Brouwer不动点定理的推广及其应用

本文证明了当算子定义域的要求由紧凸集放宽到紧星形体时,Brouwer不动点定理的结论仍然成立,作为推广的Brouwer不动点定理的一个应用,得到了一类非线性方程组解的存在性的一个新结果.

开普勒猜想:历史与现状

1611年,著名天文学家开普勒(J.Kepler)断言: 球堆积的最大密度是π/(18)^(1/2)。换句话说,在一个大立方体中堆放同样的小球,小球总体积与立方体体积之比不超过最佳上界π/(18)^(1/2)(≈0.74048)。这就是困扰世人近四个世纪的著名猜想——开普勒猜想。从开普勒猜想到希尔伯特问题在过去的近四个世纪中,许多科学家通过实验来验证这一断言。在一个大的容器中装满同样的小金属球,得到一个局部球堆积。装入水后。

cytoplasmic domain of tissue factor promotes liver fibrosis in mice

To evaluate the role of tissue factor (TF) and protease activated receptor (PAR)-2 in liver fibrosis. METHODSUsing CCl4 administration for eight weeks, we induced hepatic fibrosis in wild-type C57BL/6 mice and in mice with deletion of the cytoplasmic signalling domain of TF (TF§CT/§CT), deletion of PAR-2 (PAR-2-/-) and combined deletion of TF signalling domain and PAR-2 (TF§CT/§CT/PAR-2-/-). Hepatic fibrosis area was assessed by quantitative imaging of picrosirius red staining. Hepatic collagen content was assessed by hydroxyproline levels. Hepatic stellate cells (αSMA positive) and hepatic macrophages (CD68 positive) were identified by immunohistochemistry. Hepatic gene expression was determined by PCR and liver TGFβ1 content by ELISA. RESULTSCCl4 treated mice with deletion of the PAR-2 gene (PAR-2-/-) and the cytoplasmic domain of TF (TF§CT/§CT) developed significantly less hepatic fibrosis, characterised by reduced liver fibrosis area and hydroxyproline content, compared to control wildtype mice treated with CCl4. The observed reduction in histological fibrosis was accompanied by a significant decrease in the hepatic content of TGFβ, the prototypic fibrogenic cytokine, as well as fewer activated hepatic stellate cells and hepatic macrophages. Deletion of the TF cytoplasmic signalling domain reduced hepatic fibrosis to levels similar to those observed in mice lacking PAR-2 signalling but combined deletion provided no added protection against fibrosis indicating a lack of mutual modulating effects that have been observed in other contexts such as angiogenic responses. CONCLUSIONTissue factor cytoplasmic domain is involved in TF-PAR-2 signalling initiating hepatic fibrosis and is a potential therapeutic target, as its deletion would not impact coagulation.

Effect of ligand of peroxisome proliferator-activated receptor γ on the biological characters of hepatic stellate cells

AIM： To study the effect of rosiglitazone, which is a ligand of peroxisome proliferator-activated receptor gamma （PPARy）, on the expression of PPARy in hepatic stellate cells （HSCs） and on the biological characteristics of HSCs. METHODS： The activated HSCs were divided into three groups： control group, 3 μmol/L rosiglitazone group, and 10 μmol/L rosiglitazone group. The expression of PPARγ, α-smooth muscle actin （α-SMA）, and type Ⅰ and Ⅲ collagen was detected by RT-PCR, Western blot and immunocytochemical staining, respectively. Cell proliferation was determined with methylthiazolyltetrazolium （MTT） colodmetric assay. Cell apoptosis was demonstrated with flow cytometry. RESULTS： The expression of PPARγ at mRNA and protein level markedly increased in HSCs of 10 μmol/L rosiglitazone group （tvalue was 10.870 and 4.627 respectively, P〈0.01 in both）. The proliferation of HSCs in 10 μmol/L rosiglitazone group decreased significantly （t = 5.542, P〈0.01）, α-SMA expression level and type Ⅰ collagen synthesis ability were also reduced VS controls （tvalue = 10.256 and 14.627 respectively, P〈0.01 in both）. The apoptotic rate of HSCs significantly increased in 10 μmol/L rosiglitazone group vs control （X^2= 16.682, P〈0.01）. CONCLUSION： By increasing expression of PPARγ in activated HSCs, rosiglitazone, an agonist of PPARγ, decreases α-SNA expression and type Ⅰ collagen synthesis, inhibits cell proliferation, and induces cell apoptosis.

