Theory of the frustration effect. II. Ising spins on a square lattice

Thermal stability and secondary aggregation of self-limiting, geometrically frustrated assemblies: Chain assembly of incommensurate polybricks

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multisubunit size which results from the competition between the elastic costs of frustration within an assembly and the surface energy at its boundaries. Physical realizations-from ill-fitting particle assemblies to self-twisting protein superstructures-are capable of multiple mechanisms of escaping the cumulative costs of frustration, resulting in unlimited equilibrium assembly, including elastic modes of "shape flattening" and the formation of weak, defective bonds that screen intra-assembly stresses. Here we study a model of one-dimensional chain assembly of incommensurate "polybricks" and determine its equilibrium assembly as a function of temperature, concentration, degree of shape frustration, elasticity, and interparticle binding, notably focusing on how weakly cohesive, defective bonds give rise to strongly temperature-dependent assembly. Complex assembly behavior derives from the competition between multiple distinct local minima in the free-energy landscape, including self-limiting chains, weakly bound aggregates of self-limiting chains, and strongly bound, elastically defrustrated assemblies. We show that this scenario, in general, gives rise to anomalous multiple aggregation behavior, in which disperse subunits (stable at low concentration and high temperature) first exhibit a primary aggregation transition to self-limiting chains (at intermediate concentration and temperature) which are ultimately unstable to condensation into unlimited assembly of finite-chains through weak binding beyond a secondary aggregation transition (at low temperature and high concentration). We show that window of stable self-limitation is determined both by the elastic costs of frustration in the assembly as well as energetic and entropic features of intersubunit binding.

Planar Spin Glass with Topologically Protected Mazes in the Liquid Crystal Targeting for Reconfigurable Micro Security Media

The planar spin glass pattern is widely known for its inherent randomness, resulting from the geometrical frustration. As such, developing physical unclonable functions (PUFs)-which operate with device randomness-with planar spin glass patterns is a promising candidate for an advanced security systems in the upcoming digitalized society. Despite their inherent randomness, traditional magnetic spin glass patterns pose considerable obstacles in detection, making it challenging to achieve authentication in security systems. This necessitates the development of facilely observable mimetic patterns with similar randomness to overcome these challenges. Here, a straightforward approach is introduced using a topologically protected maze pattern in the chiral liquid crystals (LCs). This maze exhibits a comparable level of randomness to magnetic spin glass and can be reliably identified through the combination of optical microscopy with machine learning-based object detection techniques. The "information" embedded in the maze can be reconstructed through thermal phase transitions of the LCs in tens of seconds. Furthermore, incorporating various elements can enhance the optical PUF, resulting in a multi-factor security medium. It is expected that this security medium, based on microscopically controlled and macroscopically uncontrolled topologically protected structures, may be utilized as a next-generation security system.

Pattern of frustration formation in the functional brain network

The brain is a frustrated system that contains conflictual link arrangements named frustration. The frustration as a source of disorder prevents the system from settling into low-energy states and provides flexibility for brain network organization. In this research, we tried to identify the pattern of frustration formation in the brain at the levels of region, connection, canonical network, and hemisphere. We found that frustration formation has no uniform pattern. Some subcortical elements have an active role in frustration formation, despite low contributions from many cortical elements. Frustrating connections are mostly between-network connections, and triadic frustrations are mainly formed between three regions from three distinct canonical networks. We did not find any significant differences between brain hemispheres or any robust differences between the frustration formation patterns of various life-span stages. Our results may be interesting for those who study the organization of brain links and promising for those who want to manipulate brain networks.

