Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.Comment: 36 pages, 10 figures, accepted on International Journal of Bifurcation and Chaos. arXiv admin note: substantial text overlap with arXiv:1401.285

Relevance of the 1:1 resonance in galactic dynamics

This paper aims to illustrate the applications of resonant Hamiltonian normal forms to some problems of galactic dynamics. We detail the construction of the 1:1 resonant normal form corresponding to a wide class of potentials with self-similar elliptical equi-potentials and apply it to investigate relevant features of the orbit structure of the system. We show how to compute the bifurcation of the main periodic orbits in the symmetry planes of a triaxial ellipsoid and in the meridional plane of an axi-symmetric spheroid and briefly discuss how to refine these results with higher-order approaches.Comment: Corrected typos, to appear on the European Physical Journal Plus. arXiv admin note: text overlap with arXiv:0906.3138v

An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z_2 X Z_2 symmetry

We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under $\Z_2\times\Z_2$ symmetry. The rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods. The geometric approach readily allows to find an energy-momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features. Quadrature formulas for the actions, periods and rotation number are also provided.Comment: 22 pages, 3 figures, 1 tabl

Management of type II Diabetes Mellitus

There is currently no cure for diabetes mellitus (DM). Irrespective of whether type I or type II diabetes is treated, the overall goals of management and therapy are targeted towards patient well being and may be summarised as follows.peer-reviewe

Theoretical evidence for the semi-insulating character of AlN

We present ab initio density-functional calculations for acceptors, donors, and native defects in aluminum nitride, showing that acceptors are deeper (Be ~ 0.25 eV, Mg_ 0.45 eV) and less soluble than in GaN; at further variance with GaN, both the extrinsic donors Si_Al and C_Al, and the native donor V_N (the anion vacancy) are found to be deep (about 1 to 3 eV below the conduction). We thus predict that doped AlN will generally turn out to be semi-insulating in the normally achieved Al-rich conditions, in agreement with the known doping difficulties of high-x AlGaN alloys.Comment: RevTeX 3 pages, 1 figur

Chemical Synthesis of the Thymocyte Differentiation Antigen 1 (Thy-1) N-glycoprotein

