Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Targeting aberrant kinase activity in myeloid leukaemias

Acute myeloid leukaemia (AML) is the most common form of acute leukaemia in adults. Its treatment has remained largely unchanged for the past 30 years. Chronic myeloid leukaemia (CML) represents a tremendous success story in the era of targeted therapy but significant challenges remain including the development of drug resistance and disease persistence due to presence of CML stem cells. The Aurora family of kinases is essential for cell cycle regulation and their aberrant expression in cancer prompted the development of small molecules that selectively inhibit their activity. Chapter 2 of this thesis outlines the efficacy and mechanism of action of alisertib, a novel inhibitor of Aurora A kinase, in preclinical models of CML. Alisertib possessed equipotent activity against CML cells expressing unmutated and mutated forms of BCR-ABL. Notably, this agent retained high activity against the T315I and E255K BCR-ABL mutations, which confer the greatest degree of resistance to standard CML therapy. Chapter 3 explores the activity of alisertib in preclinical models of AML. Alisertib disrupted cell viability, diminished clonogenic survival, induced expression of the forkhead box O3 (FOXO3a) targets p27 and BCL-2 interacting mediator (BIM), and triggered apoptosis. A link between Aurora A expression and sensitivity to ara-C was established. Chapter 4 outlines the role of the proto-oncogene serine/threonine-protein (PIM) kinases in resistance to ara-C in AML. We report that the novel small molecule PIM kinase inhibitor SGI-1776 disrupted cell viability and induced apoptosis in AML. We establish a link between ara-C resistance and PIM over-expression. Finally, chapter 5 explores how the preclinical work outlined in this thesis may be translated into clinical studies that may lead to novel therapeutic approaches for patients with refractory myeloid leukaemia.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Characterisation of the non-muscle α-actinins

Actinins are cytoskeleton proteins that cross-link actin filaments. Evolution of the actinin family resulted in the formation of Ca++-insensitive muscle isoforms (actinin-2 and- 3) and Ca++-sensitive non-muscle isoforms (actinin-1 and -4) with regard to their actin-binding function. Despite high sequence similarity, unique properties have been ascribed to actinin-4 compared with actinin-1. Actinin-4 is the predominant isoform reported to be associated with the cancer phenotype. Actinin-4, but not actinin-1, is essential for normal glomerular function in the kidney and and is able to translocate to the nucleus to regulate transcription. To understand the molecular basis for such isoform-specific functions I have comprehensively compared these proteins in terms of localisation, migration, alternative splicing, actin-binding properties, heterodimer formation and molecular interactions for the first time. This work characterises a number of commercially available actinin antibodies and in doing so, identifies actinin-1, -2 and -4 isoform-specific antibodies that enabled studies of actinin expression and localisation. This work identifies the actinin rod domain as the predominant domain that influences actinin localisation however localisation is likely to be effected by the entire actinin protein. si-RNA- mediated knockdown of actinin-1 and -4 did not affect migration in a number of cell lines highlighting that migration may only require a fraction of total non-muscle actinin levels. This work finds that the Ca++-insensitive variant of actinin-4 is expressed only in the nervous system and thus cannot be regarded as a smooth muscle isoform, as is the case for the Ca++-insensitive variant of actinin-1. This work also identifies a previously unreported exon 19a+19b expressing variant of actinin-4 in human skeletal muscle. This work finds that alternative splice variants of actinin-1 and -4 are co-expressed in a number of tissues, in particular the brain. In contrast to healthy brain, glioblastoma cells express Ca++-sensitive variants of both actinin-1 and -4. Actin-binding properties of actinin-1 and -4 are similar and are unlikely to explain isoform-specific functions. Surprisingly, this work reveals that actinin-1/-4 heterodimers, rather than homodimers, are the most abundant form of actinin in many cancer cell lines. Taken together this data suggests that actinin-1 and -4 cannot be viewed as distinct entities from each other but rather as proteins that can exist in both homodimeric and heterodimeric forms. Finally, this work employs yeast two-hybrid and proteomic approaches to identify actinin-interacting proteins. In doing so, this work identifies a number of putative actinin-4 specific interacting partners that may help to explain some of the unique functions attributed the actinin-4. The observation of alternative splice variants of actinin-1 and -4 combined with the observed potential of these proteins to form homodimers and heterodimers suggests that homodimers and heterodimers with novel actin-binding properties and interaction networks may exist. The ability to behave in this manner may have functional implications. This may be of importance considering that these proteins are central to such processes as cell migration and adhesion. This significantly alters our view of the non-muscle actinins.

