Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Biological analysis of the in-vitro effects of homologous recombination inhibition and its use in cancer treatment through synthetic lethality

Synthetic lethality represents an anticancer strategy that targets tumor specific gene defects. One of the most studied application is the use of PARP inhibitors (e.g. olaparib) in BRCA1/2-less cancer cells. In BRCA2-defective tumors, olaparib (OLA) inhibits DNA single-strand break repair, while BRCA2 mutations hamper homologous recombination (HR) repair. The simultaneous impairment of those pathways leads BRCA-less cells to death by synthetic lethality. The projects described in this thesis were aimed at extending the use of OLA in cancer cells that do not carry a mutation in BRCA2 by combining this drug with compounds that could mimic a BRCA-less environment via HR inhibition. We demonstrated the effectiveness of our “fully small-molecule induced synthetic lethality” by using two different approaches. In the direct approach (Project A), we identified a series of neo-synthesized compounds (named RAD51-BRCA2 disruptors) that mimic BRCA2 mutations by disrupting the RAD51-BRCA2 interaction and thus the HR pathway. Compound ARN 24089 inhibited HR in human pancreatic adenocarcinoma cell line and triggered synthetic lethality by synergizing with OLA. Interestingly, the observed synthetic lethality was triggered by tackling two biochemically different mechanisms: enzyme inhibition (PARP) and protein-protein disruption (RAD51-BRCA2). In the indirect approach (Project B), we inhibited HR by interfering with the cellular metabolism through inhibition of LDH activity. The obtained data suggest an LDH-mediated control on HR that can be exerted by regulating either the energy supply needed to this repair mechanism or the expression level of genes involved in DNA repair. LDH inhibition also succeeded in increasing the efficiency of OLA in BRCA-proficient cell lines. Although preliminary, these results highlight a complex relationship between metabolic reactions and the control of DNA integrity. Both the described projects proved that our “fully small-molecule-induced synthetic lethality” approach could be an innovative approach to unmet oncological needs.

Liquid biopsy for prostate cancer molecular characterization: homologous recombination system and genomic profile

Pathogenic aberrations in homologous recombination DNA repair (HRR) genes occur in approximately 1 to 4 men with advanced prostate cancer (PCa). Treatment with PARP inhibitors (PARPi) has recently been introduced for metastatic castration-resistant PCa patients, increasing clinicians' interest in the molecular characterization of all PCa patients. The limitations of using old, low-quality tumor tissue for genetic analysis, which is very common for PCa, can be overcome by using liquid biopsy as an alternative biomarker source. In this study, we aimed to evaluate the detection of molecular alterations in HRR genes on liquid biopsy compared with tumor tissue from PCa patients. Secondarily, we explored the genomic instability score (GIS), and a broader range of gene alterations for in-depth characterization of the PCa cohort. Plasma samples were collected from 63 patients with PCa. Sophia Homologous Recombination Solution (targeting 16 HRR genes) and shallow whole genome sequencing (sWGS) were used for genomic analysis of tissue DNA and circulating tumor DNA (ct). A total of 33 alterations (mainly on TP53, ATM, CHEK2, CDK12, and BRCA1/2) were identified in 28,5% of PCa plasma patients. By integrating the mutational and sWGS data, the HRR status of PCa patients was determined and a concordance agreement of 85,7% was identified with tumor tissue. A median GIS of 15 was obtained, reaching a score of 63 in 2 samples with double alterations, BRCA1 and TP53. We explored the PCa mutation landscape, and the most significant enriched pathways identified were the sphingosine 1-phosphate (S1P) receptor signaling and the PI3K-AKT-mTOR pathway. HRR analysis on FFPE and liquid biopsy samples show high concordance, demonstrating that the noninvasive ctDNA-enriched plasma can be an optimal alternative source for molecular SNV and CNV analysis. In addition, the evaluation of GIS and pathway interaction should be considered for more comprehensive molecular characterization in PCa patients.