EBC-232 and 323: A Structural Conundrum Necessitating Unification of Five In Silico Prediction and Elucidation Methods

Structurally unique halimanes EBC-232 and EBC-323, isolated from the Australian rainforest plant Croton insularis, proved considerably difficult to elucidate. The two diastereomers, which consist an unusual oxo-6,7-spiro ring system fused to a dihydrofuran, were solved by unification and consultation of five in silico NMR elucidation and prediction methods [i.e., ACDLabs, olefin strain energy (OSE), DP4, DU8+ and TD DFT CD]. Structure elucidation challenges of this nature are prime test case examples for empowering future AI learning in structure elucidation.     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the n×n external source matrix has two distinct real eigenvalues: a with multiplicity r and zero with multiplicity n−r. For a Gaussian potential, it was shown by Péché (Probab. Theory Relat. Fields 134:127–173, 2006) that when r is fixed or grows sufficiently slowly with n (a small-rank source), r eigenvalues are expected to exit the main bulk for |a| large enough. Furthermore, at the critical value of a when the outliers are at the edge of a band, the eigenvalues at the edge are described by the r-Airy kernel. We establish the universality of the r-Airy kernel for a general class of analytic potentials for r=O(n^g)r=\mathcal{O}(n^{\gamma}) for 0≤γ<1/12.     

Mechanism and stereoselectivity of a dual amino-catalyzed robinson annulation: rare duumvirate stereocontrol

Computational study of the mechanisms and stereoselectivities of a dual amino-catalyzed synthesis of cyclohexenones containing all-carbon γ-quaternary and ?-tertiary stereocenters is reported. Extensive conformational search with density functional theory optimizations, the high-accuracy SCS-MP2/cc-pV∞Z energies, and PCM solvation corrections were used to characterize all intermediates and transition states. Six mechanisms were considered, all consistent with available experiments. The reaction proceeds via sequential Michael and Mannich conjugate additions whereby the primary amine activates the aldehyde and the catalyst activates the pentenone. We have discovered a rare duumvirate stereocontrol: the Michael reaction sets the enantioselectivity, but both the Michael and the Mannich reactions control the diastereoselectivity.     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.     

Chiral prostanoid intermediates from aucubin

Several potentially useful prostanoid intermediates have been prepared from aucubin. Dry DMSO-NBS converts enol ethers to α-bromoesters in one step.     

Mechanistic implications for the formation of the diiron cluster in ribonucleotide reductase provided by quantitative EPR spectroscopy

The small subunit of Escherichia coli ribonucleotide reductase (R2) is a homodimeric (betabeta) protein, in which each beta-peptide contains a diiron cluster composed of two inequivalent iron sites. R2 is capable of reductively activating O(2) to produce a stable tyrosine radical (Y122*), which is essential for production of deoxyribonucleotides on the larger R1 subunit. In this work, the paramagnetic Mn(II) ion is used as a spectroscopic probe to characterize the assembly of the R2 site with EPR spectroscopy. Upon titration of Mn(II) into samples of apoR2, we have been able to quantitatively follow three species (aquaMn(II), mononuclear Mn(II)R2, and dinuclear Mn(2)(II)R2) and fit each to a sequential two binding site model. As previously observed for Fe(II) binding within apoR2, one of the sites has a greater binding affinity relative to the other, K(1) = (5.5 +/- 1.1) x 10(5) M(-)(1) and K(2) = (3.9 +/- 0.6) x 10(4) M(-)(1), which are assigned to the B and A sites, respectively. In multiple titrations, only one dinuclear Mn(2)(II)R2 site was created per homodimer of R2, indicating that only one of the two beta-peptides of R2 is capable of binding Mn(II) following addition of Mn(II) to apoR2. Under anaerobic conditions, addition of only 2 equiv of Fe(II) to R2 (Fe(2)(II)R2) completely prevented the formation of any bound MnR2 species. Upon reaction of this sample with O(2) in the presence of Mn(II), both Y122* and Mn(2)(II)R2 were produced in equal amounts. Previous stopped-flow absorption spectroscopy studies have indicated that apoR2 undergoes a protein conformational change upon binding of metal (Tong et al. J. Am. Chem. Soc. 1996, 118, 2107-2108). On the basis of these observations, we propose a model for R2 metal incorporation that invokes an allosteric interaction between the two beta-peptides of R2. Upon binding the first equiv of metal to a beta-peptide (beta(I)), the aforementioned protein conformational change prevents metal binding in the adjacent beta-peptide (beta(II)) approximately 25 A away. Furthermore, we show that metal incorporation into beta(II) occurs only during the O(2) activation chemistry of the beta(I)-peptide. This is the first direct evidence of an allosteric interaction between the two beta-peptides of R2. Furthermore, this model can explain the generally observed low Fe occupancy of R2. We also demonstrate that metal uptake and this newly observed allosteric effect are buffer dependent. Higher levels of glycerol cause loss of the allosteric effect. Reductive cycling of samples in the presence of Mn(II) produced a novel mixed metal Fe(III)Mn(III)R2 species within the active site of R2. The magnitude of the exchange coupling (J) determined for both the Mn(2)(II)R2 and Fe(III)Mn(III)R2 species was determined to be -1.8 +/- 0.3 and -18 +/- 3 cm(-)(1), respectively. Quantitative spectral simulations for the Fe(III)Mn(III)R2 and mononuclear Mn(II)R2 species are provided. This work represents the first instance where both X- and Q-band simulations of perpendicular and parallel mode spectra were used to quantitatively predict the concentration of a protein bound mononuclear Mn(II) species.     

Realistic Dirac leptogenesis

We present a model of leptogenesis that preserves lepton number. The model maintains the important feature of more traditional leptogenesis scenarios: The decaying particles that provide the CP violation necessary for baryogenesis also provide the explanation for the smallness of the neutrino Yukawa couplings. This model clearly demonstrates that, contrary to conventional wisdom, neutrinos need not be Majorana in nature in order to help explain the baryon asymmetry of the universe.     

Invariants of linear maps on matrix algebras

Let L be a linear map on the space of n×n matrices over a field. We determine the structure of the maps L that preserve commutativity. We also determine the structure of all linear maps on complex matrices that preserve the higher numerical range. The main tool is the Fundamental Theorem of Projective Geometry.