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.

A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

Molecular cloning and functional analysis of SUT-1, a sulfate transporter from human high endothelial venules

High endothelial venules (HEV) are specialized postcapillary venules found in lymphoid organs and chronically inflamed tissues that support high levels of lymphocyte extravasation from the blood. One of the major characteristics of HEV endothelial cells (HEVEC) is their capacity to incorporate large amounts of sulfate into sialomucin-type counter-receptors for the lymphocyte homing receptor L-selectin. Here, we show that HEVEC express two functional classes of sulfate transporters defined by their differential sensitivity to the anion-exchanger inhibitor 4,4′-diisothiocyanostilbene-2,2′-disulfonic acid (DIDS), and we report the molecular characterization of a DIDS-resistant sulfate transporter from human HEVEC, designated SUT-1. SUT-1 belongs to the family of Na+-coupled anion transporters and exhibits 40–50% amino acid identity with the rat renal Na+/sulfate cotransporter, NaSi-1, as well as with the human and rat Na+/dicarboxylate cotransporters, NaDC-1/SDCT1 and NaDC-3/SDCT2. Functional expression studies in cRNA-injected Xenopus laevis oocytes showed that SUT-1 mediates high levels of Na+-dependent sulfate transport, which is resistant to DIDS inhibition. The SUT-1 gene mapped to human chromosome 7q33. Northern blotting analysis revealed that SUT-1 exhibits a highly restricted tissue distribution, with abundant expression in placenta. Reverse transcription–PCR analysis indicated that SUT-1 and the diastrophic dysplasia sulfate transporter (DTD), one of the two known human DIDS-sensitive sulfate transporters, are coexpressed in HEVEC. SUT-1 and DTD could correspond, respectively, to the DIDS-resistant and DIDS-sensitive components of sulfate uptake in HEVEC. Together, these results demonstrate that SUT-1 is a distinct human Na+-coupled sulfate transporter, likely to play a major role in sulfate incorporation in HEV.

Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x ○ y) = H(f(x), f(y)) (x, y ∈ S) is investigated, where H is a homogeneous function and ○ is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Activation of human monocytes induces differential resistance to apoptosis with rapid down regulation of caspase-8/FLICE

Cells of the monocyte/macrophage lineage play a central role in both innate and acquired immunity of the host. However, the acquisition of functional competence and the ability to respond to a variety of activating or modulating signals require maturation and differentiation of circulating monocytes and entail alterations in both biochemical and phenotypic profiles of the cells. The process of activation also confers survival signals essential for the functional integrity of monocytes enabling the cells to remain viable in microenvironments of immune or inflammatory lesions that are rich in cytotoxic inflammatory mediators and reactive free-radical species. However, the molecular mechanisms of activation-induced survival signals in monocytes remain obscure. To define the mechanistic basis of activation-induced resistance to apoptosis in human monocytes at the molecular level, we evaluated the modulation of expression profiles of genes associated with the cellular apoptotic pathways upon activation and demonstrate the following: (i) activation results in selective resistance to apoptosis particularly to that induced by signaling via death receptors and DNA damage; (ii) concurrent with activation, the most apical protease in the death receptor pathway, caspase-8/FLICE is rapidly down-regulated at the mRNA level representing a novel regulatory mechanism; and (iii) activation of monocytes also leads to dramatic induction of the Bfl-1 gene, an anti apoptotic member of the Bcl-2 family. Our findings thus provide a potential mechanistic basis for the activation-induced resistance to apoptosis in human monocytes.

Differential binding to HLA-C of p50-activating and p58-inhibitory natural killer cell receptors

Natural killer (NK) cell cytotoxicity is regulated in large part by the expression of NK cell receptors able to bind class I major histocompatibility complex glycoproteins. The receptors associated with recognition of HLA-C allospecificities are the two-domain Ig-like molecules, p50 and p58 proteins, with highly homologous extracellular domains but differing in that they have either an activating or inhibitory function, respectively, depending on the transmembrane domain and cytoplasmic tails that they possess. We have compared the binding to HLA-Cw7 of an inhibitory p58 molecule, NKAT2, the highly homologous activating p50 molecule, clone 49, and a second activating p50 molecule, clone 39, which has homologies to both NKAT1 and NKAT2. NKAT2 binds to HLA-Cw7 with very rapid association and dissociation rates. However, the p50 receptors bind only very weakly, if at all, to HLA-C. The molecular basis of this difference is analyzed, and the functional significance of these observations is discussed.

