Complex dynamic behaviour of an economic cycle model

In this paper, we investigate the dynamics of a nonlinear economic cycle model. The necessary and sufficient conditions are given to guarantee the existence and stability of the fixed point. It is also shown that the system undergoes a Neimark–Sacker bifurcation by using center manifold theorem and bifurcation theory. Furthermore, Marotto’s chaos is proved when certain conditions are satisfied. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviour, such as the period-10, -16, -20 orbits, attracting invariant cycles, quasi-periodic orbits, 10-coexisting chaotic attractors, and boundary crisis. Specifically, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method.     

Pseudoverticin, a novel benzoquinone-derived ansamycin antibiotic obtained as new cell cycle inhibitor from Streptomyces pseudoverticillus YN17707

Pseudoverticin (1), a novel benzoquinone-derived ansamycin antibiotic showing cell cycle inhibitory activity, was isolated from the fermentation broth of Streptomyces pseudoverticillus YN17707 together with the known ansamycin antibiotic geldanamycin (2) through a bioassay-guided separation procedure. The structure of 1 was elucidated by spectroscopic methods, being characterized by an ansa bridge the same as that in 2 and a novel benzoquinone-derived moiety. Pseudoverticin (1) arrested the cell cycle of tsFT210 cells at the G0/G1 phase with the MIC value of 2.5 μM.     

Arginine Deiminase Induces Immunogenic Cell Death and Is Enhanced by N-acetylcysteine in Murine MC38 Colorectal Cancer Cells and MDA-MB-231 Human Breast Cancer Cells In Vitro

The use of arginine deiminase (ADI) for arginine depletion therapy is an attractive anticancer approach. Combination strategies are needed to overcome the resistance of severe types of cancer cells to this monotherapy. In the current study, we report, for the first time, that the antioxidant N-acetylcysteine (NAC), which has been used in therapeutic practices for several decades, is a potent enhancer for targeted therapy that utilizes arginine deiminase. We demonstrated that pegylated arginine deiminase (ADI-PEG 20) induces apoptosis and G0/G1 phase arrest in murine MC38 colorectal cancer cells; ADI-PEG 20 induces Ca²⁺ overload and decreases the mitochondrial membrane potential in MC38 cells. ADI-PEG 20 induced the most important immunogenic cell death (ICD)-associated feature: cell surface exposure of calreticulin (CRT). The antioxidant NAC enhanced the antitumor activity of ADI-PEG 20 and strengthened its ICD-associated features including the secretion of high mobility group box 1 (HMGB1) and adenosine triphosphate (ATP). In addition, these regimens resulted in phagocytosis of treated MC38 cancer cells by bone marrow-derived dendritic cells (BMDCs). In conclusion, we describe, for the first time, that NAC in combination with ADI-PEG 20 not only possesses unique cytotoxic anticancer properties but also triggers the hallmarks of immunogenic cell death. Hence, ADI-PEG 20 in combination with NAC may represent a promising approach to treat ADI-sensitive tumors while preventing relapse and metastasis.     

Cytotoxicity and Apoptosis Effects of Curcumin Analogue (2E,6E)-2,6-Bis(2,3-Dimethoxybenzylidine) Cyclohexanone (DMCH) on Human Colon Cancer Cells HT29 and SW620 In Vitro

