Some mildly wild circles in Sn arising from algebraic K-Theory

We study wild embeddings of S ¹ in S ⁿ which are tame in a sense introduced by Quinn. We show that if is a finitely presented group with H ₁()=H ₂()=0, then any finiteness obstruction K ₀() can be realized on the complement of such an embedded S ¹. We also realize trivially symmetric K _–1() obstructions on the complements of such embeddings. For trivially symmetric , the embeddings constructed are shown to be isotopy homogeneous.     

A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Existence of generic homoclinic tangencies for henon mappings

It is an open question whether there is a strange attractor for the Henon mapping. We show that for certain maps close to the Henon map there are strange attractors.     

Anti-HIV Active Naphthyl Analogues of HEPT and DABO

Summary.  5-Isopropyl-6-naphthyl uracil and 5-isopropyl-6-naphthyl-2-thiouracil were alkylated to give N-1-(ethoxymethyl and methylthiomethyl) uracil and S²-cyclohexyl-thiouracil, respectively. 5-Ethyl-6-naphthyl uracil and 5-ethyl-6-naphthyl-2-thiouracil afforded N-1-(ethoxymethyl, methoxy-methyl, methylthiomethyl, acetoxyethoxy methyl and hydroxyethoxy methyl) uracil and S²-((2,2- diethoxyethyl), methoxycarbonylmethyl, ethoxycarbonylpropyl, methylthiomethyl, ethoxymethyl, methyl and cyclohexyl)-thiouracil upon alkylation. Received September 25, 2001. Accepted (revised) December 3, 2001     

Liquid chromatographic analysis of vitamin B6 in reconstituted infant formula: collaborative study

A liquid chromatographic (LC) method was validated for the determination of total vitamin B6 in infant formula. Total vitamin B6 was quantified by converting the phosphorylated and free vitamers into pyridoxine. Pyridoxine was determined by ion pair reversed-phase LC with fluorescence detection. The method was subjected to an AOAC collaborative study involving a factory-manufactured, milk- and soy-based infant formula. Each was spiked at 3 concentrations in the range of 0-1 microg/g and sent as blind duplicate to participant laboratories. Nine laboratories returned valid data which were statistically analyzed for outliers and precision parameters. The repeatability relative standard deviation (RSD(r)) ranges were 2.0-4.0 and 3.5-5.9% for fortified milk- and soy-based formulas, respectively. The reproducibility relative standard deviation (RSD(R)) ranges were 8.2-8.4 and 6.7-11.2% for fortified milk- and soy-based formulas, respectively. HORRAT values ranged from 0.42 to 0.53, indicating that the precision of the method is acceptable. The mean RSD(r):RSD(R) values were 0.60 and 0.55 for milk- and soy-based formulas, respectively. As expected, RSDs for the unfortified samples were higher, but their HORRAT values (0.81 and 2.06) helped define a realistic limit of quantitation as 0.05 microg/g. Recovery data were quantitative and varied between 81.4 and 98.0% (mean = 89.8%) for each of 6 spiked materials.     

Towards Predicting Partitioning of Enzymes between Macromolecular Phases: Effects of Polydispersity on the Phase Behavior of Nonadditive Hard Spheres in Solution

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.     

Heteroarylation of unactivated C–H bonds suitable for late-stage functionalization

The late-stage introduction of diverse heterocycles onto complex small molecules enables efficient access to new medicinally relevant compounds. An attractive approach to such a transformation would utilize the ubiquitous aliphatic C–H bonds of a complex substrate. Herein, we report a system that enables direct C–H heteroarylation using a stable, commercially available O-alkenylhydroxamate with heterocyclic sulfone partners. The C–H heteroarylation proceeds efficiently with a range of aliphatic substrates and common heterocycles, and is a rare example of heteroarylation of strong C–H bonds. Importantly, the present approach is amenable to late-stage functionalization as the substrate is the limiting reagent in all cases.

The late-stage introduction of diverse heterocycles onto complex small molecules enables efficient access to new medicinally relevant compounds.     

Cancer-Associated Mutations of the Adenosine A2A Receptor Have Diverse Influences on Ligand Binding and Receptor Functions

The adenosine A_2A receptor (A_2AAR) is a class A G-protein-coupled receptor (GPCR). It is an immune checkpoint in the tumor micro-environment and has become an emerging target for cancer treatment. In this study, we aimed to explore the effects of cancer-patient-derived A_2AAR mutations on ligand binding and receptor functions. The wild-type A_2AAR and 15 mutants identified by Genomic Data Commons (GDC) in human cancers were expressed in HEK293T cells. Firstly, we found that the binding affinity for agonist NECA was decreased in six mutants but increased for the V275A mutant. Mutations A165V and A265V decreased the binding affinity for antagonist ZM241385. Secondly, we found that the potency of NECA (EC₅₀) in an impedance-based cell-morphology assay was mostly correlated with the binding affinity for the different mutants. Moreover, S132L and H278N were found to shift the A_2AAR towards the inactive state. Importantly, we found that ZM241385 could not inhibit the activation of V275A and P285L stimulated by NECA. Taken together, the cancer-associated mutations of A_2AAR modulated ligand binding and receptor functions. This study provides fundamental insights into the structure–activity relationship of the A_2AAR and provides insights for A_2AAR-related personalized treatment in cancer.     

Functional Bacterial Amyloids: Understanding Fibrillation,Regulating Biofilm Fibril Formation and Organizing Surface Assemblies

Functional amyloid is produced by many organisms but is particularly well understood in bacteria, where proteins such as CsgA (E. coli) and FapC (Pseudomonas) are assembled as functional bacterial amyloid (FuBA) on the cell surface in a carefully optimized process. Besides a host of helper proteins, FuBA formation is aided by multiple imperfect repeats which stabilize amyloid and streamline the aggregation mechanism to a fast-track assembly dominated by primary nucleation. These repeats, which are found in variable numbers in Pseudomonas, are most likely the structural core of the fibrils, though we still lack experimental data to determine whether the repeats give rise to β-helix structures via stacked β-hairpins (highly likely for CsgA) or more complicated arrangements (possibly the case for FapC). The response of FuBA fibrillation to denaturants suggests that nucleation and elongation involve equal amounts of folding, but protein chaperones preferentially target nucleation for effective inhibition. Smart peptides can be designed based on these imperfect repeats and modified with various flanking sequences to divert aggregation to less stable structures, leading to a reduction in biofilm formation. Small molecules such as EGCG can also divert FuBA to less organized structures, such as partially-folded oligomeric species, with the same detrimental effect on biofilm. Finally, the strong tendency of FuBA to self-assemble can lead to the formation of very regular two-dimensional amyloid films on structured surfaces such as graphite, which strongly implies future use in biosensors or other nanobiomaterials. In summary, the properties of functional amyloid are a much-needed corrective to the unfortunate association of amyloid with neurodegenerative disease and a testimony to nature’s ability to get the best out of a protein fold.