Genome characterization through a mathematical model of the genetic code: an analysis of the whole chromosome 1 of A. thaliana

The objective of this work is to characterize the genome of the chromosome 1 of A.thaliana, a small flowering plants used as a model organism in studies of biology and genetics, on the basis of a recent mathematical model of the genetic code. I analyze and compare different portions of the genome: genes, exons, coding sequences (CDS), introns, long introns, intergenes, untranslated regions (UTR) and regulatory sequences. In order to accomplish the task, I transformed nucleotide sequences into binary sequences based on the definition of the three different dichotomic classes. The descriptive analysis of binary strings indicate the presence of regularities in each portion of the genome considered. In particular, there are remarkable differences between coding sequences (CDS and exons) and non-coding sequences, suggesting that the frame is important only for coding sequences and that dichotomic classes can be useful to recognize them. Then, I assessed the existence of short-range dependence between binary sequences computed on the basis of the different dichotomic classes. I used three different measures of dependence: the well-known chi-squared test and two indices derived from the concept of entropy i.e. Mutual Information (MI) and Sρ, a normalized version of the “Bhattacharya Hellinger Matusita distance”. The results show that there is a significant short-range dependence structure only for the coding sequences whose existence is a clue of an underlying error detection and correction mechanism. No doubt, further studies are needed in order to assess how the information carried by dichotomic classes could discriminate between coding and noncoding sequence and, therefore, contribute to unveil the role of the mathematical structure in error detection and correction mechanisms. Still, I have shown the potential of the approach presented for understanding the management of genetic information.

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.

Next-Generation Sequencing-Based Mutations Scanning Strategy of the BCR-ABL Kinase Domain in Patients with PhiladelPhia-Chromosome Positive Leukemias Treated with Tyrosine Kinase Inhibitors

In chronic myeloid leukemia and Philadelphia-positive acute lymphoblastic leukemia patients resistant to tyrosine kinase inhibitors (TKIs), BCR-ABL kinase domain mutation status is an essential component of the therapeutic decision algorithm. The recent development of Ultra-Deep Sequencing approach (UDS) has opened the way to a more accurate characterization of the mutant clones surviving TKIs conjugating assay sensitivity and throughput. We decided to set-up and validated an UDS-based for BCR-ABL KD mutation screening in order to i) resolve qualitatively and quantitatively the complexity and the clonal structure of mutated populations surviving TKIs, ii) study the dynamic of expansion of mutated clones in relation to TKIs therapy, iii) assess whether UDS may allow more sensitive detection of emerging clones, harboring critical 2GTKIs-resistant mutations predicting for an impending relapse, earlier than SS. UDS was performed on a Roche GS Junior instrument, according to an amplicon sequencing design and protocol set up and validated in the framework of the IRON-II (Interlaboratory Robustness of Next-Generation Sequencing) International consortium.Samples from CML and Ph+ ALL patients who had developed resistance to one or multiple TKIs and collected at regular time-points during treatment were selected for this study. Our results indicate the technical feasibility, accuracy and robustness of our UDS-based BCR-ABL KD mutation screening approach. UDS was found to provide a more accurate picture of BCR-ABL KD mutation status, both in terms of presence/absence of mutations and in terms of clonal complexity and showed that BCR-ABL KD mutations detected by SS are only the “tip of iceberg”. In addition UDS may reliably pick 2GTKIs-resistant mutations earlier than SS in a significantly greater proportion of patients.The enhanced sensitivity as well as the possibility to identify low level mutations point the UDS-based approach as an ideal alternative to conventional sequencing for BCR-ABL KD mutation screening in TKIs-resistant Ph+ leukemia patients