On the number of lattice points between two enlarged and randomly shifted,copies of an oval

Summary Let A be an oval with a nice boundary in ²,R a large positive number,c>0 some fixed number and a uniformly distributed random vector in the unit square [0,1]². We are interested in the number of lattice points in the shifted annular region consisting of the difference of the sets {(R+c/R)A–} and {(R–c/R)A–}. We prove that whenR tends to infinity, the expectation and the variance of this random variable tend to 4c times the area of the set A, i.e. to the area of the domain where we are counting the number of lattice points. This is consistent with computer studies in the case of a circle or an ellipse which indicate that the distribution of this random variable tends to the Poisson law. We also make some comments about possible generalizations.     

Discrepancy in arithmetic progressions

It is proven that there is a two-coloring of the first integers for which all arithmetic progressions have discrepancy less than . This shows that a 1964 result of K. F. Roth is, up to constants, best possible.

     

Synthesis of(±)-descarboxylquadrone

The synthesis of a biologically active anlogue of the antitumor agent quadrone, termed descarboxylquadrone ($\text{3}$), is described.     

Arresting cancer proliferation by small-molecule gene regulation

A small library of pyrrole-imidazole polyamide-DNA alkylator (chlorambucil) conjugates was screened for effects on morphology and growth characteristics of a human colon carcinoma cell line, and a compound was identified that causes cells to arrest in the G2/M stage of the cell cycle. Microarray analysis indicates that the histone H4c gene is significantly downregulated by this polyamide. RT-PCR and Western blotting experiments confirm this result, and siRNA to H4c mRNA yields the same cellular response. Strikingly, reduction of H4 protein by >50% does not lead to widespread changes in global gene expression. Sequence-specific alkylation within the coding region of the H4c gene in cell culture was confirmed by LM-PCR. The compound is active in a wide range of cancer cell lines, and treated cells do not form tumors in nude mice. The compound is also active in vivo, blocking tumor growth in mice, without obvious animal toxicity.     

The nexus between alternatives assessment and green chemistry: supporting the development and adoption of safer chemicals

ABSTRACT

Alternatives assessment and green chemistry share a common goal of supporting the transition to safer, more sustainable chemicals, materials, and products. Yet the two fields, and their respective scientific communities, are not well integrated. To better understand the nexus between alternatives assessment and green chemistry as complementary approaches to support the development and adoption of safer, more sustainable chemicals for specific functional uses, this article discusses the foundations of the two fields and examines two case examples in which companies have utilized the tools and approaches of both disciplines in developing safer chemical solutions. This research demonstrates the importance and utility of the overlapping skillsets and tools of the two disciplines and the potential benefit of educational opportunities and collaborative spaces in jointly strengthening both fields. Additionally, the literature and case examples identify a number of research and practice needs that would bolster the application of both alternatives assessment and green chemistry in supporting the transition to safer, more sustainable chemistry, including: clearer definitions and criteria of what is ‘safer’; improved approaches to evaluate potential unintended consequences of chemical applications; and more effective tools to evaluate toxicity, consider inherent exposure trade-offs, and combine multiple attributes to make an informed decision.     

Dynamic mechanism of E2020 binding to acetylcholinesterase: a steered molecular dynamics simulation

The unbinding process of E2020 ((R,S)-1-benzyl-4-[(5,6-dimethoxy-1-indanon)-2-yl]-methylpiperidine) leaving from the long active site gorge of Torpedo californica acetylcholinesterase (TcAChE) was studied by using steered molecular dynamics (SMD) simulations on a nanosecond scale with different velocities, and unbinding force profiles were obtained. Different from the unbinding of other AChE inhibitors, such as Huperzine A that undergoes the greatest barrier located at the bottleneck of the gorge, the major resistance preventing E2020 from leaving the gorge is from the peripheral anionic site where E2020 interacts intensively with several aromatic residues (e.g., Tyr70, Tyr121, and Trp279) through its benzene ring and forms a strong direct hydrogen bond and a water bridge with Ser286 via its O24. These interactions cause the largest rupture force, approximately 550 pN. It was found that the rotatable bonds of the piperidine ring to the benzene ring and dimethoxyindanone facilitate E2020 to pass the bottleneck through continuous conformation change by rotating those bonds to avoid serious conflict with Tyr121 and Phe330. The aromatic residues lining the gorge wall are the major components contributing to hydrophobic interactions between E2020 and TcAChE. Remarkably, these aromatic residues, acting in three groups as "sender" and "receiver", compose a "conveyer belt" for E2020 entering and leaving the TcAChE gorge.     

Enantioselective organocatalytic indole alkylations. Design of a new and highly effective chiral amine for iminium catalysis

The indole framework has become widely identified as a "privileged" structure with representation in over 3000 natural isolates and 40 medicinal agents of diverse therapeutic action. A new strategy for asymmetric access to this important pharmacaphore has been accomplished that involves the amine catalyzed alkylation of indoles with alpha,beta-unsaturated aldehydes. Central to these studies has been the design of a new chiral amine catalyst that exhibits improved reactivity and selectivity for iminium catalysis. This new (2S,5S)-5-benzyl-2-tert-butyl-imidazolidinone catalyst has enabled the conjugate addition of a variety of indole systems to a diverse range of alpha,beta-unsaturated aldehydes in high yield and with excellent levels of enantiocontrol (70-97% yield, 84-97% ee). A demonstration of the utility of this new organocatalytic alkylation for the rapid construction of biomedically relevant molecules is presented in the enantioselective synthesis of an indolobutyric acid COX-2 inhibitor.