Interestingly, dietary Se restriction of Sepp1(-/-) mice maintains relatively high concentrations of selenium in the CNS (Sepp1(-/-) 86 ± 12 ng Se/g, Sepp1(+/+) 99 ± 27 ng Se/g) compared to other tissues that often show 50– 90% reduction in Se content (kidney, testis, liver) . Thus, the CNS appears to demonstrate a priority for sele- nium that goes beyond the capability for selenoprotein P- dependent selenium delivery. Furthermore, Se deficiency induced through dietary restrictions results in disruption of motor function and memory formation [16,25], but these observation may be a result of neuronal cell death in the CNS. Thus, the present studies were performed in order to better define the contribution of selenoprotein P to synaptic function beyond selenium delivery . We find distinct behavioral phenotypic similarities and differences between Sepp1(-/-) mice and selenium defi- ciency. For example, Sepp1(-/-) show normal overall activ- ity and no change in anxiety. In contrast, selenium deficiency in mice have reported decreased activity in the open field test and increased anxiety demonstrated as decreased entry to the center of the field . This sug- gests that cerebellar function is especially sensitive to reduced selenium, which is supported by the deficit in balance and coordination determined by the cerebellum- dependant rotorod test. Spatial learning assessed with the Morris hidden platform test is disrupted in both Sepp1(-/- ) mice and selenium-deficient mice, although the deficit in Sepp1(-/-) mice is subtle and can be overcome with con-
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In Table 3, the associations between mean erythrocyte GPX enzyme activity, concentrations of whole blood selen- ium and plasma selenoprotein P, and the studied polymor- phisms, and within-subject effects between genotype and time for the intervention group, are shown. A difference in mean GPX enzyme activity at baseline was found for the GPX1/rs1050450 polymorphism among participants who were randomized to the intervention ( P = 0.044). This dif- ference in enzyme activity persisted after 13 and 26 weeks’ intervention, resulting in no statistically significant differ- ence in response to the increased selenium intake between genotypes. Mean GPX enzyme activity at baseline among CC homozygotes was 104.1 and 84.0 U/g Hb among vari- ant T-allele carriers (intervention group only — results not shown). There was no interaction between any of the stud- ied polymorphisms and whole blood selenium or plasma selenoprotein P concentrations (Table 3). However, there was a statistically significant difference of − 4.68 ng/mL (95% CI − 8.49, − 0.871) between mean concentration of plasma selenoprotein P at week 26 for variant T-allele and CC homozygotes of the SELENOP /rs3877899 polymorph- ism (Table 3). A mean difference in whole blood selenium for the SELENOP /rs3877899 polymorphism was also seen; however, this association was not statistically significant (difference between means − 5.76 (95% CI − 12.5, 1.01). Results for the control group are presented in Additional file 2. None of the polymorphisms among participants in the control group differed for either of the outcome measures as expected.
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patients also have compromised antioxidant defenses as the result of nutritional deficiencies. The micronutrient selenium is essential for selenoprotein production and is transported from the liver to target tissues via selenoprotein P (SEPP1). Target tissues also produce SEPP1, which is thought to possess an endogenous antioxidant function. Here, we have shown that mice with Sepp1 haploinsufficiency or mutations that disrupt either the selenium transport or the enzymatic domain of SEPP1 exhibit increased colitis-associated carcinogenesis as the result of increased genomic instability and promotion of a protumorigenic microenvironment. Reduced SEPP1 function markedly increased M2-polarized macrophages, indicating a role for SEPP1 in macrophage polarization and immune function. Furthermore, compared with partial loss, complete loss of SEPP1 substantially reduced tumor burden, in part due to increased apoptosis. Using intestinal organoid cultures, we found that, compared with those from WT animals, Sepp1-null cultures display increased stem cell characteristics that are coupled with increased ROS production, DNA damage, proliferation, decreased cell survival, and modulation of WNT signaling in response to H 2 O 2 -mediated oxidative stress. Together, these data demonstrate that SEPP1 influences inflammatory tumorigenesis by affecting genomic stability, the inflammatory microenvironment, and epithelial stem cell functions.
