This study was conducted to investigate how the activity and expression of certain paramount antioxidant enzymes respond to grape seed extract (GSE) addition in primary muscle cells of goats. Gluteal primary muscle cells (PMCs) isolated from a 3-week old goat were cultivated as an unstressed cell model, or they were exposed to 100 µM H2O2 to establish a H2O2-stimulated cell model. The activities of catalase (CAT), superoxide dismutases (SOD) and glutathione peroxidases (GPx) in combination with other relevant antioxidant indexes [i.e., reduced glutathione (GSH) and total antioxidant capacity (TAOC)] in response to GSE addition were tested in the unstressed and H2O2-stimulated cell models, and the relative mRNA levels of the CAT, GuZu-SOD, and GPx-1 genes were measured by qPCR. In unstressed PMCs, GSE addition at the dose of 10 µg/ml strikingly attenuated the expression levels of CAT and CuZn-SOD as well as the corresponding enzyme activities. By contrast, in cells pretreated with 100 µM H2O2, the expression and activity levels of these two antioxidant enzymes were enhanced by GSE addition at 10 µg/ml. GSE addition promoted GPx activity in both unstressed and stressed PMCs, while the expression of the GPx 1 gene displayed partial divergence with GPx activity, which was mitigated by GSE addition at 10 µg/ml in unstressed PMCs. GSH remained comparatively stable except for GSE addition to H2O2-stimulated PMCs at 60 µg/ml, in which a dramatic depletion of GSH occurred. Moreover, GSE addition enhanced TAOC in unstressed (but not H2O2-stimulated) PMCs. GSE addition exerted a bidirectional modulating effect on the mRNA levels and activities of CAT and SOD in unstressed and stressed PMCs at a moderate dose, and it only exhibited a unidirectional effect on the promotion of GPx activity, reflecting its potential to improve antioxidant protection in ruminants.

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In this paper we introduce an autoregressive model with seasonal dummy variables in which coe¢ cients of seasonal dummies vary smoothly and deterministically over time. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed, the decomposition being similar to that in well known ARCH and GARCH models. This variance is also allowed to be smoothly and deterministically time-varying. Under regularity conditions, consistency and asymptotic normality of the maximum likelihood estimators of parameters of this model is proved. A test of constancy of the seasonal coe¢ cients is derived. The test is generalised to specifying the parametric structure of the model. A test of constancy over time of the heteroskedastic error variance is presented. The purpose of building this model is to use it for describing changing seasonality in the wellknown monthly central England temperature series. More speci…cally, the idea is to …nd out in which way and by how much the monthly temperatures are varying over time during the period of more than 240 years, if they do. Misspeci…cation tests are applied to the estimated model and the …ndings discussed.

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