Functional redundancy of acetylcholinesterase and neuroligin in mammalian neuritogenesis

Accumulated evidence attributes noncatalytic morphogenic activitie(s) to acetylcholinesterase (AChE). Despite sequence homologies, functional overlaps between AChE and catalytically inactive AChE-like cell surface adhesion proteins have been demonstrated only for the Drosophila protein neurotactin. Furthermore, no mechanism had been proposed to enable signal transduction by AChE, an extracellular enzyme. Here, we report impaired neurite outgrowth and loss of neurexin Iα mRNA under antisense suppression of AChE in PC12 cells (AS-ACHE cells). Neurite growth was partially rescued by addition of recombinant AChE to the solid substrate or by transfection with various catalytically active and inactive AChE variants. Moreover, overexpression of the homologous neurexin I ligand, neuroligin-1, restored both neurite extension and expression of neurexin Iα. Differential PCR display revealed expression of a novel gene, nitzin, in AS-ACHE cells. Nitzin displays 42% homology to the band 4.1 protein superfamily capable of linking integral membrane proteins to the cytoskeleton. Nitzin mRNA is high throughout the developing nervous system, is partially colocalized with AChE, and increases in rescued AS-ACHE cells. Our findings demonstrate redundant neurite growth-promoting activities for AChE and neuroligin and implicate interactions of AChE-like proteins and neurexins as potential mediators of cytoarchitectural changes supporting neuritogenesis.

Multiple imprinted sense and antisense transcripts, differential methylation and tandem repeats in a putative imprinting control region upstream of mouse Igf2

The mouse insulin-like growth factor 2 (Igf2) locus is a complex genomic region that produces multiple transcripts from alternative promoters. Expression at this locus is regulated by parental imprinting. However, despite the existence of putative imprinting control elements in the Igf2 upstream region, imprinted transcriptional repression is abolished by null mutations at the linked H19 locus. To clarify the extent to which the Igf2 upstream region contains autonomous imprinting control elements we have performed functional and comparative analyses of the region in the mouse and human. Here we report the existence of multiple, overlapping imprinted (maternally repressed) sense and antisense transcripts that are associated with a tandem repeat in the mouse Igf2 upstream region. Regions flanking the repeat exhibit tissue-specific parental allelic methylation patterns, suggesting the existence of tissue-specific control elements in the upstream region. Studies in H19 null mice indicate that both parental allelic methylation and monoallelic expression of the upstream transcripts depends on an intact H19 gene acting in cis. The homologous region in human IGF2 is structurally conserved, with the significant exception that it does not contain a tandem repeat. Our results support the proposal that tandem repeats act to target methylation to imprinted genetic loci.

Differential Epitope Tagging of Actin in Transformed Drosophila Produces Distinct Effects on Myofibril Assembly and Function of the Indirect Flight Muscle

We have tested the impact of tags on the structure and function of indirect flight muscle (IFM)-specific Act88F actin by transforming mutant Drosophila melanogaster, which do not express endogenous actin in their IFMs, with tagged Act88F constructs. Epitope tagging is often the method of choice to monitor the fate of a protein when a specific antibody is not available. Studies addressing the functional significance of the closely related actin isoforms rely almost exclusively on tagged exogenous actin, because only few antibodies exist that can discriminate between isoforms. Thereby it is widely presumed that the tag does not significantly interfere with protein function. However, in most studies the tagged actin is expressed in a background of endogenous actin and, as a rule, represents only a minor fraction of the total actin. The Act88F gene encodes the only Drosophila actin isoform exclusively expressed in the highly ordered IFM. Null mutations in this gene do not affect viability, but phenotypic effects in transformants can be directly attributed to the transgene. Transgenic flies that express Act88F with either a 6x histidine tag or an 11-residue peptide derived from vesicular stomatitis virus G protein at the C terminus were flightless. Overall, the ultrastructure of the IFM resembled that of the Act88F null mutant, and only low amounts of C-terminally tagged actins were found. In contrast, expression of N-terminally tagged Act88F at amounts comparable with that of wild-type flies yielded fairly normal-looking myofibrils and partially reconstituted flight ability in the transformants. Our findings suggest that the N terminus of actin is less sensitive to modifications than the C terminus, because it can be tagged and still polymerize into functional thin filaments.

Differential Expression and Functions of Cortical Myosin IIA and IIB Isotypes during Meiotic Maturation, Fertilization, and Mitosis in Mouse Oocytes and Embryos

To explore the role of nonmuscle myosin II isoforms during mouse gametogenesis, fertilization, and early development, localization and microinjection studies were performed using monospecific antibodies to myosin IIA and IIB isotypes. Each myosin II antibody recognizes a 205-kDa protein in oocytes, but not mature sperm. Myosin IIA and IIB demonstrate differential expression during meiotic maturation and following fertilization: only the IIA isoform detects metaphase spindles or accumulates in the mitotic cleavage furrow. In the unfertilized oocyte, both myosin isoforms are polarized in the cortex directly overlying the metaphase-arrested second meiotic spindle. Cortical polarization is altered after spindle disassembly with Colcemid: the scattered meiotic chromosomes initiate myosin IIA and microfilament assemble in the vicinity of each chromosome mass. During sperm incorporation, both myosin II isotypes concentrate in the second polar body cleavage furrow and the sperm incorporation cone. In functional experiments, the microinjection of myosin IIA antibody disrupts meiotic maturation to metaphase II arrest, probably through depletion of spindle-associated myosin IIA protein and antibody binding to chromosome surfaces. Conversely, the microinjection of myosin IIB antibody blocks microfilament-directed chromosome scattering in Colcemid-treated mature oocytes, suggesting a role in mediating chromosome–cortical actomyosin interactions. Neither myosin II antibody, alone or coinjected, blocks second polar body formation, in vitro fertilization, or cytokinesis. Finally, microinjection of a nonphosphorylatable 20-kDa regulatory myosin light chain specifically blocks sperm incorporation cone disassembly and impedes cell cycle progression, suggesting that interference with myosin II phosphorylation influences fertilization. Thus, conventional myosins break cortical symmetry in oocytes by participating in eccentric meiotic spindle positioning, sperm incorporation cone dynamics, and cytokinesis. Although murine sperm do not express myosin II, different myosin II isotypes may have distinct roles during early embryonic development.