Development and characterization of novel transgenic techniques for the study of neuronal circuitry

Modern neuroscience relies heavily on sophisticated tools that allow us to visualize and manipulate cells with precise spatial and temporal control. Transgenic mouse models, for example, can be used to manipulate cellular activity in order to draw conclusions about the molecular events responsible for the development, maintenance and refinement of healthy and/or diseased neuronal circuits. Although it is fairly well established that circuits respond to activity-dependent competition between neurons, we have yet to understand either the mechanisms underlying these events or the higher-order plasticity that synchronizes entire circuits. In this thesis we aimed to develop and characterize transgenic mouse models that can be used to directly address these outstanding biological questions in different ways. We present SLICK-H, a Cre-expressing mouse line that can achieve drug-inducible, widespread, neuron-specific manipulations in vivo. This model is a clear improvement over existing models because of its particularly strong, widespread, and even distribution pattern that can be tightly controlled in the absence of drug induction. We also present SLICK-V::Ptox, a mouse line that, through expression of the tetanus toxin light chain, allows long-term inhibition of neurotransmission in a small subset (<1%) of fluorescently labeled pyramidal cells. This model, which can be used to study how a silenced cell performs in a wildtype environment, greatly facilitates the in vivo study of activity-dependent competition in the mammalian brain. As an initial application we used this model to show that tetanus toxin-expressing CA1 neurons experience a 15% - 19% decrease in apical dendritic spine density. Finally, we also describe the attempt to create additional Cre-driven mouse lines that would allow conditional alteration of neuronal activity either by hyperpolarization or inhibition of neurotransmission. Overall, the models characterized in this thesis expand upon the wealth of tools available that aim to dissect neuronal circuitry by genetically manipulating neurons in vivo.

Identification of novel innate immune mechanisms regulating inflammation in the gastrointestinal tract

The Gastro-Intestinal (GI) tract is a unique region in the body. Our innate immune system retains a fine homeostatic balance between avoiding inappropriate inflammatory responses against the myriad commensal microbes residing in the gut while also remaining active enough to prevent invasive pathogenic attack. The intestinal epithelium represents the frontline of this interface. It has long been known to act as a physical barrier preventing the lumenal bacteria of the gastro-intestinal tract from activating an inflammatory immune response in the immune cells of the underlying mucosa. However, in recent years, an appreciation has grown surrounding the role played by the intestinal epithelium in regulating innate immune responses, both in the prevention of infection and in maintaining a homeostatic environment through modulation of innate immune signalling systems. The aim of this thesis was to identify novel innate immune mechanisms regulating inflammation in the GI tract. To achieve this aim, we chose several aspects of regulatory mechanisms utilised in this region by the innate immune system. We identified several commensal strains of bacteria expressing proteins containing signalling domains used by Pattern Recognition Receptors (PRRs) of the innate immune system. Three such bacterial proteins were studied for their potentially subversive roles in host innate immune signalling as a means of regulating homeostasis in the GI tract. We also examined differential responses to PRR activation depending on their sub-cellular localisation. This was investigated based on reports that apical Toll-Like Receptor (TLR) 9 activation resulted in abrogation of inflammatory responses mediated by other TLRs in Intestinal Epithelial Cells (IECs) such as basolateral TLR4 activation. Using the well-studied invasive intra-cellular pathogen Listeria monocytogenes as a model for infection, we also used a PRR siRNA library screening technique to identify novel PRRs used by IECs in both inhibition and activation of inflammatory responses. Many of the PRRs identified in this screen were previously believed not to be expressed in IECs. Furthermore, the same study has led to the identification of the previously uncharacterised TLR10 as a functional inflammatory receptor of IECs. Further analysis revealed a similar role in macrophages where it was shown to respond to intracellular and motile pathogens such as Gram-positive L.monocytogenes and Gram negative Salmonella typhimurium. TLR10 expression in IECs was predominantly intracellular. This is likely in order to avoid inappropriate inflammatory activation through the recognition of commensal microbial antigens on the apical cell surface of IECs. Moreover, these results have revealed a more complex network of innate immune signalling mechanisms involved in both activating and inhibiting inflammatory responses in IECs than was previously believed. This contribution to our understanding of innate immune regulation in this region has several direct and indirect benefits. The identification of several novel PRRs involved in activating and inhibiting inflammation in the GI tract may be used as novel therapeutic targets in the treatment of disease; both for inducing tolerance and reducing inflammation, or indeed, as targets for adjuvant activation in the development of oral vaccines against pathogenic attack.