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Die biochemischen Mechanismen, die zu einer Verbesserung des klinischen Verlaufs bei höheren Selenkonzentrationen, z. B. durch eine Selensubstitution führen, sind derzeit nicht vollends geklärt (94) und werden wohl aufgrund der beschriebenen multiplen Funktionen und Regulationsmechanismen auch in Kürze nicht lückenlos zu erfassen sein. Angenommen werden kann aber, dass die gesteigerte Aktivität von Selenoenzymen, wie der Glutathionperoxidase, der Thioredoxinreduktase und dem Selenoprotein P, sowie die direkte antioxidative Kapazität des verabreichten Selens das Redoxgleichgewicht positiv beeinflussen, indem freie Radikale und Zwischenprodukte des Cyclooxigenase- und Lipooxygenase Pathways reduziert und die Ausschüttung von Prostaglandinen und Leukotrienen gemindert werden und es dadurch zu einer protektiven Funktion vor oxidativen Schäden am Endothel kommt (34), (35), (37), (38), (39). In einer 2007 groß angelegten Multicenterstudie, die die Wirksamkeit einer Hochdosisergänzung mit Selen bei Patienten im septischen Schock stärkt, wird die Überlegung geäußert, dass Selenoprotein P unter einer Selensupplementierung schnell zum Schutz der Endothelzellen gebildet wird (94). In Tierversuchen kam es nach Selengabe zu einer Aktivitätssteigerung der Selenoenzyme mit resultierender verminderten NF-ϰB- assoziierten Zytokinausbildung, gefolgt von weniger Gewebeschaden (94). Neben seiner essentiellen Bedeutung für die Aktivität der Selenoproteine führt Selen auch zu einer Verbesserung verschiedener anderer Funktionen des Immunsystems, wie der Phagozytose, sowie der Bildung von Zellen der unspezifischen Abwehr und Antikörpern (38), (81), (94). Das könnte die Folgen der posttraumatischen Phase der Immunparalyse mindern.
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ABSTRACT Selenoprotein P (Sepp) is an extracellular glycoprotein which functions principally as a selenium (Se) transporter and antioxidant. In order to assess the spatiotemporal expression of the Sepp gene during mouse embryogenesis, quantitative RT-PCR and in situ hybridization analyses were conducted in embryos and extraembryonic tissues, including placenta. Sepp mRNA expression was detected in all embryos and extraembryonic tissues on embryonic days (E) 7.5 to 18.5. Sepp mRNA levels were high in extraembryonic tissues, as compared to embryos, on E 7.5- 13.5. However, the levels were higher in embryos than in extraembryonic tissues on E 14.5-15.5, but were similar in both tissues during the subsequent periods prior to birth. According to the results of in situ hybridization, Sepp mRNA was expressed principally in the ectoplacental cone and neural ectoderm, including the neural tubes and neural folds. In whole embryos, Sepp mRNA was expressed abundantly in nervous tissues on E 9.5-12.5. Sepp mRNA was also expressed in forelimb and hindlimb buds on E 10.5-12.5. In the sectioned embryos, on E 13.5-18.5, Sepp mRNA was expressed persistently in the developing limbs, gastrointestinal tract, nervous tissue, lung, kidney and liver. On E 16.5-18.5, Sepp mRNA expression in the submandibular gland, whisker follicles, pancreas, urinary bladder and skin was apparent. In particular, Sepp mRNA was detected abundantly in blood cells during all the observed developmental periods. These results show that Sepp may function as a transporter of selenium, as well as an antioxidant, during embryogenesis.
ABSTRACT: Effects of different forms of dietary selenium (Se) supplementation on gene expression of cyto- plasmic thioredoxin reductase (TrxR1), selenoprotein P (SelP), and selenoprotein W (SelW) in broilers were investigated. A total of six hundred Ross 308 broilers (1-day-old) with similar body weight were randomly divided into three groups, each of which included 5 replicates of 40 birds. These three treatments received the same basal diet with only background Se level of 0.04 mg Se/kg, supplemented with 0.15 mg Se/kg as sodium selenite (SS) or l-selenomethionine (l-Se-Met) or d-selenomethionine (d-Se-Met) for 42 days. The SS sup- plemented diet increased TrxR1 activity in liver (P < 0.01) and kidney (P < 0.01) as well as SelP concentration in serum (P < 0.05) and liver (P < 0.01) more than the d-Se-Met supplemented diet. The addition of SS also highly increased liver (P < 0.01) and kidney (P < 0.01) TrxR1 activities of broilers in comparison with broilers fed l-Se-Met diet. In addition, liver TrxR1 activity in l-Se-Met group was higher than that in d-Se-Met group (P < 0.05). Liver and kidney mRNA levels of TrxR1 and SelP as well as breast muscle SelW mRNA level were significantly increased by l- and d-Se-Met supplementation in comparison with SS supplementation (P < 0.01), while the d-Se-Met group showed more effective (P < 0.01) than the l-Se-Met group in increasing the mRNA levels of TrxR1 and SelP in liver and kidney. Therefore, dietary l-Se-Met and d-Se-Met supplementation could improve mRNA levels of different selenoproteins studied and reduce amounts of TrxR1 and SelP in broilers compared with SS. Besides, l-Se-Met is more effective than d-Se-Met in raising TrxR1 activity and decreasing mRNA abundance of TrxR1 and SelP in broilers.
