Global systematics of arc volcano position

Global systematics in the location of volcanic arcs above subduction zones are widely considered to be a clue to the melting processes that occur at depth, and the locations of the arcs have often been explained in terms of the release of hydrous fluids near the top of the subducting slab (see, for example, refs 3-6). Grove et al. conclude that arc volcano location is controlled by melting in the mantle at temperatures above the water-saturated upper-mantle solidus and below the upper limit of stability of the mineral chlorite and in particular, that the arc fronts lie directly above the shallowest point of such melt regions in the mantle. Here we show that this conclusion is incorrect because the calculated arc locations of Grove et al. are in error owing to the inadequate spatial resolution of their numerical models, and because the agreement that they find between predicted and observed systematics arises from a spurious correlation between calculated arc location and slab dip. A more informative conclusion to draw from their experiments is that the limits of chlorite stability (figure 1b of ref. 7) cannot explain the global systematics in the depth to the slab beneath the sharply localized arc fronts.     

<Emphasis Type="Italic">The Mathematical Intelligencer</Emphasis> Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.     

Toward a History of Mathematics Focused on Procedures

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework.     

Mid-anaphase arrest in S. cerevisiae cells eliminated for the function of Cin8 and dynein

S. cerevisiae anaphase spindle elongation is accomplished by the overlapping function of dynein and the kinesin-5 motor proteins, Cin8 and Kip1. Cin8 and dynein are synthetically lethal, yet the arrest phenotypes of cells eliminated for their function had not been identified. We found that at a non-permissive temperature, dyn1Δ cells that carry a temperature-sensitive cin8 – 3 mutation arrest at mid-anaphase with a unique phenotype, which we named TAN (two microtubule asters in one nucleus). These cells enter anaphase, but fail to proceed through the slow phase of anaphase B. At a permissive temperature, dyn1Δ, cin8 – 3 or dyn1Δcin8 – 3 cells exhibit perturbed spindle midzone morphologies, with dyn1Δcin8 – 3 anaphase spindles also being profoundly bent and nonrigid. Sorbitol, which has been suggested to stabilize microtubules, corrects these defects and suppresses the TAN phenotype. We conclude that dynein and Cin8 cooperate in anaphase midzone organization and influence microtubule dynamics, thus enabling progression through the slow phase of anaphase B. Received 10 August 2008; received after revision 22 October 2008; accepted 27 October 2008     

Subunits beta gamma of heterotrimeric G protein activate beta 2 isoform of phospholipase C.

The activation of heterotrimeric G proteins results in the exchange of GDP bound to the alpha-subunit for GTP and the subsequent dissociation of a complex of the beta- and gamma-subunits (G beta gamma). The alpha-subunits of different G proteins interact with a variety of effectors, but less is known about the function of the free G beta gamma complex. G beta gamma has been implicated in the activation of a cardiac potassium channel, a retinal phospholipase A2 (ref. 9) and a specific receptor kinase, and in vitro reconstitution experiments indicate that the G beta gamma complex can act with G alpha subunit to modulate the activity of different isoforms of adenylyl cyclase. Of two phospholipase activities that can be separated in extracts of HL-60 cells, purified G beta gamma is found to activate one of them. Here we report that in co-transfection assays G beta gamma subunits specifically activate the beta 2 and not the beta 1 isoform of phospholipase, which acts on phosphatidylinositol. We use transfection assays to show also that receptor-mediated release of G beta gamma from G proteins that are sensitive to pertussis toxin can result in activation of the phospholipase. This effect may be the basis of the pertussis-toxin-sensitive phospholipase C activation seen in some cell systems (reviewed in refs 13 and 14).     

BAX activation is initiated at a novel interaction site

BAX is a pro-apoptotic protein of the BCL-2 family that is stationed in the cytosol until activated by a diversity of stress stimuli to induce cell death. Anti-apoptotic proteins such as BCL-2 counteract BAX-mediated cell death. Although an interaction site that confers survival functionality has been defined for anti-apoptotic proteins, an activation site has not been identified for BAX, rendering its explicit trigger mechanism unknown. We previously developed stabilized alpha-helix of BCL-2 domains (SAHBs) that directly initiate BAX-mediated mitochondrial apoptosis. Here we demonstrate by NMR analysis that BIM SAHB binds BAX at an interaction site that is distinct from the canonical binding groove characterized for anti-apoptotic proteins. The specificity of the human BIM-SAHB-BAX interaction is highlighted by point mutagenesis that disrupts functional activity, confirming that BAX activation is initiated at this novel structural location. Thus, we have now defined a BAX interaction site for direct activation, establishing a new target for therapeutic modulation of apoptosis.