Simple polytopes without small separators

We show that by cutting off the vertices and then the edges of neighborly cubical polytopes, one obtains simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least Ω(n/log^3/2 n). This disproves a conjecture by Kalai from 1991/2004.     

Synthetic Matching of Complex Monoterpene Indole Alkaloid Chemical Space

Monoterpene indole alkaloids (MIAs) are endowed with high structural and spatial complexity and characterized by diverse biological activities. Given this complexity-activity combination in MIAs, rapid and efficient access to chemical matter related to and with complexity similar to these alkaloids would be highly desirable, since such compound classes might display novel bioactivity. We describe the design and synthesis of a pseudo-natural product (pseudo-NP) collection obtained by the unprecedented combination of MIA fragments through complexity-generating transformations, resulting in arrangements not currently accessible by biosynthetic pathways. Cheminformatic analyses revealed that both the pseudo-NPs and the MIAs reside in a unique and common area of chemical space with high spatial complexity-density that is only sparsely populated by other natural products and drugs. Investigation of bioactivity guided by morphological profiling identified pseudo-NPs that inhibit DNA synthesis and modulate tubulin. These results demonstrate that the pseudo-NP collection occupies similar biologically relevant chemical space that Nature has endowed MIAs with.     

Unusually Strong Long‐Distance Metal–Metal Coupling in Bis(ferrocene)‐Containing BOPHY: An Introduction to Organometallic BOPHYs

The first organometallic BOPHY (BOPHY=bis(difluoroboron)‐1,2‐bis{(pyrrol‐2‐yl)methylene}hydrazine) containing two ferrocene substituents was prepared through a Knoevenagel condensation between tetramethyl substituted BOPHY and ferrocene carboxaldehyde. An unprecedentedly strong long‐range (≈17.2 Å) metal–metal coupling in this new complex was investigated using electrochemical, spectroelectrochemical, and chemical oxidation methods. Electrochemical data is indicative of a 200 mV separation between the first and the second ferrocene‐centered oxidation processes. Formation of the mixed‐valence states and appearance and disappearance of two NIR bands were observed during stepwise oxidation of the first organometallic BOPHY. The electronic structure and the nature of the excited states in this new chromophore were studied by DFT and TDDFT calculations.     

(−)‐Englerin A is a Potent and Selective Activator of TRPC4 and TRPC5 Calcium Channels

Current therapies for common types of cancer such as renal cell cancer are often ineffective and unspecific, and novel pharmacological targets and approaches are in high demand. Here we show the unexpected possibility for the rapid and selective killing of renal cancer cells through activation of calcium‐permeable nonselective transient receptor potential canonical (TRPC) calcium channels by the sesquiterpene (?)‐englerin A. This compound was found to be a highly efficient, fast‐acting, potent, selective, and direct stimulator of TRPC4 and TRPC5 channels. TRPC4/5 activation through a high‐affinity extracellular (?)‐englerin A binding site may open up novel opportunities for drug discovery aimed at renal cancer.     

Biology‐Oriented Synthesis of a Withanolide‐Inspired Compound Collection Reveals Novel Modulators of Hedgehog Signaling

Biology‐oriented synthesis employs the structural information encoded in complex natural products to guide the synthesis of compound collections enriched in bioactivity. The trans‐hydrindane dehydro‐δ‐lactone motif defines the characteristic scaffold of the steroid‐like withanolides, a plant‐derived natural product class with a diverse pattern of bioactivity. A withanolide‐inspired compound collection was synthesized by making use of three key intermediates that contain this characteristic framework derivatized with different reactive functional groups. Biological evaluation of the compound collection in cell‐based assays that monitored biological signal‐transduction processes revealed a novel class of Hedgehog signaling inhibitors that target the protein Smoothened.     

Arguments for and against Engesser's buckling formulas

Summary To account for shear in buckling pioblems, one uses either the approach of Engesser or the socalled modified approach, proposed by Haringx in connection with helical springs. Both are based on onedimensional reasoning. While most authors seem to prefer the second method, Nänni [4] has shown by means of the three-dimensional theory of elasticity that, for bars, the first one is superior. The present paper is based on a more fundamental one-dimensional approach and confirms Nänni's and hence Engesser's results. It also shows that, together with shear, shortening of the bar must be taken into account, and it improves Engesser's formulas accordingly. It finally shows why Haringx' approach is correct for springs.

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Argumente für und gegen Engessers Knickformeln

Übersicht Um bei Knickproblemen den Schub zu berücksichtigen, verwendet man entweder das Engessersche oder das sogenannte modifizierte Verfahren, das von Haringx zur Behandlung von Schraubenfedern vorgeschlagen worden ist. Während die meisten Autoren die zweite Methode vorzuziehen scheinen, hat Nänni [4] mittels der dreidimensionalen Elastizitätstheorie gezeigt, daß bei Stäben die erste überlegen ist. Die vorliegende Arbeit stützt sich auf ein fundamentaleres eindimensionales Verfahren und bestätigt Nännis und damit Engessers Ergebnisse. Sie zeigt auch, daß mit dem Schub zusammen die Verkürzung des Stabes zu berücksichtigen ist, und sie verbessert Engessers Formeln dementsprechend. Schließlich zeigt sie, weshalb das Verfahren von Haringx bei Federn korrekt ist.