susceptibility to colon cancer. Three selenoproteins have been implicated in both prevention and promotion of cancer: the 15kDa selenoprotein (Sep15) [5–7], thioredoxin reductase 1 (Txnrd1, TR1) , and glutathione peroxidase 2 (GPx2) . Furthermore, studies of single nu- cleotide polymorphisms revealed an association of both TR1 and selenoprotein P (SEPP1) with advanced colorectal adenomas in humans . We previously examined the dual personalities of the first two selenoproteins [7,8,11,12], and here, we have further investigated their interac- tions in their regulation of colon cancer. Sep15 and TR1 belong to the thiol-oxidoreductase group of selenoproteins . TR1 is a major redox-regulator in mammalian cells and is also in- volved in cell proliferation, angiogenesis, transcription, and DNA repair [14,15]. The physio- logical function of Sep15 remains poorly understood, but it may be involved in rearrangement of disulfide bonds or serve as a reductase for incorrectly formed disulfide bonds in misfolded glycoproteins bound to UDP-glucose:glycoprotein-glucosyl-transferase (UGGT) .
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The essential trace element selenium (Se), in the form of selenoproteins, plays a pivotal role in the antioxidant defense system of cell. There are at least 55 selenoproteins that have been identified in mammals. Some antioxidative selenoproteins, such as glutathione peroxidase (GPX), thioredoxin reductase (TrxR), and selenoprotein P (SelP), play a key role in removing potentially damaging lipid hydro-peroxides and hydrogen peroxides and pro- tecting cell from oxidative damage. Some studies indicated that Se supplementation reduced the incidence and severity of mastitis (Yang and Li 2015) and a significant negative correlation ex- isted between whole blood GPX activity and bulk tank milk somatic cell counts (Weiss et al. 1990). Se protected bovine aortic endothelial cells from oxidative damage induced by t-butyl hydroperoxide by increasing GPX1, GPX4, and TrxR1 activities (Miller et al. 2001). The mammary tissue of dairy cattle can express GPX1, GPX4, and TrxR1 (Bru- zelius et al. 2007) and there exists a significant positive correlation between the gene expression for these antioxidative enzymes and proinflamma- tory cytokines (Aitken et al. 2009). These studies suggested that Se may attenuate oxidative stress and decrease the incidence of mastitis through manipulating the gene expression and activities of the key antioxidant selenoprotein enzymes in mammary tissue or mammary epithelial cells of dairy cows. However, the exact mechanism is unclear and needs to be further investigated.