The glycosylation of the proteins is a common post-translational modification found in eukaryotic cells. Glycosylated proteins play a crucial role in cell adhesion, cell-matrix interaction, and immune response. Several studies suggest that the overexpression of these glycoconjugates is linked to many diseases, inflammation, viral infections, cancer metastasis, and cellular apoptosis among other pathologies. Over the years, the scientific community has tried to answer questions about the influence of the oligosaccharides on the protein structure or the relationship between the oligosaccharide structure and glycoproteins function. The main limitation to study these important aspects is the difficulty to obtain homogeneous isoforms of glycoproteins due to the lack of genetic control in the biosynthesis. The crescent interest in the understanding of structure-activity relationship of glycoproteins has led to the development of new technologies to obtain complex glycans and proteins. In this work, different methodologies were investigated to synthesize defined isoforms of the ubiquitous glycoprotein called Thy-1 or CD90. This heavily glycosylated protein was first discovered in 1964 in mouse T lymphocytes and later detected in human fibroblast neurons, blood stem cells, and endothelial cells. The 25kDa glycoprotein is translated as a 161 and 160 amino acids length protein in humans and mouse, respectively. The protein is transferred from ribosomes into the ER and receives several post-translational modifications including N-glycosylation at three different asparagine residues and a glypiation at the C-terminal cysteine residue. Several studies showed the association between the expression of Thy-1 and T cell activation, neurite outgrowth, apoptosis, leukocyte and melanoma cell adhesion and migration, tumor suppression, and fibroblast proliferation. The exploration of the structure-activity relationship to determine the role of the glycosylation on this protein required defined glycoprotein and motivated this work to develop a de novo synthesis of the Thy-1 pure glycoforms. The retrosynthesis of the mature glycoprotein was designed considering three key steps: 1) the assembly of the primary sequence of the protein; 2) the introduction of glycans into the protein; 3) the differentiation of the oligosaccharides at the glycosylation sites. The primary sequence of the glycoprotein was obtained using a sequential native chemical ligation (NCL) of three segments: the peptide fragment (1-18), the glycopeptide (19-84) having two N glycosylations, and the glycopeptide (85-110) containing one N glycosylation. The three peptide fragments were synthesized by solid-phase peptide synthesis (SPPS) and were obtained having a hydrazide moiety on the C-terminus that was converted into a thioester prior to the NCL. For this purpose, a Wang and a trityl resin were functionalized with hydrazine and modified manually with the amino acid on the C-termini. The protecting acetamidomethyl group was used to mask the thiol of the N-terminal cysteine residues in the fragment (19-84) and (85-110) to allow the stepwise ligation of the fragments. The elongation of the polypeptide chains was carried out in the microwave-assisted synthesizer and careful optimization of deprotection and coupling cycles was executed for the three fragments. The incorporation of amino acids was performed considering the common problems that affect the peptide synthesis including the cyclization reaction on asparagine and aspartic acid, and the racemization of cysteine and histidine at temperatures higher than 50°C. These precautions were not enough to obtain the Thy-1 glycopeptide fragments in high yield and with desired quality. The synthesis of the designed peptides required multiple optimizations to avoid side reactions. Some general requirements were established. Hindered amino acids (glutamic acid, isoleucine, and phenylalanine) required double coupling to assure complete attachment to the growing chain. Vicinal identical amino acids (e.g. serine 25-serine 26) were introduced using single coupling for the first residue in the sequence and a double coupling for the following residue. One of the most crucial point for the optimization of the synthesis was the minimization of the aspartimide formation involving the cyclization of the aspartic acid. Among different cocktails for the removal of the Fmoc group promising the suppression of this side reaction, the best results were obtained by using 20% piperidine and 0.7% of formic acid in dimethylformamide, which reduced the aspartimide formation up to 70%. The glycosylations were introduced following two approaches to allow differentiation between the glycan at each glycosylation site. In the cassette-method, a glycosylated asparagine was synthesized and incorporated in the corresponding glycosylation site during the assembly of the peptides. Different procedures were evaluated and optimized for the synthesis of the N-acetyl-O-per-acetylated glucosaminyl asparagine 2 and its introduction into SPPS to get the fragments 6a-c (19-84) and 37a-b (85-110) with a peracetylated glucosamine on each glycosylation site. The convergent approach was used to synthesize fragment 6b (19-84) having the peracetylated N acetylglucosamine 2 in one glycosylation site and an unprotected N-acetylglucosamine, installed via Lansbury aspartylation on the second site. The Lansbury strategy required the formation of the amide bond between the free carboxylate at an aspartic acid and the N-acetylglucosamine amine. The reaction was performed on the fully protected peptide fragment and required the synthesis of two building blocks, an orthogonal protected aspartic acid 3, and a pseudoproline dipeptide 4. The aspartic acid was synthesized with a photolabile protecting group on the side chain, which was selectively removed on resin to give a free carboxylic acid. To avoid the undesired rearrangement of the amino acid, the protected pseudoproline dipeptide Thr-Ser(Me,MePro) was incorporated before the aspartic acid. The three (glyco)peptides were efficiently synthesized by a combination of manual and automated processes and were characterized by their challenging purifications. The difficulties in obtaining the isoforms from the Thy-1 fragment (19-84) glycopeptides 6a-b, were related to the low solubility of the generated glycopeptides and the loss of acetyl groups on the peracetylated glucosamine. The analysis of these problems led to the design of the optimal strategy to synthesize in high yield the fragment 6c having a protected and non-protected N‑acetylglucosamine. The synthesis of glycoform 6c involved the coupling of a per-acetylated N-acetylglucosaminyl asparagine building block in the peptide sequence that was de-acetylated before the introduction of the second glycosylated asparagine residue. The assembly of the Thy-1 glycoprotein involved the ligation of the synthesized fragments by the chemoselective reaction between the C-terminal peptide thioester in one peptide fragment and the free N-terminal cysteine residue of another fragment. The process required the conversion of the synthesized peptide hydrazides into the corresponding thioesters prior to each ligation and the removal of the Acm-group of the fragments having the N-terminal cysteine. Two combinations were studied to ligate the three fragments: from C- to N-terminus and from N- to the C-terminus. The first approach consisted of the initial ligation of the glycopeptides 6a-c (19-84) and 37a-b (85-110) and the subsequent ligation with the peptide 1 (1-18). The second strategy involved the reaction of peptide 1 (1-18) with the glycopeptide 6a-c (19-84) and the following ligation with the fragment 37a-b (85-110). The ligation conditions were investigated, and the strategy was selected considering factors such as the availability and solubility of the fragments, number of steps and the efficiency of the processes. The N-to C-strategy was the first approach adopted. The hydrazide precursor 6a was converted into the thioester fragment 38 by formation of the peptide azide at low pH and thiolysis with the corresponding thiol. The Acm group from the cysteine in 37b was removed with mercury (II) acetate and reduction of the sulfur-mercury complex with mercaptoethanol. The ligation of the fragments delivered the glycoprotein 40 and the hydrolysed fragment 38 as by-product. The low solubility of the glycoprotein 40 hampered the isolation of the product and suggested the need of more polar fragment. For this purpose, glycoform 6b was converted into the thioester 41 and reacted with fragment 37a having a free N-terminal cysteine. Surprisingly, this ligation did not proceed suggesting that the treatment with mercury (II) acetate could be beneficial for the ligation. A N- to C- ligation of fragment 6c treated with the mercury (II) acetate with the thioester of fragment 1 proceeded successfully and the isolation of the ligation product yielded the glycoprotein 45, confirming the better behaviour of polar fragments and reactivity of the cysteine-containing fragments treated with mercury. A ligation of the MPAA thioester of Thy-1 fragment (1-84) with 37b to obtain the full glycoprotein Thy-1 (1-120) was hindered by the poor solubility of thioester 46 in the ligation media. A new C- to N- ligation involving the polar glycoform 6c with the fragment 37b delivered the glycoprotein 49 that was treated in one-pot with PdCl2 to release the N-terminal cysteine and get 50. Finally, a methyl 3-mercaptopropionate MMP thioester of fragment 1-18 (51) was ligated with glycoprotein fragment 50 to obtain the desired Thy-1 glycoprotein (1-120) having three glycosylations. In this work was presented the design and evaluation of different strategies for the synthesis of the glycoprotein Thy-1. The assembly of the 13kDa glycoprotein required different steps and the optimized synthesis of amino acid building blocks for the solid-phase assembly of glycopeptides. Various methods were applied for the generation of glycopeptides, the exploration of the chemical properties of the obtained fragments, and the modulation of the chemical conditions for the ligation of the peptide fragments to get the target glycoprotein. This work focused on the production of homogeneous glycoforms of Thy-1. However, the synthetic methods and protocols established in this work are applicable for the synthesis of any peptides and glycopeptides and contribute to the chemical synthesis of other important glycoproteins

