Lie algebras and triple systems

This thesis is dedicated to the Tits-Kantor-Koecher (TKK) construction which establishes a bijective correspondence between unital Jordan algebras and shortly graded Lie algebras with Z-grading induced by an sl_2-triple. It is based on the observation that if g is a Lie algebra with a short Z-grading and f lies in g_1, then the formula ab=[[a,f],b] defines a structure of a Jordan algebra on g_{-1}. The TKK construction has been extended to Jordan triple systems and, more recently, to the so-called Kantor triple systems. These generalizations are studied in the thesis.

An in vitro triple cell co-culture model with primary cells mimicking the human alveolar epithelial barrier

A triple cell co-culture model was recently established by the authors, consisting of either A549 or 16HBE14o- epithelial cells, human blood monocyte-derived macrophages and dendritic cells, which offers the possibility to study the interaction of xenobiotics with those cells. The 16HBE14o- containing co-culture model mimics the airway epithelial barrier, whereas the A549 co-cultures mimic the alveolar type II-like epithelial barrier. The goal of the present work was to establish a new triple cell co-culture model composed of primary alveolar type I-like cells isolated from human lung biopsies (hAEpC) representing a more realistic alveolar epithelial barrier wall, since type I epithelial cells cover >93% of the alveolar surface. Monocultures of A549 and 16HBE14o- were morphologically and functionally compared with the hAEpC using laser scanning microscopy, as well as transmission electron microscopy, and by determining the epithelial integrity. The triple cell co-cultures were characterized using the same methods. It could be shown that the epithelial integrity of hAEpC (mean ± SD, 1180 ± 188 Ω cm(2)) was higher than in A549 (172 ± 59 Ω cm(2)) but similar to 16HBE14o- cells (1469 ± 156 Ω cm(2)). The triple cell co-culture model with hAEpC (1113 ± 30 Ω cm(2)) showed the highest integrity compared to the ones with A549 (93 ± 14 Ω cm(2)) and 16HBE14o- (558 ± 267 Ω cm(2)). The tight junction protein zonula occludens-1 in hAEpC and 16HBE14o- were more regularly expressed but not in A549. The epithelial alveolar model with hAEpC combined with two immune cells (i.e. macrophages and dendritic cells) will offer a novel and more realistic cell co-culture system to study possible cell interactions of inhaled xenobiotics and their toxic potential on the human alveolar type I epithelial wall.

Gonadotropin-releasing hormone type II antagonist induces apoptosis in MCF-7 and triple-negative MDA-MB-231 human breast cancer cells in vitro and in vivo

Triple-negative breast cancer does not express estrogen and progesterone receptors, and no overexpression/amplification of the HER2-neu gene occurs. Therefore, this subtype of breast cancer lacks the benefits of specific therapies that target these receptors. Today chemotherapy is the only systematic therapy for patients with triple-negative breast cancer. About 50% to 64% of human breast cancers express receptors for gonadotropin-releasing hormone (GnRH), which might be used as a target. New targeted therapies are warranted. Recently, we showed that antagonists of gonadotropin-releasing hormone type II (GnRH-II) induce apoptosis in human endometrial and ovarian cancer cells in vitro and in vivo. This was mediated through activation of stress-induced mitogen-activated protein kinases (MAPKs) p38 and c-Jun N-terminal kinase (JNK), followed by activation of proapoptotic protein Bax, loss of mitochondrial membrane potential, and activation of caspase-3. In the present study, we analyzed whether GnRH-II antagonists induce apoptosis in MCF-7 and triple-negative MDA-MB-231 human breast cancer cells that express GnRH receptors. In addition, we ascertained whether knockdown of GnRH-I receptor expression affects GnRH-II antagonist-induced apoptosis and apoptotic signaling.

Molecular Dynamics Simulation of a PNA·DNA·PNA Triple Helix in Aqueous Solution

Molecular dynamics simulations have been used to explore the conformational flexibility of a PNA·DNA·PNA triple helix in aqueous solution. Three 1.05 ns trajectories starting from different but reasonable conformations have been generated and analyzed in detail. All three trajectories converge within about 300 ps to produce stable and very similar conformational ensembles, which resemble the crystal structure conformation in many details. However, in contrast to the crystal structure, there is a tendency for the direct hydrogen-bonds observed between the amide hydrogens of the Hoogsteen-binding PNA strand and the phosphate oxygens of the DNA strand to be replaced by water-mediated hydrogen bonds, which also involve pyrimidine O2 atoms. This structural transition does not appear to weaken the triplex structure but alters groove widths and so may relate to the potential for recognition of such structures by other ligands (small molecules or proteins). Energetic analysis leads us to conclude that the reason that the hybrid PNA/DNA triplex has quite different helical characteristics from the all-DNA triplex is not because the additional flexibility imparted by the replacement of sugar−phosphate by PNA backbones allows motions to improve base-stacking but rather that base-stacking interactions are very similar in both types of triplex and the driving force comes from weak but definate conformational preferences of the PNA strands.

Molecular Dynamics Simulations of the d(TAT) Triple Helix

Molecular dynamics (MD) simulations have been used to study the dynamical and time-averaged characteristics of the DNA triple helix d(T)10âd(A)10âd(T)10. The structures sampled during the trajectory resemble closely the B-type model for the DNA triplex proposed on the basis of NMR data, although there are some subtle differences. Alternative P- and A-type conformations for the triplex, suggested from X-ray experiments, are not predicted to contribute significantly to the structure of the DNA triplex in solution. Comparison with the best available experimental data supports the correctnes of the MD-generated structures. The analysis of the collected data gives a detailed picture of the characteristics of triple-helix DNA. A new and interesting pattern of hydration, specific for triplex DNA, is an important observation. The results suggest that molecular dynamics can be useful for the study of novel nucleic acid structures.

Decompression during Late Proterozoic Al2SiO5 Triple-Point Metamorphism at Cerro Colorado, New Mexico

An outstanding problem in understanding the late Proterozoic tectonic assembly of the southwest is identifying the tectonic setting associated with regional metamorphism at 1.4 Ga. Both isobaric heating and cooling, and counter-clockwise looping PT paths are proposed for this time. We present a study of the Proterozoic metamorphic and deformation history of the Cerro Colorado area, southern Tusas Mountains, New Mexico, which shows that the metamorphism in this area records near-isothermal decompression from 6 to 4 kbar at ca. 1.4 Ga. We do not see evidence for isobaric heating at this time. Decompression from peak pressures is recorded by the reaction Ms + Grt = St + Bt, with a negative slope in PT space; the reaction Ms + Grt = Sil + Bt, which is nearly horizontal in PT space; and partial to total pseudomorphing of kyanite by sillimanite during the main phase of deformation. The clearest reaction texture indicating decompression near peak metamorphic temperature is the replacement of garnet by clots of sillimanite, which are surrounded by halos of biotite. The sillimanite clots, most without relict garnet in the cores and with highly variable aspect ratios, are aligned. They define a lineation that formed with the dominant foliation. An inverted metamorphic gradient is locally defined by sillimanite-garnet schists (625 degrees C) structurally above staurolite-garnet schists (550 degrees C) and implies ductile thrusting during the main phase of deformation. The exhumation that led to the recorded decompression was likely in response to crustal thickening due to ductile thrusting and subsequent denudation.

Triple innominate osteotomy for Legg-Calvé-Perthes disease in children: does the lateral coverage change with time?

Triple innominate osteotomy (TIO) is one of the modalities of surgical containment in Legg-Calvé-Perthes disease (LCPD). However, overcoverage with TIO can lead to pincer impingement.