Aspects of PT-symmetric quantum mechanics

PT-symmetric quantum mechanics is an alternative to the usual hermitian quantum mechanics. We will start this thesis by taking an overview of the subject, seeing some of the elementary consequences of this different approach. The main part of the work will be an depth study of a specific Hamiltonian(diagram) This is a generalisation of the well understood harmonic oscillator with angular momentum. By making this generalisation we break the hermiticity of the problem. This leads to some intriguing results. We will be particularly interested in the merging of eigenvalues for M <1.We study the problem using a number of techniques. First the Hamiltonian is studied at the classical level and the behaviour of a particle moving in the corresponding potential is studied. Having seen the consequences at the classical level we return to the quantum case. The Hamiltonian is first solved perturbativly. This method is shown to be valid for PT-symmetric quantum mechanics. It is shown that asymptotic limits of the matrix do not capture the full behaviour of the energy levels. We then move on to study the problem considering techniques arising from the ODE/IM correspondence. Using this approach we are able to give an analytic description of the phenomena and explain the merging of eigenvalues

Nav1.5 regulates breast tumor growth and metastatic dissemination in vivo

Voltage-gated Na(+) channels (VGSCs) mediate action potential firing and regulate adhesion and migration in excitable cells. VGSCs are also expressed in cancer cells. In metastatic breast cancer (BCa) cells, the Na(v)1.5 α subunit potentiates migration and invasion. In addition, the VGSC-inhibiting antiepileptic drug phenytoin inhibits tumor growth and metastasis. However, the functional activity of Na(v)1.5 and its specific contribution to tumor progression in vivo has not been delineated. Here, we found that Na(v)1.5 is up-regulated at the protein level in BCa compared with matched normal breast tissue. Na(+) current, reversibly blocked by tetrodotoxin, was retained in cancer cells in tumor tissue slices, thus directly confirming functional VGSC activity in vivo. Stable down-regulation of Na(v)1.5 expression significantly reduced tumor growth, local invasion into surrounding tissue, and metastasis to liver, lungs and spleen in an orthotopic BCa model. Na(v)1.5 down-regulation had no effect on cell proliferation or angiogenesis within the in tumors, but increased apoptosis. In vitro, Na(v)1.5 down-regulation altered cell morphology and reduced CD44 expression, suggesting that VGSC activity may regulate cellular invasion via the CD44-src-cortactin signaling axis. We conclude that Na(v)1.5 is functionally active in cancer cells in breast tumors, enhancing growth and metastatic dissemination. These findings support the notion that compounds targeting Na(v)1.5 may be useful for reducing metastasis

in breast cancer

PSMD9 expression predicts radiotherapy respons

MiR-19b non-canonical binding is directed by HuR and confers chemosensitivity through regulation of P-glycoprotein in breast cancer

MicroRNAs and RNA-binding proteins exert regulation on >60% of coding genes, yet interplay between them is little studied. Canonical microRNA binding occurs by base-pairing of microRNA 3′-ends to complementary “seed regions” in mRNA 3′UTRs, resulting in translational repression. Similarly, regulatory RNA-binding proteins bind to mRNAs, modifying stability or translation. We investigated post-transcriptional regulation acting on the xenobiotic pump ABCB1/P-glycoprotein, which is implicated in cancer therapy resistance. We characterised the ABCB1 UTRs in primary breast cancer cells and identified UTR sequences that responded to miR-19b despite lacking a canonical binding site. Sequences did, however, contain consensus sites for the RNA-binding protein HuR. We demonstrated that a tripartite complex of HuR, miR-19b and UTR directs repression of ABCB1/P-glycoprotein expression, with HuR essential for non-canonical miR-19b binding thereby controlling chemosensitivity of breast cancer cells. This exemplifies a new cooperative model between RNA-binding proteins and microRNAs to expand the repertoire of mRNAs that can be regulated. This study suggests a novel therapeutic target to impair P-glycoprotein mediated drug efflux, and also indicates that current microRNA binding predictions that rely on seed regions alone may be too conservative

A Case Matched Gender Comparison Transcriptomic Screen Identifies eIF4E and eIF5 as Potential Prognostic and Tractable Biomarkers in Male Breast Cancer

Purpose: Breast cancer (BC) affects both genders, but is understudied in men. Although still rare, male BC is being diagnosed more frequently. Treatments are wholly informed by clinical studies conducted in women, based on assumptions that underlying biology is similar. Experimental design: A transcriptomic investigation of male and female BC was performed, confirming transcriptomic data in silico. Biomarkers were immunohistochemically assessed in 697 MBCs (n=477, training; n=220, validation set) and quantified in pre- and post-treatment samples from a male BC patient receiving Everolimus and PI3K/mTOR inhibitor. Results: Gender-specific gene expression patterns were identified. eIF transcripts were up-regulated in MBC. eIF4E and eIF5 were negatively prognostic for overall survival alone (Log rank; p=0.013; HR=1.77, 1.12-2.8 and p=0.035; HR=1.68, 1.03-2.74, respectively), or when co-expressed (p=0.01; HR=2.66, 1.26-5.63), confirmed in the validation set. This remained upon multivariate Cox regression analysis (eIF4E p=0.016; HR 2.38 (1.18-4.8), eIF5 p=0.022; HR 2.55 (1.14-5.7); co-expression p=0.001; HR=7.04 (2.22-22.26)). Marked reduction in eIF4E and eIF5 expression was seen post BEZ235/Everolimus, with extended survival. Conclusions: Translational initiation pathway inhibition could be of clinical utility in male BC patients overexpressing eIF4E and eIF5. With mTOR inhibitors which target this pathway now in the clinic, these biomarkers may represent new targets for therapeutic intervention, although further independent validation is required

Retrospective observational study of HER2 immunohistochemistry in borderline breast cancer patients undergoing neoadjuvant therapy, with an emphasis on Group 2 (HER2/CEP17 ratio ≥2.0, HER2 copy number <4.0 signals/cell) cases.