(SelW) and selenoprotein P (SelP), participate in intra- cellular redox homeostasis and play antioxidative roles [3-6]. Tanis, the homolog of Selenoprotein S (SelS), was first characterized as a transmembrane protein in the liver of the Israeli sand rat, Psammomys obesus . SelS expression was later found in a pancreatic β cell line, endothelial cells (ECs), human adipose tissue and skeletal muscle tissue [8-10]. The expression of SelS is related to inflammation and insulin resistance (IR) in liver and adipose tissue [8,11,12]. High expression of SelS protected the pancreatic β cell line, Min6, from oxidative damage induced by H 2 O 2 . Reduced expression of SelS led
ited thyroid dysfunction (raised T4, normal T3, raised reverse T3) suggestive of impaired deiodinase activity in combination with low plasma selenium levels, reflecting deficiencies of circulating red cell GPx, plasma GPx, and selenoprotein P (SEPP1) (Table 1 and Fig- ure 2B), as seen in cases with SECISBP2 mutations. Muscle imaging showed mild signal intensity change (Supplemental Figure 1A; sup- plemental material available online with this article; doi:10.1172/ JCI84747DS1), with negligible SEPN1 expression in his dermal fibroblasts (Figure 2B). Endogenous H 2 O 2 levels in fibroblasts from the proband and a SECISBP2-deficient patient were comparably elevated, consistent with impaired antioxidant defence in both contexts (Supplemental Figure 1B). However, comparison of sele- noprotein expression profiles revealed significant differences, with preservation of housekeeping selenoproteins (e.g., TrxRs, Figure 2, A and B; GPx4, Figure 2B) in cells from the proband compared with SECISBP2 deficiency cases. In contrast, expression of stress-related selenoproteins (e.g., GPx1, GPx3, SEPW1) was similarly reduced in both contexts. Furthermore, comparison of mRNA expression pat- terns indicated markedly reduced transcript levels for some sele- noproteins in SECISBP2 deficiency cases, consistent with known propensity to NMD-mediated mRNA instability in this context (1, 4), whereas selenoprotein mRNA levels in the proband were either normal or slightly increased (Figure 2C). These findings, together with normal SECISBP2 protein expression in the proband (Figure 2B) and failure to identify abnormalities with SECISBP2 sequenc- ing, suggested a defect elsewhere in the Sec-insertion pathway.
Although Se levels in blood and blood compartments are easily accessible markers of human Se nutritional status, Se level itself does not reflect its functional significance. Plasma or serum Se, very often used in various Se inves- tigations, reflects rather short-term Se status, while platelet, leukocyte, and erythrocyte Se reflects its longer-term sta- tus. Two best known selenoprotein biomarkers that have been widely used in discriminating of Se status are as follows: plasma selenoprotein P (SePP1) level and plasma glutathione peroxidase (GPx3) activity. In healthy humans, plasma Se is incorporated as Sec in two selenoproteins: SePP1 (40–70%), GPx3 (20–40%), while 6–10% of Se is bound to albumin in the form of selenomethionine, through the replacement of methionine. Free Se accounts for less than 1% of total plasma Se (Vincent and Forceville 2008). These biomarkers generally reflect the major sources of human body Se, because GPx3 and SePP1 are the unique secreted selenoproteins. GPx3 is mainly synthesized in kidney, where it is produced by the cells of proximal tubular ephitelium and by parietal cells of Bowman’s capsule and then it is released into the plasma (Grom- adzinska et al. 2008; Reeves and Hoffmann 2009). Mam- malian SePP1 that contains multiple Sec residues (10 Sec residues in humans and rodents) is synthesized in liver and then secreted into the blood and transported to other tis- sues. Therefore, SePP1 serves as Se transporter and Se body distribution controller. Recently, specific apolipo- protein E receptor-2 (ApoER2) for SePP1 uptake in brain and testis and ApoER2 homolog—megalin—for SePP1 uptake in kidney proximal tubule epithelial cells were found, suggesting receptor-mediated uptake of Se in these organs (Burk and Hill 2009).
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Certain trace minerals, such as selenium (Se), could be effective in reducing oxidative stress and the severity of several pro-inflammatory-based dairy cow diseases such as mastitis and metritis (Sordillo and Aitken 2009). Se in the form of se- lenoproteins plays a range of biological functions. Certain selenoproteins associated with antioxi- dant functions in dairy cows such as glutathione peroxidase (GPx), thioredoxin reductase (TrxR), and selenoprotein P (SelP) can clean oxygen free radicals and maintain redox balance in tissues and cells. Most studies about rat aortas (Stupin et al. 2017), mice liver (Murano et al. 2018), chicken dendritic cells (Sun et al. 2017), and bovine vascular endothelial cells (Sunde et al. 2009) indicated that the lack of Se or Se supplementation significantly decreased or increased the mRNA level and the activity of GPx1. Lack of Se significantly decreased the mRNA level of TrxR2 in Caco-2 cells of human colonic mucosa (Pagmantidis et al. 2005) and Se supplementation increased the mRNA level of TrxR1 in human Caco-2 cells (Barrera et al. 2012). Se supplementation significantly increased the mRNA level of SelP in human liver and endothe- lial cells (Steinbrenner et al. 2006; Zhang et al. 2017). These results demonstrate that Se may af- fect the antioxidant function of animal tissues or cells by regulating the synthesis of selenoprotein. However, little information is available about the effects of Se on the selenoproteins synthesis and antioxidant functions of BMECs. Based on these observations, a hypothesis is proposed that the antioxidant function and selenoprotein synthesis in BMECs are regulated by Se.
