Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Type I interferon-driven susceptibility to Mycobacterium tuberculosis is mediated by IL-1Ra.

The bacterium Mycobacterium tuberculosis (Mtb) causes tuberculosis and is responsible for more human mortality than any other single pathogen1. Progression to active disease occurs in only a fraction of infected individuals and is predicted by an elevated type I interferon (IFN) response2-7. Whether or how IFNs mediate susceptibility to Mtb has been difficult to study due to a lack of suitable mouse models6-11. Here, we examined B6.Sst1S congenic mice that carry the 'susceptible' allele of the Sst1 locus that results in exacerbated Mtb disease12-14. We found that enhanced production of type I IFNs was responsible for the susceptibility of B6.Sst1S mice to Mtb. Type I IFNs affect the expression of hundreds of genes, several of which have previously been implicated in susceptibility to bacterial infections6,7,15-18. Nevertheless, we found that heterozygous deficiency in just a single IFN target gene, Il1rn, which encodes interleukin-1 receptor antagonist (IL-1Ra), is sufficient to reverse IFN-driven susceptibility to Mtb in B6.Sst1S mice. In addition, antibody-mediated neutralization of IL-1Ra provided therapeutic benefit to Mtb-infected B6.Sst1S mice. Our results illustrate the value of the B6.Sst1S mouse to model IFN-driven susceptibility to Mtb, and demonstrate that IL-1Ra is an important mediator of type I IFN-driven susceptibility to Mtb infections in vivo

STING-dependent recognition of cyclic di-AMP mediates type I interferon responses during Chlamydia trachomatis infection.

UnlabelledSTING (stimulator of interferon [IFN] genes) initiates type I IFN responses in mammalian cells through the detection of microbial nucleic acids. The membrane-bound obligate intracellular bacterium Chlamydia trachomatis induces a STING-dependent type I IFN response in infected cells, yet the IFN-inducing ligand remains unknown. In this report, we provide evidence that Chlamydia synthesizes cyclic di-AMP (c-di-AMP), a nucleic acid metabolite not previously identified in Gram-negative bacteria, and that this metabolite is a prominent ligand for STING-mediated activation of IFN responses during infection. We used primary mouse lung fibroblasts and HEK293T cells to compare IFN-β responses to Chlamydia infection, c-di-AMP, and other type I IFN-inducing stimuli. Chlamydia infection and c-di-AMP treatment induced type I IFN responses in cells expressing STING but not in cells expressing STING variants that cannot sense cyclic dinucleotides but still respond to cytoplasmic DNA. The failure to induce a type I IFN response to Chlamydia and c-di-AMP correlated with the inability of STING to relocalize from the endoplasmic reticulum to cytoplasmic punctate signaling complexes required for IFN activation. We conclude that Chlamydia induces STING-mediated IFN responses through the detection of c-di-AMP in the host cell cytosol and propose that c-di-AMP is the ligand predominantly responsible for inducing such a response in Chlamydia-infected cells.ImportanceThis study shows that the Gram-negative obligate pathogen Chlamydia trachomatis, a major cause of pelvic inflammatory disease and infertility, synthesizes cyclic di-AMP (c-di-AMP), a nucleic acid metabolite that thus far has been described only in Gram-positive bacteria. We further provide evidence that the host cell employs an endoplasmic reticulum (ER)-localized cytoplasmic sensor, STING (stimulator of interferon [IFN] genes), to detect c-di-AMP synthesized by Chlamydia and induce a protective IFN response. This detection occurs even though Chlamydia is confined to a membrane-bound vacuole. This raises the possibility that the ER, an organelle that innervates the entire cytoplasm, is equipped with pattern recognition receptors that can directly survey membrane-bound pathogen-containing vacuoles for leaking microbe-specific metabolites to mount type I IFN responses required to control microbial infections

Venture capitalists in Asia: a comparison with the U.S. and Europe.

This research utilizes an institutional perspective to examine the behavior of venture capital professionals in three distinct regions of the world (Asia, U.S., Europe). Based upon a mail survey, we find reasonably consistent views around the world on the relative importance of various venture capitalist roles. However, we find that how those roles are implemented is shaped by cognitive institutional influences in the given region. We find that a model developed in the U.S. to predict the amount of venture capitalist/CEO interaction is not valid in Asia. Further, Asian boards have much greater insider representation than do U.S. or European boards. We attribute these difference to the greater emphasis in Asia on the importance of collective action

DICER-LIKE2 plays a primary role in transitive silencing of transgenes in Arabidopsis.

