Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

De Novo Design of secondary structures: Synthesis and conformational studies

Chemists have long sought to extrapolate the power of biological catalysis and recognition to synthetic systems. These efforts have focused largely on low molecular weight catalysts and receptors; however, biological systems themselves rely almost exclusively on polymers, proteins and RNA, to perform complex chemical functions. Proteins and RNA are unique in their ability to adopt compact, well-ordered conformations, and specific folding provides precise spatial orientation of the functional groups that comprise the “active site”. These features suggest that identification of new polymer backbones with discrete and predictable folding propensities (“foldamers”) will provide a basis for design of molecular machines with unique capabilities. The foldamer approach complements current efforts to design unnatural properties into polypeptides and polynucleotides. The aim of this thesis is the synthesis and conformational studies of new classes of foldamers, using a peptidomimetic approach. Moreover their attitude to be utilized as ionophores, catalysts, and nanobiomaterials were analyzed in solution and in the solid state. This thesis is divided in thematically chapters that are reported below. It begins with a very general introduction (page 4) which is useful, but not strictly necessary, to the expert reader. It is worth mentioning that paragraph I.3 (page 22) is the starting point of this work and paragraph I.5 (page 32) isrequired to better understand the results of chapters 4 and 5. In chapter 1 (page 39) is reported the synthesis and conformational analysis of a novel class of foldamers containing (S)-β3-homophenylglycine [(S)-β3-hPhg] and D- 4-carboxy-oxazolidin-2-one (D-Oxd) residues in alternate order is reported. The experimental conformational analysis performed in solution by IR, 1HNMR, and CD spectroscopy unambiguously proved that these oligomers fold into ordered structures with increasing sequence length. Theoretical calculations employing ab initio MO theory suggest a helix with 11-membered hydrogenbonded rings as the preferred secondary structure type. The novel structures enrich the field of peptidic foldamers and might be useful in the mimicry of native peptides. In chapter 2 cyclo-(L-Ala-D-Oxd)3 and cyclo-(L-Ala-DOxd) 4 were prepared in the liquid phase with good overall yields and were utilized for bivalent ions chelation (Ca2+, Mg2+, Cu2+, Zn2+ and Hg2+); their chelation skill was analyzed with ESI-MS, CD and 1HNMR techniques and the best results were obtained with cyclo-(L-Ala-D-Oxd)3 and Mg2+ or Ca2+. Chapter 3 describes an application of oligopeptides as catalysts for aldol reactions. Paragraph 3.1 concerns the use of prolinamides as catalysts of the cross aldol addition of hydroxyacetone to aromatic aldeydes, whereas paragraphs 3.2 and 3.3 are about the catalyzed aldol addition of acetone to isatins. By means of DFT and AIM calculations, the steric and stereoelectronic effects that control the enantioselectivity in the cross-aldol addition of acetone to isatin catalysed by L-proline have been studied, also in the presence of small quantities of water. In chapter 4 is reported the synthesis and the analysis of a new fiber-like material, obtained from the selfaggregation of the dipeptide Boc-L-Phe-D-Oxd-OBn, which spontaneously forms uniform fibers consisting of parallel infinite linear chains arising from singleintermolecular N-H···O=C hydrogen bonds. This is the absolute borderline case of a parallel β-sheet structure. Longer oligomers of the same series with general formula Boc-(L-Phe-D-Oxd)n-OBn (where n = 2-5), are described in chapter 5. Their properties in solution and in the solid state were analyzed, in correlation with their attitude to form intramolecular hydrogen bond. In chapter 6 is reported the synthesis of imidazolidin-2- one-4-carboxylate and (tetrahydro)-pyrimidin-2-one-5- carboxylate, via an efficient modification of the Hofmann rearrangement. The reaction affords the desired compounds from protected asparagine or glutamine in good to high yield, using PhI(OAc)2 as source of iodine(III).

Myc-mediated control of gene transcription in cancer cells

The Myc oncoproteins belong to a family of transcription factors composed by Myc, N-Myc and L-Myc. The most studied components of this family are Myc and N-Myc because their expressions are frequently deregulated in a wide range of cancers. These oncoproteins can act both as activators or repressors of gene transcription. As activators, they heterodimerize with Max (Myc associated X-factor) and the heterodimer recognizes and binds a specific sequence elements (E-Box) onto gene promoters recruiting histone acetylase and inducing transcriptional activation. Myc-mediated transcriptional repression is a quite debated issue. One of the first mechanisms defined for the Myc-mediated transcriptional repression consisted in the interaction of Myc-Max complex Sp1 and/or Miz1 transcription factors already bound to gene promoters. This interaction may interfere with their activation functions by recruiting co-repressors such as Dnmt3 or HDACs. Moreover, in the absence of , Myc may interfere with the Sp1 activation function by direct interaction and subsequent recruitment of HDACs. More recently the Myc/Max complex was also shown to mediate transcriptional repression by direct binding to peculiar E-box. In this study we analyzed the role of Myc overexpression in Osteosarcoma and Neuroblastoma oncogenesis and the mechanisms underling to Myc function. Myc overexpression is known to correlate with chemoresistance in Osteosarcoma cells. We extended this study by demonstrating that c-Myc induces transcription of a panel of ABC drug transporter genes. ABCs are a large family trans-membrane transporter deeply involved in multi drug resistance. Furthermore expression levels of Myc, ABCC1, ABCC4 and ABCF1 were proved to be important prognostic tool to predict conventional therapy failure. N-Myc amplification/overexpression is the most important prognostic factor for Neuroblastoma. Cyclin G2 and Clusterin are two genes often down regulated in neuroblastoma cells. Cyclin G2 is an atypical member of Cyclin family and its expression is associated with terminal differentiation and apoptosis. Moreover it blocks cell cycle progression and induces cell growth arrest. Instead, CLU is a multifunctional protein involved in many physiological and pathological processes. Several lines of evidences support the view that CLU may act as a tumour suppressor in Neuroblastoma. In this thesis I showed that N-Myc represses CCNG2 and CLU transcription by different mechanisms. • N-Myc represses CCNG2 transcription by directly interacting with Sp1 bound in CCNG2 promoter and recruiting HDAC2. Importantly, reactivation of CCNG2 expression through epigenetic drugs partially reduces N-Myc and HDAC2 mediated cell proliferation. • N-Myc/Max complex represses CLU expression by direct binding to a peculiar E-box element on CLU promoter and by recruitment of HDACs and Polycomb Complexes, to the CLU promoter. Overall our findings strongly support the model in which Myc overexpression/amplification may contribute to some aspects of oncogenesis by a dual action: i) transcription activation of genes that confer a multidrug resistant phenotype to cancer cells; ii), transcription repression of genes involved in cell cycle inhibition and cellular differentiation.

Characterization of the genetic control of fruit flesh color in peach

The analysis of a carotenoid cleavage dioxygenase gene in a pool of peach cultivars revealed the existence of a functional allele (W1), associated with the white flesh trait, and three independent mutations associated with the yellow phenotype: a 2 bp insertion within a repetitive sequence (y1), a large transposable element within the intron (y2) and a single base substitution generating a premature stop codon (y3). Based on these evidences, the yellow flesh phenotype seems to have arisen from at least three independent mutational events.