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The physiological role of the unfolded protein response in the nervous system
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作者 Shuangchan Wu Wensheng Lin 《Neural Regeneration Research》 SCIE CAS CSCD 2024年第11期2411-2420,共10页
The unfolded protein response(UPR)is a cellular stress response pathway activated when the endoplasmic reticulum,a crucial organelle for protein folding and modification,encounters an accumulation of unfolded or misfo... The unfolded protein response(UPR)is a cellular stress response pathway activated when the endoplasmic reticulum,a crucial organelle for protein folding and modification,encounters an accumulation of unfolded or misfolded proteins.The UPR aims to restore endoplasmic reticulum homeostasis by enhancing protein folding capacity,reducing protein biosynthesis,and promoting protein degradation.It also plays a pivotal role in coordinating signaling cascades to determine cell fate and function in response to endoplasmic reticulum stress.Recent research has highlighted the significance of the UPR not only in maintaining endoplasmic reticulum homeostasis but also in influencing various physiological processes in the nervous system.Here,we provide an overview of recent findings that underscore the UPR’s involvement in preserving the function and viability of neuronal and myelinating cells under physiological conditions,and highlight the critical role of the UPR in brain development,memory storage,retinal cone development,myelination,and maintenance of myelin thickness. 展开更多
关键词 MYELIN NEURON OLIGODENDROCYTE Schwann cell unfolded protein response
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The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization 被引量:1
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作者 Hong-Fei Xiao Qing-Xian Zhang +5 位作者 He-Yi Tan Bin Shi Jun Chen Zhi-Qiang Cheng Jian Zhang Rui Yang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第4期149-160,共12页
The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In or... The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%. 展开更多
关键词 Particle swarm optimization Maximum likelihood expectation maximization Neutron spectrum unfolding Bonner spheres spectrometer Monte Carlo method
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基于Fast Unfolding算法的情感词典扩展方法研究
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作者 陈力 黄树成 《计算机与数字工程》 2023年第2期405-410,共6页
随着互联网技术的发展,越来越多的互联网产品出现了,极大地改变了人们的生活方式。越来越多的人选择在网络上发表自己的观点,分享自己的生活。这些行为带来了大量的数据,其中蕴含着丰富的商业和社会价值。对这些数据进行情感分析就是挖... 随着互联网技术的发展,越来越多的互联网产品出现了,极大地改变了人们的生活方式。越来越多的人选择在网络上发表自己的观点,分享自己的生活。这些行为带来了大量的数据,其中蕴含着丰富的商业和社会价值。对这些数据进行情感分析就是挖掘其背后隐藏价值的过程。论文在SO-PMI算法的基础上,提出将Fast Unfolding算法与PMI相结合,设计并实现FU-PMI算法,并使用准确率、召回率及F1值对算法的有效性进行评判。对比实验表明,论文提出的算法构建的情感词典相比于SO-PMI算法构建的情感词典效果更好,验证了FU-PMI算法的有效性。 展开更多
关键词 情感词典 情感分析 Fast unfolding SO-PMI
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Hypoxia Affects Autophagy in Human Umbilical Vein Endothelial Cells via the IRE1 Unfolded Protein Response
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作者 Zi-qi TAO Bao-zhu WEI +3 位作者 Min ZHAO Xin-xin ZHANG Ya ZHONG Jing WAN 《Current Medical Science》 SCIE CAS 2023年第4期689-695,共7页
Objective:The purpose of this study was to investigate the role of the unfolded protein response,specifically the inositol-requiring enzyme 1(IRE1)signaling pathway,in hypoxia-induced autophagy in human umbilical veno... Objective:The purpose of this study was to investigate the role of the unfolded protein response,specifically the inositol-requiring enzyme 1(IRE1)signaling pathway,in hypoxia-induced autophagy in human umbilical venous endothelial cells(HUVECs).Methods:The expression of IRE1 and autophagy relative protein in HUVECs with hypoxia was explored by Western blotting,qRT-PCR and confocal microscopy.Further,we evaluated the biological effects of HUVECs by tube formation assay and wound healing assay in vitro.Finally,we examined the function of IRE1 in local blood vessels through animal models,Results:Hypoxia activated the IRE1 signaling pathway and induced autophagy in a time-dependent manner in HUVECs and further influenced the biological effects of HUVECs.Intraperitoneal injection of IRE1 inhibitors inhibited local vascular autophagy levels and lipid accumulation in model animals.Conclusion:Hypoxia can induce autophagy and activate the IRE1 signaling pathway in HUVECs and the IRE1 signaling pathway is involved in autophagy in hypoxic conditions. 展开更多