Investigation of p75 neurotrophin receptor and the role of its post-translational modifications in tumour cell motility and invasiveness

The p75 neurotrophin receptor (p75NTR) is a member of the tumour necrosis factor superfamily, which relies on the recruitment of cytosolic protein partners - including the TNF receptor associated factor 6 (TRAF6) E3 ubiquitin ligase - to produce cellular responses such as apoptosis, survival, and inhibition of neurite outgrowth. Recently,p75NTR was also shown to undergo γ-secretase-mediated regulated intramembrane proteolysis, and the receptor ICD was found to migrate to the nucleus where it regulates gene transcription. Moreover, γ-secretase-mediated proteolysis was shown to be involved in glioblastoma cell migration and invasion. In this study we report that TRAF6-mediated K63-linked polyubiquitination at multiple or alternative lysine residues influences p75NTR-ICD stability in vitro. In addition, we found that TRAF6-mediated ubiquitination of p75NTR is not influenced by inhibition of dynamin. Moreover, we report beta-transducin repeats-containing protein (β-TrCP) as a novel E3- ligase that ubiquitinates p75NTR, which is independent of serine phosphorylation of the p75NTR destruction motif. In contrast to its influence on other substrates, co-expression of β-TrCP did not reduce p75NTR stability. We created U87-MG glioblastoma cell lines stably expressing wild type, γ-secretaseresistant and constitutively cleaved receptor, as well as the ICD-stabilized mutant K301R. Interestingly, only wild-type p75NTR induces increased glioblastoma cell migration, which could be reversed by application of γ-secretase inhibitor. Microarray and qRT-PCR analysis of mRNA transcripts in these cell lines yielded several promising genes that might be involved in glioblastoma cell migration and invasion, such as cadherin 11 and matrix metalloproteinase 12. Analysis of potential transcription factor binding sites revealed that transcription of these genes might be regulated by well known p75NTR signalling cascades such as NF-κB or JNK signalling, which are independent of γ-secretase-mediated cleavage of the receptor. In contrast, while p75NTR overexpression was confirmed in melanoma cell lines and a patient sample of melanoma metastasis to the brain, inhibition of γ-secretase did not influence melanoma cell migration. Collectively, this study provides several avenues to better understand the physiological importance of posttranslational modifications of p75NTR and the significance of the receptor in glioblastoma cell migration and invasion.

Parents' experiences of child growth and development concerns: an interpretative phenomenological analysis

Background: Assessing child growth and development is complex. Delayed identification of growth or developmental problems until school entry has health, educational and social consequences for children and families. Health care professionals (HCPs), including Public Health Nurses work with parents to elicit and attend to their growth and development concerns. It is known that parents have concerns about their children’s growth and development which are not expressed in a timely manner. Measuring parental concern has not been fully effective to date and little is known about parents’ experiences of expressing concerns. Aim: To understand how parents make sense of child growth or development concerns. Method: The study was qualitative using Interpretative Phenomenological Analysis (IPA). A purposeful sample of 15 parents of pre-school children referred by their PHN to second tier services was used. Data were collected by semi-structured interviews. NVivo version 10 was used for data management purposes and IPA for analysis. Findings: Findings yielded two contextual themes which captured how parents described The Concern – ‘telling it as it is’ and their experiences of being Referred on. Four superordinate themes were found which encapsulated the Uncertainty – ‘a little bit not sure’ of parents as they made sense of the child’s growth and development problems. They were influenced by Parental Knowledge – ‘being and getting in the know’ which aided their sense-making before being prompted by Triggers to action. Parents then described Getting the child’s problem checked out as they went to express their concerns to HCPs. Conclusion and Implications: Parental expression of concerns about their child is a complex process that may not be readily understood by HCPs. A key implication of findings is to reappraise how parental concern is elicited and attended to in order to promote early referral and intervention of children who may have growth and development problems.

