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.

Abnormal skeletal patterning in embryos lacking a single Cbp allele: A partial similarity with Rubinstein–Taybi syndrome

CBP is a transcriptional coactivator required by many transcription factors for transactivation. Rubinstein–Taybi syndrome, which is an autosomal dominant syndrome characterized by abnormal pattern formation, has been shown to be associated with mutations in the Cbp gene. Furthermore, Drosophila CBP is required in hedgehog signaling for the expression of decapentapleigic, the Drosophila homologue of bone morphogenetic protein. However, no direct evidence exists to indicate that loss of one copy of the mammalian Cbp gene affects pattern formation. Here, we show that various abnormalities occur at high frequency in the skeletal system of heterozygous Cbp-deficient mice resulting from a C57BL/6-CBA × BALB/c cross. In support of a conserved signaling pathway for pattern formation in insects and mammals, the expression of Bmp7 was found to be reduced in the heterozygous mutants. The frequency of the different abnormalities was significantly lower in a C57BL/6-CBA background, suggesting that the genetic background is an important determinant of the variability and severity of the anomalies seen in Rubinstein–Taybi syndrome patients.

Incomplete penetrance of familial retinoblastoma linked to germ-line mutations that result in partial loss of RB function

To study the molecular basis for the clinical phenotype of incomplete penetrance of familial retinoblastoma, we have examined the functional properties of three RB mutations identified in the germ line of five different families with low penetrance. RB mutants isolated from common adult cancers and from classic familial retinoblastoma (designated as classic RB mutations) are unstable and generally do not localize to the nucleus, do not undergo cyclin-dependent kinase (cdk)-mediated hyperphosphorylation, show absent protein “pocket” binding activity, and do not suppress colony growth of RB(−) cells. In contrast, two low-penetrant alleles (661W and “deletion of codon 480”) retained the ability to localize to the nucleus, showed normal cdk-mediated hyperphosphorylation in vivo, exhibited a binding pattern to simian virus 40 large T antigen using a quantitative yeast two-hybrid assay that was intermediate between classic mutants (null) and wild-type RB, and had absent E2F1 binding in vitro. A third, low-penetrant allele, “deletion of RB exon 4,” showed minimal hyperphosphorylation in vivo but demonstrated detectable E2F1 binding in vitro. In addition, each low-penetrant RB mutant retained the ability to suppress colony growth of RB(−) tumor cells. These findings suggest two categories of mutant, low-penetrant RB alleles. Class 1 alleles correspond to promoter mutations, which are believed to result in reduced or deregulated levels of wild-type RB protein, whereas class 2 alleles result in mutant proteins that retain partial activity. Characterization of the different subtypes of class 2 low-penetrant genes may help to define more precisely functional domains within the RB product required for tumor suppression.

Altered peptide ligands act as partial agonists by inhibiting phospholipase C activity induced by myasthenogenic T cell epitopes

Myasthenia gravis (MG) is a T cell-regulated, antibody-mediated autoimmune disease. Two peptides representing sequences of the human acetylcholine receptor α-subunit, p195–212 and p259–271, previously were shown to stimulate the proliferation of peripheral blood lymphocytes of patients with MG and were found to be immunodominant T cell epitopes in SJL and BALB/c mice, respectively. Single amino acid-substituted analogs of p195–212 and p259–271, as well as a dual analog composed of the tandemly arranged two single analogs, were shown to inhibit, in vitro and in vivo, MG-associated autoimmune responses. Stimulation of T cells through the antigen-specific T cell receptor activates tyrosine kinases and phospholipase C (PLC). Therefore, in attempts to understand the mechanism of action of the analogs, we first examined whether the myasthenogenic peptides trigger tyrosine phosphorylation and activation of phospholipase C. For that purpose, we measured generation of inositol phosphates and tyrosine phosphorylation of PLC after stimulation of the p195–212- and p259–271-specific T cell lines with these myasthenogenic peptides. Both myasthenogenic peptides stimulated generation of inositol phosphates as well as tyrosine phosphorylation of PLC. However, the single and dual analogs, although inducing tyrosine phosphorylation of PLC, could not induce PLC activity. Furthermore, the single and dual analogs inhibited the induced PLC activity whereas they could not inhibit tyrosine phosphorylation of PLC that was caused by the myasthenogenic peptides. Thus, the altered peptides and the dual analog act as partial agonists. The down-regulation of PLC activity by the analogs may account for their capacity to inhibit in vitro MG-associated T cell responses.