关键词 HYPOXIA AUTOPHAGY endoplasmic reticulum stress unfolded protein response IREl JNK
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Manifold Structure Analysis of Tactical Network Traffic Matrix Based on Maximum Variance Unfolding Algorithm
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作者 Hao Shi Guofeng Wang +2 位作者 Rouxi Wang Jinshan Yang Kaishuan Shang 《Journal of Electronic Research and Application》 2023年第6期42-49,共8页
As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becomin... As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments. 展开更多
关键词 Manifold learning Maximum Variance unfolding(MVU)algorithm Nonlinear dimensionality reduction
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The Role and Mechanism of Unfolded Protein Response Pathway in Tumor Drug Resistance
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作者 Yaqi Han Bingjuan Zhou +2 位作者 Haizhi Qiao Lingyan Wang Jinku Zhang 《Proceedings of Anticancer Research》 2023年第6期65-71,共7页
In the process of tumor proliferation and metastasis,tumor cells encounter hypoxia,low glucose,acidosis,and other stressful environments.These conditions prompt tumor cells to generate endoplasmic reticulum stress(ERS... In the process of tumor proliferation and metastasis,tumor cells encounter hypoxia,low glucose,acidosis,and other stressful environments.These conditions prompt tumor cells to generate endoplasmic reticulum stress(ERS).As a signal mechanism that mitigates ERS in eukaryotic cells,the unfolded protein response(UPR)pathway can activate cells and tissues,regulating pathological activities in various cells,and maintaining ER homeostasis.It forms the most crucial adaptive and defensive mechanism for cells.However,under the continuous influence of chemotherapy drugs,the quantity of unfolded proteins and erroneous proteins produced by tumor cells significantly increases,surpassing the normal regulatory range of UPR.Consequently,ERS fails to function properly,fostering tumor cell proliferation and the development of drug resistance.This review delves into the study of three UPR pathways(PERK,IRE1,and ATF6),elucidating the mechanisms of drug resistance and research progress in the signal transduction pathway of UPR related to cancers.It provides a profound understanding of the role and relationship between UPR and anti-tumor drugs,offering a new direction for effective clinical treatment. 展开更多
关键词 unfolder protein response(UPR) Tumor resistance Activating transcription factor 6(ATF6) Protein kinase RNA-like endoplasmic reticulum kinase(PERK) Inositol requiring enzyme 1(IRE1)
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论Folding/Unfolding程序转换的能力
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作者 朱鸿 《软件学报》 EI CSCD 北大核心 1991年第2期31-41,共11页
本文讨论Burstall与Darlington提出的folding/unfolding系统的程序转换能力,即讨论从一个给定的程序可以推导出什么样的程序。因此,这是正确性与完备性问题的推广。本文证明了可推导性的一个必要条件,并由此得到了该系统提高程序效率的... 本文讨论Burstall与Darlington提出的folding/unfolding系统的程序转换能力,即讨论从一个给定的程序可以推导出什么样的程序。因此,这是正确性与完备性问题的推广。本文证明了可推导性的一个必要条件,并由此得到了该系统提高程序效率的一个界限。该系统的部分正确性和不完备性也均是该条件的推论。 展开更多
关键词 程序转换 FOLDING unfoldING
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Unfolding算法实现的高速并行CRC电路的VLSI设计 被引量:3
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作者 程超 程善美 《微电子学与计算机》 CSCD 北大核心 2002年第12期68-69,共2页
文章通过分析Unfolding算法和被广泛应用的串行CRC校验电路,提出了一种新的高速并行CRC电路,给出了推导过程,并对它的优缺点进行了讨论。
关键词 unfolding算法 高速并行CRC电路 VLSI 设计 超大规模集成电路
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Improvement of Artificial Foldable Wing Models by Mimicking the Unfolding/Folding Mechanism of a Beetle Hind Wing 被引量:6
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作者 Azhar Muhammad Quoc Viet Nguyen +3 位作者 Hoon Cheol Park Do Y.Hwang Doyoung Byun Nam Seo Goo 《Journal of Bionic Engineering》 SCIE EI CSCD 2010年第2期134-141,共8页
