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枸杞多糖通过GPX4/AIF通路改善Immp2l^(-/-)小鼠睾丸损伤的研究 被引量:3
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作者 刘春莲 张倩 +5 位作者 张少华 母春兰 陈耀平 焦海燕 徐仙 霍正浩 《中华男科学杂志》 CAS CSCD 北大核心 2021年第5期387-393,共7页
目的:探讨枸杞多糖(LBP)对氧化应激(OS)模型小鼠睾丸生精功能损伤的保护作用及其机制。方法:利用线粒体内膜肽样-2突变(Immp2l^(-/-))小鼠作为独特的OS动物模型,以野生型Immp2l^(+/+)作为正常对照、Immp2l^(-/-)突变小鼠作为阴性对照,... 目的:探讨枸杞多糖(LBP)对氧化应激(OS)模型小鼠睾丸生精功能损伤的保护作用及其机制。方法:利用线粒体内膜肽样-2突变(Immp2l^(-/-))小鼠作为独特的OS动物模型,以野生型Immp2l^(+/+)作为正常对照、Immp2l^(-/-)突变小鼠作为阴性对照,通过饮水喂养给予1.5月龄Immp2l^(-/-)小鼠20 mg/kg浓度LBP作为治疗干预组,3组小鼠于13月龄处死,采用HE染色检测睾丸组织病理变化情况,获取小鼠附睾精子计算其精子常规参数,荧光TUNEL法检测睾丸组织生精细胞凋亡情况,通过免疫组化和Western印迹检测谷胱甘肽过氧化物酶4(GPX4)和凋亡诱导因子(AIF)表达水平。结果:Immp2l^(-/-)小鼠睾丸组织皮质变薄,内见大量空泡样变性且生殖细胞减少,管腔内长形精子数量降低,LBP干预后睾丸组织空泡样病理变化减少,各级生精细胞排列较为整齐。与野生型Immp2l^(+/+)小鼠比较,Immp2l^(-/-)小鼠精子计数[(20.78±1.45)×10^(6)vs(72.89±8.28)×10^(6),P<0.01]、活率[(18.37±2.67)%vs(58.62±6.15)%,P<0.01]和正常形态精子百分率[(20.33±3.17)%vs(65.81±7.69),P<0.01]均显著降低,LBP干预后显著提高了Immp2l^(-/-)小鼠精子计数[(45.25±3.39)×10^(6),P<0.05]、活率[(36.34±4.56)%,P<0.05]和正常形态精子百分率[(38.72±3.63)%,P<0.05]。Immp2l^(-/-)小鼠睾丸组织生精细胞凋亡显著增加,与Immp2l^(+/+)相比具有显著性差异[(7.14±0.78)%vs(1.45±0.43)%,P<0.01],LBP干预Immp2l^(-/-)小鼠后凋亡率显著降低[(2.28±0.07)%,P<0.01]。免疫组化结果显示,LBP干预Immp2l^(-/-)小鼠后GPX4表达显著增加[(1.43±0.17)vs(2.75±0.48),P<0.05],AIF表达显著降低[(2.43±0.15)vs(1.35±0.51),P<0.05]。Western印迹结果显示,LBP可显著提高GPX4并降低AIF在Immp2l^(-/-)小鼠中的表达(P<0.01)。结论:20 mg/kg LBP可能通过GPX4-AIF通路改善Immp2l^(-/-)OS小鼠睾丸生精损伤。 展开更多
关键词 氧化应激 immp2l^(-/-)小鼠 枸杞多糖 睾丸 谷胱甘肽过氧化物酶4/凋亡诱导因子通路
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Expression of Angiopoietin-1/-2 in the Process of Mouse Embryo Implantation 被引量:1
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作者 马华刚 朱桂金 《Journal of Huazhong University of Science and Technology(Medical Sciences)》 SCIE CAS 2007年第2期200-202,共3页
This study examined the expression and distribution of angiopoietin-1/-2 (Ang-1/-2) in the endometrium of early pregnant mice. The expression of Ang-1/-2 was detected by immunohistochemical staining and in situ hybr... This study examined the expression and distribution of angiopoietin-1/-2 (Ang-1/-2) in the endometrium of early pregnant mice. The expression of Ang-1/-2 was detected by immunohistochemical staining and in situ hybridization respectively. Computerized image analysis system was used to measure the average optical intensity of Ang-1/-2 in endometria at different time points after gestation. Mice were randomly divided into 5 groups: control group, D2 group (2 days after pregnancy), D4 group (4 days after pregnancy), D6 group (6 days after pregnancy) and D8 group (8 days after pregnancy), each containing 15 mice. The results showed that the expression of Ang-1 and Ang-2 was very different among 4 groups (P〈0.01). Immunohistochemical staining revealed that Ang-1 was localized in the cytoplasma of stromal cells 2 days after pregnancy (day 2), and in luminal epithelial cells on day 4. The protein of Ang-2 was mainly expressed in the cytoplasma of glandular epithelia and stromal cells. With gestation time, the positive reactions of Ang-1/-2 were stronger in the endometria of the pregnant mice (P〈0.01). In situ hybridization showed Ang-I mRNA in stromal cells on day 2. Hybridization signal was localized in both stromal cells and vessel epithelial cells on day 4; Ang-2 mRNA was expressed in stromal cells and glandular epithelia on day 2; high mRNA levels appeared in stromal cells, glandular epithelia and vascular endothelia on day 4; an increasing in mRNA expression of Ang-1/-2 was observed on day 6 and day 8 (P〈0.01). It is suggested that Ang-1/-2 may play an important role in the cross-talk between blastocyst and maternal endometrium during the process of embryo implantation. 展开更多