BACKGROUND: The ASCO/CAP guidance on HER2 testing in breast cancer (BC) has recently changed. Group 2 tumours with immunohistochemistry score 2+ and HER2/CEP17 ratio ≥2.0 and HER2 copy number <4.0 signals/cell were re-classified as HER2 negative. This study aims to examine the response of Group 2 tumours to neoadjuvant chemotherapy (NACT). METHODS: 749 BC cases were identified from 11 institutions. The association between HER2 groups and pathological complete response (pCR) was assessed. RESULTS: 54% of immunohistochemistry HER2 positive (score 3+) BCs showed pCR, compared to 19% of immunohistochemistry 2+ FISH amplified cases. 27% of Group 2 treated with HER2 targeted therapy achieved pCR, compared to 19 and 11% in the combined Groups 1 + 3 and Groups 4 + 5, respectively. No difference in pCR rates was identified between Group 2 and Group 1 or combined Groups 1 + 3. However, Group 2 response rate was higher than Groups 4 + 5 (p = 0.017). CONCLUSION: No difference in pCR was detected in tumours with a HER2/CEP17 ratio ≥2.0 and a HER2 score 2+ by IHC when stratified by HER2 gene copy number. Our data suggest that ASCO/CAP HER2 Group 2 carcinomas should be evaluated further with respect to eligibility for HER2 targeted therapy

Expression of phosphorylated eIF4E-binding protein 1, but not of eIF4E itself, predicts survival in male breast cancer

Background: Male breast cancer is rare and treatment is based on data from females. High expression/activity of eukaryotic initiation factor 4E (eIF4E) denotes a poor prognosis in female breast cancer, and the eIF4E pathway has been targeted therapeutically. eIF4E activity in female breast cancer is deregulated by eIF4E over-expression and by phosphorylation of its binding protein, 4E-BP1, which relieves inhibitory association between eIF4E and 4E-BP1. The relevance of the eIF4E pathway in male breast cancer is unknown. Methods: We have assessed expression levels of eIF4E, 4E-BP1, 4E-BP2 and phosphorylated 4E-BP1 (p4E-BP1) using immunohistochemistry in a large cohort of male breast cancers (n=337) and have examined correlations with prognostic factors and survival. Results: Neither eIF4E expression or estimated eIF4E activity were associated with prognosis. However, a highly significant correlation was found between p4E-BP1 expression and disease-free survival, linking any detectable p4E-BP1 with poor survival (univariate log rank p=0.001; multivariate HR 8.8, p=0.0001). Conclusions: Our data provide no support for direct therapeutic targeting of eIF4E in male breast cancer, unlike in females. However, as p4E-BP1 gives powerful prognostic insights that are unrelated to eIF4E function, p4E-BP1 may identify male breast cancers potentially suitable for therapies directed at the upstream kinase, mTOR

Down-Regulation of miR-92 in Breast Epithelial Cells and in Normal but Not Tumour Fibroblasts Contributes to Breast Carcinogenesis

Background MicroRNA (miR) expression is commonly dysregulated in many cancers, including breast. MiR–92 is one of six miRs encoded by the miR-17-92 cluster, one of the best-characterised oncogenic miR clusters. We examined expression of miR–92 in the breast epithelium and stroma during breast cancer progression. We also investigated the role of miR–92 in fibroblasts in vitro and showed that down-regulation in normal fibroblasts enhances the invasion of breast cancer epithelial cells. Methodology/Principal Findings We used laser microdissection (LMD) to isolate epithelial cells from matched normal, DCIS and invasive tissue from 9 breast cancer patients and analysed miR–92 expression by qRT-PCR. Expression of ERβ1, a direct miR–92 target, was concurrently analysed for each case by immunohistochemistry. LMD was also used to isolate matched normal (NFs) and cancer-associated fibroblasts (CAFs) from 14 further cases. Effects of miR–92 inhibition in fibroblasts on epithelial cell invasion in vitro was examined using a Matrigel™ assay. miR– 92 levels decreased in microdissected epithelial cells during breast cancer progression with highest levels in normal breast epithelium, decreasing in DCIS (p<0.01) and being lowest in invasive breast tissue (p<0.01). This was accompanied by a shift in cell localisation of ERβ1 from nuclear expression in normal breast epithelium to increased cytoplasmic expression during progression to DCIS (p = 0.0078) and invasive breast cancer (p = 0.031). ERβ1 immunoreactivity was also seen in stromal fibroblasts in tissues. Where miR–92 expression was low in microdissected NFs this increased in matched CAFs; a trend also seen in cultured primary fibroblasts. Down-regulation of miR–92 levels in NFs but not CAFs enhanced invasion of both MCF–7 and MDA-MB–231 breast cancer epithelial cells. Conclusions miR–92 is gradually lost in breast epithelial cells during cancer progression correlating with a shift in ERβ1 immunoreactivity from nuclei to the cytoplasm. Our data support a functional role in fibroblasts where modification of miR–92 expression can influence the invasive capacity of breast cancer epithelial cells. However in silico analysis suggests that ERβ1 may not be the most important miR–92 target in breast cancer

Beyond the WKB approximation in PT-symmetric quantum mechanics

The mergings of energy levels associated with the breaking of symmetry in the model of Bender and Boettcher, and in its generalization to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrödinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero