Bulk and boundary scattering in the q-state potts mode

This thesis is concerned with the properties of 1 + 1 dimensional massive field theories in both infinite and semi-infinite geometries. Chapters 1, 2 and 3 develop the necessary theoretical framework and review existing work by Chim and Zamolodchikov [1] on integrable perturbations of the (bulk) q-state Potts model, the particular model under consideration in this thesis. Chapter 4 consists of a detailed analysis of the bootstrap for this model, during the course of which unexpected behaviour arises. The treatment of 1] has consequently been revised, but further investigation will be necessary before complete understanding of this behaviour can be reached. In the final chapter, attention turns to the imposition of boundary conditions on two dimensional systems. After looking at this from a statistical mechanical point of view, a brief review of boundary conformal held theory and its integrable perturbations is given. This leads once more to a consideration of the q-state Potts model. After summarising [2], where fixed and free boundary conditions are considered, a third and previously untreated boundary condition is discussed

Dissipative Pairing Interactions: Quantum Instabilities, Topological Light, and Volume-Law Entanglement

We analyze an unusual class of bosonic dynamical instabilities that arise from dissipative (or non-Hermitian) pairing interactions. We show that, surprisingly, a completely stable dissipative pairing interaction can be combined with simple hopping or beam-splitter interactions (also stable) to generate instabilities. Further, we find that the dissipative steady state in such a situation remains completely pure up until the instability threshold (in clear distinction from standard parametric instabilities). These pairing-induced instabilities also exhibit an extremely pronounced sensitivity to wavefunction localization. This provides a simple yet powerful method for selectively populating and entangling edge modes of photonic (or more general bosonic) lattices having a topological bandstructure. The underlying dissipative pairing interaction is experimentally resource-friendly, requiring the addition of a single additional localized interaction to an existing lattice, and is compatible with a number of existing platforms, including superconducting circuits

The proteomes of neurotransmitter receptor complexes form modular networks with distributed functionality underlying plasticity and behaviour

Neuronal synapses play fundamental roles in information processing, behaviour and disease. Neurotransmitter receptor complexes, such as the mammalian N-methyl-D-aspartate receptor complex (NRC/MASC) comprising 186 proteins, are major components of the synapse proteome. Here we investigate the organisation and function of NRC/MASC using a systems biology approach. Systematic annotation showed that the complex contained proteins implicated in a wide range of cognitive processes, synaptic plasticity and psychiatric diseases. Protein domains were evolutionarily conserved from yeast, but enriched with signalling domains associated with the emergence of multicellularity. Mapping of protein–protein interactions to create a network representation of the complex revealed that simple principles underlie the functional organisation of both proteins and their clusters, with modularity reflecting functional specialisation. The known functional roles of NRC/MASC proteins suggest the complex co-ordinates signalling to diverse effector pathways underlying neuronal plasticity. Importantly, using quantitative data from synaptic plasticity experiments, our model correctly predicts robustness to mutations and drug interference. These studies of synapse proteome organisation suggest that molecular networks with simple design principles underpin synaptic signalling properties with important roles in physiology, behaviour and disease

Gender differences in CNV burden do not confound schizophrenia CNV associations

Compared with the general population, an excess of rare copy number variants (CNVs) has been identified in people with schizophrenia. Females with neurodevelopmental disorders and in the general population have been reported to carry more large, rare CNVs than males. Given that many schizophrenia datasets do not have equal gender ratios in cases and controls, sex differences in CNV burden might have impacted on estimates of case-related CNV burden and also on associations to individual loci. In a sample of 13,276 cases and 17,863 controls, we observed a small but significant excess of large (≥500 Kb), rare (<1%) CNVs in females compared with males in both cases and controls (OR = 1.17, P = 0.0012 for controls; OR = 1.11, P = 0.045 for cases). The burden of 11 schizophrenia-associated CNVs was significantly higher in female cases compared with male cases (OR = 1.38, P = 0.0055), but after accounting for the rates of CNVs in controls, we found no significant gender difference in the risk conferred by these loci. Controlling for gender had a negligible effect on the significance of association between specific CNVs and schizophrenia. The female excess of large CNVs in both cases and controls suggests a female protective mechanism exists for deleterious CNVs that may extend beyond neurodevelopmental phenotypes

Neurotransmitters Drive Combinatorial Multistate Postsynaptic Density Networks

The mammalian postsynaptic density (PSD) comprises a complex collection of ~1100 proteins. Despite extensive knowledge of individual proteins, the overall organization of the PSD is poorly understood. Here, we define maps of molecular circuitry within the PSD based on phosphorylation of postsynaptic proteins. Activation of a single neurotransmitter receptor, the N-methyl-D-aspartate receptor (NMDAR), changed the phosphorylation status of 127 proteins. Stimulation of ionotropic and metabotropic glutamate receptors and dopamine receptors activated overlapping networks with distinct combinatorial phosphorylation signatures. Using peptide array technology, we identified specific phosphorylation motifs and switching mechanisms responsible for the integration of neurotransmitter receptor pathways and their coordination of multiple substrates in these networks. These combinatorial networks confer high information-processing capacity and functional diversity on synapses, and their elucidation may provide new insights into disease mechanisms and new opportunities for drug discover