关键词 Ang-1/-2 IMMUNOHISTOCHEMISTRY in situ hybridization ENDOMETRIUM KM mouse
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Comparative effects of α2δ-1 ligands in mouse models of colonic hypersensitivity
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作者 Mathieu Meleine Ludivine Boudieu +8 位作者 Agathe Gelot Emilie Muller Amandine Lashermes Julien Matricon Celine Silberberg Vassilia Theodorou Alain Eschalier Denis Ardid Frederic A Carvalho 《World Journal of Gastroenterology》 SCIE CAS 2016年第31期7111-7123,共13页
AIM: To investigate anti-hypersensitive effects of α2δ-1 ligands in non-inflammatory and inflammationassociated colonic hypersensitivity(CHS) mouse models.METHODS: To induce an inflammation-associated CHS, 1% dextra... AIM: To investigate anti-hypersensitive effects of α2δ-1 ligands in non-inflammatory and inflammationassociated colonic hypersensitivity(CHS) mouse models.METHODS: To induce an inflammation-associated CHS, 1% dextran sulfate sodium(DSS) was administered to C57Bl/6J male mice, in drinking water, for 14 d. Regarding the non-inflammatory neonatal maternal separation(NMS)-induced CHS model, wild-type C57BI/6J pups were isolated from their mother from day 2 to day 14(P2 to P14), three hours per day(from 9:00 a.m. to 12:00 p.m.). Colorectal distension was performed by inflating distension probe from 20 μL to 100 μL by 20 μL increment step every 10 s. After a first colorectal distension(CRD), drugs were administered subcutaneously, in a cumulative manner,(Gabapentin at 30 mg/kg and 100 mg/kg; Pregabalin at 10 mg/kg and 30 mg/kg; Carbamazepine at 10 mg/kg and 30 mg/kg) and a second CRD was performed one hour after each injection.RESULTS: The visceromotor response(VMR) to CRD was increased by our NMS paradigm protocol in comparison to non-handled(NH) mice, considering the highest distension volumes(80 μL: 0.783 ± 0.056 mV /s vs 0.531 ± 0.034 m V/s, P < 0.05 and 100 μL: 1.087 ± 0.056 m V/s vs 0.634 ± 0.038 m V/s, P < 0.05 for NMS and NH mice, respectively). In the inflammationassociated CHS, DSS-treated mice showed a dramatic and significant increase in VMR at 60 and 80 μL distension volumes when compared to control mice(60 μL: 0.920 ± 0.079 m V/s vs 0.426 ± 0.100 m V/s P < 0.05 and 80 μL: 1.193 ± 0.097 mV /s vs 0.681 ± 0.094 mV /s P < 0.05 for DSS- and Water-treated mice, respectively). Carbamazepine failed to significantly reduce CHS in both models. Gabapentin significantly reduced CHS in the DSS-induced model for both subcutaneous injections at 30 or 100 mg/kg. Pregabalin s i g n i f i c a n t l y r e d u c e d V M R t o C R D i n t h e n o n-inflammatory NMS-induced CHS model for the acute subcutaneous administration of the highest cumulative dose(30 mg/kg) and significantly reduced CHS in lowdose DSS-treated mice in a dose-dependent manner. Finally, the percent decrease of AUC induced by acute GBP or Pregabalin treatment were higher in the inflammatory DSS-induced CHS model in comparison to the non-inflammatory NMS-induced CHS model.CONCLUSION: This preclinical study demonstrates α2δ-1 ligands efficacy on inflammation-associated CHS, highlighting their potential clinical interest in patients with chronic abdominal pain and moderate intestinal inflammation. 展开更多
关键词 NEONATAL maternal separation DEXTRAN sulfate sodium COLONIC HYPERSENSITIVITY mouse models Colorectal DISTENSION α2δ-1 LIGANDS
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l^2-范数下的非线性测度 被引量:5
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作者 王凯明 胡新利 贾双盈 《纺织高校基础科学学报》 CAS 2004年第3期198-200,共3页
考察了l2-范数下非线性算子的测度.类似于矩阵测度对线性系统稳定性的判定,得到了非线性测度对于非线性微分方程系统稳定性的判定定理.
关键词 l^2-范数 非线性测度 稳定性
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一类耦合非线性Schrdinger方程组的L^2-集中性质 被引量:1
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作者 李晓光 张健 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2006年第3期501-506,共6页
在RN(N≥2)空间中讨论一类非线性Schr dinger方程组,得到其整体解的存在性及解的爆破性质,并进一步研究了解的爆破点与L2-集中性质.
关键词 非线性SCHROEDINGER方程 整体解 爆破 爆破点 L^2-集中
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基于TV模型和L^2-模型的图像去噪方案 被引量:4
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作者 杨奋林 郭二冬 《吉首大学学报(自然科学版)》 CAS 2016年第3期39-41,共3页
TV模型是图像去噪中保持图像边缘的模型之一.运用L2-模型从观察图像中提取光滑的草图,然后利用TV模型从残余图像中恢复一些丢失的有用信息,从而有效地避免TV模型的阶梯效应,使得恢复后的图像具有很好的视觉效果.
关键词 图像去噪 L^2-模型 TV模型 阶梯效应
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两两NQD阵列加权和的L^2-收敛性 被引量:1
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作者 李春丽 《湖北大学学报(自然科学版)》 CAS 北大核心 2005年第3期215-217,221,共4页
利用两两NQD列的Kolmogorov不等式,讨论了两两NQD阵列的加权和在Ces?ro一致可积、(H1)或(H2)条件下的L2-收敛性,改进并推广了鞅差阵列加权和的相应结果.
关键词 两两NQD列 CES No.ro→致可积 L^2-收敛
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关于非协调 Wilson 元及其改进型的分析──Ⅰ . 矩形网格部分 : 免于闭锁的 L^2-型误差估计
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作者 冷向 《安徽建筑工业学院学报(自然科学版)》 1997年第2期3-18,共16页
首先证明了经典的非协调Wilson矩形元的逼近阶是1而不是通常被普遍认为的2,其次讨论了非协调Wilson矩形元为什么在计算线性弹性平面应变时会免于闭锁,最后给出了非协调Wilson矩形元的L2-型误差估计。
关键词 WILSON元 逼近性 闭锁 L^2-误差估计
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SYNERGIC CYTOTOXICITY TO GASTRIC CANCER CELLS BY COMBINED USE OF TRICHOSANTHIN ANDRECOMBINANT INTERFERON α-2B
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作者 胡梅洁 张曙 +1 位作者 吴裕忻 江石湖 《Medical Bulletin of Shanghai Jiaotong University》 CAS 2000年第1期44-47,共4页
Objective To investigate a new approach of the combined use of trichosanthin (TCS) andrecombinant interferon alpha - 2b (rIFN α- 2b) against digestive system cancer cells. Methods Detect separatelythe cytotoxicity of... Objective To investigate a new approach of the combined use of trichosanthin (TCS) andrecombinant interferon alpha - 2b (rIFN α- 2b) against digestive system cancer cells. Methods Detect separatelythe cytotoxicity of TCS, rIFN α- 2b and their combination against digestive system cancer cell SGC- 7901.Results In the experiment in vitro, TCS, rIFN α- 2b both had direct, dose dependent cytotoxicity againstSGC - 7901. Their combined use demonstrated a toxicity signijicantly higher than that of the two drugs used alone,showing a signilicant synergic effect. This synergic cytotoxicity was confirmed in the animal experiment.Conclusion Combined use of TCS and rIFN α - 2b decreases the therapeutic dose of TCS and its toxic adverseellect, and this synergic effect is favorable to the clinical use of TCS protein against gastric cancer. 展开更多
关键词 trichosanthin synergic cytotoxicity recombinant interferon α-2b gastric carcinoma nude mouse
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广义BBM-Burgers方程稀疏波解的稳定性(英文) 被引量:1
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作者 蒋咪娜 徐艳玲 《华中师范大学学报(自然科学版)》 CAS CSCD 北大核心 2002年第3期276-280,共5页
考察了如下广义BBM Burgres方程ut+f(u) x =uxx+uxxt,u|t =0 =uo(x)→u±,x→∞ . ( 1)稀疏波解的稳定性 ,即在u-<u+的假设条件下 ,当t→∞ 时 ,Cauchy问题 ( 1)的解满足supx∈R|u(x ,t) -uR(x/t)|→ 0 ,其中uR(x/t)是无粘Bur... 考察了如下广义BBM Burgres方程ut+f(u) x =uxx+uxxt,u|t =0 =uo(x)→u±,x→∞ . ( 1)稀疏波解的稳定性 ,即在u-<u+的假设条件下 ,当t→∞ 时 ,Cauchy问题 ( 1)的解满足supx∈R|u(x ,t) -uR(x/t)|→ 0 ,其中uR(x/t)是无粘Burgers方程黎曼问题ut+f(u) x =0 ,u|t=0 =uR0 (x) =u-,x<0 ,u+,x >0 ,的解 . 展开更多
关键词 广义BBM-BURGERS方程 稀疏波解 稳定性 先验估计 L^2-能量方法 CAUCHY问题 无粘Burgers方程
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带排斥势的非线性Schrdinger方程爆破解的L^2集中率
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作者 罗宏 《应用数学》 CSCD 北大核心 2008年第4期712-717,共6页
本文在RN(N≥2)中研究了临界带排斥势的非线性Schrdinger方程的爆破解,建立了其径向对称爆破解的集中速率的下界.
关键词 非线性SCHRODINGER方程 爆破 L^2-集中率
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抛物-双曲耦合方程组的Crank-Nicolson特征差分格式
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作者 鲁淑霞 《河北大学学报(自然科学版)》 CAS 2002年第3期225-228,共4页
针对抛物 -双曲耦合方程组提出了一种Crank_Nicolson类型的特征差分格式 ,证明了该格式按离散L2 模是收敛的 ,且其收敛阶为O(Δt2 +h2 ) .
关键词 抛物-双曲耦合方程组 Crank-Nicolson特征差分格式 二阶精度 收敛性 离散L^2 收敛阶
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Tumor-associated autoantibodies are useful biomarkers in immunodiagnosis of α-fetoprotein-negative hepatocellular carcinoma 被引量:9
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作者 Ting Wang Mei Liu +11 位作者 Su-Jun Zheng Dan-Dan Bian Jin-Yan Zhang Jia Yao Qing-Fen Zheng A-Meng Shi Wen-Han Li Lu Li Yu Chen Jin-Hai Wang Zhong-Ping Duan Lei Dong 《World Journal of Gastroenterology》 SCIE CAS 2017年第19期3496-3504,共9页
AIM To determine the prevalence and diagnostic value of autoantibodies inα-fetoprotein(AFP)-negative hepatocellular carcinoma(HCC).METHODS Fifty-six serum samples from AFP-negative HCC cases,86 from AFP-positive HCC ... AIM To determine the prevalence and diagnostic value of autoantibodies inα-fetoprotein(AFP)-negative hepatocellular carcinoma(HCC).METHODS Fifty-six serum samples from AFP-negative HCC cases,86 from AFP-positive HCC cases,168 from chronic liver disease cases,and 59 from normal human controls were included in this study.Autoantibodies to nucleophosmin(NPM)1,14-3-3zeta and mouse double minute 2 homolog(MDM2)proteins in AFP-negative HCC serum were evaluated by enzymelinked im munosorbent assay.Partially positive sera were further evaluated by western blotting.Immunohistochemistry was used to detect the expression