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number of cases of adult-onset diabetes in subjects supplemented with Se alone (200 m g/day as selenomethionine)  that diminished further on follow-up for an additional 18 months . To advance our understanding of the effect of Se on the risk of type-2 diabetes, we used stored plasma samples from the UK PRECISE (PREvention of Cancer by Intervention with SElenium) pilot study to test the effect of Se supplementation on plasma adiponectin, a strong independent predictor of type-2 diabetes risk [16–20]. Adiponectin sensitizes skeletal muscle and liver to the action of insulin and stimulates glucose uptake via the cellular fuel sensor, AMP-activated protein kinase (AMPK) [21;22]. Adipo- nectin has been linked to Se or selenoproteins in a number of ways, though as with the epidemiology, the relationship is not straightforward: (i) circulating selenoprotein P was negatively associated with circulating adiponectin in patients with type-2 diabetes ; (ii) patients with markedly reduced expression of selenoproteins due to a rare defect in the SECISBP2 gene had elevated blood adiponectin and enhanced insulin signalling ; (iii) selenoprotein P knock-out mice had significantly higher blood adiponectin levels than wild-type mice ; (iv) Se supplementation of macrophages increases the production of 15-deoxy-Delta12,14- prostaglanin J2 (15d-PGJ2), an activator of peroxisome prolif- erator-activated nuclear receptor-c (PPAR-c) ; this is relevant because PPAR-c agonists have been shown to increase the expression and protein levels of adiponectin [25,26]; (v) knock- down of selenoprotein P in adipocytes markedly lowered the expression of both adiponectin and PPAR-c . Furthermore, both Se/selenoprotein P and adiponectin are associated with raised HDL cholesterol [20,28,29] and reduced inflammation [20,28,30], and both can affect AMPK, though in opposite directions [4,22]. Most importantly for our study, adiponectin is a useful biomarker of type-2 diabetes risk in non-fasted plasma samples, which ours are, as diurnal variability is minor and there is no noticeable effect of food intake [16,31,32].
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Only a very limited number of studies have explored whether allelic variants of SNPs in selenoprotein genes are associated with altered disease susceptibility, and only three studies have investigated association with CRC or adenoma risk. Variants of a SNP in the promoter of the selenoprotein P gene (SEPP1) were not associated with altered risk of CRC , but a more recent study indicated that three variants in SEPP1 and one in the thioredoxin reductase 1 gene TXNRD1 showed an association with risk of adenoma . In addition, a relatively small case–con- trol study in the United Kingdom showed an association of the C variant of rs713041 in GPX4 with increased risk of CRC . The aim of the present work was to extend these studies by investigating the association between a series of SNPs and CRC risk, focusing on SNPs present in seleno- protein genes and known to be functional. To do this, we analysed DNA from a case–control study of a Korean population.
Während in allen bisher untersuchten prokaryontischen Systemen die SECIS-Elemente innerhalb der codierenden Region der mRNA lokalisiert sind, befinden sie sich in Archaeen im 3'-nicht- translatierten Bereich der mRNA. Folgende Resultate unterstützen diese Tatsache: (a) Die postulierten SECIS-Elemente haben die Merkmale in silico stabile Sekundärstukturen auszubilden, die stark konservierte Bereiche enthalten (siehe Abb. 2). Es konnte gezeigt werden, dass das fruA-SECIS-Element von M. jannaschii in der Tat in vivo auf der mRNA vorhanden ist, als auch, dass es die durch Vorhersagen erwartete Sekundärstruktur einnimmt (Rother et al. 2001a). (b) Die vermuteten SECIS-Elemente sind beschränkt auf den 3'-nicht-translatierten Bereich von potentiellen Selenoprotein-Genen; 3' von anderen Leserahmen finden sie sich nicht. (c) In anderen methanogenen Archaea lassen sich sehr ähnliche Strukturen im 3'-nicht- translatierten Bereich von mRNAs für Selenoproteine ableiten (Halboth und Klein 1992; Vorholt et al. 1997). (d) Die heterologe Expression eines Selenoprotein-Gens aus M. jannaschii in M. maripaludis war nur möglich, wenn das dazugehörige SECIS-Element im 3'-nicht-translatierten Bereich der mRNA vorhanden war. Damit konnte die Natur der archaeellen SECIS-Elemente bewiesen werden.