Designing Magnetism in High Entropy Oxides

In magnetic systems, spin and exchange disorder can provide access to quantum criticality, frustration, and spin dynamics, but broad tunability of these responses and a deeper understanding of strong limit disorder are lacking. Here, it is demonstrated that high entropy oxides present a previously unexplored route to designing materials in which the presence of strong local compositional disorder may be exploited to generate tunable magnetic behaviors-from macroscopically ordered states to frustration-driven dynamic spin interactions. Single-crystal La(Cr_0.2 Mn_0.2 Fe_0.2 Co_0.2 Ni_0.2 )O₃ films are used as a model system hosting a magnetic sublattice with a high degree of microstate disorder in the form of site-to-site spin and exchange type inhomogeneity. A classical Heisenberg model simplified to represent the highest probability microstates well describes how compositionally disordered systems can paradoxically host magnetic uniformity and demonstrates a path toward continuous control over ordering types and critical temperatures. Model-predicted materials are synthesized and found to possess an incipient quantum critical point when magnetic ordering types are designed to be in direct competition, this leads to highly controllable exchange bias behaviors previously accessible only in intentionally designed bilayer heterojunctions.

An Annealing Accelerator for Ising Spin Systems Based on In-Memory Complementary 2D FETs

Metaheuristic algorithms such as simulated annealing (SA) are often implemented for optimization in combinatorial problems, especially for discreet problems. SA employs a stochastic search, where high-energy transitions ("hill-climbing") are allowed with a temperature-dependent probability to escape local optima. Ising spin glass systems have properties such as spin disorder and "frustration" and provide a discreet combinatorial problem with a high number of metastable states and ground-state degeneracy. In this work, subthreshold Boltzmann transport is exploited in complementary 2D field-effect transistors (p-type WSe₂ and n-type MoS₂ ) integrated with an analog, nonvolatile, and programmable floating-gate memory stack to develop in-memory computing primitives necessary for energy- and area-efficient hardware acceleration of SA for Ising spin systems. Search acceleration of >800× is demonstrated for 4 × 4 ferromagnetic, antiferromagnetic, and spin glass systems using SA compared to an exhaustive search using a brute force trial at miniscule total energy expenditure of ≈120 nJ. The hardware-realistic numerical simulations further highlight the astounding benefits of SA in accelerating the search for larger spin lattices.

Localization of Energetic Frustration in Proteins

We present a detailed heuristic method to quantify the degree of local energetic frustration manifested by protein molecules. Current applications are realized in computational experiments where a protein structure is visualized highlighting the energetic conflicts or the concordance of the local interactions in that structure. Minimally frustrated linkages highlight the stable folding core of the molecule. Sites of high local frustration, in contrast, often indicate functionally relevant regions such as binding, active, or allosteric sites.

Coupling disorder in a population of swarmalators

We consider a population of two-dimensional oscillators with random couplings and explore the collective states. The coupling strength between oscillators is randomly quenched with two values, one of which is positive while the other is negative, and the oscillators can spatially move depending on the state variables for phase and position. We find that the system shows the phase transition from the incoherent state to the fully synchronized one at a proper ratio of the number of positive couplings to the total. The threshold is numerically measured and analytically predicted by the linear stability analysis of the fully synchronized state. It is found that the random couplings induce the long-term state patterns appearing for constant strength. The oscillators move to the places where the randomly quenched couplings work as if annealed. We further observe that the system with mixed randomnesses for quenched couplings shows the combination of the deformed patterns understandable with each annealed average.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Resilience of the topological phases to frustration

Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.

Tropical Tensor Network for Ground States of Spin Glasses

We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the tropical algebra defined on the semiring of (R∪{-∞},⊕,⊙). Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the ordinary algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes the computational power of graphical processing units (GPUs). For applications, we compute the exact ground state energy of Ising spin glasses on square lattice up to 1024 spins, on cubic lattice up to 216 spins, and on three regular random graphs up to 220 spins, on a single GPU; we obtain exact ground state energy of ±J Ising spin glass on the chimera graph of D-Wave quantum annealer of 512 qubits in less than 100 s and investigate the exact value of the residual entropy of ±J spin glasses on the chimera graph; finally, we investigate ground-state energy and entropy of three-state Potts glasses on square lattices up to size 18×18. Our approach provides baselines and benchmarks for exact algorithms for spin glasses and combinatorial optimization problems, and for evaluating heuristic algorithms and mean-field theories.