of three tumor-associated antigens(TAAs)in AFP-negative HCC and normal control tissues.RESULTS The frequency of autoantibodies to the three TAAs in AFP-negative HCC sera was 21.4%,19.6%and 19.6%,which was significantly higher than in the chronic liver disease cases and normal human controls(P<0.01)as well as AFP-positive HCC cases.The sensitivity of the three autoantibodies for diagnosis of AFP-negative HCC ranged from 19.6%to 21.4%,and the specificity was approximately 95%.When the three autoantibodies were combined,the sensitivity reached 30.4%and the specificity reached 91.6%.CONCLUSION Autoantibodies to NPM1,14-3-3zeta and MDM2 may be useful biomarkers for immunodiagnosis of AFP-negative HCC. 展开更多
关键词 α-fetoprotein Nucleophosmin 1 14-3-3zeta mouse double minute 2 homolog IMMUNODIAGNOSIS AUTOANTIBODY Hepatocellular carcinoma
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Isatin decreases Bax protein expression in the substantia nigra of a mouse model of Parkinson's disease 被引量:3
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作者 Jiguo Zhang Fang Zhang +1 位作者 Yanlong Qiu Wang Yue 《Neural Regeneration Research》 SCIE CAS CSCD 2011年第26期2022-2025,共4页
The present study observed the action of 1H-indole-2, 3-dione (isatin) on Bax protein expression in the substantia nigra of a Parkinson's disease animal model. Parkinson's disease-like behaviors were induced in C5... The present study observed the action of 1H-indole-2, 3-dione (isatin) on Bax protein expression in the substantia nigra of a Parkinson's disease animal model. Parkinson's disease-like behaviors were induced in C57BL/6J mice treated with 1-methyl-4-phenyl-1,2, 3, 6-tetrahydropyridine (MPTP) Bax protein expression was significantly reduced in isatin (100, 200 mg/kg)-pretreated mice. Results demonstrate that isatin plays a neuroprotective role in mice treated with MPTP by down-regulating Bax protein expression. 展开更多
关键词 1H-indole-2 3-dione (isatin) Parkinson's disease 1-methyl-4-phenyl-1 2 3 6- tetrahydropyridine Bax mouse neurodegenerative disease neural regeneration
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L^2调和形式与具有常平均曲率的稳定超曲面
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作者 杜伟平 《高校应用数学学报(A辑)》 CSCD 北大核心 2005年第2期225-232,共8页
设M为(n+1)维流形N中完备、非紧、定向的、具有常平均曲率H的强稳定超曲面,文中证明了若N的双Ricci曲率沿M不小于-n2H2,则M上不存在非平凡的L2调和1-形式.
关键词 常平均曲率 强稳定 双Ricci曲率 L^2调和1-形式
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某些平均压缩迭代函数系的不变测度的L^2维数的估计
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作者 孙妍 《数学杂志》 CSCD 北大核心 2004年第6期695-700,共6页
假设F ={f1 ,… ,fm}是定义在Rd上的m个Lipschitz函数 ,形如fi(x) =λ- 1 i x +bi(λi∈Z ) .假定由F产生的迭代函数系 (IFS)是平均压缩的 .本文给出了这种迭代函数系的不变测度的L2 -维数的上、下界的估计 .
