Asymmetric cycloadditions of o-quinone methides employing chiral ammonium fluoride precatalysts

The catalytic, enantioselective, [4 + 2] cycloaddition reaction of ortho-quinone methides with silyl ketene acetals is described. This mechanistically interesting reaction, initiated by a chiral cinchona alkaloid-derived ammonium fluoride "precatalyst" complex, affords a variety of alkyl- and aryl-substituted 3,4-dihydrocoumarin products in excellent yield and with good enantioselectivity.     

Assessment of intracellular methotrexate and methotrexate-polyglutamate metabolite concentrations in erythrocytes by ultrafast matrix-assisted laser desorption/ionization triple quadrupole tandem mass spectrometry

A new ultrafast quantitative and high‐throughput mass spectrometric method using matrix‐assisted laser desorption/ionization triple quadrupole tandem mass spectrometry has been developed and validated for determination of intracellular erythrocyte concentrations of the antifolate drug methotrexate (MTX) and its polyglutamate metabolites. The method consists of a solid‐phase extraction of MTX and MTX‐polyglutamate metabolites from deproteinized erythrocyte lysates spiked with aminopterin as internal standard. The newly developed method was validated according to the most recent FDA guidelines on linearity, recovery, within‐run and between‐run accuracy and precision and stability of the analytes. The low limit of quantification (LLOQ) was 10 nmol/L for all analytes while the limit of detection (LOD) determined at a signal‐to‐noise (S/N) ratio = 3:1 in drug‐ free erythrocyte lysate was on average 0.3 nmol/L. After validation, the new method was used in the measurement of intracellular erythrocyte concentrations of MTX and MTX‐polyglutamate metabolites (MTXPG2 to MTXPG7) in packed human erythrocyte samples collected from patients with rheumatoid arthritis receiving low‐dose oral methotrexate therapy. Mean (SD) intracellular erythrocyte concentrations observed in patient samples were 12.8 (12.6), 12.4 (9.4), 44.4 (30.0), 33.6 (35.9) and 9.4 (8.2) nmol/L for MTX to MTXPG5, respectively, in 10⁶ erythrocytes. The highest observed glutamylation degree of MTX was MTXPG5, the very long chain MTX‐polyglutamate metabolites MTXPG6 and MTXPG7 were not detected in the packed erythrocyte pellets collected from rheumatoid arthritis patients. Copyright © 2011 John Wiley & Sons, Ltd.     

Two classes of quasi-steady-state model reductions for stochastic kinetics

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case.     

Impact of woven fabric: Experiments and mesostructure-based continuum-level simulations

Woven fabric is an increasingly important component of many defense and commercial systems, including deployable structures, restraint systems, numerous forms of protective armor, and a variety of structural applications where it serves as the reinforcement phase of composite materials. With the prevalence of these systems and the desire to explore new applications, a comprehensive, computationally efficient model for the deformation of woven fabrics is needed. However, modeling woven fabrics is difficult due, in particular, to the need to simulate the response both at the scale of the entire fabric and at the meso-level, the scale of the yarns that compose the weave. Here, we present finite elements for the simulation of the three-dimensional, high-rate deformation of woven fabric. We employ a continuum-level modeling technique that, through the use of an appropriate unit cell, captures the evolution of the mesostructure of the fabric without explicitly modeling every yarn. Displacement degrees of freedom and degrees of freedom representing the change in crimp amplitude of each yarn family fully determine the deformed geometry of the mesostructure of the fabric, which in turn provides, through the constitutive relations, the internal nodal forces. In order to verify the accuracy of the elements, instrumented ballistic impact experiments with projectile velocities of 22-550 m/s were conducted on single layers of Kevlar^® fabric. Simulations of the experiments demonstrate that the finite elements are capable of efficiently simulating large, complex structures.     

The stochastic quasi-steady-state assumption: reducing the model but not the noise

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution.     

Singular rational curves with points of nearly-maximal weight

In this article we study rational curves with a unique unibranch genus-g singularity, which is of κ-hyperelliptic type in the sense of [27]; we focus on the cases $\kappa =0$ and $\kappa =1$, in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality.