Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

Synthetic and mechanistic investigation of new radical processes: reaction of organic azides with group-XIII Lewis acids

Dichloroindium hydride revealed to be a valid alternative to tributyltin hydride for radical reduction of organic (alkyl, aryl, acyl, solfonyl) azides. The new approach entails mild reaction conditions and provides high yields of the corresponding amines and amides, also showing high degrees of selectivity. The system dichloroindium hydride / azides can be utilised in fivemembered ring closures of g-azidonitriles, as a new source of aminyl radicals for the attractive synthesis of interesting amidine compounds in the absence of both toxic reagents and tedious purification procedures. Allylindium dichloride seems a good substitute for dichloroindium hydride for generation of indium centred radicals under photolytic conditions, since it allows allylation of electrophilic azides (e.g. phenylsulfonyl azide) and halogen or ester δ-substituted azides, the latter through a 1,5-H transfer rearrangement mechanism. Evidences of the radical nature of the reactions mechanism were provided by ESR spectroscopy, furthermore the same technique, allowed to discover that the reaction of azides with indium trichloride and other group XIII Lewis acids, in particular gallium trichloride, gives rise to strongly coloured, persistent paramagnetic species, whose structure is consistent with the radical cation of the head-to-tail dimer of the aniline corresponding to the starting azide.

Studio della subunità epsilon della DNA polimerasi III di Escherichia coli: stabilità e interazione con la subunità polimerasica

Faithful replication of DNA from one generation to the next is crucial for long-term species survival. Genomic integrity in prokaryotes, archaea and eukaryotes is dependent on efficient and accurate catalysis by multiple DNA polymerases. Escherichia coli possesses five known DNA polymerases (Pol). DNA polymerase III holoenzyme is the major replicative polymerase of the Escherichia coli chromosome (Kornberg, 1982). This enzyme contains two Pol III cores that are held together by a t dimer (Studwell-Vaughan and O’Donnell, 1991). The core is composed of three different proteins named α-, ε- and θ-subunit. The α-subunit, encoded by dnaE, contains the catalytic site for DNA polymerisation (Maki and Kornberg, 1985), the ε-subunit, encoded by dnaQ, contains the 3′→5′ proofreading exonuclease (Scheuermann, et al., 1983) and the θ-subunit, encoded by hole, that has no catalytic activity (Studwell-Vaughan, and O'Donnell, 1983). The three-subunit α–ε–θ DNA pol III complex is the minimal active polymerase form purified from the DNA pol III holoenzyme complex; these three polypeptides are tightly associated in the core (McHenry and Crow, 1979) Despite a wealth of data concerning the properties of DNA polymerase III in vitro, little information is available on the assembly in vivo of this complex enzyme. In this study it is shown that the C-terminal region of the proofreading subunit is labile and that the ClpP protease and the molecular chaperones GroL and DnaK control the overall concentration in vivo of ε. Two α-helices (comprising the residues E311-M335 and G339-D353, respectively) of the N-terminal region of the polymerase subunit were shown to be essential for the binding to ε. These informations could be utilized to produce a conditional mutator strain in which proofreading activity would be titrated by a a variant that can only bind e and that is polymerase-deficient. In this way the replication of DNA made by DNA Pol-III holoenzyme would accordingly become error-prone.