Investigating the invasive and cytoprotective properties of the heme binding protein HRG-1 in cancer cells

This thesis investigates the mechanisms by which HRG-1 contributes to the invasive and cytoprotective signalling pathways in cancer cells through its effects on VATPase activity and heme transport. Plasma membrane-localised V-ATPase activity correlates with enhanced metastatic potential in cancer cells, which is attributed to extrusion of protons into the extracellular space and activation of pH-sensitive, extracellular matrix degrading-proteases. We found that HRG-1 is co-expressed with the V-ATPase at the plasma membrane of certain aggressive cancer cell types. Modulation of HRG-1 expression altered both the localisation and activity of the VATPase. We also found that HRG-1 enhances trafficking of essential transporters such as the glucose transporter (GLUT-1) in cancer cells, and increases glucose uptake, which is required for cancer cell growth, metabolism and V-ATPase assembly. Heme is potentially cytotoxic, owing to its iron moiety, and therefore the trafficking of heme is tightly controlled in cells. We hypothesised that HRG-1 is required for the transport of heme to intracellular compartments. Importantly, we found that HRG-1 interacts with the heme oxygenases that are necessary for heme catabolism. HRG-1 is also required for trafficking of both heme-bound and nonheme-bound receptors and suppression of HRG-1 results in perturbed receptor trafficking to the lysosome. Suppression of HRG-1 in HeLa cells increases toxic heme accumulation, reactive oxygen species accumulation, and DNA damage resulting in caspasedependent cell death. Mutation of essential heme binding residues in HRG-1 results in decreased heme binding to HRG-1. Interestingly, cells expressing heme-binding HRG-1 mutants exhibit decreased internalisation of the transferrin receptor compared to cells expressing wildtype HRG-1. These findings suggest that HRG- 1/heme trafficking contributes to a hitherto unappreciated aspect of receptormediated endocytosis. Overall, the findings of this thesis show that HRG-1-mediated regulation of intracellular and extracellular pH through V-ATPase activity is essential for a functioning endocytic pathway. This is critical for cells to acquire nutrients such as folate, iron and glucose and to mediate signalling in response to growth factor activation. Thus, HRG-1 facilitates enhanced metabolic activity of cancer cells to enable tumour growth and metastasis.

Thuricin CD: a potential therapeutic targeted against Clostridium difficile-associated diarrhea (CDAD)

Clostridium difficile is mainly a nosocomial pathogen and is a significant cause of antibioticassociated diarrhea. It is also implicated in the majority of cases of pseudomembranous colitis. The main etiological agent of C. difficile-associated diarrhea (CDAD) is perturbations to the gut microbiota by broad-spectrum antibiotics. Recently, thuricin CD, a two-peptide narrow spectrum sactibiotic bacteriocin with potent activity against C. difficile has been discovered. It is produced by Bacillus thuringiensis DPC6431. The efficacy of thuricin CD against a range of C. difficile clinical isolates has been determined in the form of minimum inhibitory concentration (MIC) values and compared to metronidazole, vancomycin, ramoplanin and actagardine in this thesis. Furthermore, by assessing paired combinations of the above-mentioned antimicrobials, it was determined that ramoplanin and actagardine function in a synergistic manner against the majority of C. difficile isolates. The functions of the genes in the thuricin CD gene cluster have also been elucidated by cloning the cluster and expressing thuricin CD in a heterologous Bacillus subtilis host and are described herein. In addition, the immunity mechanisms employed by the B. thuringiensis DPC6431 producer to protect itself from the antimicrobial actions of thuricin CD have also been elucidated. It has been shown that a small immunity peptide, TrnI, is involved in thuricin CD immunity, most likely by intercepting the thuricin CD peptides and/or blocking their access to the thuricin CD receptor. This immunity peptide and also the ABC-transporter system TrnFG serve to protect the B. thuringiensis host against thuricin CD.

Investigations into the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy and maternal immune activation

