In this work we explore the preservation of quasiconvexity and ∞-Poincaré inequality under sphericalization and flattening in the metric setting. The results developed in [22] show the preservation of Ahlfors regularity, doubling property and the p-Poincaré inequality for 1 ≤ p < ∞ under the sphericalization and flattening transformations provided the underlying metric space is annularly quasicovex. In this work, we propose a weaker assumption to still preserve quasiconvexity and ∞-Poincaré inequality, called radially star-like quasiconvexity (corresponding to sphericalization) and meridian-like quasiconvexity (corresponding to flattening) extending in particular a result in [8] to a wider class of metric spaces and covering the case p = ∞ in [22].

Cadmium (Cd) is a major heavy metal pollutant, and Cd toxicity is a serious cause of abiotic stress in the environment. Plants protect themselves against Cd stress through a variety of pathways. In a recent study, we found that mitochondrial pyruvate carriers (MPCs) are involved in Cd tolerance in Arabidopsis (Arabidopsis thaliana). Following the identification of MPCs in yeast (Saccharomyces cerevisiae) in 2012, most studies have focused on the function of MPCs in animals, as a possible approach to reduce the risk of cancer developing. The results of this study show that AtMPC protein complexes are required for Cd tolerance and prevention of Cd accumulation in Arabidopsis. AtMPC complexes are composed of two elements, AtMPC1 and AtMPC2 (AtNRGA1 or AtMPC3). When the formation of AtMPCs was interrupted by the loss of AtMPC1, glutamate could supplement the synthesis of acetyl-coenzyme A and sustain the TCA cycle. With the up-regulation of glutathione synthesis following exposure to Cd stress, the supplementary pathway could not efficiently drive the tricarboxylic acid cycle without AtMPC. The ATP content decreased concomitantly with the deletion of tricarboxylic acid activity, which led to Cd accumulation in Arabidopsis. More importantly, ScMPCs were also required for Cd tolerance in yeast. Our results suggest that the mechanism of Cd tolerance may be similar in other species.

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi-De León, solutions by considering the Dirichlet problem for p-harmonic functions, p > 1, and letting p → 1. Tools developed and used in this paper include the inner perimeter measure of a domain.

Obesity is a serious metabolic syndrome characterized by high levels of cholesterol, lipids in the blood, and intracellular fat accumulation in adipose tissues. It is known that the suppression of adipogenic protein expression is an effective approach for the treatment of obesity, and regulates fatty acid storage and transportation in adipose tissues. The 60% ethanol extract of Grateloupia elliptica (GEE), a red seaweed from Jeju Island in Korea, was shown to exert anti-adipogenic activity in 3T3-L1 cells and in mice with high-fat diet (HFD)-induced obesity. GEE inhibited intracellular lipid accumulation in 3T3-L1 cells, and significantly reduced expression of adipogenic proteins. In vivo experiments indicated a significant reduction in body weight, as well as white adipose tissue (WAT) weight, including fatty liver, serum triglycerides, total cholesterol, and leptin contents. The expression of the adipogenic proteins, SREBP-1 and PPAR-γ, was significantly decreased by GEE, and the expression of the metabolic regulator protein was increased in WAT. The potential of GEE was shown in WAT, with the downregulation of PPAR-γ and C/EBP-α mRNA; in contrast, in brown adipose tissue (BAT), the thermogenic proteins were increased. Collectively, these research findings suggest the potential of GEE as an effective candidate for the treatment of obesity-related issues via functional foods or pharmaceutical agents.

Obesity is associated with several health complications and can lead to the development of metabolic syndrome. Some of its deleterious consequences are related to insulin resistance, which adversely affects blood glucose regulation. At present, there is a growing concern regarding healthy food consumption, owing to awareness about obesity. Seaweeds are well-known for their nutritional benefits. The brown alga Ishige okamurae (IO) has been studied as a dietary supplement and exhibits various biological activities in vitro and in vivo. The bioactive compounds isolated from IO extract are known to possess anti-obesity and anti-diabetic properties, elicited via the regulation of lipid metabolism and glucose homeostasis. This review focuses on IO extract and its bioactive compounds that exhibit therapeutic effects through several cellular mechanisms in obesity and diabetes. The information discussed in the present review may provide evidence to develop nutraceuticals from IO.