A T42A Ran Mutation: Differential Interactions with Effectors and Regulators, and Defect in Nuclear Protein Import

Ran, the small, predominantly nuclear GTPase, has been implicated in the regulation of a variety of cellular processes including cell cycle progression, nuclear-cytoplasmic trafficking of RNA and protein, nuclear structure, and DNA synthesis. It is not known whether Ran functions directly in each process or whether many of its roles may be secondary to a direct role in only one, for example, nuclear protein import. To identify biochemical links between Ran and its functional target(s), we have generated and examined the properties of a putative Ran effector mutation, T42A-Ran. T42A-Ran binds guanine nucleotides as well as wild-type Ran and responds as well as wild-type Ran to GTP or GDP exchange stimulated by the Ran-specific guanine nucleotide exchange factor, RCC1. T42A-Ran·GDP also retains the ability to bind p10/NTF2, a component of the nuclear import pathway. In contrast to wild-type Ran, T42A-Ran·GTP binds very weakly or not detectably to three proposed Ran effectors, Ran-binding protein 1 (RanBP1), Ran-binding protein 2 (RanBP2, a nucleoporin), and karyopherin β (a component of the nuclear protein import pathway), and is not stimulated to hydrolyze bound GTP by Ran GTPase-activating protein, RanGAP1. Also in contrast to wild-type Ran, T42A-Ran does not stimulate nuclear protein import in a digitonin permeabilized cell assay and also inhibits wild-type Ran function in this system. However, the T42A mutation does not block the docking of karyophilic substrates at the nuclear pore. These properties of T42A-Ran are consistent with its classification as an effector mutant and define the exposed region of Ran containing the mutation as a probable effector loop.

Molecular cloning of a cytochrome P450 taxane 10β-hydroxylase cDNA from Taxus and functional expression in yeast

The early steps in the biosynthesis of Taxol involve the cyclization of geranylgeranyl diphosphate to taxa-4(5),11(12)-diene followed by cytochrome P450-mediated hydroxylation at C5, acetylation of this intermediate, and a second cytochrome P450-dependent hydroxylation at C10 to yield taxadien-5α-acetoxy-10β-ol. Subsequent steps of the pathway involve additional cytochrome P450 catalyzed oxygenations and CoA-dependent acylations. The limited feasibility of reverse genetic cloning of cytochrome P450 oxygenases led to the use of Taxus cell cultures induced for Taxol production and the development of an approach based on differential display of mRNA-reverse transcription-PCR, which ultimately provided full-length forms of 13 unique but closely related cytochrome P450 sequences. Functional expression of these enzymes in yeast was monitored by in situ spectrophotometry coupled to in vivo screening of oxygenase activity by feeding taxoid substrates. This strategy yielded a family of taxoid-metabolizing enzymes and revealed the taxane 10β-hydroxylase as a 1494-bp cDNA that encodes a 498-residue cytochrome P450 capable of transforming taxadienyl acetate to the 10β-hydroxy derivative; the identity of this latter pathway intermediate was confirmed by chromatographic and spectrometric means. The 10β-hydroxylase represents the initial cytochrome P450 gene of Taxol biosynthesis to be isolated by an approach that should provide access to the remaining oxygenases of the pathway.

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.

Differential synaptic localization of two major gamma-aminobutyric acid type A receptor alpha subunits on hippocampal pyramidal cells.

Hippocampal pyramidal cells, receiving domain specific GABAergic inputs, express up to 10 different subunits of the gamma-aminobutyric acid type A (GABAA) receptor, but only 3 different subunits are needed to form a functional pentameric channel. We have tested the hypothesis that some subunits are selectively located at subsets of GABAergic synapses. The alpha 1 subunit has been found in most GABAergic synapses on all postsynaptic domains of pyramidal cells. In contrast, the alpha 2 subunit was located only in a subset of synapses on the somata and dendrites, but in most synapses on axon initial segments innervated by axo-axonic cells. The results demonstrate that molecular specialization in the composition of postsynaptic GABAA receptor subunits parallels GABAergic cell specialization in targeting synapses to a specific domain of postsynaptic cortical neurons.