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

The greatest catch:Big game fishing for mRNA-bound proteins

Purification of proteins cross-linked to mRNAs has identified 800 mRNA-binding proteins and their characteristics

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

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

Heteromeric RNP Assembly at LINEs Controls Lineage-Specific RNA Processing.

Long mammalian introns make it challenging for the RNA processing machinery to identify exons accurately. We find that LINE-derived sequences (LINEs) contribute to this selection by recruiting dozens of RNA-binding proteins (RBPs) to introns. This includes MATR3, which promotes binding of PTBP1 to multivalent binding sites within LINEs. Both RBPs repress splicing and 3' end processing within and around LINEs. Notably, repressive RBPs preferentially bind to evolutionarily young LINEs, which are located far from exons. These RBPs insulate the LINEs and the surrounding intronic regions from RNA processing. Upon evolutionary divergence, changes in RNA motifs within LINEs lead to gradual loss of their insulation. Hence, older LINEs are located closer to exons, are a common source of tissue-specific exons, and increasingly bind to RBPs that enhance RNA processing. Thus, LINEs are hubs for the assembly of repressive RBPs and also contribute to the evolution of new, lineage-specific transcripts in mammals. VIDEO ABSTRACT

A lactate shuttle system between tumour and stromal cells is associated with poor prognosis in prostate cancer

Background In a malignant tumour, cancer cells are embedded in stromal cells, namely cancer-associated fibroblasts (CAFs). These CAFs are now accepted as important players in cancer dynamics, being involved in tumour growth and progression. Although there are various reports on the interaction between tumour and stromal cells, the clinico-pathological significance of this cross-talk is still largely unknown. In this study, we aimed to characterise the expression of key metabolic proteins involved in glucose transport, pyruvate/lactate shuttle system, glycolytic metabolism and fatty acid oxidation in CAFs and tumour cells in different stages of malignant transformation. We further aimed to contextualise the clinico-pathological significance of these protein expression profiles with reference to known prognostic indicators, including biochemical recurrence in pT stage. Methods Prostate tissues were obtained from 480 patients with a median age of 64 years following radical prostatectomy with no previous hormonal therapy. Tissues were analysed for the expression of several key metabolism-related proteins in glands and surrounding fibroblasts by immunohistochemistry. Reliable markers of prognosis such as pT stage and biochemical recurrence were assessed for each case. Results We observed that prostate cancer cells did not rely mainly on glycolytic metabolism, while there was a high expression of MCT4 and CAIX - in CAFs. This corroborates the hypothesis of the "Reverse Warburg effect" in prostate cancer, in which fibroblasts are under oxidative stress and express CAIX, an established hypoxia marker. We found that alterations in the expression of metabolism-related proteins were already evident in the early stages of malignant transformation, suggesting the continuing alteration of CAFs from an early stage. Additionally, and for the first time, we show that cases showing high MCT4 expression in CAFs with concomitant strong MCT1 expression in prostate cancer (PCa) cells are associated with poor clinical outcome, namely pT3 stage of the tumour. Conclusions In summary, this work demonstrates for the first time the clinico-pathological significance of the lactate shuttle in prostate cancer. It also suggests that other alterations in CAFs may be useful prognostic factors, and further supports the use of MCT1/MCT4 as targets for PCa therapy.NPG received a fellowship from the Portuguese Foundation for Science and Technology (FCT), refs. SFRH/BD/61027/2009. This work was supported by the FCT grant ref. PTDC/SAUMET/113415/2009, under the scope of "Programa Operacional Tematico Factores de Competitividade" (COMPETE) of "Quadro Comunitario de Apoio III" and co-financed by Fundo Comunitario Europeu FEDER. JA was supported by a Boehringer Ingelheim Fonds fellowship