Amination of ethers using chloramine-T hydrate and a copper(I) catalyst

Amination of C-H bonds activated by ether oxygen atoms is facile with chloramine-T as nitrene source and copper(I) chloride in acetonitrile as catalyst. For cyclic ethers the hemiaminal products are generally stable and can be isolated pure. For acyclic ethers, the hemiaminal products, as expected, fragment with elimination of alcohol to yield imines. When activation of benzylic positions is remote through a conjugated system, stable benzylamine derivatives are isolated. Mechanistic studies are consistent with concerted insertion of an electrophilic nitrenoid into the C-H bond in the rate-determining step, though in an asynchronous manner with a more activated substrate.     

Arithmetic Properties of Non-Squashing Partitions into Distinct Parts

A partition with is non-squashing if On their way towards the solution of a certain box-stacking problem, Sloane and Sellers were led to consider the number b(n) of non-squashing partitions of n into distinct parts. Sloane and Sellers did briefly consider congruences for b(n) modulo 2. In this paper we show that 2^r-2 is the exact power of 2 dividing the difference b(2^r+1n)–b(2^r-1n) for n odd and r 2.     

Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

Polariton emission in GaN microcavities

We present a detailed experimental study aimed at demonstrating the polariton nature of the photoluminescence emission in a bulk GaN microcavity grown on (111) silicon. The comparison of the photoluminescence with coincident reflectivity measurements at different temperatures shows an anticrossing behaviour with a Rabi splitting of the order of 35 meV up to room temperature. Relevant confirmations of the mixing between excitons and photons are found in the analysis of the spectral linewidth and of the time resolved kinetics.     

Invariant circles for the piecewise linear standard map

We investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus. We show that invariant circles of all types and rotation numbers occur and we classify them into families. We compute parameter ranges in which there are no invariant circles.     

Detection of halogenated organic compounds using immobilized thermophilic dehalogenase

Environmental pollutants containing halogenated organic compounds can cause a plethora of health problems. Detection, quantification, and eventual remediation of halogenated pollutants in the environment are important to human well-being. Toward this end, we previously identified a haloacid dehalogenase, L-HAD_ST, from the thermophile Sulfolobus tokodaii. This thermophilic enzyme is extremely stable and catalyzes, stereospecifically, the dehalogenation of l-2-haloacids. In the current study, we covalently linked L-HAD_ST to an N-hydroxysuccinimidyl Sepharose resin to construct a highly specific sensor with long shelf life for the detection of l-2-haloacids. The enzyme-modified resin was packed into disposable columns. Samples containing l-2-haloacids were first incubated in the column, and were then collected to quantify the chloride produced through the breakdown of the substrate. The optimum pH of the immobilized enzyme is around 9.5, similar to that of the soluble protein. Its catalytic activity increased with temperature up to the highest temperature measured (50 °C). The resin could be fully regenerated after multiple reaction cycles and retained 70% of the initial activity after being stored at 4 °C for 6 months. The L-HAD_ST-modified resin could be used to breakdown and quantify l-2-haloacids spiked in the simulated environmental samples, indicating dehalogenases from extremophiles can potentially be employed in the detection and decontamination of l-2-haloacids.     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Engineering enzyme specificity using computational design of a defined-sequence library

Engineered biosynthetic pathways have the potential to produce high-value molecules from inexpensive feedstocks, but a key limitation is engineering enzymes with high activity and specificity for new reactions. Here, we developed a method for combining structure-based computational protein design with library-based enzyme screening, in which inter-residue correlations favored by the design are encoded into a defined-sequence library. We validated this approach by engineering a glucose 6-oxidase enzyme for use in a proposed pathway to convert D-glucose into D-glucaric acid. The most active variant, identified after only one round of diversification and screening of only 10,000 wells, is approximately 400-fold more active on glucose than is the wild-type enzyme. We anticipate that this strategy will be broadly applicable to the discovery of new enzymes for engineered biological pathways.     

Torsion in biochemical reaction networks

This article starts in Part I with a simple example of two biochemical reaction networks that are indistinguishable at the macroscopic level but are different at the molecular level and are shown to have significantly different kinetic properties. So, if one completely ignores the fact that reactions advance in discrete steps at the molecular level, then one can fail to distinguish between networks with widely different kinetics. In part II biochemical reaction networks are treated in a general way to discover what property of a network, only seen at the molecular level, affects its kinetics. It is shown that every such network has a unique torsion group which can be described numerically and readily determined by a programmable computation. If the group is found to be the singleton {0} (as is most often the case in practice), then the network is said to be torsion-free and its kinetic properties unaffected by ignoring its discrete character. A chemical reaction network has to be represented algebraically to calculate its torsion group. If the network is to be understood only at the macroscopic level, it can be placed in the context of real vector spaces, but to recognize its discrete character and its torsion group, each vector space is replaced by a discrete subset of that space, where each molecule can be recognized as a distinct and indivisible entity. Next, the process of calculating a torsion group is shown in several cases, including the example in part I. In this particular case it is shown to have the torsion group with 2 elements, reflecting the fact that the substrate molecules become product molecules 2 at a time, with the result that the overall macroscopic reaction is R ⇔ T, whereas at the molecular level it is 2R ⇔ 2T. In general, however, the torsion group of a biochemical reaction network can be any finite additive group, which is a property of the network that can only be seen at the molecular level. Finally, this fact is demonstrated by showing how to construct a hypothetical, but plausible, biochemical reaction network that has any given finite additive group as its torsion group.