Prolonged activation of the N-methyl-d-aspartate receptor–Ca2+ transduction pathway causes spontaneous recurrent epileptiform discharges in hippocampal neurons in culture

The molecular basis for developing symptomatic epilepsy (epileptogenesis) remains ill defined. We show here in a well characterized hippocampal culture model of epilepsy that the induction of epileptogenesis is Ca2+-dependent. The concentration of intracellular free Ca2+ ([Ca2+]i) was monitored during the induction of epileptogenesis by prolonged electrographic seizure activity induced through low-Mg2+ treatment by confocal laser-scanning fluorescent microscopy to directly correlate changes in [Ca2+]i with alterations in membrane excitability measured by intracellular recording using whole-cell current–clamp techniques. The induction of long-lasting spontaneous recurrent epileptiform discharges, but not the Mg2+-induced spike discharges, was prevented in low-Ca2+ solutions and was dependent on activation of the N-methyl-d-aspartate (NMDA) receptor. The results provide direct evidence that prolonged activation of the NMDA–Ca2+ transduction pathway causes a long-lasting plasticity change in hippocampal neurons causing increased excitability leading to the occurrence of spontaneous, recurrent epileptiform discharges.

Lune/eye gone, a Pax-like protein, uses a partial paired domain and a homeodomain for DNA recognition

Pax proteins, characterized by the presence of a paired domain, play key regulatory roles during development. The paired domain is a bipartite DNA-binding domain that contains two helix–turn–helix domains joined by a linker region. Each of the subdomains, the PAI and RED domains, has been shown to be a distinct DNA-binding domain. The PAI domain is the most critical, but in specific circumstances, the RED domain is involved in DNA recognition. We describe a Pax protein, originally called Lune, that is the product of the Drosophila eye gone gene (eyg). It is unique among Pax proteins, because it contains only the RED domain. eyg seems to play a role both in the organogenesis of the salivary gland during embryogenesis and in the development of the eye. A high-affinity binding site for the Eyg RED domain was identified by using systematic evolution of ligands by exponential enrichment techniques. This binding site is related to a binding site previously identified for the RED domain of the Pax-6 5a isoform. Eyg also contains another DNA-binding domain, a Prd-class homeodomain (HD), whose palindromic binding site is similar to other Prd-class HDs. The ability of Pax proteins to use the PAI, RED, and HD, or combinations thereof, may be one mechanism that allows them to be used at different stages of development to regulate various developmental processes through the activation of specific target genes.

A Mutant of Arp2p Causes Partial Disassembly of the Arp2/3 Complex and Loss of Cortical Actin Function in Fission Yeast

The Arp2/3 complex is an essential component of the yeast actin cytoskeleton that localizes to cortical actin patches. We have isolated and characterized a temperature-sensitive mutant of Schizosaccharomyces pombe arp2 that displays a defect in cortical actin patch distribution. The arp2+ gene encodes an essential actin-related protein that colocalizes with actin at the cortical actin patch. Sucrose gradient analysis of the Arp2/3 complex in the arp2-1 mutant indicated that the Arp2p and Arc18p subunits are specifically lost from the complex at restrictive temperature. These results are consistent with immunolocalization studies of the mutant that show that Arp2-1p is diffusely localized in the cytoplasm at restrictive temperature. Interestingly, Arp3p remains localized to the cortical actin patch under the same restrictive conditions, leading to the hypothesis that loss of Arp2p from the actin patch affects patch motility but does not severely compromise its architecture. Analysis of the mutant Arp2 protein demonstrated defects in ATP and Arp3p binding, suggesting a possible model for disruption of the complex.

Ocular cicatricial pemphigoid antigen: Partial sequence and biochemical characterization

Ocular cicatricial pemphigoid (OCP) is an autoimmune disease that affects mainly conjunctiva and other squamous epithelia. OCP is histologically characterized by a separation of the epithelium from underlying tissues within the basement membrane zone. Immunopathological studies demonstrate the deposition of anti-basement membrane zone autoantibodies in vivo. Purified IgG from sera of patients with active OCP identified a cDNA clone from a human keratinocyte cDNA library that had complete homology with the cytoplasmic domain of β4-integrin. The sera recognized a 205-kDa protein in human epidermal, human conjunctiva, and tumor cell lysates that was identified as β4-integrin by its reaction with polyclonal and monoclonal antibodies to human β4-integrin. Sera from patients with bullous pemphigoid, pemphigus vulgaris, and cicatricial pemphigoid-like diseases did not recognize the 205-kDa protein, indicating the specificity of the binding. These data strongly implicate a role for human β4-integrin in the pathogenesis of OCP. It should be emphasized that multiple antigens in the basement membrane zone of squamous epithelia may serve as targets for a wide spectrum of autoantibodies observed in vesiculobullous diseases. Molecular definition of these autoantigens will facilitate the classification and characterization of subsets of cicatricial pemphigoid and help distinguishing them from bullous pemphigoid. This study highlights the function and importance of β4-integrin in maintaining the attachment of epithelial cells to the basement membrane.

Sequencing of 3-O sulfate containing heparin decasaccharides with a partial antithrombin III binding site

Heparin- and heparan sulfate-like glycosaminoglycans (HLGAGs) represent an important class of molecules that interact with and modulate the activity of growth factors, enzymes, and morphogens. Of the many biological functions for this class of molecules, one of its most important functions is its interaction with antithrombin III (AT-III). AT-III binding to a specific heparin pentasaccharide sequence, containing an unusual 3-O sulfate on a N-sulfated, 6-O sulfated glucosamine, increases 1,000-fold AT-III's ability to inhibit specific proteases in the coagulation cascade. In this manner, HLGAGs play an important biological and pharmacological role in the modulation of blood clotting. Recently, a sequencing methodology was developed to further structure-function relationships of this important class of molecules. This methodology combines a property-encoded nomenclature scheme to handle the large information content (properties) of HLGAGs, with matrix-assisted laser desorption ionization MS and enzymatic and chemical degradation as experimental constraints to rapidly sequence picomole quantities of HLGAG oligosaccharides. Using the above property-encoded nomenclature-matrix-assisted laser desorption ionization approach, we found that the sequence of the decasaccharide used in this study is ΔU2SHNS,6SI2SHNS,6SI2SHNS,6SIHNAc,6SGHNS,3S,6S (±DDD4–7). We confirmed our results by using integral glycan sequencing and one-dimensional proton NMR. Furthermore, we show that this approach is flexible and is able to derive sequence information on an oligosaccharide mixture. Thus, this methodology will make possible both the analysis of other unusual sequences in HLGAGs with important biological activity as well as provide the basis for the structural analysis of these pharamacologically important group of heparin/heparan sulfates.

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.

Ts1Cje, a partial trisomy 16 mouse model for Down syndrome, exhibits learning and behavioral abnormalities

A mouse model for Down syndrome, Ts1Cje, has been developed. This model has made possible a step in the genetic dissection of the learning, behavioral, and neurological abnormalities associated with segmental trisomy for the region of mouse chromosome 16 homologous with the so-called “Down syndrome region” of human chromosome segment 21q22. Tests of learning in the Morris water maze and assessment of spontaneous locomotor activity reveal distinct learning and behavioral abnormalities, some of which are indicative of hippocampal dysfunction. The triplicated region in Ts1Cje, from Sod1 to Mx1, is smaller than that in Ts65Dn, another segmental trisomy 16 mouse, and the learning deficits in Ts1Cje are less severe than those in Ts65Dn. In addition, degeneration of basal forebrain cholinergic neurons, which was observed in Ts65Dn, was absent in Ts1Cje.

Decreased ability of HIV-1 Tat protein-treated accessory cells to organize cellular clusters is associated with partial activation of T cells

It has been shown in several animal models that HIV infection of accessory cells (ACs) plays an important role in development of AIDS. Here, we report that ACs treated with HIV-1 Tat protein (Tat-ACs) have a decreased ability to organize cellular aggregates as compared with untreated ACs, resulting in incomplete activation of T cells in responses to anti-CD3 mAb or staphylococcal enterotoxin B stimulation. The T cells failed to up-regulate adhesion molecules CD11a and CD2 on the cell surface and had reduced proliferative responses, as determined by [3H]thymidine incorporation, but they obtained lymphoblast-like morphology and expressed early activation antigens on the cell surface such as Fas and CD69 and interleukin 2 receptor, at comparable levels as those T cells undergoing a maximal proliferation. These results suggest that the Tat-AC-induced defect occurs in the late, but not in the early, phases of T cell activation. Normal expression of cell surface Fas antigen accompanied by defects in late activation thus may result in the susceptibility of these T cells to apoptosis. Our studies suggest that dysfunction, hyperactivation, and susceptibility to apoptosis, as observed with T cells isolated from HIV-infected individuals, may be, at least in part, a consequence of abnormal functions of ACs.

Lack of agreement between tonometric and gastric juice partial carbon dioxide tension

Our goal was to compare measurement of tonometered saline and gastric juice partial carbon dioxide tension (PCO2). In this prospective observational study, 112 pairs of measurements were simultaneously obtained under various hemodynamic conditions, in 15 critical care patients. Linear regression analysis showed a significant correlation between the two methods of measuring PCO2 (r 2 = 0.43; P < 0.0001). However, gastric juice PCO2 was systematically higher (mean difference 51 mmHg). The 95% limits of agreement were 315 mmHg and the dispersion increased as the values of PCO2 increased. Tonometric and gastric juice PCO2 cannot be used interchangeably. Gastric juice PCO2 measurement should be interpreted with caution.