Colorectal cancer (CRC) is the third most common type of cancer worldwide and a leading cause of cancer death. According to the Malaysian National Cancer Registry Report 2012–2016, colorectal cancer was the second most common cancer in Malaysia after breast cancer. Recent treatments for colon cancer cases have caused side effects and recurrence in patients. One of the alternative ways to fight cancer is by using natural products. Curcumin is a compound of the rhizomes of Curcuma longa that possesses a broad range of pharmacological activities. Curcumin has been studied for decades but due to its low bioavailability, its usage as a therapeutic agent has been compromised. This has led to the development of a chemically synthesized curcuminoid analogue, (2E,6E)-2,6-bis(2,3-dimethoxybenzylidine) cyclohexanone (DMCH), to overcome the drawbacks. This study aims to examine the potential of DMCH for cytotoxicity, apoptosis induction, and activation of apoptosis-related proteins on the colon cancer cell lines HT29 and SW620. The cytotoxic activity of DMCH was evaluated using the [3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide] (MTT) cell viability assay on both of the cell lines, HT29 and SW620. To determine the mode of cell death, an acridine orange/propidium iodide (AO/PI) assay was conducted, followed by Annexin V/FITC, cell cycle analysis, and JC-1 assay using a flow cytometer. A proteome profiler angiogenesis assay was conducted to determine the protein expression. The inhibitory concentration (IC₅₀) of DMCH in SW620 and HT29 was 7.50 ± 1.19 and 9.80 ± 0.55 µg/mL, respectively. The treated cells displayed morphological features characteristic of apoptosis. The flow cytometry analysis confirmed that DMCH induced apoptosis as shown by an increase in the sub-G0/G1 population and an increase in the early apoptosis and late apoptosis populations compared with untreated cells. A higher number of apoptotic cells were observed on treated SW620 cells as compared to HT29 cells. Human apoptosis proteome profiler analysis revealed upregulation of Bax and Bad proteins and downregulation of Livin proteins in both the HT29 and SW620 cell lines. Collectively, DMCH induced cell death via apoptosis, and the effect was more pronounced on SW620 metastatic colon cancer cells, suggesting its potential effects as an antimetastatic agent targeting colon cancer cells.     

Metformin Inhibits the Urea Cycle and Reduces Putrescine Generation in Colorectal Cancer Cell Lines

The urea cycle (UC) removes the excess nitrogen and ammonia generated by nitrogen-containing compound composites or protein breakdown in the human body. Research has shown that changes in UC enzymes are not only related to tumorigenesis and tumor development but also associated with poor survival in hepatocellular, breast, and colorectal cancers (CRC), etc. Cytoplasmic ornithine, the intermediate product of the urea cycle, is a specific substrate for ornithine decarboxylase (ODC, also known as ODC1) for the production of putrescine and is required for tumor growth. Polyamines (spermidine, spermine, and their precursor putrescine) play central roles in more than half of the steps of colorectal tumorigenesis. Given the close connection between polyamines and cancer, the regulation of polyamine metabolic pathways has attracted attention regarding the mechanisms of action of chemical drugs used to prevent CRC, as the drug most widely used for treating type 2 diabetes (T2D), metformin (Met) exhibits antitumor activity against a variety of cancer cells, with a vaguely defined mechanism. In addition, the influence of metformin on the UC and putrescine generation in colorectal cancer has remained unclear. In our study, we investigated the effect of metformin on the UC and putrescine generation of CRC in vivo and in vitro and elucidated the underlying mechanisms. In nude mice bearing HCT116 tumor xenografts, the administration of metformin inhibited tumor growth without affecting body weight. In addition, metformin treatment increased the expression of monophosphate (AMP)-activated protein kinase (AMPK) and p53 in both HCT116 xenografts and colorectal cancer cell lines and decreased the expression of the urea cycle enzymes, including carbamoyl phosphate synthase 1 (CPS1), arginase 1 (ARG1), ornithine trans-carbamylase (OTC), and ODC. The putrescine levels in both HCT116 xenografts and HCT116 cells decreased after metformin treatment. These results demonstrate that metformin inhibited CRC cell proliferation via activating AMPK/p53 and that there was an association between metformin, urea cycle inhibition and a reduction in putrescine generation.     

