Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

As part of our attempts at understanding fundamental principles that underlie the generation of nondividing terminally differentiated progeny from dividing precursor cells, we have developed approaches to a quantitative analysis of proliferation and differentiation of oligodendrocyte type 2 astrocyte (O-2A) progenitor cells at the clonal level. Owing to extensive previous studies of clonal differentiation in this lineage, O-2A progenitor cells represent an excellent system for such an analysis. Previous studies have resulted in two competing hypotheses; one of them suggests that progenitor cell differentiation is symmetric, the other hypothesis introduces an asymmetric process of differentiation. We propose a general model that incorporates both such extreme hypotheses as special cases. Our analysis of experimental data has shown, however, that neither of these extreme cases completely explains the observed kinetics of O-2A progenitor cell proliferation and oligodendrocyte generation in vitro. Instead, our results indicate that O-2A progenitor cells become competent for differentiation after they complete a certain number of critical mitotic cycles that represent a period of symmetric development. This number varies from clone to clone and may be thought of as a random variable; its probability distribution was estimated from experimental data. Those O-2A cells that have undergone the critical divisions then may differentiate into an oligodendrocyte in each of the subsequent mitotic cycles with a certain probability, thereby exhibiting the asymmetric type of differentiation.

Telomerase expression and activity are coupled with myocyte proliferation and preservation of telomeric length in the failing heart

The role and even the existence of myocyte proliferation in the adult heart remain controversial. Documentation of cell cycle regulators, DNA synthesis, and mitotic images has not modified the view that myocardial growth can only occur from hypertrophy of an irreplaceable population of differentiated myocytes. To improve understanding the biology of the heart and obtain supportive evidence of myocyte replication, three indices of cell proliferation were analyzed in dogs affected by a progressive deterioration of cardiac performance and dilated cardiomyopathy. The magnitude of cycling myocytes was evaluated by the expression of Ki67 in nuclei. Ki67 labeling of left ventricular myocytes increased 5-fold, 12-fold, and 17-fold with the onset of moderate and severe ventricular dysfunction and overt failure, respectively. Telomerase activity in vivo is present only in multiplying cells; this enzyme increased 2.4-fold and 3.1-fold in the decompensated heart, preserving telomeric length in myocytes. The contribution of cycling myocytes to telomerase activity was determined by the colocalization of Ki67 and telomerase in myocyte nuclei. More than 50% of Ki67-positive cells expressed telomerase in the overloaded myocardium, suggesting that these myocytes were the morphological counterpart of the biochemical assay of enzyme activity. Moreover, we report that 20–30% of canine myocytes were telomerase competent, and this value was not changed by cardiac failure. In conclusion, the enhanced expression of Ki67 and telomerase activity, in combination with Ki67-telomerase labeling of myocyte nuclei, support the notion that myocyte proliferation contributes to cardiac hypertrophy of the diseased heart.

IL-7 is critical for homeostatic proliferation and survival of naïve T cells

In T cell-deficient conditions, naïve T cells undergo spontaneous “homeostatic” proliferation in response to contact with self-MHC/peptide ligands. With the aid of an in vitro system, we show here that homeostatic proliferation is also cytokine-dependent. The cytokines IL-4, IL-7, and IL-15 enhanced homeostatic proliferation of naïve T cells in vitro. Of these cytokines, only IL-7 was found to be critical; thus, naïve T cells underwent homeostatic proliferation in IL-4− and IL-15− hosts but proliferated minimally in IL-7− hosts. In addition to homeostatic proliferation, the prolonged survival of naïve T cells requires IL-7. Thus, naïve T cells disappeared gradually over a 1-month period upon adoptive transfer into IL-7− hosts. These findings indicate that naïve T cells depend on IL-7 for survival and homeostatic proliferation.

Chloroplast DNA evidence of colonization, adaptive radiation, and hybridization in the evolution of the Macaronesian flora.

Most evolutionary studies of oceanic islands have focused on the Pacific Ocean. There are very few examples from the Atlantic archipelagos, especially Macaronesia, despite their unusual combination of features, including a close proximity to the continent, a broad range of geological ages, and a biota linked to a source area that existed in the Mediterranean basin before the late Tertiary. A chloroplast DNA (cpDNA) restriction site analysis of Argyranthemum (Asteraceae: Anthemideae), the largest endemic genus of plants of any volcanic archipelago in the Atlantic Ocean, was performed to examine patterns of plant evolution in Macaronesia. cpDNA data indicated that Argyranthemum is a monophyletic group that has speciated recently. The cpDNA tree showed a weak correlation with the current sectional classification and insular distribution. Two major cpDNA lineages were identified. One was restricted to northern archipelagos--e.g., Madeira, Desertas, and Selvagens--and the second comprised taxa endemic to the southern archipelago--e.g., the Canary Islands. The two major radiations identified in the Canaries are correlated with distinct ecological habitats; one is restricted to ecological zones under the influence of the northeastern trade winds and the other to regions that are not affected by these winds. The patterns of phylogenetic relationships in Argyranthemum indicate that interisland colonization between similar ecological zones is the main mechanism for establishing founder populations. This phenomenon, combined with rapid radiation into distinct ecological zones and interspecific hybridization, is the primary explanation for species diversification.