Female hepatology:Favorable role of estrogen in chronic liver disease with hepatitis B virus infection

Chronic hepatitis B virus (HBV) infection is the most common cause of hepatic fibrosis and hepatocellular carcinoma (HCC),mainly as a result of chronic necroinflammatory liver disease. A characteristic feature of chronic hepatitis B infection,alcoholic liver disease and nonalcoholic fatty liver disease (NAFLD) is hepatic steatosis. Hepatic steatosis leads to an increase in lipid peroxidation in hepatocytes,which,in turn,activates hepatic stellate cells (HSCs). HSCs are the primary target cells for inflammatory and oxidative stimuli,and these cells produce extracellular matrix components. Chronic hepatitis B appears to progress more rapidly in males than in females,and NAFLD,cirrhosis and HCC are predominately diseases that tend to occur in men and postmenopausal women. Premenopausal women have lower hepatic iron stores and a decreased production of proinflammatory cytokines. Hepatic steatosis has been observed in aromatase-deficient mice,and has been shown to decrease in animals after estradiol treatment. Estradiol is a potent endogenous antioxidant which suppresses hepatic fibrosis in animal models,and attenuates induction of redox sensitive transcription factors,hepatocyte apoptosis and HSC activation by inhibiting a generation of reactive oxygen species in primary cultures. Variant estrogen receptors are expressed to a greater extent in male patients with chronic liver disease than in females. These lines of evidence suggest that the greater progression of hepatic fibrosis and HCC in men and postmenopausal women may be due,at least in part,to lower production of estradiol and a reduced response to the action of estradiol. A better understanding of the basic mechanisms underlying the sex-associated differences in hepatic fibrogenesis and carciogenesis may open up new avenues for the prevention and treatment of chronic liver disease.

RELATIONSHIP BETWEEN SOMATOSTATIN RECEPTORS AND ACTIVATION OF HEPATIC STELLATE CELL

Objective To investigate the relationship between expression of somatostatin receptors(SSTRs) and activation of rat hepatic stellate cell (HSC). Methods HSCs were isolated from rats by in situ perfusion and single-step density gradient centrifugation, and then SSTR1-5 mRNA levels in the differentiated first passage HSCs were detected by means of reverse transcription polymerase chain reaction. On the other hand, hepatic fibrosis was induced in adult male Sprague-Dawley rats by carbon tetrachloride intoxication, and the expression of SSTR1-5 in normal as well as fibrotic liver was measured by immunohistochemical staining. Results SSTR mR-NA and SSTR could not be found in freshly isolated rat HSCs and normal rat liver. But SSTR1-3 mRNA appeared as HSCs became wholly activated, and SSTR1-3 could also be identified on the membrane of activated HSCs in the peri-sinusoid space, fibrous septa, etc. Conclusion The expression of SSTR1-3 in the rat HSC is closely related to its activation. This may reflect one of the main negative regulation mechanisms in the course of HSC activation.

TRPC3 is required for the survival, pluripotency and neural differentiation of mouse embryonic stem cells(mESCs)

Transient receptor potential canonical subfamily member 3(TRPC3) is known to be important for neural development and the formation of neuronal networks. Here, we investigated the role of TRPC3 in undifferentiated mouse embryonic stem cells(mESCs) and during the differentiation of mESCs into neurons. CRISPR/Cas9-mediated knockout(KO) of TRPC3 induced apoptosis and the disruption of mitochondrial membrane potential both in undifferentiated mESCs and in those undergoing neural differentiation. In addition, TRPC3 KO impaired the pluripotency of mESCs. TRPC3 KO also dramatically repressed the neural differentiation of mESCs by inhibiting the expression of markers for neural progenitors, neurons, astrocytes and oligodendrocytes.Taken together, our new data demonstrate an important function of TRPC3 with regards to the survival, pluripotency and neural differentiation of mESCs.

A review for dynamics of collective behaviors of network of neurons

The nervous system is composed of a large number of neurons, and the electrical activities of neurons can present multiple modes during the signal transmission between neurons by changing intrinsic bifurcation parameters or under appropriate external forcing. In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons. Finally, some open problems in this field such as electromagnetic radiation on electrical activities of neuron, energy consumption in neurons are presented.

The global star formation law of galaxies revisited in the radio continuum

We study the global star formation law, the relation between the gas and star formation rate （SFR） in a sample of 130 local galaxies with infrared （IR） luminosities spanning over three orders of magnitude （109-1012 Lo）, which includes 91 normal spiral galaxies and 39 （ultra）luminous IR galaxies [（U）LIRGs]. We derive their total （atomic and molecular） gas and dense molecular gas masses using newly available HI, CO and HCN data from the literature. The SFR of galaxies is determined from total IR （8-1000 μm） and 1.4 GHz radio continuum （RC） luminosities. The galaxy disk sizes are defined by the de-convolved elliptical Gaussian FWHM of the RC maps. We derive the galaxy disk-averaged SFRs and various gas surface densities, and investigate their relationships. We find that the galaxy disk-averaged surface density of dense molecular gas mass has the tightest correlation with that of SFR （scatter -0.26 dex）, and is linear in log-log space （power-law slope of N=1.03±0.02） across the full galaxy sample. The correlation between the total gas and SFR surface densities for the full sample has a somewhat larger scatter （-0.48 dex）, and is best fit by a power-law with slope 1.45±0.02. However, the slope changes from -1 when only normal spirals are considered, to -1.5 when more and more （U）LIRGs are included in the fitting. When different CO-to-H2 conversion factors are used to infer molecular gas masses for normal galaxies and （U）LIRGs, the bi-modal relations claimed recently in CO observations of high-redshift galaxies appear to also exist in local populations of star-forming galaxies.