Analogue of the degree conjecture over function fields

Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.

     

Effect of the polyethylene confinement and topology on its crystallisation within semicrystalline ABC triblock copolymers

The isothermal crystallisation behaviour of the polyethylene block within polystyrene-b-polyethylene-b-poly(ε-caprolactone), SEC, triblock copolymers was studied by differential scanning calorimetry. The morphology was observed by transmission electron microscopy. Melting scans after isothermal crystallisation performed at different times were employed to determine the crystallisation kinetics one step at a time (“isothermal step crystallisation”). Double melting endotherms were observed after isothermal crystallisation and they were interpreted as a result of the melting of two lamellar populations. These arise from the intrinsic short chain branching distribution within the hydrogenated polybutadiene chains that conform the PE blocks and from their location within the copolymer microdomains. The Hoffman-Weeks procedure failed to yield reasonable values for the equilibrium melting point of the PE blocks as a result of the distribution of linear sequences present in these blocks. The results indicate that as the degree of PE confinement increases the Avrami index decreases to values that are even lower than 1, a result that can be explained by the nature of the homogeneous nucleation process that is in between sporadic and instantaneous.     

Profiling and comprehensive expression analysis of ABC transporter solute-binding proteins of Bacillus subtilis membrane based on a proteomic approach

We analyzed ABC transporter solute-binding proteins (SBPs) of the Bacillus subtilis membrane using a proteomic approach. We prepared a washed cell membrane fraction that was insoluble in 134 mM nondetergent sulfobetaine and then extracted proteins using mixtures of detergents in a stepwise manner. The membrane proteins were resolved by three two-dimensional polyacrylamide gel electrophoresis (2-D PAGE) or two one-dimensional (1-D) PAGE procedures, electroblotted, and digested in the presence of 5% or 80% acetonitrile. Thereafter, matrix-assisted laser desorption/ionization-time of flight-mass spectrometry (MALDI-TOF MS) identified 637 proteins corresponding to 15.9% of the total cellular proteins. We predicted that among these, 256 were membrane proteins, 101 were lipoproteins or secretory proteins and 280 were soluble proteins containing peripheral proteins that function in both the cytoplasm and the cell membrane such as SecA and FtsY. Among the 637 proteins, we identified 30 SBPs among 38 importers predicted by a bioinformatic search of the genome. We confirmed expression of the genes for the 30 SBPs using DNA microarray analysis. We compared the 2-D gel separation profiles of submembrane fractions solubilized by 1% n-dodecyl-beta-D-maltoside from cells cultured on Luria Bertani (LB), S7, and S7 medium without glutamate as well as DNA microarray data on LB and S7. The results suggested that YcdH, YtmK and YurO are binding proteins for Mn(++), glutamate and glucose, respectively, and that YqiX and YxeM are binding proteins for amino acids (tryptophan in S7 medium).     

Facile Syntheses of ABC Ring Skeleton of Camptothecin and Related Alkaloids

Abstract

Facile synthetic approaches toward the preparation of ABC ring of camptothecin and related alkaloids starting from cheaper and readily available chemical reagents.     

ABC Triblock Copolymer Micelles: Spherical Versus Worm‐Like Micelles Depending on the Preparation Method

Well‐defined ABC triblock copolymers based on two hydrophilic blocks, A and C, and a hydrophobic block B are synthesized and their self‐assembly behavior is investigated. Interestingly, at the same solvent, concentration, pH, and temperature, different shape micelles are observed, spherical and worm‐like micelles, depending on the preparation method. Specifically, spherical micelles are observed with bulk rehydration while both spherical and worm‐like micelles are observed with film rehydration.

     

Computational Insights into Allosteric Conformational Modulation of P-Glycoprotein by Substrate and Inhibitor Binding

The ATP-binding cassette (ABC) transporter P-glycoprotein (P-gp) is a physiologically essential membrane protein that protects many tissues against xenobiotic molecules, but limits the access of chemotherapeutics into tumor cells, thus contributing to multidrug resistance. The atomic-level mechanism of how substrates and inhibitors differentially affect the ATP hydrolysis by P-gp remains to be elucidated. In this work, atomistic molecular dynamics simulations in an explicit membrane/water environment were performed to explore the effects of substrate and inhibitor binding on the conformational dynamics of P-gp. Distinct differences in conformational changes that mainly occurred in the nucleotide-binding domains (NBDs) were observed from the substrate- and inhibitor-bound simulations. The binding of rhodamine-123 can increase the probability of the formation of an intermediate conformation, in which the NBDs were closer and better aligned, suggesting that substrate binding may prime the transporter for ATP hydrolysis. By contrast, the inhibitor QZ-Leu stabilized NBDs in a much more separated and misaligned conformation, which may result in the deficiency of ATP hydrolysis. The significant differences in conformational modulation of P-gp by substrate and inhibitor binding provided a molecular explanation of how these small molecules exert opposite effects on the ATPase activity. A further structural analysis suggested that the allosteric communication between transmembrane domains (TMDs) and NBDs was primarily mediated by two intracellular coupling helices. Our computational simulations provide not only valuable insights into the transport mechanism of P-gp substrates, but also for the molecular design of P-gp inhibitors.     

The ABC Conjecture Implies Vojta's Height Inequality for Curves

Following Elkies (Internat. Math. Res. Notices7 (1991) 99-109) and Bombieri (Roth's theorem and the abc-conjecture, preprint, ETH Zürich, 1994), we show that the ABC conjecture implies the one-dimensional case of Vojta's height inequality. The main geometric tool is the construction of a Belyǐ function. We take care to make explicit the effectivity of the result: we show that an effective version of the ABC conjecture would imply an effective version of Roth's theorem, as well as giving an (in principle) explicit bound on the height of rational points on an algebraic curve of genus at least two.     

On the Brocard–Ramanujan Diophantine Equation n! + 1 = m2

In 1876, H. Brocard posed the problem of finding all integral solutions to n! + 1 = m². In 1913, unaware of Brocard's query, S. Ramanujan gave the problem in the form, The number 1 + n! is a perfect square for the values 4, 5, 7 of n. Find other values. We report on calculations up to n = 10⁹ and briefly discuss a related problem.     

互补共形匹配层研究

在运用数值方法求解开域散射问题时,需采用虚拟边界截断分析区域,这不可避免会造成人工反射。比较已存在的吸收边界条件,介绍了一种新型的吸收边界条件。这种方法基于特性互补的两种边界。分别求解两种边界条件下的解然后取平均,可以完全消除人工边界的一次反射。数值结果表明与其它广泛使用的边界条件相比这种方法可以显著减小由反射造成的误差。