Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Function of the PDLIM2 protein in oncogenic Wnt signalling pathways

Aberrant regulation of the Wnt signalling pathway is a recurrent theme in cancer biology. Hyper activation due to oncogenic mutations and paracrine activity has been found in both colon cancer and breast cancer, and continues to evolve as a central mechanism in oncogenesis. PDLIM2, a cytoskeletal PDZ protein, is an IGF-1 regulated gene that is highly expressed in cancer cell lines derived from metastatic tumours. Suppression of PDLIM2 inhibits polarized cell migration, reverses the Epithelial to Mesenchymal transition (EMT) phenotype, suppresses the transcription of β-catenin target genes, and regulates gene expression of key transcription factors in EMT. This thesis investigates the mechanism by which PDLIM2 contributes to the maintenance of Wnt signalling in cancer cells. Here we show that PDLIM2 is a critical regulator of the Wnt pathway by regulating β-catenin at the adherens juctions, as also its transcriptional activity by the interaction of PDLIM2 with TCF4 at the nucleus. Evaluation of PDLIM2 in macrophages and co-culture studies with cancer cells and fibroblasts showed the influence exerted on PDLIM2 by paracrine cues. Thus, PDLIM2 integrates cytoskeleton signalling with gene expression by modulating the Wnt signalling pathway and reconciling microenvironmental cues with signals in epithelial cells. Negative correlation of mRNA and protein levels in the triple negative breast cancer cell BT549 suggests that PDLIM2 is part of a more complex mechanism that involves transcription and posttranslational modifications. GST pulldown studies and subsequent mass spectrometry analysis showed that PDLIM2 interacts with 300 proteins, with a high biological function in protein biosynthesis and Ubiquitin/proteasome pathways, including 13 E3 ligases. Overall, these data suggest that PDLIM2 has two distinct functions depending of its location. Located at the cytoplasm mediates cytoskeletal re-arrangements, whereas at the nucleus PDLIM2 acts as a signal transduction adaptor protein mediating transcription and ubiquitination of key transcription factors in cancer development.