Polygenic risk for schizophrenia and subcortical brain anatomy in the UK Biobank cohort

Research has shown differences in subcortical brain volumes between participants with schizophrenia and healthy controls. However, none of these differences have been found to associate with schizophrenia polygenic risk. Here, in a large sample (n = 14,701) of unaffected participants from the UK Biobank, we test whether schizophrenia polygenic risk scores (PRS) limited to specific gene-sets predict subcortical brain volumes. We compare associations with schizophrenia PRS at the whole genome level (‘genomic’, including all SNPs associated with the disorder at a p-value threshold < 0.05) with ‘genic’ PRS (based on SNPs in the vicinity of known genes), ‘intergenic’ PRS (based on the remaining SNPs), and genic PRS limited to SNPs within 7 gene-sets previously found to be enriched for genetic association with schizophrenia (‘abnormal behaviour,’ ‘abnormal long-term potentiation,’ ‘abnormal nervous system electrophysiology,’ ‘FMRP targets,’ ‘5HT2C channels,’ ‘CaV2 channels’ and ‘loss-of-function intolerant genes’). We observe a negative association between the ‘abnormal behaviour’ gene-set PRS and volume of the right thalamus that survived correction for multiple testing (ß = −0.031, pFDR = 0.005) and was robust to different schizophrenia PRS p-value thresholds. In contrast, the only association with genomic PRS surviving correction for multiple testing was for right pallidum, which was observed using a schizophrenia PRS p-value threshold < 0.01 (ß = −0.032, p = 0.0003, pFDR = 0.02), but not when using other PRS P-value thresholds. We conclude that schizophrenia PRS limited to functional gene sets may provide a better means of capturing differences in subcortical brain volume than whole genome PRS approaches

Dynamic expression of genes associated with schizophrenia and bipolar disorder across development

Common genetic variation contributes a substantial proportion of risk for both schizophrenia and bipolar disorder. Furthermore, there is evidence of significant, but not complete, overlap in genetic risk between the two disorders. It has been hypothesised that genetic variants conferring risk for these disorders do so by influencing brain development, leading to the later emergence of symptoms. The comparative profile of risk gene expression for schizophrenia and bipolar disorder across development over different brain regions however remains unclear. Using genotypes derived from genome-wide associations studies of the largest available cohorts of patients and control subjects, we investigated whether genes enriched for schizophrenia and bipolar disorder association show a bias for expression across any of 13 developmental stages in prefrontal cortical and subcortical brain regions. We show that genetic association with schizophrenia is positively correlated with expression in the prefrontal cortex during early midfetal development and early infancy, and negatively correlated with expression during late childhood, which stabilises in adolescence. In contrast, risk-associated genes for bipolar disorder did not exhibit a bias towards expression at any prenatal stage, although the pattern of postnatal expression was similar to that of schizophrenia. These results highlight the dynamic expression of genes harbouring risk for schizophrenia and bipolar disorder across prefrontal cortex development and support the hypothesis that prenatal neurodevelopmental events are more strongly associated with schizophrenia than bipolar disorder

Pharmacogenomic variants and drug interactions identified through the genetic analysis of clozapine metabolism

Objective: Clozapine is the only effective medication for treatment-resistant schizophrenia, but its worldwide use is still limited because of its complex titration protocols. While the discovery of pharmacogenomic variants of clozapine metabolism may improve clinical management, no robust findings have yet been reported. This study is the first to adopt the framework of genome-wide association studies (GWASs) to discover genetic markers of clozapine plasma concentrations in a large sample of patients with treatment-resistant schizophrenia. Methods: The authors used mixed-model regression to combine data from multiple assays of clozapine metabolite plasma concentrations from a clozapine monitoring service and carried out a genome-wide analysis of clozapine, norclozapine, and their ratio on 10,353 assays from 2,989 individuals. These analyses were adjusted for demographic factors known to influence clozapine metabolism, although it was not possible to adjust for all potential mediators given the available data. GWAS results were used to pinpoint specific enzymes and metabolic pathways and compounds that might interact with clozapine pharmacokinetics. Results: The authors identified four distinct genome-wide significant loci that harbor common variants affecting the metabolism of clozapine or its metabolites. Detailed examination pointed to coding and regulatory variants at several CYP* and UGT* genes as well as corroborative evidence for interactions between the metabolism of clozapine, coffee, and tobacco. Individual effects of single single-nucleotide polymorphisms (SNPs) fine-mapped from these loci were large, such as the minor allele of rs2472297, which was associated with a reduction in clozapine concentrations roughly equivalent to a decrease of 50 mg/day in clozapine dosage. On their own, these single SNPs explained from 1.15% to 9.48% of the variance in the plasma concentration data. Conclusions: Common genetic variants with large effects on clozapine metabolism exist and can be found via genome-wide approaches. Their identification opens the way for clinical studies assessing the use of pharmacogenomics in the clinical management of patients with treatment-resistant schizophrenia