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.

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.

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.

Two gonadotropin-releasing hormone receptor subtypes with distinct ligand selectivity and differential distribution in brain and pituitary in the goldfish (Carassius auratus)

In the goldfish (Carassius auratus) the two endogenous forms of gonadotropin-releasing hormone (GnRH), namely chicken GnRH II ([His5,Trp7,Tyr8]GnRH) and salmon GnRH ([Trp7,Leu8]GnRH), stimulate the release of both gonadotropins and growth hormone from the pituitary. This control is thought to occur by means of the stimulation of distinct GnRH receptors. These receptors can be distinguished on the basis of differential gonadotropin and growth hormone releasing activities of naturally occurring GnRHs and GnRHs with variant amino acids in position 8. We have cloned the cDNAs of two GnRH receptors, GfA and GfB, from goldfish brain and pituitary. Although the receptors share 71% identity, there are marked differences in their ligand selectivity. Both receptors are expressed in the pituitary but are differentially expressed in the brain, ovary, and liver. Thus we have found and cloned two full-length cDNAs that appear to correspond to different forms of GnRH receptor, with distinct pharmacological characteristics and tissue distribution, in a single species.

Differential Responses of Abaxial and Adaxial Guard Cells of Broad Bean to Abscisic Acid and Calcium1

Regulation by abscisic acid (ABA) and Ca2+ of broad bean (Vicia faba) abaxial and adaxial guard cell movements and inward K+ currents were compared. One millimolar Ca2+ in the bathing medium inhibited abaxial stomatal opening by 60% but only inhibited adaxial stomatal opening by 15%. The addition of 1 μm ABA in the bathing medium resulted in 80% inhibition of abaxial but only 45% inhibition of adaxial stomatal opening. Similarly, ABA and Ca2+ each stimulated greater abaxial stomatal closure than adaxial stomatal closure. Whole-cell patch-clamp results showed that the inward K+ currents of abaxial guard cells were inhibited by 60% (−180 mV) in the presence of 1.5 μm Ca2+ in the cytoplasm, whereas the inward K+ currents of adaxial guard cells were not affected at all by the same treatment. Although 1 μm ABA in the cytoplasm inhibited the inward K+ currents to a similar extent for both abaxial and adaxial guard cells, the former were more sensitive to ABA applied externally. These results suggest that the abaxial stomata are more sensitive to Ca2+ and ABA than adaxial stomata in regard to stomatal opening and closing processes and that the regulation of the inward K+ currents by ABA may not proceed via a Ca2+-signaling pathway in adaxial guard cells. Therefore, there may be different pathways for ABA- and Ca2+-mediated signal transduction in abaxial and adaxial guard cells.

Differential Control of Xanthophylls and Light-Induced Stress Proteins, as Opposed to Light-Harvesting Chlorophyll a/b Proteins, during Photosynthetic Acclimation of Barley Leaves to Light Irradiance

Barley (Hordeum vulgare L.) plants were grown at different photon flux densities ranging from 100 to 1800 μmol m−2 s−1 in air and/or in atmospheres with reduced levels of O2 and CO2. Low O2 and CO2 partial pressures allowed plants to grow under high photosystem II (PSII) excitation pressure, estimated in vivo by chlorophyll fluorescence measurements, at moderate photon flux densities. The xanthophyll-cycle pigments, the early light-inducible proteins, and their mRNA accumulated with increasing PSII excitation pressure irrespective of the way high excitation pressure was obtained (high-light irradiance or decreased CO2 and O2 availability). These findings indicate that the reduction state of electron transport chain components could be involved in light sensing for the regulation of nuclear-encoded chloroplast gene expression. In contrast, no correlation was found between the reduction state of PSII and various indicators of the PSII light-harvesting system, such as the chlorophyll a-to-b ratio, the abundance of the major pigment-protein complex of PSII (LHCII), the mRNA level of LHCII, the light-saturation curve of O2 evolution, and the induced chlorophyll-fluorescence rise. We conclude that the chlorophyll antenna size of PSII is not governed by the redox state of PSII in higher plants and, consequently, regulation of early light-inducible protein synthesis is different from that of LHCII.

