirality induces structural frustration in liquid crystal systems, producing various kinds of chiral frustrated phases, for example, twist grain boundary (TGB) phases, blue phases (BPs) and dark conglomerate (DC) phases. Almost all molecules exhibiting these frustrated phases have a rigid shape. Especially, a bent–core unit is regarded as a key structure for BPs and DC phases. This paper describes that some flexible liquid crystal oligomers being far from a rigid bent–core molecule stabilise these phases. The LC oligomers have a supermolecular structure in which mesogenic units are connected via flexible spacers. By designing intermolecular interactions, they can exhibit various molecular packing structures in the liquid-crystalline phases as follows: chiral dimers inducing TGB phases, U-shaped and T-shaped oligomers stabilising BPs and achiral liquid crystal trimers exhibiting DC phases. I discuss how the designed liquid crystal oligomers produce the chiral frustrated phases.

Crystal Structure and Spin Frustration Behavior of an Oxo‐centered Trinuclear Chromium(III) Complex

A trinuclear chromium(III) complex, [Cr3O(HCO2)6(CH3OH)3]NO3·H2O·CH3OH (1), is synthesized and structurally characterized by single‐crystal X‐ray diffraction. Three chromium(III) ions are bridged by one oxygen atom in the center, forming a triangular structure. The HCOO − anion acts as bidentate ligand and bridges couples of Cr(III) ions. Magnetic susceptibility measurement indicates that a strong antiferromagnetic interaction is operative between chromium(III) ions, and the S = 1/2 ground state reveals normal spin frustration behavior.