The Methionine 549 and Leucine 552 Residues of Friedelin Synthase from Maytenus ilicifolia Are Important for Substrate Binding Specificity

Friedelin, a pentacyclic triterpene found in the leaves of the Celastraceae species, demonstrates numerous biological activities and is a precursor of quinonemethide triterpenes, which are promising antitumoral agents. Friedelin is biosynthesized from the cyclization of 2,3-oxidosqualene, involving a series of rearrangements to form a ketone by deprotonation of the hydroxylated intermediate, without the aid of an oxidoreductase enzyme. Mutagenesis studies among oxidosqualene cyclases (OSCs) have demonstrated the influence of amino acid residues on rearrangements during substrate cyclization: loss of catalytic activity, stabilization, rearrangement control or specificity changing. In the present study, friedelin synthase from Maytenus ilicifolia (Celastraceae) was expressed heterologously in Saccharomyces cerevisiae. Site-directed mutagenesis studies were performed by replacing phenylalanine with tryptophan at position 473 (Phe473Trp), methionine with serine at position 549 (Met549Ser) and leucine with phenylalanine at position 552 (Leu552Phe). Mutation Phe473Trp led to a total loss of function; mutants Met549Ser and Leu552Phe interfered with the enzyme specificity leading to enhanced friedelin production, in addition to α-amyrin and β-amyrin. Hence, these data showed that methionine 549 and leucine 552 are important residues for the function of this synthase.     

Synthesis,characterization, and X-ray crystallographic structure of 1,3-dimethyl-2(3H)-imidazoleselone

The reaction of elemental Se with 1,3-dimethylimidazolium iodide in methanolic K₂CO₃ yields 1,3-dimethyl-2(3H)-imidazoleselone for which three addition products, two with bromine and one with iodomethane, have been synthesized and for which X-ray crystallographic analysis shows the structure to consist of a selenium-substituted planar heterocyclic ring with bond distances and angles significantly different from those noted for the previously reported sulfur analog [1,3-dimethyl-2(3H)-imidazolethione, dmit]. Crystal data: C₅H₈N₂Se, space group C mcm, M = 175.03, a = 8.625(3), b = 11.447(6), c = 6.900(4) Å, V = 681.24 ų, Z = 4, D_c = 1.707 g cm⁻³, D₀ = 1.68 g cm⁻³, λ = 0.71073 Å (Mo-K_α), μ = 5.35 mm⁻¹, R = 0.034, and R_w = 0.031.     

Student Strategy Choices on a Constructed Response Algebra Problem

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th‐, 9th‐, and 10th‐grade students in five different school systems over three consecutive years on the same algebra problem. We also analyzed connections between their strategies and their success on the problem. Our findings suggest that many students continued to struggle with algebraic problems, even after several years of instruction in algebra. Students did not reflect the anticipated growth toward the consistent use of efficient strategies deemed appropriate in solving this problem. Instead a surprisingly large number of students continued to rely on strategies such as guessing and checking, or offered solutions that were unintelligible or meaningless and not useful to the researchers. Even those students who used algebraic strategies consistently did not show the anticipated improvement of performance that would be expected from several years of continuing to study mathematics.     

A formula of two-partition Hodge integrals

Motivated by the Mariño-Vafa formula of Hodge integrals and physicists' predictions on local Gromov-Witten invariants of toric Fano surfaces in a Calabi-Yau threefold, the third author conjectured a formula of certain Hodge integrals in terms of certain Chern-Simons invariants of the Hopf link. We prove this formula by virtual localization on moduli spaces of relative stable morphisms.

     

A Survey on Mixed Spin P-Fields

The mixed spin P-fields (MSP for short) theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variables.It starts with Wittens vision and the P-fields treatment of GW invariants and FJRW invariants.Then it briefly discusses the master space technique and its application to the set-up of the MSP moduli.Some key results in MSP theory are explained and some examples are provided.     

A comparative investigation of the presence of psychological conditions in high achieving eighth graders from TIMSS 2007 Mathematics

This study is a second analysis of Trends in International Mathematics and Science Study (TIMSS) 2007 background questionnaires to investigate high achieving eighth-grade students’ possession of three elements of Krutetskii’s (The Psychology of Mathematical Abilities in Schoolchildren, The University of Chicago, 1976) psychological conditions. Analyses were made between high achieving eighth graders and their lower achieving counterparts, and between Korean high achievers and their high achieving peers across ten high performing TIMSS participating countries. After reviewing 44,643 students across selected countries, we conclude that a larger percentage of students with mathematical talent demonstrate positive attitudes toward mathematics, value mathematics, and have self-confidence in their ability to learn mathematics than their peers without high achievement in mathematics. However, a larger portion of high achieving Korean students displayed low self-confidence and valued mathematics less than their peers from other high performing countries. Findings from this study will provide insight into some educational issues in science, technology, engineering and mathematics education.     

Semiclassical <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> Estimates of Quasimodes on Curved Hypersurfaces

Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L ² normalized family of functions such that P(h)u(h) is O(h) in L ²(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L ^p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch ^−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator.