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Ginsenoside Rk3 modulates gut microbiota and regulates immune response of group 3 innate lymphoid cells to against colorectal tumorigenesis 被引量:1
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作者 Xue Bai Rongzhan Fu +5 位作者 yannan liu Jianjun Deng Qiang Fei Zhiguang Duan Chenhui Zhu Daidi Fan 《Journal of Pharmaceutical Analysis》 SCIE CAS CSCD 2024年第2期259-275,共17页
The gut microbiota plays a pivotal role in the immunomodulatory and protumorigenic microenvironment of colorectal cancer(CRC).However,the effect of ginsenoside Rk3(Rk3)on CRC and gut microbiota remains unclear.Therefo... The gut microbiota plays a pivotal role in the immunomodulatory and protumorigenic microenvironment of colorectal cancer(CRC).However,the effect of ginsenoside Rk3(Rk3)on CRC and gut microbiota remains unclear.Therefore,the purpose of this study is to explore the potential effect of Rk3 on CRC from the perspective of gut microbiota and immune regulation.Our results reveal that treatment with Rk3 significantly suppresses the formation of colon tumors,repairs intestinal barrier damage,and regulates the gut microbiota imbalance caused by CRC,including enrichment of probiotics such as Akkermansia muciniphila and Barnesiella intestinihominis,and clearance of pathogenic Desulfovibrio.Subsequent metabolomics data demonstrate that Rk3 can modulate the metabolism of amino acids and bile acids,particularly by upregulating glutamine,which has the potential to regulate the immune response.Furthermore,we elucidate the regulatory effects of Rk3 on chemokines and inflammatory factors associated with group 3 innate lymphoid cells(ILC3s)and T helper 17(Th17)signaling pathways,which inhibits the hyperactivation of the Janus kinase-signal transducer and activator of transcription 3(JAK-STAT3)signaling pathway.These results indicate that Rk3 modulates gut microbiota,regulates ILC3s immune response,and inhibits the JAK-STAT3 signaling pathway to suppress the development of colon tumors.More importantly,the results of fecal microbiota transplantation suggest that the inhibitory effect of Rk3 on colon tumors and its regulation of ILC3 immune responses are mediated by the gut microbiota.In summary,these findings emphasize that Rk3 can be utilized as a regulator of the gut microbiota for the prevention and treatment of CRC. 展开更多
关键词 Colorectal cancer GINSENOSIDE Immune cells Gut microbiota
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Research on Chaos of Nonlinear Singular Integral Equation
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作者 yannan liu Yu Wang 《Journal of Applied Mathematics and Physics》 2023年第4期1152-1159,共8页
In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of... In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method. 展开更多
关键词 Lagrange Interpolation Method Nonlinear Singular Integral Equation Iterative Method
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Ginsenoside Rk3 is a novel PI3K/AKT-targeting therapeutics agent that regulates autophagy and apoptosis in hepatocellular carcinoma 被引量:3
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作者 Linlin Qu yannan liu +2 位作者 Jianjun Deng Xiaoxuan Ma Daidi Fan 《Journal of Pharmaceutical Analysis》 SCIE CAS CSCD 2023年第5期463-482,共20页
Hepatocellular carcinoma(HCC)is the third leading cause of cancer death worldwide.Ginsenoside Rk3,an important and rare saponin in heat-treated ginseng,is generated from Rg1 and has a smaller molecular weight.However,... Hepatocellular carcinoma(HCC)is the third leading cause of cancer death worldwide.Ginsenoside Rk3,an important and rare saponin in heat-treated ginseng,is generated from Rg1 and has a smaller molecular weight.However,the anti-HCC efficacy and mechanisms of ginsenoside Rk3 have not yet been characterized.Here,we investigated the mechanism by which ginsenoside Rk3,a tetracyclic triterpenoid rare ginsenoside,inhibits the growth of HCC.We first explored the possible potential targets of Rk3 through network pharmacology.Both in vitro(HepG2 and HCC-LM3 cells)and in vivo(primary liver cancer mice and HCC-LM3 subcutaneous tumor-bearing mice)studies revealed that Rk3 significantly inhibits the proliferation of HCC.Meanwhile,Rk3 blocked the cell cycle in HCC at the G1 phase and induced autophagy and apoptosis in HCC.Further proteomics and siRNA experiments showed that Rk3 regulates the phosphatidylinositol 3-kinase(PI3K)/protein kinase B(AKT)pathway to inhibit HCC growth,which was validated by molecular docking and surface plasmon resonance.In conclusion,we report the discovery that ginsenoside Rk3 binds to PI3K/AKT and promotes autophagy and apoptosis in HCC.Our data strongly support the translation of ginsenoside Rk3 into novel PI3K/AKT-targeting therapeutics for HCC treatment with low toxic side effects. 展开更多
关键词 Hepatocellular carcinoma Ginsenoside Rk3 APOPTOSIS AUTOPHAGY PI3K/AKT pathway
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Recent advances in systemic and local delivery of ginsenosides using nanoparticles and nanofibers 被引量:4
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作者 Jing Zhao Zhiguang Duan +2 位作者 Xiaoxuan Ma yannan liu Daidi Fan 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2021年第2期291-300,共10页
Ginsenosides are the main pharmacologically active constituents of ginseng which have been used in East Asian countries for centuries to modulate blood pressure,metabolism and immune function.Following the technologic... Ginsenosides are the main pharmacologically active constituents of ginseng which have been used in East Asian countries for centuries to modulate blood pressure,metabolism and immune function.Following the technological advances in isolation,purification and mass production,their mechanisms of action are gradually elucidated,providing solid basis for clinical applications.Ginseng extracts(total ginsenosides)and ginsenoside Rg3,CK,Rd have been marketed or entered clinical trials as drugs or dietary supplements.Despite the proven safety and efficacy of some ginsenosides,their applications are hindered by inferior pharmacokinetics such as low solubility,poor membrane permeability and metabolic instability.Nanoparticle formulation of drugs and implantable drug depots are effective strategies to improve the pharmacokinetics of therapeutic agents by enhancing solubility,providing protection,facilitating intracellular transport,and enabling sustained and controlled release.This mini-review summarizes the recent advances in systemic delivery of ginsenosides using liposomes,micelles,albumin-based nanoparticles,and inorganic nanoparticles,as well as local delivery of ginsenosides by electronspun fibrous membranes and hydrogels. 展开更多
关键词 GINSENOSIDES NANOPARTICLES NANOFIBERS Drug delivery
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Translating bacteriophage-derived depolymerases into antibacterial therapeutics:Challenges and prospects 被引量:1
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作者 Honglan Wang yannan liu +1 位作者 Changqing Bai Sharon Shui Yee Leung 《Acta Pharmaceutica Sinica B》 SCIE CAS CSCD 2024年第1期155-169,共15页
Predatory bacteriophages have evolved a vast array of depolymerases for bacteria capture and deprotection.These depolymerases are enzymes responsible for degrading diverse bacterial surface carbohydrates.They are expl... Predatory bacteriophages have evolved a vast array of depolymerases for bacteria capture and deprotection.These depolymerases are enzymes responsible for degrading diverse bacterial surface carbohydrates.They are exploited as antibiofilm agents and antimicrobial adjuvants while rarely inducing bacterial resistance,making them an invaluable asset in the era of antibiotic resistance.Numerous depolymerases have been investigated preclinically,with evidence indicating that depolymerases with appropriate dose regimens can safely and effectively combat different multidrug-resistant pathogens in animal infection models.Additionally,some formulation approaches have been developed for improved stability and activity of depolymerases.However,depolymerase formulation is limited to liquid dosage form and remains in its infancy,posing a significant hurdle to their clinical translation,compounded by challenges in their applicability and manufacturing.Future development must address these obstacles for clinical utility.Here,after unravelling the history,diversity,and therapeutic use of depolymerases,we summarized the preclinical efficacy and existing formulation findings of recombinant depolymerases.Finally,the challenges and perspectives of depolymerases as therapeutics for humans were assessed to provide insights for their further development. 展开更多
