Electronic Spectra: Topology, Supersymmetry, and Statistics

The description of electronic behavior within solids is a major part of modern Condensed Matter Physics. It is well known that depending on the precise conditions, very diverse phenomena arise from the interacting electrons in the material. To make predictions, it is therefore crucial to understand the electronic structure in a material and to compute its electronic spectrum. This thesis discusses three different aspects of electronic spectra including their numerical solution, each highlighting a distinct approach. In a first part, this thesis presents a numerical solution of many-electron spectra on small clusters of IrO6 octahedra. Such clusters are relevant in the field of strongly coupled matter as they give rise to the elementary building blocks of many topological spin systems, localized j = 1/2 moments. Exact diagonalization of the full many-electron interaction Hamiltonian is utilized to compute multi-particle spectra with respective eigenstates. Subsequently, these eigenstates are further used for numerical calculations of resonant inelastic X-ray scattering (RIXS) amplitudes. The numerical approach is versatile enough to be applied to different examples in this thesis, covering single-site RIXS spectra as in Ba2CeIrO6, materials with local clusters like Ba3InIr2O9 and Ba3Ti3−xIrxO9 and Kitaev materials such as Na2IrO3 and α-RuCl3. In particular, interference effects in the RIXS amplitudes are shown to play a crucial role of determining the nature of delocalized eigenstates in these materials. In a second part, supersymmetry is used to link the spectra of electronic lattice models with bosonic counterparts. To this endeavor, an exact lattice construction is introduced, underlying the supersymmetric identification and providing a visual representation of the supersymmetric matching. As a first instance of the supersymmetric map, it will be shown that models of complex fermions and models of complex bosons are supersymmetrically related if they reside on the two sublattices of a bipartite lattice. Another similar identification is introduced for Majorana fermions on a bipartite lattice which can be related to real boson models on one of the sublattices, allowing for the explicit construction of related mechanical models. As examples of this classical construction, the Kitaev model and a second order topological insulator with floppy corner modes are discussed. In both examples, the supersymmetrically related mechanical model is shown to exhibit the same spectral properties as its quantum mechanical analogue and even inherit topologically protected localized corner modes. In a third part, the electronic spectra of general Moiré materials are investigated at the example of twisted bilayer graphene. This part demonstrates that statistical principles are best suited to describe the vast number of bands originating from the large Moiré unit cells. The statistical description reveals a localization mechanism in momentum space which is investigated and described. The mechanism does not only apply to all parts of the spectrum in twisted bilayer graphene but is also believed to apply to generic Moiré materials. Moreover, exceptions from this general mechanism in twisted bilayer graphene are discussed in detail which turn out to be described by harmonic oscillator states

Topological Mechanics from Supersymmetry

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples we discuss mechanical analogues of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.Comment: 8 pages, 6 figure

Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids

In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models which admit topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by the SUSY are isospectral except for zero modes, such as flat bands, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences and discuss further ramifications such as the definition of supersymmetric topological invariants for generic bosonic systems. Notably, a Hermitian form of the supercharge operator, the generator of the SUSY, can itself be interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to identify a wide class of interconnected lattices whose tight-binding Hamiltonians are superpartners of one another or can be derived via squaring or square-rooting their energy spectra all the while preserving band topology features. We introduce a five-fold way symmetry classification scheme of these SUSY lattice correspondences, including cases with a non-zero Witten index, based on a topological classification of the underlying Hermitian supercharge operator. These concepts are illustrated for various explicit examples including frustrated magnets, Kitaev spin liquids, and topological superconductors.Comment: 37 pages, 27 figure

Nuclear matrix protein Matrin3 regulates alternative splicing and forms overlapping regulatory networks with PTB.

Matrin3 is an RNA- and DNA-binding nuclear matrix protein found to be associated with neural and muscular degenerative diseases. A number of possible functions of Matrin3 have been suggested, but no widespread role in RNA metabolism has yet been clearly demonstrated. We identified Matrin3 by its interaction with the second RRM domain of the splicing regulator PTB. Using a combination of RNAi knockdown, transcriptome profiling and iCLIP, we find that Matrin3 is a regulator of hundreds of alternative splicing events, principally acting as a splicing repressor with only a small proportion of targeted events being co-regulated by PTB. In contrast to other splicing regulators, Matrin3 binds to an extended region within repressed exons and flanking introns with no sharply defined peaks. The identification of this clear molecular function of Matrin3 should help to clarify the molecular pathology of ALS and other diseases caused by mutations of Matrin3.We thank Nejc Haberman (UCL) for assisting in the generation of the splicing maps and preparation of the iCLIP data. This work was supported by Wellcome Trust programme grants to CWJS (077877 and 092900), and by grants to EE and NB BIO2011-23920 and RNAREG (CSD2009-00080) from the Spanish Government and by the Sandra Ibarra Foundation for Cancer (FSI2013). JA was supported by a Boehringer Ingelheim Fonds studentship.This is the final version of the article. It first appeared from EMBO Press/Wiley via http://dx.doi.org/10.15252/embj.20148985