Frustration in Fuzzy Protein Complexes Leads to Interaction Versatility

Disordered proteins frequently serve as interaction hubs involving a constrained variety of partners. Complexes with different partners frequently exhibit distinct binding modes, involving regions that remain disordered in the bound state. While the conformational properties of disordered proteins are well-characterized in their free states, less is known about the molecular mechanisms by which specificity can be achieved not with one but with multiple partners. Using the energy landscape theory concept of protein frustration, we demonstrate that complexes of disordered proteins exhibit a high degree of local frustration, especically at the binding interface. These suboptimal interactions lead to the possibility of multiple bound substates, each displaying distinct frustration patterns, which are differently populated in complexes with different partners. These results explain how specificity of disordered proteins can be achieved without a single common bound conformation and how the confliict between different interactions can be used to control the binding to multiple partners.

Structural stability predictions and molecular dynamics simulations of RBD and HR1 mutations associated with SARS-CoV-2 spike glycoprotein

The COVID-19 pandemic is caused by human transmission and infection of Severe Acute Respiratory Syndrome Corona Virus-2 (SARS-CoV-2). There is no trusted drug against the virus; hence, efforts are on discovering novel inhibitors for the virus. The entry of a SARS-CoV-2 virus particle into a host cell is initiated by its spike glycoprotein and host Angiotensin-Converting Enzyme 2 (ACE2) receptor interaction. Spike glycoprotein domains, namely, the Receptor Binding Domain (RBD) and Heptad Repeat (HR) domains, are essential for this activity. We have studied the impact of mutations such as A348T, N354D, D364Y, G476S, V483A, S494D in the RBD (319-591), and S939F, S940T, T941A, S943P (912-984) in the HR1 domains of spike glycoprotein. Summarily, we utilized the computational screening algorithms to rank the deleterious, damaging and disease-associated spike glycoprotein mutations. Subsequently, to understand the changes in conformation, flexibility and function of the spike glycoprotein mutants, Molecular Dynamics (MD) simulations were performed. The computational predictions and analysis of the MD trajectories suggest that the RBD and HR1 mutations induce significant phenotypic effects on the pre-binding spike glycoprotein structure, which are presumably consequential to its binding to the receptor and provides lead to design inhibitors against the binding.Communicated by Ramaswamy H. Sarma.

A molecular journey to check the conformational dynamics of tau tubulin kinase 2 mutations associated with Alzheimer's disease

Proteins are one of the most vital components of biological functions. Proteins have evolutionarily conserved structures as the shape and folding pattern predominantly determine their function. Considerable research efforts have been made to study the protein folding mechanism. The misfolding of protein intermediates of large groups form polymers with unwanted aggregates that may initiate various diseases. Amongst the diseases caused by misfolding of proteins, Alzheimer's disease (AD) is one of the most prevalent neuro-disorders which has a worldwide impact on human health. The disease is associated with several vital proteins and single amino acid mutations. Tau tubulin kinase 2 (TTBK2) is one of the kinases which is known to phosphorylate tau and tubulin. The literature strongly supports that the mutations-K50E, D163A, R181E, A184E and K143E are associated with multiple important cellular processes of TTBK2. In this study, to understand the molecular basis of the functional effects of the mutations, we have performed structural modeling for TTBK2 and its mutations, using computational prediction algorithms and Molecular Dynamics (MD) simulations. The MD simulations highlighted the impact of the mutations on the Wild Type (WT) by the conformational dynamics, Free Energy Landscape (FEL) and internal molecular motions, indicating the structural de-stabilization which may lead to the disruption of its biological functions. The destabilizing effect of TTBK2 upon mutations provided valuable information about individuals carrying this mutant which could be used as a diagnostic marker in AD.