Coordinating DNA replication initiation with cell growth: differential roles for DnaA and SeqA proteins.

We describe here the development of a new approach to the analysis of Escherichia coli replication control. Cells were grown at low growth rates, in which case the bacterial cell cycle approximates that of eukaryotic cells with G1, S, and G2 phases: cell division is followed sequentially by a gap period without DNA replication, replication of the single chromosome, another gap period, and finally the next cell division. Flow cytometry of such slowly growing cells reveals the timing of replication initiation as a function of cell mass. The data show that initiation is normally coupled to cell physiology extremely tightly: the distribution of individual cell masses at the time of initiation in wild-type cells is very narrow, with a coefficient of variation of less than 9%. Furthermore, a comparison between wild-type and seqA mutant cells shows that initiation occurs at a 10-20% lower mass in the seqA mutant, providing direct evidence that SeqA is a bona fide negative regulator of replication initiation. In dnaA (Ts) mutants the opposite is found: the mass at initiation is dramatically increased and the variability in cell mass at initiation is much higher than that for wild-type cells. In contrast to wild-type and dnaA(Ts) cells, seqA mutant cells frequently go through two initiation events per cell division cycle, and all the origins present in each cell are not initiated in synchrony. The implications for the complex interplay amongst growth, cell division, and DNA replication are discussed.

Differential activation of proliferation and cytotoxicity in human T-cell lymphotropic virus type I Tax-specific CD8 T cells by an altered peptide ligand.

Human T-cell leukemia virus type I (HTLV-I) gives rise to a neurologic disease known as HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Although the pathogenesis of the disease is unknown, the presence of a remarkably high frequency of Tax-specific, cytotoxic CD8 T cells may suggest a role of these cells in the development of HAM/TSP. Antigen-mediated signaling in a CD8 T-cell clone specific for the Tax(11-19) peptide of HTLV-I was studied using analog peptides substituted in their T-cell receptor contact residues defined by x-ray crystallographic data of the Tax(11-19) peptide in the groove of HLA-A2. CD8 T-cell stimulation with the wild-type peptide antigen led to activation of p56lck kinase activity, interleukin 2 secretion, cytotoxicity, and clonal expansion. A Tax analog peptide with an alanine substitution of the T-cell receptor contact residue tyrosine-15 induced T-cell-mediated cytolysis without activation of interleukin 2 secretion or proliferation. Induction of p56lck kinase activity correlated with T-cell-mediated cytotoxicity, whereas interleukin 2 secretion correlated with [3H]thymidine incorporation and proliferation. Moreover, Tax peptide analogs that activated the tyrosine kinase activity of p56lck could induce unresponsiveness to secondary stimulation with the wild-type peptide. These observations show that a single amino acid substitution in a T-cell receptor contact residue of Tax can differentially signal CD8 T cells and further demonstrate that primary activation has functional consequences for the secondary response of at least some Tax-specific CD8 T cells to HTLV-I-infected target cells.

Mast cells express a peripheral cannabinoid receptor with differential sensitivity to anandamide and palmitoylethanolamide.

Mast cells are multifunctional bone marrow-derived cells found in mucosal and connective tissues and in the nervous system, where they play important roles in tissue inflammation and in neuroimmune interactions. Very little is known about endogenous molecules and mechanisms capable of modulating mast cell activation. Palmitoylethanolamide, found in peripheral tissues, has been proposed to behave as a local autacoid capable of downregulating mast cell activation and inflammation. A cognate N-acylamide, anandamide, the ethanolamide of arachidonic acid, occurs in brain and is a candidate endogenous agonist for the central cannabinoid receptor (CB1). As a second cannabinoid receptor (CB2) has been found in peripheral tissues, the possible presence of CB2 receptors on mast cells and their interaction with N-acylamides was investigated. Here we report that mast cells express both the gene and a functional CB2 receptor protein with negative regulatory effects on mast cell activation. Although both palmitoylethanolamide and anandamide bind to the CB2 receptor, only the former downmodulates mast cell activation in vitro. Further, the functional effect of palmitoylethanolamide, as well as that of the active cannabinoids, was efficiently antagonized by anandamide. The results suggest that (i) peripheral cannabinoid CB2 receptors control, upon agonist binding, mast cell activation and therefore inflammation; (ii) palmitoylethanolamide, unlike anandamide, behaves as an endogenous agonist for the CB2 receptor on mast cells; (iii) modulatory activities on mast cells exerted by the naturally occurring molecule strengthen a proposed autacoid local inflammation antagonism (ALIA) mechanism; and (iv) palmitoylethanolamide and its derivatives may provide antiinflammatory therapeutic strategies specifically targeted to mast cells ("ALIAmides").