In an attempt to realize a flapping wing micro-air vehicle with morphing wings, we report on improvements to our previousfoldable artificial hind wing.Multiple hinges, which were implemented to mimic the bending zone ... In an attempt to realize a flapping wing micro-air vehicle with morphing wings, we report on improvements to our previousfoldable artificial hind wing.Multiple hinges, which were implemented to mimic the bending zone of a beetle hind wing, weremade of small composite hinge plates and tiny aluminum rivets.The buck-tails of rivets were flared after the hinge plates wereassembled with the rivets so that the folding/unfolding motions could be completed in less time, and the straight shape of theartificial hind wing could be maintained after fabrication.Folding and unfolding actions were triggered by electrically-activatedShape Memory Alloy (SMA) wires.For wing folding, the actuation characteristics of the SMA wire actuator were modifiedthrough heat treatment.Through a series of flapping tests, we confirmed that the artificial wings did not fold back and arbitrarilyfluctuate during the flapping motion. 展开更多
关键词 hind wing unfoldING FOLDING shape memory alloy folding ratio artificial wing
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Acinar cell injury induced by inadequate unfolded protein response in acute pancreatitis 被引量:10
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作者 Kaylene Barrera Albert Stanek +7 位作者 Kei Okochi Zuzanna Niewiadomska Cathy Mueller Peiqi Ou Devon John Antonio E Alfonso Scott Tenner Chongmin Huan 《World Journal of Gastrointestinal Pathophysiology》 CAS 2018年第2期37-46,共10页
Acute pancreatitis (AP) is an inflammatory disorder of pancreatic tissue initiated in injured acinar cells. Severe AP remains a significant challenge due to the lack of effective treatment. The widely-accepted autodig... Acute pancreatitis (AP) is an inflammatory disorder of pancreatic tissue initiated in injured acinar cells. Severe AP remains a significant challenge due to the lack of effective treatment. The widely-accepted autodigestion theory of AP is now facing challenges, since inhibiting protease activation has negligible effectiveness for AP treatment despite numerous efforts. Furthermore, accumulating evidence supports a new concept that malfunction of a self-protective mechanism, the unfolded protein response(UPR), is the driving force behind the pathogenesis of AP. The UPR is induced by endoplasmic reticulum(ER) stress, a disturbance frequently found in acinar cells, to prevent the aggravation of ER stress that can otherwise lead to cell injury. In addition, the UPR's signaling pathways control NFκB activation and autophagy flux, and these dysregulations cause acinar cell inflammatory injury in AP, but with poorly understood mechanisms. We therefore summarize the protective role of the UPR in AP, propose mechanistic models of how inadequate UPR could promote NFκB's pro-inflammatory activity and impair autophagy's protective function in acinar cells, and discuss its relevance to current AP treatment. We hope that insight provided in this review will help facilitate the research and management of AP. 展开更多
关键词 ACUTE PANCREATITIS Endoplasmic reticulum stress unfolded PROTEIN response Acinar cell INJURY AUTOPHAGY
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TAR~*:an improved process similarity measure based on unfolding of Petri nets 被引量:4
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作者 WANG Wen-xing 《计算机集成制造系统》 EI CSCD 北大核心 2012年第8期1774-1784,共11页
Determining the similarity degree between process models was very important for their management,reuse,and analysis.Current approaches either focused on process model's structural aspect,or had inefficiency or imp... Determining the similarity degree between process models was very important for their management,reuse,and analysis.Current approaches either focused on process model's structural aspect,or had inefficiency or imprecision in behavioral similarity.Aiming at these problems,a novel similarity measure which extended an existing method named Transition Adjacent Relation(TAR) with improved precision and efficiency named TAR * was proposed.The ability of measuring similarity was extended by eliminating the duplicate tasks without impacting the behaviors.For precision,TARs was classified into repeatable and unrepeatable ones to identify whether a TAR was involved in a loop.Two new kinds of TARs were added,one related to the invisible tasks after the source place and before sink place,and the other representing implicit dependencies.For efficiency,all TARs based on unfolding instead of its reach ability graph of a labeled Petri net were calculated to avoid state space explosion.Experiments on artificial and real-world process models showed the effectiveness and efficiency of the proposed method. 展开更多
关键词 transition adjacent relation unfoldING Petri nets behavioral similarity
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Calibration and Unfolding of the Pulse Height Spectra of Liquid Scintillator-Based Neutron Detectors Using Photon Sources 被引量:3
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作者 谢旭飞 袁熙 +3 位作者 张兴 樊铁栓 陈金象 李湘庆 《Plasma Science and Technology》 SCIE EI CAS CSCD 2012年第6期553-557,共5页
An accurate energy calibration of a 5"× 2" BC501A liquid scintillator-based neutron detector by means of photon sources and the unfolding of pulse height spectra are described. The photon responses were measure... An accurate energy calibration of a 5"× 2" BC501A liquid scintillator-based neutron detector by means of photon sources and the unfolding of pulse height spectra are described. The photon responses were measured with 22Na, 137Cs and 54Mn photon sources and simulated using the GRESP code, which was developed at the Physiknlisch Technische Bundesanstalt in Germany. Pulse height spectra produced by three different photon sources were employed to investigate the effects of the unfolding techniques. It was found that the four unfolding codes of the HEPRO and UMG3.3 packages, including GRAVEL, UNFANA, MIEKE and MAXED, performed well with the test spectra and produced generally consistent results. They could therefore be used to obtain neutron energy spectra in toknmak experiments. 展开更多
关键词 liquid scintillation detector CALIBRATION pulse height spectra unfolding methods
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Unfolding neutron spectra from water-pumping-injection multilayered concentric sphere neutron spectrometer using self-adaptive differential evolution algorithm 被引量:4
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作者 Rui Li Jian-Bo Yang +2 位作者 Xian-Guo Tuo Jie Xu Rui Shi 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2021年第3期41-51,共11页
A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neut... A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neutron spectrometer(WMNS).Specifically,the neutron fluence bounds are estimated to accelerate the algorithm convergence,and the minimum error between the optimal solution and input neutron counts with relative uncertainties is limited to 10^(-6)to avoid unnecessary calculations.Furthermore,the crossover probability and scaling factor are self-adaptively controlled.FLUKA Monte Carlo is used to simulate the readings of the WMNS under(1)a spectrum of Cf-252 and(2)its spectrum after being moderated,(3)a spectrum used for boron neutron capture therapy,and(4)a reactor spectrum.Subsequently,the measured neutron counts are unfolded using the SDENUA.The uncertainties of the measured neutron count and the response matrix are considered in the SDENUA,which does not require complex parameter tuning or an a priori default spectrum.The results indicate that the solutions of the SDENUA agree better with the IAEA spectra than those of MAXED and GRAVEL in UMG 3.1,and the errors of the final results calculated using the SDENUA are less than 12%.The established SDENUA can be used to unfold spectra from the WMNS. 展开更多
关键词 Water-pumping-injection multilayered spectrometer Neutron spectrum unfolding Differential evolution algorithm Self-adaptive control
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The unfolded protein response signaling and retinal Müller cell metabolism 被引量:2
