Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Mass spectrometry-based protein profiling strategies for biomarker discovery in liver and inflammatory bowel diseases

The study of protein expression profiles for biomarker discovery in serum and in mammalian cell populations needs the continuous improvement and combination of proteins/peptides separation techniques, mass spectrometry, statistical and bioinformatic approaches. In this thesis work two different mass spectrometry-based protein profiling strategies have been developed and applied to liver and inflammatory bowel diseases (IBDs) for the discovery of new biomarkers. The first of them, based on bulk solid-phase extraction combined with matrix-assisted laser desorption/ionization - Time of Flight mass spectrometry (MALDI-TOF MS) and chemometric analysis of serum samples, was applied to the study of serum protein expression profiles both in IBDs (Crohn’s disease and ulcerative colitis) and in liver diseases (cirrhosis, hepatocellular carcinoma, viral hepatitis). The approach allowed the enrichment of serum proteins/peptides due to the high interaction surface between analytes and solid phase and the high recovery due to the elution step performed directly on the MALDI-target plate. Furthermore the use of chemometric algorithm for the selection of the variables with higher discriminant power permitted to evaluate patterns of 20-30 proteins involved in the differentiation and classification of serum samples from healthy donors and diseased patients. These proteins profiles permit to discriminate among the pathologies with an optimum classification and prediction abilities. In particular in the study of inflammatory bowel diseases, after the analysis using C18 of 129 serum samples from healthy donors and Crohn’s disease, ulcerative colitis and inflammatory controls patients, a 90.7% of classification ability and a 72.9% prediction ability were obtained. In the study of liver diseases (hepatocellular carcinoma, viral hepatitis and cirrhosis) a 80.6% of prediction ability was achieved using IDA-Cu(II) as extraction procedure. The identification of the selected proteins by MALDITOF/ TOF MS analysis or by their selective enrichment followed by enzymatic digestion and MS/MS analysis may give useful information in order to identify new biomarkers involved in the diseases. The second mass spectrometry-based protein profiling strategy developed was based on a label-free liquid chromatography electrospray ionization quadrupole - time of flight differential analysis approach (LC ESI-QTOF MS), combined with targeted MS/MS analysis of only identified differences. The strategy was used for biomarker discovery in IBDs, and in particular of Crohn’s disease. The enriched serum peptidome and the subcellular fractions of intestinal epithelial cells (IECs) from healthy donors and Crohn’s disease patients were analysed. The combining of the low molecular weight serum proteins enrichment step and the LCMS approach allowed to evaluate a pattern of peptides derived from specific exoprotease activity in the coagulation and complement activation pathways. Among these peptides, particularly interesting was the discovery of clusters of peptides from fibrinopeptide A, Apolipoprotein E and A4, and complement C3 and C4. Further studies need to be performed to evaluate the specificity of these clusters and validate the results, in order to develop a rapid serum diagnostic test. The analysis by label-free LC ESI-QTOF MS differential analysis of the subcellular fractions of IECs from Crohn’s disease patients and healthy donors permitted to find many proteins that could be involved in the inflammation process. Among them heat shock protein 70, tryptase alpha-1 precursor and proteins whose upregulation can be explained by the increased activity of IECs in Crohn’s disease were identified. Follow-up studies for the validation of the results and the in-depth investigation of the inflammation pathways involved in the disease will be performed. Both the developed mass spectrometry-based protein profiling strategies have been proved to be useful tools for the discovery of disease biomarkers that need to be validated in further studies.

New analytical LC-mass spectrometry methodologies for the quali-quantitative determination of natural substances and drugs in complex matrices

This thesis reports an integrated analytical and physicochemical approach for the study of natural substances and new drugs based on mass spectrometry techniques combined with liquid chromatography. In particular, Chapter 1 concerns the study of Berberine a natural substance with pharmacological activity for the treatment of hepatobiliary and intestinal diseases. The first part focused on the relationships between physicochemical properties, pharmacokinetics and metabolism of Berberine and its metabolites. For this purpose a sensitive HPLC-ES-MS/MS method have been developed, validated and used to determine these compounds during their physicochemical properties studies and plasma levels of berberine and its metabolites including berberrubine(M1), demethylenberberine(M3), and jatrorrhizine(M4) in humans. Data show that M1, could have an efficient intestinal absorption by passive diffusion due to a keto-enol tautomerism confirmed by NMR studies and its higher plasma concentration. In the second part of Chapter 1, a comparison between M1 and BBR in vivo biodistribution in rat has been studied. In Chapter 2 a new HPLC-ES-MS/MS method for the simultaneous determination and quantification of glucosinolates, as glucoraphanin, glucoerucin and sinigrin, and isothiocyanates, as sulforaphane and erucin, has developed and validated. This method has been used for the analysis of functional foods enriched with vegetable extracts. Chapter 3 focused on a physicochemical study of the interaction between the bile acid sequestrants used in the treatment of hypercholesterolemia including colesevelam and cholestyramine with obeticolic acid (OCA), potent agonist of nuclear receptor farnesoid X (FXR). In particular, a new experimental model for the determination of equilibrium binding isotherm was developed. Chapter 4 focused on methodological aspects of new hard ionization coupled with liquid chromatography (Direct-EI-UHPLC-MS) not yet commercially available and potentially useful for qualitative analysis and for “transparent” molecules to soft ionization techniques. This method was applied to the analysis of several steroid derivatives.