Graphs in the COVID-19 news: a mathematics audit of newspapers in Korea.

Visual displays in the news media become critical during escalating events such as the COVID-19 pandemic, as they facilitate the communication of complex information to the public. This article investigates the use of graphs in Korea's news media during the COVID-19 outbreak. We selected 12 dates that represent turning points in the outbreak of the disease and collected news stories including graphs from seven Korean daily newspapers issued on those dates. First, we analyzed the usage of graphs in COVID-19 news stories. Quantitative analysis of the types and frequency of graphs used in COVID-19 news stories and qualitative analysis of the content of news stories containing graphs were conducted. Second, we identified cases in which readers may be biased by the mathematical misuse of graphs in the news stories covering COVID-19. The implications of these findings for future teaching and learning of graph literacy in school mathematics courses are discussed.

Functionalization of a Triazine Dendrimer Presenting Four Maleimides on the Periphery and a DOTA Group at the Core.

A readily and rapidly accessible triazine dendrimer was manipulated in four steps with 23% overall yield to give a construct displaying four maleimide groups and DOTA. The maleimide groups of the dendrimer are sensitive to hydrolysis under basic conditions. The addition of up to four molecules of water can be observed via mass spectrometry and HPLC. The evolution in the alkene region of the ¹H-NMR--the transformation of the maleimide singlet to the appearance of two doublets--is consistent with imide hydrolysis and not the Michael addition. The hydrolysis events that proceeded over hours are sufficiently slower than the desired thiol addition reactions that occur in minutes. The addition of thiols to maleimides can be accomplished in a variety of solvents. The thiols examined derived from cysteine and include the protected amino acid, a protected dipeptide, and native oligopeptides containing either 9 or 18 amino acids. The addition reactions were monitored with HPLC and mass spectrometry in most cases. Complete substitution was observed for small molecule reactants. The model peptides containing nine or eighteen amino acids provided a mixture of products averaging between 3 and 4 substitutions/dendrimer. The functionalization of the chelate group with gadolinium was also accomplished easily.

Triazine-Substituted and Acyl Hydrazones: Experiment and Computation Reveal a Stability Inversion at Low pH.

Condensation of a hydrazine-substituted s-triazine with an aldehyde or ketone yields an equivalent to the widely used, acid-labile acyl hydrazone. Hydrolysis of these hydrazones using a formaldehyde trap as monitored using HPLC reveals that triazine-substituted hydrazones are more labile than acetyl hydrazones at pH>5. The reactivity trends mirror that of the corresponding acetyl hydrazones, with hydrolysis rates increasing along the series (aromatic aldehyde

Design, synthesis and biological assessment of a triazine dendrimer with approximately 16 Paclitaxel groups and 8 PEG groups.

The synthesis and characterization of a generation three triazine dendrimer that displays a phenolic group at the core for labeling, up to eight 5 kDa PEG chains for solubility, and 16 paclitaxel groups is described. Three different diamine linkers--dipiperidine trismethylene, piperazine, and aminomethylpiperidine--were used within the dendrimer. To generate the desired stoichiometric ratio of 8 PEG chains to 16 paclitaxel groups, a monochlorotriazine was prepared with two paclitaxel groups attached through their 2'-hydroxyls using a linker containing a labile disulfide. This monochlorotriazine was linked to a dichlorotriazine with aminomethylpiperidine. The resulting dichlorotriazine bearing two paclitaxel groups could be reacted with the eight amines of the dendrimer. NMR and MALDI-TOF confirm successful reaction. The eight monochlorotriazines of the resulting material are used as the site for PEGylation affording the desired 2:1 stoichiometry. The target and intermediates were amenable to characterization by (1)H and (13)C NMR, and mass spectrometry. Analysis revealed that 16 paclitaxel groups were installed along with 5-8 PEG chains. The final construct is 63% PEG, 22% paclitaxel, and 15% triazine dendrimer. Consistent with previous efforts and computational models, 5 kDa PEG groups were essential for making the target water-soluble. Molecular dynamics simulations showed a high degree of hydration of the core, and a radius of gyration of 2.8 ± 0.2 nm. The hydrodynamic radius of the target was found to be 15.8 nm by dynamic light scattering, an observation indicative of aggregation. Drug release studies performed in plasma showed slow and identical release in mouse and rat plasma (8%, respectively). SPECT/CT imaging was used to follow biodistribution and tumor uptake. Using a two component model, the elimination and distribution half-lives were 2.65 h and 38.2 h, respectively. Compared with previous constructs, this dendrimer persists in the vasculature longer (17.33 ± 0.88% ID/g at 48 h postinjection), and showed higher tumor uptake. Low levels of dendrimer were observed in lung, liver, and spleen (~6% ID/g). Tumor saturation studies of small prostate cancer tumors (PC3) suggest that saturation occurs at a dose between 23.2 mg/kg and 70.9 mg/kg.

Total synthesis of the spirocyclic imine marine toxin (-)-gymnodimine and an unnatural C4-epimer.

The first total synthesis of the marine toxin (-)-gymnodimine (1) has been accomplished in a convergent manner. A highly diastereo- and enantioselective exo-Diels-Alder reaction catalyzed by a bis-oxazoline Cu(II) catalyst enabled rapid assembly of the spirocyclic core of gymnodimine. The preparation of the tetrahydrofuran fragment utilized a chiral auxiliary based anti-aldol reaction. Two major fragments, spirolactam 56 and tetrahydrofuran 55, were then coupled through an efficient Nozaki-Hiyama-Kishi reaction. An unconventional, ambient temperature t-BuLi-initiated intramolecular Barbier reaction of alkyl iodide 64 was employed to form the macrocycle. A late stage vinylogous Mukaiyama aldol addition of a silyloxyfuran to a complex cyclohexanone 83 appended the butenolide, and a few additional steps provided (-)-gymnodimine (1). A diastereomer of the natural product was also synthesized, C4-epi-gymnodimine (90), derived from the vinylogous Mukaiyama aldol addition.

Bicyclic- and tricyclic-beta-lactones via organonucleophile-promoted bis-cyclizations of keto acids: Enantioselective synthesis of (+)-dihydroplakevulin.

A highly diastereoselective, nucleophile-promoted bis-cyclization process, employing readily available and tractable keto acid substrates, is described. This methodology provides concise access to bicyclic- and tricyclic-beta-lactones bearing tertiary carbinol centers and quaternary carbons, greatly extending the scope of previous routes to bicyclic-beta-lactones from aldehyde acid substrates. The utility of the method was demonstrated by application to an enantioselective synthesis of (+)-dihydroplakevulin A. This and related processes may be revealing a subtle interplay between [2+2] cycloaddition and nucleophile-catalyzed aldol lactonization (NCAL) reaction manifolds.