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.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

Diverse roles of the tumor necrosis factor family member TRANCE in skeletal physiology revealed by TRANCE deficiency and partial rescue by a lymphocyte-expressed TRANCE transgene

Tumor necrosis factor-related, activation-induced cytokine (TRANCE), a tumor necrosis factor family member, mediates survival of dendritic cells in the immune system and is required for osteoclast differentiation and activation in the skeleton. We report the skeletal phenotype of TRANCE-deficient mice and its rescue by the TRANCE transgene specifically expressed in lymphocytes. TRANCE-deficient mice showed severe osteopetrosis, with no osteoclasts, marrow spaces, or tooth eruption, and exhibited profound growth retardation at several skeletal sites, including the limbs, skull, and vertebrae. These mice had marked chondrodysplasia, with thick, irregular growth plates and a relative increase in hypertrophic chondrocytes. Transgenic overexpression of TRANCE in lymphocytes of TRANCE-deficient mice rescued osteoclast development in two locations in growing long bones: excavation of marrow cavities permitting hematopoiesis in the marrow spaces, and remodeling of osteopetrotic woven bone in the shafts of long bones into histologically normal lamellar bone. However, osteoclasts in these mice failed to appear at the chondroosseous junction and the metaphyseal periosteum of long bones, nor were they present in tooth eruption pathways. These defects resulted in sclerotic metaphyses with persistence of club-shaped long bones and unerupted teeth, and the growth plate defects were largely unimproved by the TRANCE transgene. Thus, TRANCE-mediated regulation of the skeleton is complex, and impacts chondrocyte differentiation and osteoclast formation in a manner that likely requires local delivery of TRANCE.

The Two Major Types of Plant Plasma Membrane H+-ATPases Show Different Enzymatic Properties and Confer Differential pH Sensitivity of Yeast Growth1

The proton-pumping ATPase (H+-ATPase) of the plant plasma membrane is encoded by two major gene subfamilies. To characterize individual H+-ATPases, PMA2, an H+-ATPase isoform of tobacco (Nicotiana plumbaginifolia), was expressed in Saccharomyces cerevisiae and found to functionally replace the yeast H+-ATPase if the external pH was kept above 5.0 (A. de Kerchove d'Exaerde, P. Supply, J.P. Dufour, P. Bogaerts, D. Thinès, A. Goffeau, M. Boutry [1995] J Biol Chem 270: 23828–23837). In the present study we replaced the yeast H+-ATPase with PMA4, an H+-ATPase isoform from the second subfamily. Yeast expressing PMA4 grew at a pH as low as 4.0. This was correlated with a higher acidification of the external medium and an approximately 50% increase of ATPase activity compared with PMA2. Although both PMA2 and PMA4 had a similar pH optimum (6.6–6.8), the profile was different on the alkaline side. At pH 7.2 PMA2 kept more than 80% of the maximal activity, whereas that of PMA4 decreased to less than 40%. Both enzymes were stimulated up to 3-fold by 100 μg/mL lysophosphatidylcholine, but this stimulation vanished at a higher concentration in PMA4. These data demonstrate functional differences between two plant H+-ATPases expressed in the same heterologous host. Characterization of two PMA4 mutants selected to allow yeast growth at pH 3.0 revealed that mutations within the carboxy-terminal region of PMA4 could still improve the enzyme, resulting in better growth of yeast cells.

Identification and Partial Characterization of the Pectin Methyltransferase “Homogalacturonan-Methyltransferase” from Membranes of Tobacco Cell Suspensions1

A membrane preparation from tobacco (Nicotiana tabacum L.) cells contains at least one enzyme that is capable of transferring the methyl group from S-adenosyl-methionine (SAM) to the C6 carboxyl of homogalacturonan present in the membranes. This enzyme is named homogalacturonan-methyltransferase (HGA-MT) to distinguish it from methyltransferases that catalyze methyletherification of the pectic polysaccharides rhamnogalacturonan I or rhamnogalacturonan II. A trichloroacetic acid precipitation assay was used to measure HGA-MT activity, because published procedures to recover pectic polysaccharides via ethanol or chloroform:methanol precipitation lead to high and variable background radioactivity in the product pellet. Attempts to reduce the incorporation of the 14C-methyl group from SAM into pectin by the addition of the alternative methyl donor 5-methyltetrahydrofolate were unsuccessful, supporting the role of SAM as the authentic methyl donor for HGA-MT. The pH optimum for HGA-MT in membranes was 7.8, the apparent Michaelis constant for SAM was 38 μm, and the maximum initial velocity was 0.81 pkat mg−1 protein. At least 59% of the radiolabeled product was judged to be methylesterified homogalacturonan, based on the release of radioactivity from the product after a mild base treatment and via enzymatic hydrolysis by a purified pectin methylesterase. The released radioactivity eluted with a retention time identical to that of methanol upon fractionation over an organic acid column. Cleavage of the radiolabeled product by endopolygalacturonase into fragments that migrated as small oligomers of HGA during thin-layer chromatography, and the fact that HGA-MT activity in the membranes is stimulated by uridine 5′-diphosphate galacturonic acid, a substrate for HGA synthesis, confirms that the bulk of the product recovered from tobacco membranes incubated with SAM is methylesterified HGA.

Interleukin 2 production, not the pattern of early T-cell antigen receptor-dependent tyrosine phosphorylation, controls anergy induction by both agonists and partial agonists.