Dicer-like (DCL) enzymes play a pivotal role in RNA silencing in plants, processing the long double-stranded RNA (dsRNA) that triggers silencing into the primary short interfering RNAs (siRNAs) that mediate it. The siRNA population can be augmented and silencing amplified via transitivity, an RNA-dependent RNA polymerase (RDR)-dependent pathway that uses the target RNA as substrate to generate secondary siRNAs. Here we report that Arabidopsis DCL2-but not DCL4-is required for transitivity in cell-autonomous, post-transcriptional silencing of transgenes. An insertion mutation in DCL2 blocked sense transgene-induced silencing and eliminated accumulation of the associated RDR-dependent siRNAs. In hairpin transgene-induced silencing, the dcl2 mutation likewise eliminated accumulation of secondary siRNAs and blocked transitive silencing, but did not block silencing mediated by primary siRNAs. Strikingly, in all cases, the dcl2 mutation eliminated accumulation of all secondary siRNAs, including those generated by other DCL enzymes. In contrast, mutations in DCL4 promoted a dramatic shift to transitive silencing in the case of the hairpin transgene and enhanced silencing induced by the sense transgene. Suppression of hairpin and sense transgene silencing by the P1/HC-Pro and P38 viral suppressors was associated with elimination of secondary siRNA accumulation, but the suppressors did not block processing of the stem of the hairpin transcript into primary siRNAs. Thus, these viral suppressors resemble the dcl2 mutation in their effects on siRNA biogenesis. We conclude that DCL2 plays an essential, as opposed to redundant, role in transitive silencing of transgenes and may play a more important role in silencing of viruses than currently thought

Rapid quantification of underivatized alloisoleucine and argininosuccinate using mixed-mode chromatography with tandem mass spectrometry

Plasma elevations of the amino acids alloisoleucine and argininosuccinic acid (ASA) are pathognomonic for maple syrup urine disease and argininosuccinate lyase deficiency, respectively. Reliable detection of these biomarkers is typically achieved using methods with tedious sample preparations or long chromatographic separations, and many published amino acid assays report poor specificity and/or sensitivity for one or both of these compounds. This report describes a novel liquid chromatography tandem mass spectrometry (LC-MS/MS) method that provides rapid quantification of alloisoleucine and ASA in human plasma. The basis of this method is a mixed-mode solid phase separation that achieves baseline resolution of alloisoleucine from isobaric interferents without the use of derivatization or ion pairing agents. The inject-to-inject time is 6 min including elution, column washing and re-equilibration. Validation studies demonstrate excellent limits of quantification (1 μmol/L), linearity (r = 0.999 from 1 to 250 μmol/L), accuracy (bias = −3.8% and −10.1%), and inter-assay imprecision (CV < 8.06%) for plasma analyses. Data from long-term clinical application confirms chromatographic consistency equivalent to more traditional reversed-phase or HILIC based columns. Additional matrix studies indicate low suppression (<10%) for a wide range of amino acids and compatibility with other matrixes such as blood spot analyses. Finally, analysis of our first 257 clinical specimens demonstrates high analytic specificity and sensitivity, allowing the detection of subtle but clinically relevant elevations of alloisoleucine and ASA that may be missed by other less sensitive methods. In conclusion, the novel LC-MS/MS method reported here overcomes a number of the challenges associated with alloisoleucine and ASA quantification. Combining this approach with published incomplete amino acid quantification methods allows, for the first time, a rapid and comprehensive LC-MS/MS analysis of underivatized amino acids without the use of ion pairing agents

Spectral-domain optical coherence tomography as a noninvasive method to assess damaged and regenerating adult zebrafish retinas.

These experiments assessed the ability of spectral-domain optical coherence tomography (SD-OCT) to accurately represent the structural organization of the adult zebrafish retina and reveal the dynamic morphologic changes during either light-induced damage and regeneration of photoreceptors or ouabain-induced inner retinal damage. Retinas of control dark-adapted adult albino zebrafish were compared with retinas subjected to 24 hours of constant intense light and recovered for up to 8 weeks or ouabain-damaged retinas that recovered for up to 3 weeks. Images were captured and the measurements of retinal morphology were made by SD-OCT, and then compared with those obtained by histology of the same eyes. Measurements between SD-OCT and histology were very similar for the undamaged, damaged, and regenerating retinas. Axial measurements of SD-OCT also revealed vitreal morphology that was not readily visualized by histology. SD-OCT accurately represented retinal lamination and photoreceptor loss and recovery during light-induced damage and subsequent regeneration. SD-OCT was less accurate at detecting the inner nuclear layer in ouabain-damaged retinas, but accurately detected the undamaged outer nuclear layer. Thus, SD-OCT provides a noninvasive and quantitative method to assess the morphology and the extent of damage and repair in the zebrafish retina

Strange hyperon and antihyperon production from quark and string-rope matter

Hyperon and antihyperon production is investigated using two microscopical models: {\bf (1)} the fast hadronization of quark matter as given by the ALCOR model; {\bf (2)} string formation and fragmentation as in the HIJING/B model. We calculate the particle numbers and momentum distributions for Pb+Pb collisions at CERN SPS energies in order to compare the two models with each other and with the available experimental data. We show that these two theoretical approaches give similar yields for the hyperons, but strongly differ for antihyperons.Comment: 11 pages, Latex, 3 EPS figures, contribution to the Proceedings of the 4th International Conference on Strangeness in Quark Matter (SQM'98), Padova, Italy, 20-24 July 199