Progettazione e sintesi di nuovi derivati azetidinonici biologicamente attivi

In this PhD-thesis new synthetic approaches towards new azetidinone derivatives are described. In particular, 4-alkyliden-β-lactams were used as starting materials for the preparation of new biologically active compounds. The carbapenem Thienamycin has got a broad spectrum of activity as antibiotic. It has got 3 stereocenters and apart of one epimer, all isomers have been synthesized. Using the 4-alkyliden-β-lactam benzilyc ester as precursor, we developed a synthesis for this missing epimer, which is described in chapter II. Biological tests in order to establish its biological activity are under way. The Hunsdiecker-Borodine reaction was extensively studied for the preparation of the mono halogenated and – surprisingly – the dihalogenated derivative from the 4-alkyliden-azetidinone carboxylic acid. The herein described synthetic procedures allowed the preparation of chloro-, bromo- and iodo derivatives in good to excellent yield. Furthermore, the reaction mechanism was investigated by NMR-experiments and is described in detail in chapter III. In chapter IV, synthetic approaches towards new β-lactam derivatives for inhibition of the histone deacetylase enzymes (HDACs) are reported. In collaboration with the company Sigma-Tau (Rome), 14 new β-lactams were synthesized. The new β-lactams were evaluated for the activity showing a promising activityparticulary, 10 of the β-lactams synthesized were evaluated for the in vitro inhibitory activity against the 11 human HDACs isoforms and they showed a selective inhibition of HDAC6 or HDAC8 in micromolar range. Finally, preliminary studies were conducted for the employment of 4-alkyliden-β-lactams as precursors for the synthesis of chiral β-amino acids by an opening of the β-lactam ring. In chapter V is described the ring opening reaction catalyzed by the enzyme lipase Cal-B. Preliminary results have shown that the enzyme not only catalyzes the ring opening of the β-lactam precursor, moreover, it leads to the formation of a cyclic dimer by the reaction of two molecules of β-amino acid obtained.

Sistemi liquido cristallini complessi: simulazioni al calcolatore e studi ESR

The aim of this PhD thesis was to study at a microscopic level different liquid crystal (LC) systems, in order to determine their physical properties, resorting to two distinct methodologies, one involving computer simulations, and the other spectroscopic techniques, in particular electron spin resonance (ESR) spectroscopy. By means of the computer simulation approach we tried to demonstrate this tool effectiveness for calculating anisotropic static properties of a LC material, as well as for predicting its behaviour and features. This required the development and adoption of suitable molecular models based on a convenient intermolecular potentials reflecting the essential molecular features of the investigated system. In particular, concerning the simulation approach, we have set up models for discotic liquid crystal dimers and we have studied, by means of Monte Carlo simulations, their phase behaviour and self­-assembling properties, with respect to the simple monomer case. Each discotic dimer is described by two oblate Gay­Berne ellipsoids connected by a flexible spacer, modelled by a harmonic "spring" of three different lengths. In particular we investigated the effects of dimerization on the transition temperatures, as well as on the characteristics of molecular aggregation displayed and the relative orientational order. Moving to the experimental results, among the many experimental techniques that are typically employed to evaluate LC system distinctive features, ESR has proved to be a powerful tool in microscopic scale investigation of the properties, structure, order and dynamics of these materials. We have taken advantage of the high sensitivity of the ESR spin probe technique to investigate increasingly complex LC systems ranging from devices constituted by a polymer matrix in which LC molecules are confined in shape of nano- droplets, as well as biaxial liquid crystalline elastomers, and dimers whose monomeric units or lateral groups are constituted by rod-like mesogens (11BCB). Reflection-mode holographic-polymer dispersed liquid crystals (H-PDLCs) are devices in which LCs are confined into nanosized (50­-300 nm) droplets, arranged in layers which alternate with polymer layers, forming a diffraction grating. We have determined the configuration of the LC local director and we have derived a model of the nanodroplet organization inside the layers. Resorting also to additional information on the nanodroplet size and shape distribution provided by SEM images of the H-PDLC cross-section, the observed director configuration has been modeled as a bidimensional distribution of elongated nanodroplets whose long axis is, on the average, parallel to the layers and whose internal director configuration is a uniaxial quasi- monodomain aligned along the nanodroplet long axis. The results suggest that the molecular organization is dictated mainly by the confinement, explaining, at least in part, the need for switching voltages significantly higher and the observed faster turn-off times in H-PDLCs compared to standard PDLC devices. Liquid crystal elastomers consist in cross-linked polymers, in which mesogens represent the monomers constituting the main chain or the laterally attached side groups. They bring together three important aspects: orientational order in amorphous soft materials, responsive molecular shape and quenched topological constraints. In biaxial nematic liquid crystalline elastomers (BLCEs), two orthogonal directions, rather than the one of normal uniaxial nematic, can be controlled, greatly enhancing their potential value for applications as novel actuators. Two versions of a side-chain BLCEs were characterized: side­-on and end­-on. Many tests have been carried out on both types of LCE, the main features detected being the lack of a significant dynamical behaviour, together with a strong permanent alignment along the principal director, and the confirmation of the transition temperatures already determined by DSC measurements. The end­-on sample demonstrates a less hindered rotation of the side group mesogenic units and a greater freedom of alignment to the magnetic field, as already shown by previous NMR studies. Biaxial nematic ESR static spectra were also obtained on the basis of Molecular Dynamics generated biaxial configurations, to be compared to the experimentally determined ones, as a mean to establish a possible relation between biaxiality and the spectral features. This provides a concrete example of the advantages of combining the computer simulation and spectroscopic approaches. Finally, the dimer α,ω-bis(4'-cyanobiphenyl-4-yl)undecane (11BCB), synthesized in the "quest" for the biaxial nematic phase has been analysed. Its importance lies in the dimer significance as building blocks in the development of new materials to be employed in innovative technological applications, such as faster switching displays, resorting to the easier aligning ability of the secondary director in biaxial phases. A preliminary series of tests were performed revealing the population of mesogenic molecules as divided into two groups: one of elongated straightened conformers sharing a common director, and one of bent molecules, which display no order, being equally distributed in the three dimensions. Employing this model, the calculated values show a consistent trend, confirming at the same time the transition temperatures indicated by the DSC measurements, together with rotational diffusion tensor values that follow closely those of the constituting monomer 5CB.