Full activation of T cells requires signaling through the T-cell antigen receptor (TCR) and additional surface molecules interacting with ligands on the antigen-presenting cell. TCR recognition of agonist ligands in the absence of accessory signals frequently results in the induction of a state of unresponsiveness termed anergy. However, even in the presence of costimulation, anergy can be induced by TCR partial agonists. The unique pattern of early receptor-induced tyrosine phosphorylation events induced by partial agonists has led to the hypothesis that altered TCR signaling is directly responsible for the development of anergy. Here we show that anergy induction is neither correlated with nor irreversibly determined by the pattern of early TCR-induced phosphorylation. Rather, it appears to result from the absence of downstream events related to interleukin 2 receptor occupancy and/or cell division. This implies that the anergic state can be manipulated independently of the precise pattern of early biochemical changes following TCR occupancy, a finding with implications for understanding the induction of self-tolerance and the use of partial agonist ligands in the treatment of autoimmune diseases.

Chromosomal localization of the mammalian peptide-methionine sulfoxide reductase gene and its differential expression in various tissues.

Peptide methionine sulfoxide reductase (MsrA; EC 1.8.4.6) is a ubiquitous protein that can reduce methionine sulfoxide residues in proteins as well as in a large number of methyl sulfoxide compounds. The expression of MsrA in various rat tissues was determined by using immunocytochemical staining. Although the protein was found in all tissues examined, it was specifically localized to renal medulla and retinal pigmented epithelial cells, and it was prominent in neurons and throughout the nervous system. In addition, blood and alveolar macrophages showed high expression of the enzyme. The msrA gene was mapped to the central region of mouse chromosome 14, in a region of homology with human chromosomes 13 and 8p21.

Potent immunogenicity of the B subunits of Escherichia coli heat-labile enterotoxin: receptor binding is essential and induces differential modulation of lymphocyte subsets.

The importance of receptor binding in the potent immunogenicity of Escherichia coli heat-labile enterotoxin B subunit (EtxB) was tested by comparing its immunogical properties with those of a receptor binding mutant, EtxB(G33D). Subcutaneous immunization of EtxB(G33D) resulted in 160-fold reduction in antibody titer compared with wild-type EtxB, whereas its oral delivery failed to provoke any detectable secretory or serum anti-B subunit responses. Moreover, the two proteins induced strikingly different effects on lymphocyte cultures in vitro. EtxB, in comparison with EtxB(G33D), caused an increase in the proportion of B cells, many of which were activated (CD25+); the complete depletion of CD8+ T cells; an increase in the activation of CD4+ T cells; and an increase in interleukin 2 and a decrease in interferon gamma. These data indicate that EtxB exerts profound effects on immune cells, suggesting that its potent immunogenicity is dependent not only on efficient receptor-mediated uptake, but also on direct receptor-mediated immunomodulation of lymphocyte subsets.

Selenophosphate synthetase: detection in extracts of rat tissues by immunoblot assay and partial purification of the enzyme from the archaean Methanococcus vannielii.

In Escherichia coli and Salmonella typhimurium it has been shown that selenophosphate serves as the selenium donor for the conversion of seryl-tRNA to selenocysteyl-tRNA and for the synthesis of 2-selenouridine, a modified nucleoside present in tRNAs. Although selenocysteyl-tRNA also is formed in eukaryotes and is used for the specific insertion of selenocysteine into proteins, the precise mechanism of its biosynthesis from seryl-tRNA in these systems is not known. Because selenophosphate is extremely oxygen labile and difficult to identify in biological systems, we used an immunological approach to detect the possible presence of selenophosphate synthetase in mammalian tissues. With antibodies elicited to E. coli selenophosphate synthetase the enzyme was detected in extracts of rat brain, liver, kidney, and lung by immunoblotting. Especially high levels were detected in Methanococcus vannielii, a member of the domain Archaea, and the enzyme was partially purified from this source. It seems likely that the use of selenophosphate as a selenium donor is widespread in biological systems.

Bridging grafts and transient nerve growth factor infusions promote long-term central nervous system neuronal rescue and partial functional recovery.

Grafts of favorable axonal growth substrates were combined with transient nerve growth factor (NGF) infusions to promote morphological and functional recovery in the adult rat brain after lesions of the septohippocampal projection. Long-term septal cholinergic neuronal rescue and partial hippocampal reinnervation were achieved, resulting in partial functional recovery on a simple task assessing habituation but not on a more complex task assessing spatial reference memory. Control animals that received transient NGF infusions without axonal-growth-promoting grafts lacked behavioral recovery but also showed long-term septal neuronal rescue. These findings indicate that (i) partial recovery from central nervous system injury can be induced by both preventing host neuronal loss and promoting host axonal regrowth and (ii) long-term neuronal loss can be prevented with transient NGF infusions.

Rescue, propagation, and partial purification of a helper virus-dependent adenovirus vector.

Adenoviral vectors are widely used as highly efficient gene transfer vehicles in a variety of biological research strategies including human gene therapy. One of the limitations of the currently available adenoviral vector system is the presence of the majority of the viral genome in the vector, resulting in leaky expression of viral genes particularly at high multiplicity of infection and limited cloning capacity of exogenous sequences. As a first step to overcome this problem, we attempted to rescue a defective human adenovirus serotype 5 DNA, which had an essential region of the viral genome (L1, L2, VAI + II, pTP) deleted and replaced with an indicator gene. In the presence of wild-type adenovirus as a helper, this DNA was packaged and propagated as transducing viral particles. After several rounds of amplification, the titer of the recombinant virus reached at least 4 x 10(6) transducing particles per ml. The recombinant virus could be partially purified from the helper virus by CsCl equilibrium density-gradient centrifugation. The structure of the recombinant virus around the marker gene remained intact after serial propagation, while the pBR sequence inserted in the E1 region was deleted from the recombinant virus. Our results suggest that it should be possible to develop a helper-dependent adenoviral vector, which does not encode any viral proteins, as an alternative to the currently available adenoviral vector systems.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.