Isogenies of elliptic curves and the Morava stabilizer group

Let S₂ be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over , O the ring of endomorphisms of C, and ? a topological generator of (or if p=2). We show that for p>2 the group Γ⊆O[1/?]^× of quasi-endomorphisms of degree a power of ? is dense in S₂. For p=2, we show that Γ is dense in an index 2 subgroup of S₂.     

Spectral asymptotics for Kac–Murdock–Szegő matrices

Szeg?’s First Limit Theorem provides the limiting statistical distribution of the eigenvalues of large Toeplitz matrices. Szeg?’s Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order correction to the First Limit Theorem, and allows one to calculate asymptotics for the determinants of large Toeplitz matrices. In this paper we survey results extending the First and Second Limit Theorems to Kac–Murdock–Szeg? (KMS) matrices. These are matrices whose entries along the diagonals are not necessarily constants, but modeled by functions. We clarify and extend some existing results, and explain some apparently contradictory results in the literature.     

The plus-construction, Bousfield localization, and derived completion

We define a plus-construction on connective augmented algebras over operads in symmetric spectra using Quillen homology. For associative and commutative algebras, we show that this plus-construction is related to both Bousfield localization and Carlsson’s derived completion.     

Isolation and Synthesis of Novel Meroterpenoids from Rhodomyrtus tomentosa: Investigation of a Reactive Enetrione Intermediate

Rhodomyrtusials A–C, the first examples of triketone‐sesquiterpene meroterpenoids featuring a unique 6/5/5/9/4 fused pentacyclic ring system were isolated from Rhodomyrtus tomentosa, along with several biogenetically‐related dihydropyran isomers. Two bis‐furans and one dihydropyran isomer showed acetylcholinesterase (AChE) inhibitory activity. Structures of the isolates were unambiguously established by a combination of spectroscopic data, ECD analysis, and total synthesis. Bioinspired total syntheses of six isolates were achieved in six steps utilizing a reactive enetrione intermediate generated in situ from a readily available hydroxy‐endoperoxide precursor.     

Exosome isolation and purification via hydrophobic interaction chromatography using a polyester,capillary‐channeled polymer fiber phase

Extracellular vesicles, including microvesicles and exosomes, are lipidic membrane‐derived vesicles that are secreted by most cell types. Exosomes, one class of these vesicles that are 30–100 nm in diameter, hold a great deal of promise in disease diagnostics, as they display the same protein biomarkers as their originating cell. For exosomes to become useful in disease diagnostics, and as burgeoning drug delivery platforms, they must be isolated efficiently and effectively without compromising their structure. Most current exosome isolation methods have practical problems including being too time‐consuming and labor intensive, destructive to the exosomes, or too costly for use in clinical settings. To this end, this study examines the use of poly(ethylene terephthalate) (PET) capillary‐channeled polymer (C‐CP) fibers in a hydrophobic interaction chromatography (HIC) protocol to isolate exosomes from diverse matrices of practical concern. Initial results demonstrate the ability to isolate extracellular vesicles enriched in exosomes with comparable yields and size distributions on a much faster time scale when compared to traditional isolation methods. As a demonstration of the potential analytical utility of the approach, extracellular vesicle recoveries from cell culture milieu and a mock urine matrix are presented. The potential for scalable separations covering submilliliter spin‐down columns to the preparative scale is anticipated.     

A real-time,fluorescence-based assay for Rho-associated protein kinase activity

Inhibitors of Rho-associated protein kinase (ROCK) enzymatic activity have been shown to reduce the invasive phenotype observed in metastatic hepatocellular carcinoma (HCC). We describe the design, synthesis, and evaluation of a direct probe for ROCK activity utilizing a phosphorylation-sensitive sulfonamido-oxine fluorophore, termed Sox. The Sox fluorophore undergoes an increase in fluorescence upon phosphorylation of a proximal amino acid via chelation-enhanced fluorescence (CHEF, ex. = 360 nm and em. = 485 nm), allowing for the direct visualization of the rate of phosphate addition to a peptide substrate over time. Our optimal probe design, ROCK-S1, is capable of sensitively reporting ROCK activity with a limit of detection of 10 pM and a high degree of reproducibility (Z’-factor = 0.6 at 100 pM ROCK2). As a proof-of-principle for high-throughput screening (HTS) we demonstrate the ability to rapidly assess the efficacy of a 78 member, small molecule library against ROCK2 using a robotics platform. We identify two previously unreported ROCK2 inhibitor scaffolds, PHA665752 and IKK16, with IC₅₀ values of 3.6 μM and 247 nM respectively. Lastly, we define conditions for selectively monitoring ROCK activity in the presence of potential off-target enzymes (PKCα, PKA, and PAK) with similar substrate specificities.