Global stability in chemostat-type plankton models with delayed nutrient recycling

In this paper, we consider chemostat-type plankton models in which plankton feeds on a limiting nutrient and the nutrient is supplied at a constant rate and is partially recycled after the death of plankton by bacterial decomposition. We use a distributed delay to describe nutrient recycling and a discrete delay to model the planktonic growth response to nutrient uptake. When one or both delays occur, by constructing Liapunov functionals, we obtain some sufficient conditions for the global attractivity of the positive equilibrium, which can be regarded as estimates of the delays for persistence of global attractivity

Global stability in chemostat-type competition models with nutrient recycling

Abstract. Freedman and Xu [J. Math. Biol., 31 (1993), pp. 513–527] proposed two chemostattype competition models with nutrient recycling. In the first model the recycling is instantaneous, whereas in the second, the recycling is delayed. They carried out the equilibrium analysis and obtained persistence criteria for the models. In this paper, by applying the method of Liapunov functionals we study the global asymptotic stability of the positive equilibria of the models. We also generalize the results to the multispecies competition models with instantaneous and delayed nutrient recycling, respectively. Differing from the dynamics of the usual chemostat models, we find that the competing populations could coexist if there is nutrient recycling and they compete directly. Key words. stability competition model, nutrient recycling, time delay, Liapunov functional, globa

Global stability in chemostat-type equations with distributed delays

Abstract. We consider a chemostat-type model in which a single species feeds on a limiting nutrient supplied at a constant rate. The model incorporates a general nutrient uptake function and two distributed (infinite) delays. The first delay models the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition, and the second delay indicates that the growth of the species depends on the past concentration of the nutrient. By constructing appropriate Liapunov-like functionals, we obtain sufficient conditions for local and global stability of the positive equilibrium of the model. Quantitative estimates on the size of the delays for local and global stability are also obtained with the help of the Liapunov-like functionals. The technique we use in this paper may be used as well to study global stability of other types of physical models with distributed delays

Global properties of vector-host disease models with time delays

Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector-host disease transmission dynamics. In this paper, we propose vector-host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models. The analytic results reveal that the global dynamics of such vector-host disease models with time delays are completely determined by the basic reproduction number. Some specific cases with discrete delay are studied and the corresponding results are improved

Kui Jie Tong Ameliorates Ulcerative Colitis by Regulating Gut Microbiota and NLRP3/Caspase-1 Classical Pyroptosis Signaling Pathway

Ulcerative colitis (UC) is one of the most refractory digestive diseases in the world. Kui jie tong (KJT) is an effective traditional Chinese medicine used clinically to treat UC. This study observed the regulatory effects of KJT on NIMA-related kinase 7- (NEK7-) activated nod-like receptor protein-3 (NLRP3)/caspase-1 classical pyroptosis pathway and intestinal flora in UC model rats. KJT components were analyzed using an ultraperformance liquid chromatography-tandem mass spectrometer (UPLC-MS/MS). A UC Sprague Dawley (SD) rat model was established using sodium dextran sulfate (DSS). Rats were randomly divided into four groups: control group (CG), UC model group (UG), KJT group (KG), and sulfasalazine (SASP) group (SG). After seven days of intervention, each group’s body weight, disease activity index (DAI) scores, and colon length were recorded. Intestinal mucosal injury to each group was observed using hematoxylin-eosin staining. Additionally, we investigated the expression levels of NEK7, NLRP3, ASC, caspase-1, and GSDMD in intestinal mucosa, as well as serum interleukin- (IL-) 1β, IL-18, and IL-33 proinflammatory factors. Intestinal microflora was analyzed using 16s rRNA sequencing. KJT controlled weight loss; decreased DAI scores; restored colon length; improved pathological injury in the colon; inhibited NEK7, NLRP3, ASC, caspase-1, cleaved-caspase-1, GSDMD, and GSDMD-N expression; and decreased IL-1β, IL-18, and IL-33 contents in UG rats’ serum and colon tissue (P <0.001 or P <0.05). KJT also increased Ruminococcaceae, unclassified_f_Ruminococcaceae, and unclassified_g_Ruminococcus_1 levels and decreased Erysipelotrichia, Erysipelotrichales, Erysipelotrichaceae, Turicibacter, and uncultured_bacterium_g_Turicibacter levels. KJT alleviated UC immune-inflammatory responses to NLRP3/caspase-1 by inhibiting the NEK-7-activated classic pyroptosis pathway and improving intestinal microflora

Constitutive expression of OsDof4, encoding a C2-C2 zinc finger transcription factor, confesses its distinct flowering effects under long- and short-day photoperiods in rice (Oryza sativa L.)

Abstract Background Dof (DNA binding with one finger) proteins, a class of plant-specific transcription factors which contain a conserved C2-C2-type zinc finger domain, are involved in many fundamental processes. In the Arabidopsis photoperiod response pathway, CDF (CYCLING DOF FACTOR) proteins have a primary role as acting via transcriptional repression of the direct FLOWERING LOCUS T (FT) activator CONSTANS (CO). Our previous study indicated that one of CDF homologs, OsDOf12, was involved in photoperiodic flowering. However, the functional characterization of other rice CDF like genes is still in progress. Here, we characterized the function of OsDof4 in rice. Results Phylogenic analysis indicated that OsDof4 is closely clustered into the same subgroup with CDFs and OsDof12. The subcellular localization experiment and transcriptional activity assay suggested that OsDof4 may function as a transcription factor. The diurnal expression pattern indicated that OsDof4 was regulated by endogenous circadian clock. Overexpression of OsDof4 led to earlier flowering under natural long-day field conditions (NLDs) and late flowering under natural short-day field conditions (NSDs), respectively. We compared the expression level of key floral genes in vector line and OsDof4-ox lines grown under long-day conditions (LDs) and short-day conditions (SDs). Real-time q-PCR results demonstrated that under LDs, Hd3a, RFT1 and Ehd1 were up-regulated whereas under SDs they were down-regulated. Hd1 was down-regulated at dusk period independent of photoperiods. Conclusions Taken these results together, we may speculate that the abnormal flowering responses in OsDof4-ox plants under LDs and SDs might be mediated by Ehd1 and Hd1