Engagement of p75/AIRM1 or CD33 inhibits the proliferation of normal or leukemic myeloid cells

P75/AIRM1 is a recently identified surface molecule that belongs to the sialoadhesin family and displays homology with the myeloid cell antigen CD33. In lymphoid cells, p75/AIRM1 is confined to natural killer cells and mediates inhibition of their cytolytic activity. In this study, we show that p75/AIRM1 is also expressed by cells of the myelomonocytic cell lineage, in which it appears at a later stage as compared with CD33. In vitro proliferation and differentiation of cord blood-derived CD34+ cells (induced by stem cell factor and granulocyte–macrophage colony-stimulating factor) were consistently inhibited by the addition of anti-p75/AIRM1 mAb. Engagement of CD33 led to inhibition in some experiments. A sharp decrease of cell proliferation/survival was detected in all three p75/AIRM1+ chronic myeloid leukemias analyzed when cultured in the presence of either anti-p75/AIRM1 or anti-CD33 mAbs. Thus, the present study suggests that p75/AIRM1 and CD33 may play a regulatory role in normal myelopoiesis and may be viewed as suitable target molecules to counteract the proliferation/survival of chronic myeloid leukemias.

Abnormal integrin-mediated regulation of chronic myelogenous leukemia CD34+ cell proliferation: BCR/ABL up-regulates the cyclin-dependent kinase inhibitor, p27Kip, which is relocated to the cell cytoplasm and incapable of regulating cdk2 activity

β1-integrin engagement on normal (NL) CD34+ cells increases levels of the cyclin-dependent kinase inhibitor (cdki), p27Kip, decreases cdk2 activity, and inhibits G1/S-phase progression. In contrast, β1-integrin engagement on chronic myelogenous leukemia (CML) CD34+ cells does not inhibit G1/S progression. We now show that, in CML, baseline p27Kip levels are significantly higher than in NL CD34+ cells, but adhesion to fibronectin (FN) does not increase p27Kip levels. p27Kip mRNA levels are similar in CML and NL CD34+ cells and remain unchanged after adhesion, suggesting posttranscriptional regulation. Despite the elevated p27Kip levels, cdk2 kinase activity is similar in CML and NL CD34+ cells. In NL CD34+ cells, >90% of p27Kip is located in the nucleus, where it binds to cdk2 after integrin engagement. In CML CD34+ cells, however, >80% of p27Kip is located in the cytoplasm even in FN-adherent cells, and significantly less p27Kip is bound to cdk2. Thus, presence of BCR/ABL induces elevated levels of p27Kip and relocation of p27Kip to the cytoplasm, which contributes to the loss of integrin-mediated proliferation inhibition, characteristic of CML.

Role of the arginine-nitric oxide pathway in the regulation of vascular smooth muscle cell proliferation

The objective of this study was to elucidate the mechanisms by which nitric oxide (NO) inhibits rat aortic smooth muscle cell (RASMC) proliferation. Two products of the arginine-NO pathway interfere with cell growth by distinct mechanisms. NG-hydroxyarginine and NO appear to interfere with cell proliferation by inhibiting arginase and ornithine decarboxylase (ODC), respectively. S-nitroso-N-acetylpenicillamine, (Z)-1-[N-(2-aminoethyl)-N-(2-aminoethyl)-amino]-diazen-1-ium-1,2-diolate, and a nitroaspirin derivative (NCX 4016), each of which is a NO donor agent, inhibited RASMC growth at concentrations of 1–3 μM by cGMP-independent mechanisms. The cytostatic action of the NO donor agents as well as α-difluoromethylornithine (DFMO), a known ODC inhibitor, was prevented by addition of putrescine but not ornithine. These observations suggested that NO, like DFMO, may directly inhibit ODC. Experiments with purified, recombinant mammalian ODC revealed that NO inhibits ODC possibly by S-nitrosylation of the active site cysteine in ODC. DFMO, as well as the NO donor agents, interfered with cellular polyamine (putrescine, spermidine, spermine) production. Conversely, increasing the expression and catalytic activity of arginase I in RASMC either by transfection of cells with the arginase I gene or by induction of arginase I mRNA with IL-4 resulted in increased urea and polyamine production as well as cell proliferation. Finally, coculture of rat aortic endothelial cells, which had been pretreated with lipopolysaccharide plus a cytokine mixture to induce NO synthase and promote NO production, caused NO-dependent inhibition of target RASMC proliferation. This study confirms the inhibitory role of the arginine-NO pathway in vascular smooth muscle proliferation and indicates that one mechanism of action of NO is cGMP-independent and attributed to its capacity to inhibit ODC.