Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity

The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.     

Macroscopic modelling of transport phenomena in porous media. 2: Applications to mass,momentum and energy transport

In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain. It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media.     

Separating the contribution of translational and rotational diffusion to protein association

The association of two proteins is preceded by a mutual diffusional search in solution. The role of translational and rotational diffusion in this process has been studied theoretically for many years. However, systematic experimental verification of theoretical results is still lacking. We report here measurements of association rates of the proteins beta-lactamase (TEM) and beta-lactamase inhibitor protein (BLIP) in solutions of glycerol and poly(ethylene glycol) of increasing viscosity. We also measured translational and rotational diffusion in the same solutions, using fluorescence correlation spectroscopy and fluorescence anisotropy, respectively. It is found that in glycerol both translational and rotational diffusion rates are inversely dependent on viscosity, as predicted by the classical Stokes-Einstein relations, while the association rate depends nonlinearly on viscosity. In contrast, the association rate depends only weakly on the viscosity of the polymer solutions, which results in a similar weak dependence of k(on) on viscosity. The data are modeled using the theory of diffusion-limited association. Deviations from the theory are explained by a short-range solute-induced repulsion between the proteins in glycerol solution and an attractive depletion interaction generated by the polymers. These results open the way to the creation of a unified framework for all nonspecific effects involved in the protein association process, as well as to better theoretical understanding of these effects. Further, they reflect on the complex factors controlling protein association within the crowded environment of cells and suggest that a high concentration of macromolecules does not significantly impede protein association.     

On zero-sum partitions and anti-magic trees

We study zero-sum partitions of subsets in abelian groups, and apply the results to the study of anti-magic trees. Extension to the nonabelian case is also given.     

Reactions in dry media: reactions of cholesterol and cholestanes on silica bound ferric chloride : Cholestane—diacholestene rearrangement

Reaction of cholesterol with silica bound FeCl₃ resulted in a mixture of 3β-cholesteryl chloride and dicholesteryl ether.5-Cholestene and hydroxy- and halogeno-substituted cholestane derivatives gave on heating at 100° with this reagent a 1:1 mixture of 20-epimeric diacholestenes. The 20(R)-isomer gave with meta-chloroperbenzoic acid 20(R)-α-epoxide, while the 20(S)-gave a mixture of 20(S)-α- and 20(S)-β-epoxides.5α,6β-Dihydrocholestane reacted with the FeCl₃/SiO₂ under milder conditions (50°) to give 6β-hydroxy-20(R)-diacholestene, which was converted to the 20(R)-diacholestene.     

Twentyfold increase in alkaline phosphatase activity by sequential reversible activation of the enzyme followed by coupling with a copolyme of ethylene and maleic anhydride

Alkaline phosphatase, APase, (EC 3.1.31) from calf intestine, after shifting the equilibrium by effector molecules towards the dimeric form of the enzyme, was coupled (ratio 1:2, protein: copolymer) to a copolymer of ethylene and maleic anhydride, EMA. The water-soluble APase-EMA was separated from APase and the unbound EMA by DEAE-cellulose ion exchange chromatography. The specific activity of the APase-EMA, compared to APase, increased 26-fold at pH 7.1 and 10-fold at pH 8.6. The pH optimum of APase-EMA was shifted down from pH 9.5 (native APase) to 8.6. This change could be interpreted in terms of polyelectrolyte theory. APase-EMA retained 50–70% of its optimum activity in the pH range 7–8, while APase retained only 5–15% of its optimum activity within the same pH range. Its isoelectric point, pI, was 4.2 (APase 6.0) and it migrated on polyacrylamide gel electrophoresis in a single band, anodic movement twice as fast as APase. Parallel with the kinetic measurements, the reactive-enzyme sedimentation method was used to measure S_20,w values. S_20,w values obtained for APase-EMA, activated APase, and APase dialyzed against wafer were 6.56S, 6.46S, and 5.17S, respectively. Molecular weights, M_r, were determined by equilibrium sedimentation: the values obtained were 180,000, 160,000, and 84,500. M_r values of APase-EMA and APase (native) estimated by Sepharose-4B gel filtrations were essentially the same. The above-mentioned values remained unchanged for APase-EMA after intensive dialysis against water, whereas for the activated APase, separation from the effector molecules caused the equilibrium to shift back to the monomeric, very slightly active enzyme with concomitant changes of S_20,w to 5.15 and M_r to 82,000.     

Njaoamines G and H, two new cytotoxic polycyclic alkaloids and a tetrahydroquinolone from the marine sponge Neopetrosia sp.

Two new polycyclic alkaloids, njaoamines G (1) and H (2) and 1,2,3,4-tetrahydroquinolin-4-one (3) have been isolated from the sponge Neopetrosia sp. collected at Pemba Island, Tanzania. Compounds 1 and 2 are close in structure to njaoamines A-F. Compound 3, known synthetically, is a new natural compound. The structures and relative stereochemistries of compounds 1 and 2 were elucidated on the basis of spectroscopic data. Njaoamines G and H are potent brine shrimp toxins with LD₅₀ values of 0.17 μg/mL and 0.08 μg/mL for 1 and 2, respectively.