Intergenic RNA mainly derives from nascent transcripts of known genes

BACKGROUND Eukaryotic genomes undergo pervasive transcription, leading to the production of many types of stable and unstable RNAs. Transcription is not restricted to regions with annotated gene features but includes almost any genomic context. Currently, the source and function of most RNAs originating from intergenic regions in the human genome remain unclear. RESULTSWe hypothesize that many intergenic RNAs can be ascribed to the presence of as-yet unannotated genes or the "fuzzy" transcription of known genes that extends beyond the annotated boundaries. To elucidate the contributions of these two sources, we assemble a dataset of more than 2.5 billion publicly available RNA-seq reads across 5 human cell lines and multiple cellular compartments to annotate transcriptional units in the human genome. About 80% of transcripts from unannotated intergenic regions can be attributed to the fuzzy transcription of existing genes; the remaining transcripts originate mainly from putative long non-coding RNA loci that are rarely spliced. We validate the transcriptional activity of these intergenic RNAs using independent measurements, including transcriptional start sites, chromatin signatures, and genomic occupancies of RNA polymerase II in various phosphorylation states. We also analyze the nuclear localization and sensitivities of intergenic transcripts to nucleases to illustrate that they tend to be rapidly degraded either on-chromatin by XRN2 or off-chromatin by the exosome. CONCLUSIONSWe provide a curated atlas of intergenic RNAs that distinguishes between alternative processing of well-annotated genes from independent transcriptional units based on the combined analysis of chromatin signatures, nuclear RNA localization, and degradation pathways

Tumor beta2-microglobulin and HLA-A expression is increased by immunotherapy and can predict response to CIT in association with other biomarkers

BackgroundDownregulation of MHC class I expression and/or defects in the antigen presentation pathways are commonly reported in human cancers. Numerous studies previously have explored extensively the molecular mechanisms that underlie HLA-class I and Beta2-Microglobulin (B2M) downregulation. However, the techniques presently available to detect expression of MHC class I proteins lack the robustness, specificity and sensitivity needed for systematic integration and analysis in clinical trials. Furthermore, the dynamics of HLA-class I and B2M expression have not been comprehensively studied as a potential biomarker for immunotherapy.MethodsUsing novel, validated, immunohistochemistry (IHC)-based methods for quantifying B2M and HLA-A in tumor samples from diverse cancer types, we have determined loss of B2M and HLA-A proteins in 336 archived, primary specimens and 329 biopsies from metastatic patients collected during Roche-sponsored Phase 1 clinical trials investigating novel immunotherapy candidates as monotherapy or in combination with CPI.ResultsUp to 56% of cases with B2M or HLA-A loss were noted in the investigated tumor types. The frequency of loss was dependent on indication and stage of disease and revealed heterogeneous expression patterns across patients. B2M and HLA-A loss was increased in metastatic lesions compared to primary tumors, indicating selection of MHC class I low clones in metastatic and refractory tumor cells. High on-treatment B2M expression correlated with successful clinical outcome (RECIST), while high baseline B2M did not. A treatment-induced increase of B2M expression was noted in most of the patients with low B2M levels at baseline. The triple biomarker combination of B2M, CD8 and PDL1 strongly improved response prediction to cancer immunotherapy.ConclusionOur results indicate that B2M and HLA-A loss occurs frequently in tumors and is reversed in most instances following immunotherapy which supports the conclusion that MHC class I loss is not the dominant resistance mechanism to CPI treatment. This investigation reveals a highly dynamic expression of HLA-A and B2M in tumors affected by indication, metastatic status, immunophenotype and immunotherapy treatment. Baseline expression levels of B2M on tumors may be of utility as a constituent of a biomarker panel used for selecting patients for immunotherapy clinical trials

Identification of potential therapeutic targets in prostate cancer through a cross-species approach.

Genetically engineered mouse models of cancer can be used to filter genome-wide expression datasets generated from human tumours and to identify gene expression alterations that are functionally important to cancer development and progression. In this study, we have generated RNAseq data from tumours arising in two established mouse models of prostate cancer, PB-Cre/PtenloxP/loxP and p53loxP/loxPRbloxP/loxP, and integrated this with published human prostate cancer expression data to pinpoint cancer-associated gene expression changes that are conserved between the two species. To identify potential therapeutic targets, we then filtered this information for genes that are either known or predicted to be druggable. Using this approach, we revealed a functional role for the kinase MELK as a driver and potential therapeutic target in prostate cancer. We found that MELK expression was required for cell survival, affected the expression of genes associated with prostate cancer progression and was associated with biochemical recurrence

Cap-binding protein 4EHP effects translation silencing by microRNAs

Significance miRNAs are important components of gene regulatory networks and affect all aspects of cell biology by controlling the stability and translation efficiency of their target mRNAs. Here, we identified the mRNA cap-binding eIF4E-related protein 4EHP as an effector of miRNA-mediated translation repression. Through screening for protein interactions in cells via the BioID method, we identified 4EHP as a component of the CCR4–NOT/DDX6/4E-T axis. Direct interaction between 4E-T and 4EHP increases the latter’s cap-binding affinity, suggesting that this interaction potentiates its competition with the eIF4F complex for binding to the mRNA 5′ cap. Our findings suggest that 4EHP facilitates the formation of a closed-loop structure between the 3′ UTR of the mRNA and its 5′ cap, which causes repression of mRNA translation.</jats:p

iCLIP: Protein-RNA interactions at nucleotide resolution.

RNA-binding proteins (RBPs) are key players in the post-transcriptional regulation of gene expression. Precise knowledge about their binding sites is therefore critical to unravel their molecular function and to understand their role in development and disease. Individual-nucleotide resolution UV crosslinking and immunoprecipitation (iCLIP) identifies protein-RNA crosslink sites on a genome-wide scale. The high resolution and specificity of this method are achieved by an intramolecular cDNA circularization step that enables analysis of cDNAs that truncated at the protein-RNA crosslink sites. Here, we describe the improved iCLIP protocol and discuss critical optimization and control experiments that are required when applying the method to new RBPs