Differential modulation of Th1- and Th2-related cytokine mRNA expression by a synthetic peptide homologous to a conserved domain within retroviral envelope protein.

The influence of a synthetic retroviral peptide, CKS-17, on T helper type 1 (Th1)- or Th2-related cytokines was investigated in human blood mononuclear cells. Cells were stimulated with staphylococcal enterotoxin A, anti-CD3 plus anti-CD28 monoclonal antibodies, or lipopolysaccharide to induce cytokine mRNA. mRNA was detected by a reverse transcription-polymerase chain reaction or Northern blot analysis. CKS-17 down-regulated stimulant-induced mRNA accumulation for interferon gamma (IFN-gamma), interleukin (IL)-2, and p40 heavy and p35 light chains of IL-12, a cytokine that mediates development of Th1 response. CKS-17 up-regulated stimulant-induced mRNA accumulation of IL-10 and did not suppress Th2-related cytokine (IL-4, IL-5, IL-6, or IL-13) mRNA expression. A reverse sequence of CKS-17 peptide, used as a control, showed no such action. Anti-human IL-10 monoclonal antibody blocked ability of CKS-17 to inhibit mRNA accumulation for IFN-gamma but not the CKS-17 suppressive activity of IL-12 p40 heavy chain mRNA. Thus, CKS-17-mediated suppression of IFN-gamma mRNA expression is dependent upon augmentation of IL-10 production by CKS-17. This conserved component of several retroviral envelope proteins, CKS-17, may act as an immunomodulatory epitope responsible for cytokine dysregulation that leads to suppression of cellular immunity.

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

On the acidity and reactivity of HNO in aqueous solution and biological systems

The gas phase and aqueous thermochemistry and reactivity of nitroxyl (nitrosyl hydride, HNO) were elucidated with multiconfigurational self-consistent field and hybrid density functional theory calculations and continuum solvation methods. The pKa of HNO is predicted to be 7.2 ± 1.0, considerably different from the value of 4.7 reported from pulse radiolysis experiments. The ground-state triplet nature of NO− affects the rates of acid-base chemistry of the HNO/NO− couple. HNO is highly reactive toward dimerization and addition of soft nucleophiles but is predicted to undergo negligible hydration (Keq = 6.9 × 10−5). HNO is predicted to exist as a discrete species in solution and is a viable participant in the chemical biology of nitric oxide and derivatives.

Selenoprotein oxidoreductase with specificity for thioredoxin and glutathione systems

Thioredoxin (Trx) and glutathione (GSH) systems are considered to be two major redox systems in animal cells. They are reduced by NADPH via Trx reductase (TR) or oxidized GSH (GSSG) reductase and further supply electrons for deoxyribonucleotide synthesis, antioxidant defense, and redox regulation of signal transduction, transcription, cell growth, and apoptosis. We cloned and characterized a pyridine nucleotide disulfide oxidoreductase, Trx and GSSG reductase (TGR), that exhibits specificity for both redox systems. This enzyme contains a selenocysteine residue encoded by the TGA codon. TGR can reduce Trx, GSSG, and a GSH-linked disulfide in in vitro assays. This unusual substrate specificity is achieved by an evolutionary conserved fusion of the TR and glutaredoxin domains. These observations, together with the biochemical probing and molecular modeling of the TGR structure, suggest a mechanism whereby the C-terminal selenotetrapeptide serves a role of a protein-linked GSSG and shuttles electrons from the disulfide center within the TR domain to either the glutaredoxin domain or Trx.