Simple relation between frustration and transition points in diluted spin glasses

We investigate a possible relation between frustration and phase-transition points in two-dimensional spin glasses at zero temperature. The relation consists of a condition on the average number of frustrated plaquettes and was reported to provide very good predictions for the critical points at zero temperature, for several two-dimensional lattices. Although there has been no proof of the relation, the good correspondence in several lattices suggests the validity of the relation and an important role of frustration in the phase transitions. To examine the relation further, we present a natural extension of the relation to diluted lattices and verify its effectiveness for bond-diluted square lattices. We then confirm that the resulting points are in good agreement with the phase-transition points in a wide range of dilution rate. Our result supports the suggestion from R. Miyazaki [J. Phys. Soc. Jpn. 82, 094001 (2013)JUPSAU0031-901510.7566/JPSJ.82.094001] for nondiluted lattices on the importance of frustration to the phase transition of two-dimensional spin glasses at zero temperature.

Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model

We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional ±1 random-bond Ising model. The behavior of the model is determined by the temperature T and the concentration p of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for 0≤p<p_{c}, and a spin glass for p_{c}<p≤0.5 where p_{c}≃0.222. We investigate the percolation transition of the Fortuin-Kasteleyn clusters as a function of temperature for large system sizes up to N=200^{3} spins. Except for p=0 the Fortuin-Kasteleyn percolation transition occurs at a higher temperature than the magnetic ordering temperature. This was known before for p=1/2 but here we provide evidence for a difference in transition temperatures even for p arbitrarily small. Furthermore, for all values of p>0, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for p=0 where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.

Assistance for Folding of Disease-Causing Plasma Membrane Proteins

An extensive catalog of plasma membrane (PM) protein mutations related to phenotypic diseases is associated with incorrect protein folding and/or localization. These impairments, in addition to dysfunction, frequently promote protein aggregation, which can be detrimental to cells. Here, we review PM protein processing, from protein synthesis in the endoplasmic reticulum to delivery to the PM, stressing the main repercussions of processing failures and their physiological consequences in pathologies, and we summarize the recent proposed therapeutic strategies to rescue misassembled proteins through different types of chaperones and/or small molecule drugs that safeguard protein quality control and regulate proteostasis.

Substitutional transition metal doping in MoS2: a first-principles study

Single-layer MoS2 is a direct-gap semiconductor whose band edges character is dominated by the d-orbitals of the Mo atoms. It follows that substitutional doping of the Mo atoms has a significant impact on the material’s electronic properties, namely the size of the band gap and the position of the Fermi level. Here, density functional theory is used along with the G0W0 method to examine the effects of substituting Mo with four different transition metal dopants: Nb, Tc, Ta, and Re. Nb and Ta possess one less valence electron than Mo does and are therefore p-type dopants, while Re and Tc are n-type dopants, having one more valence electron than Mo has. Four types of substitutional structures are considered for each dopant species: isolated atoms, lines, three-atom clusters centered on a S atom (c3s), and three-atom clusters centered on a hole (c3h). The c3h structure is found to be the most stable configuration for all dopant species. However, electronic structure calculations reveal that isolated dopants are preferable for efficient n- or p-type performance. Lastly, it is shown that photoluminescence measurements can provide valuable insight into the atomic structure of the doped material. Understanding these properties of substitutionally-doped MoS2 can allow for its successful implementation into cutting-edge solid state devices.

Extending the knowledge on the quaternary rare earth nickel aluminum germanides of the RENiAl4Ge2 series (RE=Y, Sm, Gd–Tm, Lu) – structural, magnetic and NMR-spectroscopic investigations