Molecular architecture of fur binding to iron-induced and - repressed genes in Helicobacter pylori

The ferric uptake regulator protein Fur regulates iron-dependent gene expression in bacteria. In the human pathogen Helicobacter pylori, Fur has been shown to regulate iron-induced and iron-repressed genes. Herein we investigate the molecular mechanisms that control this differential iron-responsive Fur regulation. Hydroxyl radical footprinting showed that Fur has different binding architectures, which characterize distinct operator typologies. On operators recognized with higher affinity by holo-Fur, the protein binds to a continuous AT-rich stretch of about 20 bp, displaying an extended protection pattern. This is indicative of protein wrapping around the DNA helix. DNA binding interference assays with the minor groove binding drug distamycin A, point out that the recognition of the holo-operators occurs through the minor groove of the DNA. By contrast, on the apo-operators, Fur binds primarily to thymine dimers within a newly identified TCATTn10TT consensus element, indicative of Fur binding to one side of the DNA, in the major groove of the double helix. Reconstitution of the TCATTn10TT motif within a holo-operator results in a feature binding swap from an holo-Fur- to an apo-Fur-recognized operator, affecting both affinity and binding architecture of Fur, and conferring apo-Fur repression features in vivo. Size exclusion chromatography indicated that Fur is a dimer in solution. However, in the presence of divalent metal ions the protein is able to multimerize. Accordingly, apo-Fur binds DNA as a dimer in gel shift assays, while in presence of iron, higher order complexes are formed. Stoichiometric Ferguson analysis indicates that these complexes correspond to one or two Fur tetramers, each bound to an operator element. Together these data suggest that the apo- and holo-Fur repression mechanisms apparently rely on two distinctive modes of operator-recognition, involving respectively the readout of a specific nucleotide consensus motif in the major groove for apo-operators, and the recognition of AT-rich stretches in the minor groove for holo-operators, whereas the iron-responsive binding affinity is controlled through metal-dependent shaping of the protein structure in order to match preferentially the major or the minor groove.