关键词 Phage-derived polysaccharide depolymerases Bacteriophage proteins Bacterial capsules Polysaccharide capsules Antibiotic resistance Biofilms Antibacterial therapy Antimicrobial adjuvants Combination treatment
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The advantages of crosstalk during the evolution of the BZR1–ARF6–PIF4 (BAP) module∞
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作者 Runjie Diao Mengru Zhao +2 位作者 yannan liu Zhenhua Zhang Bojian Zhong 《Journal of Integrative Plant Biology》 SCIE CAS CSCD 2023年第12期2631-2644,共14页
The BAP module,comprising BRASSINAZOLE RESISTANT 1(BZR1),AUXIN RESPONSE FACTOR 6(ARF6),and PHYTOCHROME‐INTERACTING FACTOR 4(PIF4),functions as a molecular hub to orchestrate plant growth and development.In Arabidopsi... The BAP module,comprising BRASSINAZOLE RESISTANT 1(BZR1),AUXIN RESPONSE FACTOR 6(ARF6),and PHYTOCHROME‐INTERACTING FACTOR 4(PIF4),functions as a molecular hub to orchestrate plant growth and development.In Arabidopsis thaliana,components of the BAP module physically interact to form a complex system that integrates light,brassinosteroid(BR),and auxin signals.Little is known about the origin and evolution of the BAP module.Here,we conducted comparative genomic and transcriptomic analyses to investigate the evolution and functional diversification of the BAP module.Our results suggest that the BAP module originated in land plants and that theζ,ε,andγwhole‐genome duplication/triplication events contributed to the expansion of BAP module components in seed plants.Comparative transcriptomic analysis suggested that the prototype BAP module arose in Marchantia polymorpha,experienced stepwise evolution,and became established as a mature regulatory system in seed plants.We developed a formula to calculate the signal transduction productivity of the BAP module and demonstrate that more crosstalk among components enables higher signal transduction efficiency.Our results reveal the evolutionary history of the BAP module and provide insights into the evolution of plant signaling networks and the strategies employed by plants to integrate environmental and endogenous signals. 展开更多
关键词 BAP module CROSSTALK origin and evolution signaling networks
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人参皂苷单体定向转化的生物催化及应用进展 被引量:9
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作者 李伟娜 蒋云云 +2 位作者 刘彦楠 李春英 范代娣 《生物工程学报》 CAS CSCD 北大核心 2019年第9期1590-1606,共17页
人参是我国传统中药,药效显著、应用广泛。通过定向修饰与转化人参皂苷糖基可产生高抗癌活性稀有人参皂苷。传统化学法由于制备工艺极其复杂、成本过高,不能应用于临床,微生物及其酶系转化成为解决该瓶颈问题的最可行手段。有关全细胞... 人参是我国传统中药,药效显著、应用广泛。通过定向修饰与转化人参皂苷糖基可产生高抗癌活性稀有人参皂苷。传统化学法由于制备工艺极其复杂、成本过高,不能应用于临床,微生物及其酶系转化成为解决该瓶颈问题的最可行手段。有关全细胞催化、糖苷酶重组表达、固定化及其催化分子识别机制和溶剂工程的生物转化已有大量综述报道,但尚无在人参皂苷转化应用中的系统研究。文中通过对人参皂苷单体生物转化理论和应用研究最新进展的回顾,结合目前广泛采用的生物催化方法的讨论,系统梳理归纳了能够改善产物专一性、提高催化效率,且具有工业应用前景的人参皂苷单体定向转化方法。基于酶分子设计以及离子液体溶剂工程,对人参皂苷单体抗癌药物和食品、保健品市场的开发、规模化制备进行了展望。 展开更多
关键词 人参皂苷 生物催化 全细胞转化 酶法转化 离子液体
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基于POI数据的郑州市主城区生活服务业空间分布特征研究 被引量:32
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作者 张家旗 刘晏男 宋斌玢 《世界地理研究》 CSSCI 北大核心 2022年第2期399-409,共11页
中国经济已经进入服务经济时代,生活服务业是服务经济的重要组成部分,也是国民经济的基础性产业。生活服务业的合理布局可以改善人居生活质量,提升资源利用效率。以郑州市主城区六类生活服务类兴趣点数据为基础,综合运用核密度分析、叠... 中国经济已经进入服务经济时代,生活服务业是服务经济的重要组成部分,也是国民经济的基础性产业。生活服务业的合理布局可以改善人居生活质量,提升资源利用效率。以郑州市主城区六类生活服务类兴趣点数据为基础,综合运用核密度分析、叠置分析、标准差椭圆分析及空间相关性分析等空间分析方法,对郑州市生活服务业空间分布格局特征进行研究。结果发现(:1)餐饮、住宿、购物、医疗、教育培训、运动健身等六类生活服务业的布局在主城区中心五区交界处都出现了连片但不连续的峰值,呈“中心混合集中,边缘分类扩散”的布局模式,且各服务业分布密度较高的地域在空间上有明显的重合性(;2)各类生活服务业之间在空间分布上存在较强相关性,其中餐饮业与其他各类服务业相关性相对较高,而住宿业与其他服务业之间的相关性相对较低(;3)各类生活服务业空间分布中心位置十分接近,均位于二七区与金水区交界处的中心点附近,且各类服务业在空间分布上的方向基本一致,呈西北-东南走向,医疗和教育培训行业的分布范围较为集中,餐饮业和购物行业的分布和服务范围最广(;4)郑州市主城区人口密度分布与生活服务业分布存在不匹配现象,而经济密度高的区域范围与各类生活服务业设施高密度区域基本重合。 展开更多
关键词 生活服务业 POI 空间分布 郑州
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In vivo oxidative stress alters thiol redox status of peroxiredoxin 1 and 6 and impairs rat sperm quality 被引量:4
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作者 yannan liu Cristian O'Flaherty 《Asian Journal of Andrology》 SCIE CAS CSCD 2017年第1期73-79,共7页
Oxidative stress, the imbalance between the production of reactive oxygen species (ROS) and antioxidant activity is a major culprit of male infertility. Peroxiredoxins (PRDXs) are major antioxidant enzymes of mamm... Oxidative stress, the imbalance between the production of reactive oxygen species (ROS) and antioxidant activity is a major culprit of male infertility. Peroxiredoxins (PRDXs) are major antioxidant enzymes of mammalian spermatozoa and are thiol oxidized and inactivated by ROS in a dose-dependent manner. Their deficiency and/or inactivation have been associated with men infertility. The aim of this study was to elucidate the impact of oxidative stress, generated by the in vivo tert-butyl hydroperoxide (tert-BHP) treatment on rat epididymal spermatozoa during their maturation process. Adult Sprague-Dawley males were treated with 300 -moles tert-BHP/kg or saline (control) per day intraperitoneal for 15 days. Lipid peroxidation (2-thibarbituric acid reactive substances assay), total amount and thiol oxidation of PRDXs along with the total amount of superoxide dismutase (SOD), motility and DNA oxidation (8-hydroxy-deoxyguanosine) were determined in epididymal spermatozoa. Total amount of PRDXs and catalase and thiol oxidation of PRDXs were determined in caput and cauda epididymis. While animals were not affected by treatment, their epididymal spermatozoa have decreased motility, increased levels of DNA oxidation and lipid peroxidation along with increased PRDXs (and not SOD) amounts. Moreover, sperm PRDXs were highly thiol oxidized. There was a differential regulation in the expression of PRDX1 and PRDX6 in the epididymis that suggests a segment-specific role for PRDXs. In conclusion, PRDXs are increased in epididymal spermatozoa in an attempt to fight against the oxidative stress generated by tert-BHP in the epididymis. These findings highlight the role of PRDXs in the protection of sperm function and DNA integrity during epididymal maturation. 展开更多
关键词 antioxidant enzymes DNA oxidation EPIDIDYMIS reactive oxygen species SPERMATOZOA thiol oxidation
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3UVH2 and SUVH9 Couple Two Essential Steps For Transcriptional Gene Silencing in Arabidopsis 被引量:2
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作者 Yuqing Jing Han Sun +5 位作者 Wei Yuan Yue Wang Qi Li yannan liu Yan Li Weiqiang Qian 《Molecular Plant》 SCIE CAS CSCD 2016年第8期1156-1167,共12页
In Arabidopsis, an RNA-directed DNA methylation pathway (RdDM) is responsible for de novo establish- ment of DNA methylation and contributes to transcriptional gene silencing. Recently, the microrchidia (MORC)-typ... In Arabidopsis, an RNA-directed DNA methylation pathway (RdDM) is responsible for de novo establish- ment of DNA methylation and contributes to transcriptional gene silencing. Recently, the microrchidia (MORC)-type ATPases were shown to play essential roles in enforcing transcriptional gene silencing of a subset of genes and transposons by regulating the formation of higher-order chromatin architecture. How- ever, how MORC proteins cooperate with the RdDM pathway components to regulate gene expression re- mains largely unclear. In this study, SUVH9 and MORC6 were identified from a screening of suppressors of idml, which is a mutant defective in active DNA demethylation. SUVH9 and MORC6 are required for silencing of two reporter genes and some endogenous genes without enhancing DNA methylation levels. SUVH9, one of SU(VAR)3-9 homologs involved in RdDM, directly interacts with MORC6 and its two close homologs, MORC1 and MORC2. Similar to MORC6, SUVH9 and its homolog SUVH2 are required for hetero- chromatin condensation and formation of 3D chromatin architecture at SDC, and Solo-LTR loci. We propose that SUVH2 and SUVH9 bind to the methylated DNA and facilitate the recruitment of a chromatin- remodeling complex to the target loci in association with MORC proteins. 展开更多