The quaternary rare earth nickel aluminum germanide series RENiAl4Ge2 (RE = Y, Sm, Gd–Tm, Lu) has been extended by several members. The compounds were synthesized from the elements by arc-melting, and single crystals of YNiAl4Ge2, GdNiAl4Ge2, and LuNiAl4Ge2 were grown from an aluminum flux. All members crystallize isostructurally in the rhombohedral SmNiAl4Ge2-type structure (R3̅m, Z = 3). The compounds can be described as a stacking of RE δ+ and [NiAl4Ge2] δ− slabs with an ABC stacking sequence, or alternatively as stacking of CsCl and CdI2 building blocks. The results of the magnetic measurements indicate that all rare earth atoms are in a trivalent oxidation state. Of the RENiAl4Ge2 series, the members with RE = Sm, Gd–Dy exhibit antiferromagnetic ordering with a maximum Néel temperature of T N = 16.4(1) K observed for GdNiAl4Ge2. 27Al NMR spectroscopic investigations yielded spectra with two distinct signals, in line with the crystal structure, however, significantly different resonance frequencies of δ iso ms(YNiAl4Ge2) = 77(1) and 482(1) ppm as well as δ iso ms(LuNiAl4Ge2) = 90(1) and 467(1) ppm were observed. These indicate significantly different s-electron densities at the two crystallographically different Al atoms, in line with the results from DFT calculations. The Bader charge analysis confirms that the present compounds must be considered as germanides, as expected from the relative electronegativities of the constituent elements, while the low charges on Al and Y indicate significant covalent bonding.

The Poincaré-Shannon Machine: Statistical Physics and Machine Learning Aspects of Information Cohomology

Previous works established that entropy is characterized uniquely as the first cohomology class in a topos and described some of its applications to the unsupervised classification of gene expression modules or cell types. These studies raised important questions regarding the statistical meaning of the resulting cohomology of information and its interpretation or consequences with respect to usual data analysis and statistical physics. This paper aims to present the computational methods of information cohomology and to propose its interpretations in terms of statistical physics and machine learning. In order to further underline the cohomological nature of information functions and chain rules, the computation of the cohomology in low degrees is detailed to show more directly that the k multivariate mutual information (Ik) are (k−1)-coboundaries. The (k−1)-cocycles condition corresponds to Ik=0, which generalizes statistical independence to arbitrary degree k. Hence, the cohomology can be interpreted as quantifying the statistical dependences and the obstruction to factorization. I develop the computationally tractable subcase of simplicial information cohomology represented by entropy Hk and information Ik landscapes and their respective paths, allowing investigation of Shannon’s information in the multivariate case without the assumptions of independence or of identically distributed variables. I give an interpretation of this cohomology in terms of phase transitions in a model of k-body interactions, holding both for statistical physics without mean field approximations and for data points. The I1 components define a self-internal energy functional Uk and (−1)kIk,k≥2 components define the contribution to a free energy functional Gk (the total correlation) of the k-body interactions. A basic mean field model is developed and computed on genetic data reproducing usual free energy landscapes with phase transition, sustaining the analogy of clustering with condensation. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, providing a trivial topological expression of the second law of thermodynamics. The local minima of free energy, related to conditional information negativity and conditional independence, characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. I give an interpretation of this complex in terms of unsupervised deep learning where the neural network architecture is given by the chain complex and conclude by discussing future supervised applications.

Ensemble allosteric model: energetic frustration within the intrinsically disordered glucocorticoid receptor

Allostery is an important regulatory phenomenon enabling precise control of biological function. Initial understanding of allostery was gained from seminal work on conformational changes exhibited by structured proteins. Within the last decade, protein allostery has also been demonstrated to occur within intrinsically disordered proteins. This emerging concept of disorder-mediated allostery can be usefully understood in the context of a thermodynamic ensemble. The advantage of this ensemble allosteric model is that it unifies the explanations of allostery occurring within both structured and disordered proteins. One central finding from this model is that energetic coupling, the transmission of a signal between separate regions (or domains) of a protein, is maximized when one or more domains are disordered. This is due to a disorder-order transition that contributes additional coupling energy to the allosteric system through formation of a molecular interaction surface or interface. A second key finding is that multiple interfaces may constructively or destructively interfere with each other, resulting in a new form of allosteric regulation called 'energetic frustration'. Articulating protein allostery in terms of the thermodynamic ensemble permits formulation of experimentally testable hypotheses which can increase fundamental understanding and direct drug-design efforts. These ideas are illustrated here with the specific case of human glucocorticoid receptor, a medically important multi-domain allosteric protein that contains both structured and disordered regions and exemplifies 'energetic frustration'.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Frustration, function and folding

Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful catalysis, are examples of basic chemical activities that the great majority of polypeptides do not display, and are thought to be the outcome of the natural history of proteins. Function, a concept genuine to Biology, is at the core of evolution and often conflicts with the physical constraints. Locating the frustration between discrepant goals in a recurrent system leads to fundamental insights about the chances and necessities that shape the encoding of biological information.