关键词 平均压缩迭代函数系 不变测度 L^2-维数
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由Ornstein-Uhlenbeck过程产生的l^2-模平方过程的增量 被引量:2
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作者 林正炎 《科学通报》 EI CAS CSCD 北大核心 1996年第1期6-10,共5页
设{Y(t),-∞<t<∞}={X_k(t),-∞<t<∞}_k=1~∞是一个系数为γ_k和λ_k,K=1,2,…的独立的Ornstein-Uhlenbeck过程序列,也就是说,X_k(·)是一个Gauss过程,EX_k(t)=0,EX_k(s)X_k(t)=γ_k/λ_kexp(λ_k|t-s|),k=1,2,…,其中... 设{Y(t),-∞<t<∞}={X_k(t),-∞<t<∞}_k=1~∞是一个系数为γ_k和λ_k,K=1,2,…的独立的Ornstein-Uhlenbeck过程序列,也就是说,X_k(·)是一个Gauss过程,EX_k(t)=0,EX_k(s)X_k(t)=γ_k/λ_kexp(λ_k|t-s|),k=1,2,…,其中λ_k≥0,λ_k>0.定义ι~2-模平方过程X^2(t)=||Y(t)||~2=sum from k=1 to ∞( X_k^2(t)),-∞<t<∞.文献[1~5]中研究过这个过程.特别是对于它的连续模,已有较理想的结果. 展开更多
关键词 增量 强极限 O-U过程 l^2-模平方过程
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Current humanized mouse models for studying human immunology and HIV-1 immuno-pathogenesis 被引量:12
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作者 MEISSNER Eric 《Science China(Life Sciences)》 SCIE CAS 2010年第2期195-203,共9页
A robust animal model for "hypothesis-testing/mechanistic" research in human immunology and immuno-pathology should meet the following criteria.First,it has well-studied hemato-lymphoid organs and target cel... A robust animal model for "hypothesis-testing/mechanistic" research in human immunology and immuno-pathology should meet the following criteria.First,it has well-studied hemato-lymphoid organs and target cells similar to those of humans.Second,the human pathogens establish infection and lead to relevant diseases.Third,it is genetically inbred and can be manipulated via genetic,immunological and pharmacological means.Many human-tropic pathogens such as HIV-1 fail to infect murine cells due to the blocks at multiple steps of their life cycle.The mouse with a reconstituted human immune system and other human target organs is a good candidate.A number of human-mouse chimeric models with human immune cells have been developed in the past 20 years,but most with only limited success due to the selective engraftment of xeno-reactive human T cells in hu-PBL-SCID mice or the lack of significant human immune responses in the SCID-hu Thy/Liv mouse.This review summarizes the current understanding of HIV-1 immuno-pathogenesis in human patients and in SIV-infected primate models.It also reviews the recent progress in the development of humanized mouse models with a functional human immune system,especially the recent progress in the immunodeficient mice that carry a defective gammaC gene.NOD/SCID/gammaC-/(NOG or NSG) or the Rag2-/-/gammaC-/double knockout (DKO) mice,which lack NK as well as T and B cells (NTB-null mice),have been used to reconstitute a functional human immune system in central and peripheral lymphoid organs with human CD34+ HSC.These NTB-hu HSC humanized models have been used to investigate HIV-1 infection,immuno-pathogenesis and therapeutic interventions.Such models,with further improvements,will contribute to study human immunology,human-tropic pathogens as well as human stem cell biology in the tissue development and function in vivo. 展开更多
关键词 HUMANIZED mouse models HIV-1 NOD/SCID/gammaC-/- Rag2-/-/gammaC-/-
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与年龄相关的非线性时变种群系统的L^2(Q)-解
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作者 庞洪博 程岩 付军 《吉林师范大学学报(自然科学版)》 2007年第2期7-9,共3页
本文讨论与年龄相关的非线性时变种群系统(P)的L2(Q)-解,为进一步研究种群系统的最优控制问题提供了必要的理论基础.
关键词 非线性种群系统 L^2(Q)-
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L^(2)-范数与L^(∞)-范数及其联合管制下的微分方程求解
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作者 杨秋花 黄晴 +1 位作者 吕玉兰 卢卫君 《数学的实践与认识》 2022年第12期169-179,共11页
主要简述Lebesgue积分意义下的L^(2)-范数与L^(k)-范数及L^(∞)-范数,分别从三个方面即环面、一般紧致流形以及向量丛,来探讨Sobolev空间中弱解的存在性问题.特别地,受到Liu Zhu利用Hodge理论求解微分方程的方法的启发,引进两个新的Gree... 主要简述Lebesgue积分意义下的L^(2)-范数与L^(k)-范数及L^(∞)-范数,分别从三个方面即环面、一般紧致流形以及向量丛,来探讨Sobolev空间中弱解的存在性问题.特别地,受到Liu Zhu利用Hodge理论求解微分方程的方法的启发,引进两个新的Green算子■*G_(■)■与■*G_(■)■并证明它们具有拟等距性质,着重讨论在L^(2)-范数与L^(∞)-范数联合限制下算子■*G_(■)■在■-微分方程■Ω+■(i_(φ)Ω)=0的全纯可解性. 展开更多
关键词 L^(2)-范数 L^(∞)-范数 SOBOLEV空间 微分方程的弱解 拟等距
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