An aqueous zinc-ion hybrid super-capacitor for achieving ultrahigh-volumetric energy density

Zinc-ion hybrid super-capacitors are regarded as promising safe energy storage systems. However, the relatively low volumetric energy density has become the main bottlenecks in practical applications of portable electronic devices. In this work, the zinc-ion hybrid super-capacitor with high volumetric energy density and superb cycle stability had been constructed which employing the high-density three-dimensional graphene hydrogel as cathode and Zn foil used as anode in 1 mol/L ZnSO₄ electrolyte. Benefiting from the abundant ion transport paths and the abundant active sites for graphene hydrogel with high density and porous structure, the zinc-ion hybrid super-capacitor exhibited an extremely high volumetric energy density of 118.42 Wh/L and a superb power density of 24.00 kW/L, as well as an excellent long cycle life (80% retention after 30,000 cycles at 10 A/g), which was superior to the volumetric energy density of the reported zinc-ion hybrid super-capacitors. This device, based on the fast ion adsorption/desorption on the capacitor-type graphene cathode and reversible Zn²⁺ plating/stripping on the battery-type Zn anode, which will inspire the development of zinc-ion hybrid super-capacitor in miniaturized devices.     

Synthesis of Co-Ni oxide microflowers as a superior anode for hybrid supercapacitors with ultralong cycle life

Li-ion hybrid capacitors (LIHCs), composing of a lithium-ion battery (LIB) type anode and a supercapacitor (SC) type cathode, gained worldwide popularity due to harmonious integrating the virtues of high energy density of LIBs with high power density of SCs. Herein, nanoflakes composed microflower-like Co-Ni oxide (CoNiO) was successfully synthesized by a simple co-precipitation method. The atomic ratio of as-synthesized CoNiO is determined to be 1:3 through XRD and XPS analytical method. As a typical battery-type material, CoNiO and capacitor-type activated polyanilinederived carbon (APDC) were used to assemble LIHCs as the anode and cathode materials, respectively. As a result, when an optimized mass ratio of CoNiO and APDC was 1:2, CoNiO//APDC LIHC could deliver a maximum energy density of 143 Wh kg^-1 at a working voltage of 1-4 V. It is worth mentioning that the LIHC also exhibits excellent cycle stability with the capacitance retention of 78.2% after 15,000 cycles at a current density of 0.5 A g^-1.     

A modified Leslie–Gower predator–prey model with ratio‐dependent functional response and alternative food for the predator

In this work, a modified Leslie–Gower predator–prey model is analyzed, considering an alternative food for the predator and a ratio‐dependent functional response to express the species interaction. The system is well defined in the entire first quadrant except at the origin ( 0 , 0 ) . Given the importance of the origin ( 0 , 0 ) as it represents the extinction of both populations, it is convenient to provide a continuous extension of the system to the origin. By changing variables and a time rescaling, we obtain a polynomial differential equations system, which is topologically equivalent to the original one, obtaining that the non‐hyperbolic equilibrium point ( 0 , 0 ) in the new system is a repellor for all parameter values. Therefore, our novel model presents a remarkable difference with other models using ratio‐dependent functional response. We establish conditions on the parameter values for the existence of up to two positive equilibrium points; when this happen, one of them is always a hyperbolic saddle point, and the other can be either an attractor or a repellor surrounded by at least one limit cycle. We also show the existence of a separatrix curve dividing the behavior of the trajectories in the phase plane. Moreover, we establish parameter sets for which a homoclinic curve exits, and we show the existence of saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation, and homoclinic bifurcation. An important feature in this model is that the prey population can go to extinction; meanwhile, population of predators can survive because of the consumption of alternative food in the absence of prey. In addition, the prey population can attain their carrying capacity level when predators go to extinction. We demonstrate that the solutions are non‐negatives and bounded (dissipativity and permanence of population in many other works). Furthermore, some simulations to reinforce our mathematical results are shown, and we further discuss their ecological meanings. Copyright © 2017 John Wiley & Sons, Ltd.     

关于1-Lipschitz函数模2~k微分的一个注记

给出了Klimov-Shamir型1-Lipschitz函数的模2~2-微分指标的一个直接计算,修正了Anashin关于模2~2-微分指标的一个结论.进一步地,利用Anashin的模2~2-微分指标定理构造了一大类形如f(x)=u(x)+u~2(x)∨5的单圈1-Lipschitz函数.