The difficult relationship between ruins and modernity: the case study of the Mother Church reconstruction in Salemi (Italy)

Located in the heart of Sicily, Salemi, a town of Arab origin and first capital of Italy, was devastated by the powerful earthquake that struck the Belice Valley in January 1968. From that moment on, its historic centre has long been abandoned; a few restoration works have been carried out as it was preferred to reconstruct affected districts in new sites. Nevertheless, Salemi has generally maintained its medieval structure, still preserving the original attractive landscape of perched village, resulting from security and control needs of an area based on agricultural and pastoral economy. At its highest point, next to the majestic Norman castle, re-erected in the 13th century by Frederick II of Swabia, stands the Mother Church, were acted the architects Alvaro Siza Vieira and Roberto Collova. Their project, drafted in the early 80's, can be considered as an emblematic case of architectural conservation and cultural preservation. Remains have been seen here in their profound value as a testimony to memory, turning them into charming and moving scenery for the new square created around. The designers considered the traumatic event has a starting point for an overhaul of the historic urban core of the city. They founded the project on the idea of "opening and offering" this sacred space to the town, accepting and integrating the earthquake effects into the architectural plans. Starting from this experience of consolidation and architectural restoration, recalling in its expression Ruskin's romantic memory, this work intends to highlight the historical and today's difficult relationship between ruins and modernity, improvement and destruction, conservation and new buildings design