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Here, we describe affected individuals from 2 families, identi- fied on the basis of elevated circulating thyroxine (T4) levels, but low levels of selenium and selenoproteins (SEPP and GPx3). Their biochemical profile, suggestive of a broader deficiency of deio- dinase enzymes as well as other selenoproteins, was analogous to the phenotype of childhood cases with defects in SECISBP2, reported previously (11, 12). Consistent with this, the probands were compound heterozygous for mutations in the SECISBP2 coding region together with missplicing of transcripts derived from the other allele. In our affected subjects, we observed clini- cal (azoospermia, axial muscular dystrophy, skin photosensitiv- ity, abnormal immune cell function, and marked insulin sensi- tivity) and cellular (increased ROS production, membrane lipid peroxidation and oxidative DNA damage, and accelerated telo- mere shortening) features that could be directly attributed to loss of selenoprotein function. We have also documented cellular deficiencies of additional members of the selenoproteome (e.g., SELH, SELT, SELW, and SELI) whose function is unknown. Our observations define a multisystem disorder involving the defec- tive biosynthesis of many selenoproteins.
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SelM was recently reported as a new selenoprotein containing a 145-amino acid open reading frame along with an in-frame TGA as a Sec codon. Further, homolo- gous SelM proteins have been found in various species, including rat, zebrafish, and other vertebrates, although Sec is conserved among these homologs . Further- more, SelM contributes to spicule formation in the demosponge Suberitesdomuncula . In addition, this protein is tightly correlated with a suppressive or pro- tective role in the pathology of patients with Alzheimer’s disease . However, global changes in total protein ex- pression have never been reported in kidney tissue from Tg rats overexpressing hSelM using 2-DE.
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Table 2 shows the genotype frequencies of SEPS1 in patients with gastric cancer and the control group. The polymorphism at position -105 of SEPS1 was typed in all 574 subjects. Among cases, the distribution of genotypes was as follows: 88.4% were GG, 11.2% were GA, and 0.4% were AA. Among controls, the distribution was as follows: 92.5% were GG, 7.2% were GA, and 0.3% were AA (Table 2). The frequency of SEPS1 polymorphism in the controls and gastric cancer patients did not deviate sig- nificantly from those expected under the Hardy-Weinberg equilibrium (p = 0.42, 0.96 respectively). Among males, compared with the GG genotype, the genotypes GA and AA combined was associated with an increased odds of gastric cancer (OR: 1.97, 95% CI 0.95–4.06, p = 0.067; Table 3).
Cells were collected in 80 μl lysis buffer containing protease inhibitors (Beyotime, China) and were sonicated (SonicsVCX105, USA). The lysate was centrifuged at 12,000 rpm for 20 min at 4 °C and the supernatant was immediately collected for use. Protein concentration was determined using the BCA kit (Beyotime, China). Fifty μg of protein were diluted in sample loading buffer and heated at 95°C for 5 min. The denatured proteins were resolved by 12% sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS–PAGE), and transferred to polyvinylidene difluoride (PVDF) membranes. The membranes were incubated for 2 h at RT in Tris-buffered saline (TBS) containing 5% milk (for SelS) or BSA (for β-actin, p38, p-p38, ERK1/2, and p-ERK1/2), and 0.1% Tween 20 (TBST), followed by overnight incubation at 4°C in specific primary antibodies (anti-SelS from Santa Cruz Biotechnology, diluted 1/500; anti-β-actin, anti-p38, anti-p-p38 anti-ERK1/2, and anti-p-ERK1/2 from Cell Signaling, diluted 1/1000). The membranes were washed and incubated in HRP-conjugated secondary antibody (polyclonal anti-rabbit–horseradish peroxidase from Sigma) at RT for 1h. The blots were visualized and analyzed by a Luminescent Image Analyzer (FUJIFILM LAS-4000) and expressed as a percentage respect to the control group.
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see [2, p. 201] for a proof of this and some related results. However, other limiting behaviours may also be of interest. For example, in the study of the regularity of solutions to the Navier–Stokes equation, it is sometimes of interest to know the limiting behaviour of the p’th power of f p
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