Genetically tunable frustration controls allostery in an intrinsically disordered transcription factor

Intrinsically disordered proteins (IDPs) present a functional paradox because they lack stable tertiary structure, but nonetheless play a central role in signaling, utilizing a process known as allostery. Historically, allostery in structured proteins has been interpreted in terms of propagated structural changes that are induced by effector binding. Thus, it is not clear how IDPs, lacking such well-defined structures, can allosterically affect function. Here, we show a mechanism by which an IDP can allosterically control function by simultaneously tuning transcriptional activation and repression, using a novel strategy that relies on the principle of ‘energetic frustration’. We demonstrate that human glucocorticoid receptor tunes this signaling in vivo by producing translational isoforms differing only in the length of the disordered region, which modulates the degree of frustration. We expect this frustration-based model of allostery will prove to be generally important in explaining signaling in other IDPs.

Proteins carry out most of the key tasks inside cells. To perform these roles, proteins must fold up to form complex three-dimensional structures. Researchers used to think that the useful parts of proteins all had set structures. However, we now know that ‘disordered’ proteins with variable structures are common and disordered parts of proteins can have vital roles.

In a process called allosteric regulation, regulator molecules can increase or decrease the activity of a protein by binding to it. This binding was thought to work by changing the structure of the protein, but it was not clear how this works in disordered proteins. To investigate, Li et al. studied a disordered protein called glucocorticoid receptor, and found that disordered regions can have opposing effects on other regions of the protein. This creates a ‘tug-of-war’ that Li et al. term “energetic frustration”, whereby the activity of the protein results from the combination of the opposing interactions.

Further investigation revealed that the glucorticoid receptor produces different versions of itself that have different degrees of energetic frustration, which alters how effectively the proteins perform their tasks. This means that the protein can regulate its own activity even in the absence of binding to regulator molecules.

The concept of energetic frustration could enhance our understanding of the many different proteins that contain disordered regions. Eventually, this knowledge could be used to develop drugs that alter the activity of these proteins and so could form part of treatments for a wide range of conditions including autoimmune diseases (such as rheumatoid arthritis and lupus), cancers, and organ rejection for transplant patients. The results presented by Li et al. suggest where more research is needed to achieve this goal. For example, we need to understand more about the stability of disordered protein regions, and to identify which surfaces of the proteins interact with each other.

On simulated annealing phase transitions in phylogeny reconstruction

Phylogeny reconstruction with global criteria is NP-complete or NP-hard, hence in general requires a heuristic search. We investigate the powerful, physically inspired, general-purpose heuristic simulated annealing, applied to phylogeny reconstruction. Simulated annealing mimics the physical process of annealing, where a liquid is gently cooled to form a crystal. During the search, periods of elevated specific heat occur, analogous to physical phase transitions. These simulated annealing phase transitions play a crucial role in the outcome of the search. Nevertheless, they have received comparably little attention, for phylogeny or other optimisation problems. We analyse simulated annealing phase transitions during searches for the optimal phylogenetic tree for 34 real-world multiple alignments. In the same way in which melting temperatures differ between materials, we observe distinct specific heat profiles for each input file. We propose this reflects differences in the search landscape and can serve as a measure for problem difficulty and for suitability of the algorithm's parameters. We discuss application in algorithmic optimisation and as a diagnostic to assess parameterisation before computationally costly, large phylogeny reconstructions are launched. Whilst the focus here lies on phylogeny reconstruction under maximum parsimony, it is plausible that our results are more widely applicable to optimisation procedures in science and industry.

Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection towards hierarchical architectures

Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary time scales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of biological networks is studied by considering a network of a few nodes embedded in a larger context. Taking into account this fact that any network under study is actually embedded in a larger context, we define network architecture, not on the basis of physical interactions alone, but rather as a specification of the manner in which constraints are placed upon the states of its nodes. We show that such network architectures possessing cycles in their topology, in contrast to those that do not, may be subjected to unsatisfiable constraints. This may be a significant factor leading to selection biased against those network architectures where such inconsistent constraints are more likely to arise. We proceed to quantify the likelihood of inconsistency arising as a function of network architecture finding that, in the absence of sampling bias over the space of possible constraints and for a given network size, networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them. Our results identify a constraint that, at least in isolation, would contribute to a bias in the evolutionary process towards more hierarchical -modular versus completely connected network architectures. Together, these results highlight the context dependence of the functionality of biological networks.

Strong magnetic frustration and anti-site disorder causing spin-glass behavior in honeycomb Li2RhO3

With large spin-orbit coupling, the electron configuration in d-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d⁵ iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li₂RhO₃, a 4d⁵ honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural 5d⁵ iridate Li₂IrO₃, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.

Ground-state phase-space structures of two-dimensional ±J spin glasses: A network approach

We illustrate a complex-network approach to study the phase spaces of spin glasses. By mapping the whole ground-state phase spaces of two-dimensional Edwards-Anderson bimodal (±J) spin glasses exactly into networks for analysis, we discovered various phase-space properties. The Gaussian connectivity distribution of the phase-space networks demonstrates that both the number of free spins and the visiting frequency of all microstates follow the Gaussian distribution. The spectra of phase-space networks are Gaussian, which is proven to be exact when the system is infinitely large. The phase-space networks exhibit community structures. By coarse graining to the community level, we constructed a network representing the entropy landscape of the ground state and discovered its scale-free property. The phase-space networks exhibit fractal structures, as a result of the rugged entropy landscape. Moreover, we show that the connectivity distribution, community structures, and fractal structures change drastically at the ferromagnetic-to-glass phase transition. These quantitative measurements of the ground states provide new insight into the study of spin glasses. The phase-space networks of spin glasses share a number of common features with those of lattice gases and geometrically frustrated spin systems and form a new class of complex networks with unique topology.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Coverage versus supply cost in facility location: physics of frustrated spin systems

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems.

The network of stabilizing contacts in proteins studied by coevolutionary data

The primary structure of proteins, that is their sequence, represents one of the most abundant sets of experimental data concerning biomolecules. The study of correlations in families of co-evolving proteins by means of an inverse Ising-model approach allows to obtain information on their native conformation. Following up on a recent development along this line, we optimize the algorithm to calculate effective energies between the residues, validating the approach both back-calculating interaction energies in a model system, and predicting the free energies associated to mutations in real systems. Making use of these effective energies, we study the network of interactions which stabilizes the native conformation of some well-studied proteins, showing that it displays different properties than the associated contact network.

Characterizing and quantifying frustration in quantum many-body systems

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.

Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.

Molecular nanomagnets and magnetic nanoparticles: the EMR contribution to a common approach

The current status and future developments of the use of electron magnetic resonance (EMR) for the investigation of magnetic nano-systems is here reviewed. The aim is to stimulate efforts to provide a unified view of the properties of magnetic nanoparticles (MNP) comprising a few hundred magnetic centres, and molecular nanomagnets which contain up to ca. one hundred magnetic centres (MNM). The size of the systems is becoming the same but the approaches to the interpretation of their properties are still different, being bottom up for the latter and top down for the former. We make the point here of the need for a common viewpoint, highlighting the status of the two fields and giving some hints for the future developments. EMR has been a powerful tool for the investigation of magnetic nano-objects and it can provide a tool of fundamental importance for the development of a unified view.