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

Sigma-2 receptors as a biomarker of proliferation in solid tumours

Over the past several years, our group has provided considerable evidence that the expression of sigma-2 (σ2) receptors may serve as a biomarker of tumour cell proliferation. In these in vitro studies, σ2receptors were expressed 8–10 times more in proliferative (P) tumour cells than in quiescent (Q) tumour cells, and the extent and kinetics of their expression were independent of a number of biological, physiological and environmental factors often found in solid tumours. Moreover, the expression of σ2receptors followed both the population growth kinetics when Q-cells were recruited into the P-cell compartment and the proliferative status of human breast tumour cells treated with cytostatic concentrations of tamoxifen. However, these in vitro studies may or may not be indicative of what might occur in solid tumours. In the present study, the σ2receptor P:Q ratio was determined for the cells from subcutaneous 66 (diploid) and 67 (aneuploid) tumours grown in female nude mice. The σ2receptor P:Q ratio of the 66 tumours was 10.6 compared to the σ2receptor P:Q ratio of 9.5 measured for the 66 tissue culture model. The σ2receptor P:Q ratio of the 67 tumours was 4.5 compared to the σ2receptor P:Q ratio of ≈ 8 measured for the 67 tissue culture model. The agreement between the solid tumour and tissue culture data indicates that: (1) the expression of σ2receptors may be a reliable biomarker of the proliferative status of solid tumours and (2) radioligands with both high affinity and high selectivity for σ2receptors may have the potential to non-invasively assess the proliferative status of human solid tumours using imaging techniques such as positron emission tomography or single-photon emission computerized tomography. © 2000 Cancer Research Campaig

Conversion of the Mycotoxin Patulin to the Less Toxic Desoxypatulinic Acid by the Biocontrol Yeast Rhodosporidium kratochvilovae Strain LS11

Se describe en este artículo el descubrimiento de la degradación de la micotoxina patulina por una levaduraThe infection of stored apples by the fungus Penicillium expansum causes the contamination of fruits and fruit-derived products with the mycotoxin patulin, which is a major issue in food safety. Fungal attack can be prevented by beneficial microorganisms, so-called biocontrol agents. Previous time-course thin layer chromatography analyses showed that the aerobic incubation of patulin with the biocontrol yeast Rhodosporidium kratochvilovae strain LS11 leads to the disappearance of the mycotoxin spot and the parallel emergence of two new spots, one of which disappears over time. In this work, we analyzed the biodegradation of patulin effected by LS11 through HPLC. The more stable of the two compounds was purified and characterized by nuclear magnetic resonance as desoxypatulinic acid, whose formation was also quantitated in patulin degradation experiments. After R. kratochvilovae LS11 had been incubated in the presence of 13C-labeled patulin, label was traced to desoxypatulinic acid, thus proving that this compound derives from the metabolization of patulin by the yeast. Desoxypatulinic acid was much less toxic than patulin to human lymphocytes and, in contrast to patulin, did not react in vitro with the thiol-bearing tripeptide glutathione. The lower toxicity of desoxypatulinic acid is proposed to be a consequence of the hydrolysis of the lactone ring and the loss of functional groups that react with thiol groups. The formation of desoxypatulinic acid from patulin represents a novel biodegradation pathway that is also a detoxification process

Effect of ploidy, recruitment, environmental factors, and tamoxifen treatment on the expression of sigma-2 receptors in proliferating and quiescent tumour cells

Recently, we demonstrated that sigma-2 receptors may have the potential to be a biomarker of tumour cell proliferation (Mach et al (1997) Cancer Res57: 156–161). If sigma-2 receptors were a biomarker of tumour cell proliferation, they would be amenable to detection by non-invasive imaging procedures, thus eliminating many of the problems associated with the flow cytometric measures of tumour cell proliferation presently used in the clinic. To be a good biomarker of tumour cell proliferation, the expression of sigma-2 receptors must be essentially independent of many of the biological, physiological, and/or environmental properties that are found in solid tumours. In the investigation reported here, the mouse mammary adenocarcinoma lines, 66 (diploid) and 67 (aneuploid), 9L rat brain tumour cells, and MCF-7 human breast tumour cells were used to study the extent and kinetics of expression of sigma-2 receptors in proliferative (P) and quiescent (Q) tumour cells as a function of species, cell type, ploidy, pH, nutrient depletion, metabolic state, recruitment from the Q-cell compartment to the P-cell compartment, and treatment with tamoxifen. In these experiments, the expression of sigma-2 receptors solely reflected the proliferative status of the tumour cells. None of the biological, physiological, or environmental properties that were investigated had a measurable effect on the expression of sigma-2 receptors in these model systems. Consequently, these data suggest that the proliferative status of tumours and normal tissues can be non-invasively assessed using radiolabelled ligands that selectively bind sigma-2 receptors. © 1999 Cancer Research Campaig

Alternate Metabolic Programs Define Regional Variation of Relevant Biological Features in Renal Cell Carcinoma Progression

ccRCC has recently been redefined as a highly heterogeneous disease. In addition to genetic heterogeneity, the tumor displays risk variability for developing metastatic disease, therefore underscoring the urgent need for tissue-based prognostic strategies applicable to the clinical setting. We’ve recently employed the novel positron emission tomography/magnetic resonance (PET/MR) image modality to enrich our understanding of how tumor heterogeneity can relate to gene expression and tumor biology to assist in defining individualized treatment plans

Turnover-Dependent Covalent Inactivation of Staphylococcus aureus Coenzyme A-Disulfide Reductase by Coenzyme A-Mimetics: Mechanistic and Structural Insights

Disruption of the unusual thiol-based redox homeostasis mechanisms in Staphylococcus aureus represents a unique opportunity to identify new metabolic processes, and new targets for intervention. Targeting uncommon aspects of CoASH biosynthetic and redox functions in S. aureus, the antibiotic CJ-15,801 has recently been demonstrated to be an antimetabolite of the CoASH biosynthetic pathway in this organism; CoAS-mimetics containing α,β-unsaturated sulfone and carboxyl moieties have also been exploited as irreversible inhibitors of S. aureus coenzyme A-disulfide reductase (SaCoADR). In this work we have determined the crystal structures of three of these covalent SaCoADR-inhibitor complexes, prepared by inactivation of wild-type enzyme during turnover. The structures reveal the covalent linkage between the active-site Cys43-Sγ and Cβ of the vinyl sulfone or carboxyl moiety. The full occupancy of two inhibitor molecules per enzyme dimer, together with kinetic analyses of the wild-type/C43S heterodimer, indicates that half-sites-reactivity is not a factor during normal catalytic turnover. Further, we provide the structures of SaCoADR active-site mutants; in particular, Tyr419′-OH plays dramatic roles in directing intramolecular reduction of the Cys43-SSCoA redox center, in the redox asymmetry observed for the two FAD per dimer in NADPH titrations, and in catalysis. The two conformations observed for the Ser43 side chain in the C43S mutant structure lend support to a conformational switch for Cys43-Sγ during its catalytic Cys43-SSCoA/Cys43-SH redox cycle. Finally, the structures of the three inhibitor complexes provide a framework for design of more effective inhibitors with therapeutic potential against several major bacterial pathogens

Gender Differences in Compensation, Job Satisfaction and Other Practice Patterns in Urology

The proportion of women in urology has increased from <0.5% in 1981 to 10% today. Furthermore, 33% of students matching in urology are now female. This analysis sought to characterize the female workforce in urology in comparison to men with regard to income, workload, and job satisfaction