关键词 EPIGENETICS DNA methylation SUVH9 (At4g13460) MORC6 (At1919100) transcriptional genesilencing chromatin remodeling
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Inhibition of cystathionine β-synthase promotes apoptosis and reduces cell proliferation in chronic myeloid leukemia 被引量:2
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作者 Dan Wang Huan Yang +8 位作者 Yun Zhang Rong Hu Dongjie Hu Qunxian Wang yannan liu Mingjing liu Zijun Meng Weihui Zhou Weihong Song 《Signal Transduction and Targeted Therapy》 SCIE CSCD 2021年第3期864-874,共11页
Increased endogenous hydrogen sulfide(H_(2)S)level by cystathionine β-synthase(CBS)has been shown to closely relate tumorigenesis.H_(2)S promotes angiogenesis,stimulates bioenergy metabolism and inhibits selective ph... Increased endogenous hydrogen sulfide(H_(2)S)level by cystathionine β-synthase(CBS)has been shown to closely relate tumorigenesis.H_(2)S promotes angiogenesis,stimulates bioenergy metabolism and inhibits selective phosphatases.However,the role of CBS and H_(2)S in chronic myeloid leukemia(CML)remains elusive.In this study,we found that CBS and H_(2)S levels were increased in the bone marrow mononuclear cells of pediatric CML patients,as well as in the CML-derived K562 cells and CBS expression levels were correlated with different disease phases.Inhibition of CBS reduced the proliferation of the CML primary bone marrow mononuclear cells and induced growth inhibition,apoptosis,cell cycle arrest,and migration suppression in K562 cells and tumor xenografts.The knockdown of CBS expression by shRNA and inhibiting CBS activity by AOAA decreased the endogenous H_(2)S levels,promoted mitochondrial-related apoptosis and inhibited the NF-xB-mediated gene expression.Our study suggests that inhibition of CBS induces cell apoptosis,as well as limits cell proliferation and migration,a potential target for the treatment of chronic myeloid leukemia. 展开更多
关键词 ENDOGENOUS MYELOID METABOLISM
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Conserved termini and adjacent variable region of Twortlikevirus Staphylococcus phages
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作者 Xianglilan Zhang Huaixing Kang +13 位作者 Yuyuan Li Xiaodong liu Yu Yang Shasha Li Guangqian Pei Qiang Sun Peng Shu Zhiqiang Mi Yong Huang Zhiyi Zhang yannan liu Xiaoping An Xiaolu Xu Yigang Tong 《Virologica Sinica》 SCIE CAS CSCD 2015年第6期433-440,共8页
Methicillin-resistant Staphylococcus aureus(MRSA) is an increasing cause of serious infection,both in the community and hospital settings. Despite sophisticated strategies and efforts, the antibiotic options for treat... Methicillin-resistant Staphylococcus aureus(MRSA) is an increasing cause of serious infection,both in the community and hospital settings. Despite sophisticated strategies and efforts, the antibiotic options for treating MRSA infection are narrowing because of the limited number of newly developed antimicrobials. Here, four newly-isolated MRSA-virulent phages, IME-SA1, IMESA2, IME-SA118 and IME-SA119, were sequenced and analyzed. Their genome termini were identified using our previously proposed "termini analysis theory". We provide evidence that remarkable conserved terminus sequences are found in IME-SA1/2/118/119, and, moreover, are widespread throughout Twortlikevirus Staphylococcus phage G1 and K species. Results also suggested that each phage of the two species has conserved 5′ terminus while the 3′ terminus is variable. More importantly, a variable region with a specific pattern was found to be present near the conserved terminus of Twortlikevirus S. phage G1 species. The clone with the longest variable region had variable terminus lengths in successive generations, while the clones with the shortest variable region and with the average length variable region maintained the same terminal length as themselves during successive generations. IME-SA1 bacterial infection experiments showed that the variation is not derived from adaptation of the phage to different host strains. This is the first study of the conserved terminus and variable region of Twortlikevirus S. phages. 展开更多
