In this paper, we prove that smooth self-shrinkers in R n+1 , that are entire graphs, are hyperplanes. Previously, Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this paper is that no growth assumption at infinity is needed.

BackgroundL-arabinose isomerase (AI) is a crucial catalyst for the biotransformation of D-galactose to D-tagatose. In previous reports, AIs from thermophilic bacterial strains had been wildly researched, but the browning reaction and by-products formed at high temperatures restricted their applications. By contrast, AIs from mesophilic Bacillus strains have some different features including lower optimal temperatures and lower requirements of metallic cofactors. These characters will be beneficial to the development of a more energy-efficient and safer production process. However, the relevant data about the kinetics and reaction properties of Bacillus AIs in D-tagatose production are still insufficient. Thus, in order to support further applications of these AIs, a comprehensive characterization of a Bacillus AI is needed.ResultsThe coding gene (1422 bp) of Bacillus coagulans NL01 AI (BCAI) was cloned and overexpressed in the Escherichia coli BL21 (DE3) strain. The enzymatic property test showed that the optimal temperature and pH of BCAI were 60 °C and 7.5 respectively. The raw purified BCAI originally showed high activity in absence of outsourcing metallic ions and its thermostability did not change in a low concentration (0.5 mM) of Mn2+ at temperatures from 70 °C to 90 °C. Besides these, the catalytic efficiencies (kcat/Km) for L-arabinose and D-galactose were 8.7 mM-1 min-1 and 1.0 mM-1 min-1 respectively. Under optimal conditions, the recombinant E. coli cell containing BCAI could convert 150 g L-1 and 250 g L-1 D-galactose to D-tagatose with attractive conversion rates of 32 % (32 h) and 27 % (48 h).ConclusionsIn this study, a novel AI from B. coagulans NL01was cloned, purified and characterized. Compared with other reported AIs, this AI could retain high proportions of activity at a broader range of temperatures and was less dependent on metallic cofactors such as Mn2+. Its substrate specificity was understood deeply by carrying out molecular modelling and docking studies. When the recombinant E. coli expressing the AI was used as a biocatalyst, D-tagatose could be produced efficiently in a simple one-pot biotransformation system.Electronic supplementary materialThe online version of this article (doi:10.1186/s12896-016-0286-5) contains supplementary material, which is available to authorized users.

The carboxyl terminus domain of Schizosaccharomyces pombe dicer (yDicerC) was expressed in Escherichia coli as an MBP-fusion protein (MBP-yDicerC). When the E. coli strain was cultured and induced at 25˚C, the MBPyDicerC was partly expressed in the soluble fraction. It was then purified by two step affinity chromatography with amylose resin and Ni-NTA His•Bind® resin. The purified MBP-yDicerC showed double-strand RNA digestion activity. siRNA-like products about 22-nt in length were generated. INTRODUCTONDicer enzymes are the key players in the RNA interference (RNAi) [1] and microRNA pathways [2,3] in eukaryote. In Schizosaccharomyces pombe, dicer is also required for the epigenetic gene silencing at centromeres [4], the initiation of heterochromatin formation [5] and the chromosome segregation [6]. Dicer enzyme belongs to the RNase III superfamily. At least three classes of RNase III have been described based on their structures [7]. The first class only contains one catalytic endonuclease domain and a dsRNA binding domain, and is represented by Escherichia coli RNase III. The second and the third classes of RNase III enzymes were described recently, and their structures are more complicated than those of the first class in that they all contain two catalytic endonuclease domains. Dicer differs from other RNase III enzymes in that it digests long dsRNAs into small interfering RNAs (siRNAs) about 22-nt in length. This is a hallmark of an RNAi response [1]. Several papers studying the mechanism of dicer enzyme have been published, but many questions remain to be answered. Blaszczyk, et al. reported the crystal structure of Aquifex aeolicus RNase III [8]. They proposed a mechanism of dicer cleavage based on the 3-D structure of Aquifex aeolicus RNase III. Carmell and Hannon proposed four possible mechanisms in their review article [7]. It is necessary to elucidate the mechanism by further studies. In this paper, we successfully expressed and purified the nuclease domain of Schizosaccharomyces pombe dicer in Escherichia coli as a Maltose Binding Protein fusion protein. The purified recombinant protein showed double-strand RNA digestion activity, and siRNA-like products about 22-nt in length were generated. As far as we know, this is the first report on expression and purification of a functional fission yeast dicer enzyme in Escherichia coli. This work has paved the way for the further studies on the mechanism of dicer enzyme activity.

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Transcription factor p53 regulates cellular responses to environmental perturbations via the transcriptional activation of downstream target genes. Inappropriate p53 activation can trigger abnormal cellular responses, therefore leading to acute or chronic tissue damage, human developmental syndromes, and neurodegenerative diseases. Antagonists of p53 transcriptional activity provide prospective therapeutic applications and molecular probes. In this article, we identified five 3-phenylquinoline derivatives as potential p53 inhibitors through screening a chemical library consisting of 120 compounds, in which PQ1 was the most active compound. PQ1 had no effect on p53 protein levels and decreased the expression of p53 target gene p21. PQ1 thermally stabilizes the wild-type p53 protein. Further, transcriptomics confirmed that PQ1 exposure generated a similar regulatory effect to transcription profiles with a reported p53 transcriptional inhibitor pifithrin-α. However, compared to pifithrin-α, PQ1 increased the sensitivity of SW480 cells to 5FU. Taken together, PQ1 was a novel antagonist of p53 transcriptional activity. We propose that PQ1 could be developed as a chemical tool to pinpoint the physiological functions of p53 and a novel lead compound for targeting dysfunctional p53 activation.