Funzioni della subunità θ e del dominio PHP della subunità α nel core catalitico della DNA polimerasi III di Escherichia coli

Il core catalitico della DNA polimerasi III, composto dalle tre subunità α, ε e θ, è il complesso minimo responsabile della replicazione del DNA cromosomiale in Escherichia coli. Nell'oloenzima, α ed ε possiedono rispettivamente un'attività 5'-3' polimerasica ed un'attività 3'-5' esonucleasica, mentre θ non ha funzioni enzimatiche. Il presente studio si è concentrato sulle regioni del core che interagiscono direttamente con ε, ovvero θ (interagente all'estremità N-terminale di ε) e il dominio PHP di α (interagente all'estremità C-terminale di ε), delle quali non è stato sinora identificato il ruolo. Al fine di assegnare loro una funzione sono state seguite tre linee di ricerca parallele. Innanzitutto il ruolo di θ è stato studiato utilizzando approcci ex-vivo ed in vivo. I risultati presentati in questo studio mostrano che θ incrementa significativamente la stabilità della subunità ε, intrinsecamente labile. Durante gli esperimenti condotti è stata anche identificata una nuova forma dimerica di ε. Per quanto la funzione del dimero non sia definita, si è dimostrato che esso è attivamente dissociato da θ, che potrebbe quindi fungere da suo regolatore. Inoltre, è stato ritrovato e caratterizzato il primo fenotipo di θ associato alla crescita. Per quanto concerne il dominio PHP, si è dimostrato che esso possiede un'attività pirofosfatasica utilizzando un nuovo saggio, progettato per seguire le cinetiche di reazione catalizzate da enzimi rilascianti fosfato o pirofosfato. L'idrolisi del pirofosfato catalizzata dal PHP è stata dimostrata in grado di sostenere l'attività polimerasica di α in vitro, il che suggerisce il suo possibile ruolo in vivo durante la replicazione del DNA. Infine, è stata messa a punto una nuova procedura per la coespressione e purificazione del complesso α-ε-θ

Studies of pure rotational spectra of isolated molecules and molecular adducts using pulsed jet Fourier transform microwave (PJ-FTM) spectroscopy

This thesis focuses on studying molecular structure and internal dynamics by using pulsed jet Fourier transform microwave (PJ-FTMW) spectroscopy combined with theoretical calculations. Several kinds of interesting chemical problems are investigated by analyzing the MW spectra of the corresponding molecular systems. First, the general aspects of rotational spectroscopy are summarized, and then the basic theory on molecular rotation and experimental method are described briefly. ab initio and density function theory (DFT) calculations that used in this thesis to assist the assignment of rotational spectrum are also included. From chapter 3 to chapter 8, several molecular systems concerning different kind of general chemical problems are presented. In chapter 3, the conformation and internal motions of dimethyl sulfate are reported. The internal rotations of the two methyl groups split each rotational transition into several components line, allowing for the determination of accurate values of the V3 barrier height to internal rotation and of the orientation of the methyl groups with respect to the principal axis system. In chapter 4 and 5, the results concerning two kinds of carboxylic acid bi-molecules, formed via two strong hydrogen bonds, are presented. This kind of adduct is interesting also because a double proton transfer can easily take place, connecting either two equivalent or two non-equivalent molecular conformations. Chapter 6 concerns a medium strong hydrogen bonded molecular complex of alcohol with ether. The dimer of ethanol-dimethylether was chosen as the model system for this purpose. Chapter 7 focuses on weak halogen…H hydrogen bond interaction. The nature of O-H…F and C-H…Cl interaction has been discussed through analyzing the rotational spectra of CH3CHClF/H2O. In chapter 8, two molecular complexes concerning the halogen bond interaction are presented.

Predictability in Social Science, The statistical mechanics approach.

The subject of this work concerns the study of the immigration phenomenon, with emphasis on the aspects related to the integration of an immigrant population in a hosting one. Aim of this work is to show the forecasting ability of a recent finding where the behavior of integration quantifiers was analyzed and investigated with a mathematical model of statistical physics origins (a generalization of the monomer dimer model). After providing a detailed literature review of the model, we show that not only such a model is able to identify the social mechanism that drives a particular integration process, but it also provides correct forecast. The research reported here proves that the proposed model of integration and its forecast framework are simple and effective tools to reduce uncertainties about how integration phenomena emerge and how they are likely to develop in response to increased migration levels in the future.