The amygdala is a limbic structure that is involved in many of our emotions and processing of these emotions such as fear, anger and pleasure. Conditions such as anxiety, autism, and also epilepsy, have been linked to abnormal functioning of the amygdala, owing to improper neurodevelopment or damage. This thesis investigated the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy (TLE) and maternal immune activation (MIA). The kainic acid (KA) model of temporal lobe epilepsy (TLE) was used to induce Ammon’s-horn sclerosis (AHS) and to investigate behavioural and cytoarchitectural changes that occur in the amygdala related to Neuropeptide Y1 receptor expression. Results showed that KA-injected animals showed increased anxiety-like behaviours and displayed histopathological hallmarks of AHS including CA1 ablation, granule cell dispersion, volume reduction and astrogliosis. Amygdalar volume and neuronal loss was observed in the ipsilateral nuclei which was accompanied by astrogliosis. In addition, a decrease in Y1 receptor expressing cells in the ipsilateral CA1 and CA3 sectors of the hippocampus, ipsi- and contralateral granule cell layer of the dentate gyrus and ipsilateral central nucleus of the amygdala was found, consistent with a reduction in Y1 receptor protein levels. The results suggest that plastic changes in hippocampal and/or amygdalar Y1 receptor expression may negatively impact anxiety levels. Gamma-aminobutyric acid (GABA) is the main inhibitory neurotransmitter in the brain and tight regulation and appropriate control of GABA is vital for neurochemical homeostasis. GABA transporter-1 (GAT-1) is abundantly expressed by neurones and astrocytes and plays a key role in GABA reuptake and regulation. Imbalance in GABA homeostasis has been implicated in epilepsy with GAT-1 being an attractive pharmacological target. Electron microscopy was used to examine the distribution, expression and morphology of GAT-1 expressing structures in the amygdala of the TLE model. Results suggest that GAT-1 was preferentially expressed on putative axon terminals over astrocytic processes in this TLE model. Myelin integrity was examined and results suggested that in the TLE model myelinated fibres were damaged in comparison to controls. Synaptic morphology was studied and results suggested that asymmetric (excitatory) synapses occurred more frequently than symmetric (inhibitory) synapses in the TLE model in comparison to controls. This study illustrated that the amygdala undergoes ultrastructural alterations in this TLE model. Maternal immune activation (MIA) is a risk factor for neurodevelopmental disorders such as autism, schizophrenia and also epilepsy. MIA was induced at a critical window of amygdalar development at E12 using bacterial mimetic lipopolysaccharide (LPS). Results showed that MIA activates cytokine, toll-like receptor and chemokine expression in the fetal brain that is prolonged in the postnatal amygdala. Inflammation elicited by MIA may prime the fetal brain for alterations seen in the glial environment and this in turn have deleterious effects on neuronal populations as seen in the amygdala at P14. These findings may suggest that MIA induced during amygdalar development may predispose offspring to amygdalar related disorders such as heightened anxiety, fear impairment and also neurodevelopmental disorders.

Redox biology of myeloid leukaemias

Internal tandem duplication of FMS-like receptor tyrosine kinase (FLT3-ITD) has been associated with an aggressive AML phenotype. FLT3-ITD expressing cell lines have been shown to generate increased levels of reactive oxygen species (ROS) and DNA double strand breaks (dsbs). However, the molecular basis of how FLT3-ITD-driven ROS leads to the aggressive form of AML is not clearly understood. Herein, we observe that the majority of H2O2 in FLT3-ITD-expressing MV4-11 cells colocalises to the endoplasmic reticulum (ER). Furthermore, ER localisation of ROS in MV4-11 cells corresponds to the localisation of p22phox, a small membrane-bound subunit of NOX complex. Furthermore, we show that 32D cells, a myeloblast-like cell line transfected with FLT3-ITD, possess higher steady protein levels of p22phox than their wild type FLT3 (FLT3-WT)-expressing counterparts. Moreover, the inhibition of FLT3-ITD, using various FLT3 tyrosine kinase inhibitors, uniformly results in a posttranslational downregulation of p22phox. We also show that depletion of NOX2 and NOX4 and p22phox, but not NOX1 proteins causes a reduction in endogenous H2O2 levels. We show that genomic instability induced by FLT3-ITD leads to an increase in nuclear levels of H2O2. The presence of H2O2 in the nucleus is largely reduced by inhibition of FLT3-ITD or NOX. Furthermore, similar results are also observed following siRNA knockdowns of p22phox or NOX4. We demonstrate that 32D cells transfected with FLT3-ITD have a higher level of DNA damage than 32D cells transfected with FLT3-WT. Additionally, inhibition of FLT3-ITD, p22phox and NOX knockdowns decrease the number of DNA dsbs. In summary, this study presents a novel mechanism of genomic instability generation in FLT3-ITD-expressing AML cells, whereby FLT3-ITD activates NOX complexes by stabilising p22phox. This in turn leads to elevated generation of ROS and DNA damage in these cells.