关键词 Twortlikevirus STAPHYLOCOCCUS PHAGE CONSERVED termini VARIABLE region
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Origin and evolution of green plants in the light of key evolutionary events
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作者 Zhenhua Zhang Xiaoya Ma +5 位作者 yannan liu Lingxiao Yang Xuan Shi Hao Wang Runjie Diao Bojian Zhong 《Journal of Integrative Plant Biology》 SCIE CAS CSCD 2022年第2期516-535,共20页
Green plants(Viridiplantae)are ancient photosynthetic organisms that thrive both in aquatic and terrestrial ecosystems,greatly contributing to the changes in global climates and ecosystems.Significant progress has bee... Green plants(Viridiplantae)are ancient photosynthetic organisms that thrive both in aquatic and terrestrial ecosystems,greatly contributing to the changes in global climates and ecosystems.Significant progress has been made toward understanding the origin and evolution of green plants,and plant biologists have arrived at the consensus that green plants first originated in marine deep-water environments and later colonized fresh water and dry land.The origin of green plants,colonization of land by plants and rapid radiation of angiosperms are three key evolutionary events during the long history of green plants.However,the comprehensive understanding of evolutionary features and molecular innovations that enabled green plants to adapt to complex and changeable environments are still limited.Here,we review current knowledge of phylogenetic relationships and divergence times of green plants,and discuss key morphological innovations and distinct drivers in the evolution of green plants.Ultimately,we highlight fundamental questions to advance our understanding of the phenotypic novelty,environmental adaptation,and domestication of green plants. 展开更多
关键词 ADAPTATION divergence times green plants key innovations PHYLOGENETICS TERRESTRIALIZATION
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Optimal global regularity for minimal graphs over convex domains in hyperbolic space
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作者 You LI yannan liu 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第5期905-914,共10页
We use the concept of the inside-(a,η,h)domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space.As an application,we prove that the Hölder exponent m... We use the concept of the inside-(a,η,h)domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space.As an application,we prove that the Hölder exponent max{1/a,1/(n+1)}for the problem is optimal for any a∈[2,+∞]. 展开更多
关键词 Minimal graph equation optimal regularity global regularity
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Evolution of hypersurfaces by powers of mean curvature minus an external force field
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作者 yannan liu 《Frontiers of Mathematics in China》 SCIE CSCD 2012年第4期717-723,共7页
In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some con... In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality. 展开更多
关键词 Parabolic equation mean curvature flow maximum principle (for tensor)
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Gradient Flow for the Helfrich Functional
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作者 yannan liu 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第6期931-940,共10页
The author studies the L2 gradient flow of the Helfrich functional, which is a functional describing the shapes of human red blood cells. For any λi ≥ 0 and co, the author obtains a lower bound on the lifespan of th... The author studies the L2 gradient flow of the Helfrich functional, which is a functional describing the shapes of human red blood cells. For any λi ≥ 0 and co, the author obtains a lower bound on the lifespan of the smooth solution, which depends only on the concentration of curvature for the initial surface. 展开更多
关键词 Geometric evolution equation Fourth order Energy estimate
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