Colored grains including red, purple, and black rice, purple corn, black barley, and black soybean contain anthocyanins. The present study was designed to (i) identify and quantify the individual anthocyanins and measure the total phenolic content (TPC), (ii) evaluate the antioxidant and alpha-glucosidase inhibitory activity, and (iii) correlate the TPC with total antioxidant activity and alpha-glucosidase inhibitory potency in these colored grains. The TPC was measured using a Folin-Ciocalteu assay, while the total antioxidant activity was determined by a method based on the 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical-scavenging activity. Among all of the studied colored grains, black rice possessed the highest TPC, which was 86 times greater than that of red rice. In addition, black rice had the highest total anthocyanin contents and alpha-glucosidase inhibitory activity. A significant positive correlation of the antioxidant activity and alpha-glucosidase inhibitory activity with total anthocyanin content and TPC was observed in this study. It is concluded that black rice possesses the highest antioxidant activity and alpha-glucosidase inhibitory among all of the colored grains tested and can be further explored as a functional food.

Eleven cultivars of celery, belonging to 2 species, were collected and analyzed for their phenolic compound composition and antioxidant activities. Major phenolic acids identified in the extracts of these celeries were caffeic acid, p-coumaric acid, and ferulic acid, while the identified flavonoids were apigenin, luteolin, and kaempferol. The contents of total phenolics were measured using a Folin-Ciocalteu assay and the total antioxidant capacity was estimated by the 1, 1-diphenyl-2-picrylhydrazyl radical (DPPH) and 2, 2'-azino-bis (3-ethylbenzthiazoline-6-sulphonic acid) (ABTS.(+)) methods. Apigenin was the major flavonoid in these samples and the most abundant phenolic acid was p-coumaric acid. Many of the investigated cultivars had high levels of phenolics and exhibited high antioxidant capacity. Among these 11 cultivars, Shengjie celery had the highest antioxidant activity whereas Tropica had the lowest. An extremely significant positive correlation between the antioxidant activity and the contents of total flavonoids, total phenolic acids, or total phenolics was observed in this study.

Mean field game theory has been developed largely following two routes. One of them, called the direct approach, starts by solving a large-scale game and next derives a set of limiting equations as the population size tends to infinity. The second route is to apply mean field approximations and formalize a fixed point problem by analyzing the best response of a representative player. This paper addresses the connection and difference of the two approaches in a linear quadratic (LQ) setting. We first introduce an asymptotic solvability notion for the direct approach, which means for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies in addition to a mild regularity requirement. We provide a necessary and sufficient condition for asymptotic solvability and show that in this case the solution converges to a mean field limit. This is accomplished by developing a rescaling method to derive a low dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role. We next compare with the fixed point approach which determines a two point boundary value (TPBV) problem, and show that asymptotic solvability implies feasibility of the fixed point approach, but the converse is not true. We further address non-uniqueness in the fixed point approach and examine the long time behavior of the non-symmetric Riccati ODE in the asymptotic solvability problem.Index Terms-Asymptotic solvability, direct approach, fixed point approach, linear quadratic, mean field game, re-scaling, Riccati differential equation.where Ψ is any matrix from A, Q i , Q i f

Aromatic polyketides from marine actinomycetes have received increasing attention due to their unusual structures and potent bioactivities. Compared to their terrestrial counterparts, marine aromatic polyketides have been less discovered and their structural and biological diversities are far from being fully investigated. In this study, we employed a PCR-based genome mining method to discover aromatic polyketides in our marine bacteria collection. Five new atypical angucyclinones, fluostatins M–Q (1–5) featuring a unique 6-5-6-6 ring skeleton, were discovered from one “positive” Streptomyces sp. PKU-MA00045. The structures of fluostatins M–Q (1–5) were elucidated based on comprehensive spectroscopic analyses and the crystallographic structure of fluostatin P (4), which contains the most oxidized A-ring, was solved by X-ray diffraction analysis with Cu Kα radiation. Compared to the published 16 fluostatin analogues, fluostatins M–Q (1–5) contained a different methoxy group attached at C-7 and hydroxy group attached at C-4, enriching the structural diversity of aromatic polyketides from marine actinomycetes. Genome sequencing of Streptomyces sp. PKU-MA00045 revealed the biosynthetic gene cluster of fluostatins M–Q (1–5), which contained different genes and gene organizations compared to known fluostatin gene clusters, facilitating the investigation of the biosynthesis of the unique 6-5-6-6 ring skeleton in all fluostatins.

Nonribosomal peptides from marine Bacillus strains have received considerable attention for their complex structures and potent bioactivities. In this study, we carried out PCR-based genome mining for potential nonribosomal peptides producers from our marine bacterial library. Twenty-one “positive” strains were screened out from 180 marine bacterial strains, and subsequent small-scale fermentation, HPLC and phylogenetic analysis afforded Bacillus sp. PKU-MA00092 and PKU-MA00093 as two candidates for large-scale fermentation and isolation. Ten nonribosomal peptides, including four bacillibactin analogues (1–4) and six bacillomycin D analogues (5–10) were discovered from Bacillus sp. PKU-MA00093 and PKU-MA00092, respectively. Compounds 1 and 2 are two new compounds and the 1H NMR and 13C NMR data of compounds 7 and 9 is first provided. All compounds 1–10 were assayed for their cytotoxicities against human cancer cell lines HepG2 and MCF7, and the bacillomycin D analogues 7–10 showed moderate cytotoxicities with IC50 values from 2.9 ± 0.1 to 8.2 ± 0.2 µM. The discovery of 5–10 with different fatty acid moieties gave us the opportunity to reveal the structure-activity relationships of bacillomycin analogues against these human cancer cell lines. These results enrich the structural diversity and bioactivity properties of nonribosomal peptides from marine Bacillus strains.