Duramycin-induced calcium release in cancer cells

Introduction: Duramycin through binding with phosphatidylethanolamine (PE) has shown potential to be an effective anti-tumour agent. However its mode of action in relation to tumour cells is not fully understood. Methods: PE expression on the surface of a panel of cancer cell lines was analysed using duramycin and subsequent antibody labelling then analysed by flow cytometry. Cell viability was also assessed via flow cytometry using annexin V and propidium iodide (PI). Calcium ion (Ca²⁺) release by tumour cells in response to duramycin was determined by spectrofluorometry following incubation with Fluo-3, AM. Confocal microscopy was performed on the cancer cell line AsPC-1 to assess real time cell response to duramycin treatment. Results: Duramycin was able to detect cell surface PE expression on all 15 cancer cell lines screened, which was shown to be duramycin concentration dependent. However higher concentrations induced necrotic cell death. Duramycin induced calcium ion (Ca²⁺) release from the cancer cell lines also in a concentration and time dependent manner. Confocal microscopy showed an influx of PI into the cells over time and induced morphological changes. Conclusion: Duramycin induces Ca²⁺ release from cancer cell lines in a time and concentration dependent relationship

Flattening a Cone

We want to manufacture a cut-off slanted cone from a flat sheet of metal. If the cone were a normal right cone we know that we would simply cut out a sector of a circle and roll it up. However the cone is slanted. We want to know what the flattened shape looks like so that we can cut it out and roll it up to closely approximate correct final shape. We also want to minimize the amount of wasted metal after the shape is cut out. The problem, and it generalizations may be solved analytically but the analytical solution is given in terms of indefinite integrals which rarely can be evaluated in closed form. The solutions may be found numerically which are good enough the create a picture of the flattened-out cone

Continuous Dependence of Solutions of Equations on Parameters

It is shown under very general conditions that the solutions of equations depend continuously on the coefficients or parameters of the equations. The standard examples are solutions of monic polynomial equations and the eigenvalues of a matrix. However, the proof methods apply to any finite map T : Cn -\u3e Cn

Constructing Kaleidscopic Tiling Polygons in the Hyperbolic Plane

We have all seen many of the beautiful patterns obtained by tiling the hyperbolic plane H by repeated reflection in the sides of a kaleidoscopic polygon. Though there are such patterns on the sphere and the euclidean plane, these positively curved and fiat geometries lack the richness we see in the hyperbolic plane. Many of these patterns have been popularized by the beautiful art of M.C. Escher. For a list of references and a more complete discussion on the construction of artistic tilings see [6]

The Birational Isomorphism Types of Smooth Real Elliptic Curves

In this note we determine all birational isomorphism types of real elliptic curves and show that it is the same as the orbit space of smooth cubic real curves in real projective space under linear projective equivalence. There are two families, each depending polynomially on a real parameter in a open subinterval of R. We further show that the complexification of a real elliptic curve has exactly two real forms. Thus the real elliptic curves come in pairs which are isomorphic over C. Finally, the map taking a real elliptic curve to its j-invariant maps the two families onto the real line in C, intersecting only at the value 1728, the special curve with 4 automorphisms and two topologically distinct real forms

Calculation of the Killing Form of a Simple Lie Group

The Killing form of a simple Lie Algebra is determined from invariants of the extended root diagrams of the Lie algebra

Topological and Hq Equivalence of Prime Cyclic p-gonal Actions on Riemann Surfaces (Corrected)

Two Riemann surfaces S1 and S2 with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S1 -\u3e S2 which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials Hq(S1) and Hq(S2). In this note we study the differences between topological equivalence and Hq equivalence of prime cyclic actions, where S1/G and S2/G have genus zero

Topological and H^q Equivalence of Cyclic n-gonal Actions on Riemann Surfaces - Part II

We consider conformal actions of the finite group G on a closed Riemann surface S, as well as algebraic actions of G on smooth, complete, algebraic curves over an arbitrary, algebraically closed field. There are several notions of equivalence of actions, the most studied of which is topological equivalence, because of its close relationship to the branch locus of moduli space. A second important equivalence relation is that induced by representation of G on spaces of holomorphic q-differentials. The notion of topological equivalence does not work well in positive characteristic. We shall discuss an alternative to topological equivalence, which we dub equisymmetry, that may be applied in all characteristics. The relation is induced by families of curves with G-action, and it works well with rotation constants and q-differentials, which are also defined in positive characteristic. After giving an overview of the various equivalence relations (conformal/algebraic, topological, q-differentials, rotation constants, equisymmetry) we focus on the interconnections among rotation constants, q-differentials, and equisymmetry