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作者 Kristen Kelly Joshua J.Wang Sarah X.Zhang 《Neural Regeneration Research》 SCIE CAS CSCD 2018年第11期1861-1870,共10页
The retina is one of the most energy demanding tissues in the body. Like most neurons in the central nervous system, retinal neurons consume high amounts of adenosine-5′-triphosphate(ATP) to generate visual signal ... The retina is one of the most energy demanding tissues in the body. Like most neurons in the central nervous system, retinal neurons consume high amounts of adenosine-5′-triphosphate(ATP) to generate visual signal and transmit the information to the brain. Disruptions in retinal metabolism can cause neuronal dysfunction and degeneration resulting in severe visual impairment and even blindness. The homeostasis of retinal metabolism is tightly controlled by multiple signaling pathways, such as the unfolded protein response(UPR), and the close interactions between retinal neurons and other retinal cell types including vascular cells and Müller glia. The UPR is a highly conserved adaptive cellular response and can be triggered by many physiological stressors and pathophysiological conditions. Activation of the UPR leads to changes in glycolytic rate, ATP production, de novo serine synthesis, and the hexosamine biosynthetic pathway, which are considered critical components of Müller glia metabolism and provide metabolic support to surrounding neurons. When these pathways are disrupted, neurodegeneration occurs rapidly. In this review, we summarize recent advance in studies of the UPR in Müller glia and highlight the potential role of the UPR in retinal degeneration through regulation of Müller glia metabolism. 展开更多
关键词 unfolded protein response RETINA Müller glia metabolism NEURODEGENERATION X-box binding protein 1 glycolysis glucose transporter
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Roles of mitochondrial unfolded protein response in mammalian stem cells 被引量:3
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作者 Li-Fang Gu Jia-Qi Chen +1 位作者 Qing-Yin Lin Yan-Zhou Yang 《World Journal of Stem Cells》 SCIE 2021年第7期737-752,共16页
The mitochondrial unfolded protein response(UPRmt)is an evolutionarily conserved adaptive mechanism for improving cell survival under mitochondrial stress.Under physiological and pathological conditions,the UPRmt is t... The mitochondrial unfolded protein response(UPRmt)is an evolutionarily conserved adaptive mechanism for improving cell survival under mitochondrial stress.Under physiological and pathological conditions,the UPRmt is the key to maintaining intracellular homeostasis and proteostasis.Important roles of the UPRmt have been demonstrated in a variety of cell types and in cell development,metabolism,and immune processes.UPRmt dysfunction leads to a variety of pathologies,including cancer,inflammation,neurodegenerative disease,metabolic disease,and immune disease.Stem cells have a special ability to selfrenew and differentiate into a variety of somatic cells and have been shown to exist in a variety of tissues.These cells are involved in development,tissue renewal,and some disease processes.Although the roles and regulatory mechanisms of the UPRmt in somatic cells have been widely reported,the roles of the UPRmt in stem cells are not fully understood.The roles and functions of the UPRmt depend on stem cell type.Therefore,this paper summarizes the potential significance of the UPRmt in embryonic stem cells,tissue stem cells,tumor stem cells,and induced pluripotent stem cells.The purpose of this review is to provide new insights into stem cell differentiation and tumor pathogenesis. 展开更多
关键词 Mitochondrial unfolded protein response MAMMALS Stem cells CANCER
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Equilibrium folding and unfolding dynamics to reveal detailed free energy landscape of src SH3 protein by magnetic tweezers 被引量:2
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作者 苏环环 孙皓 +3 位作者 洪海燕 郭子龙 余平 陈虎 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第7期595-599,共5页
Src SH3 protein domain is a typical two-state protein which has been confirmed by research of denaturant-induced unfolding dynamics.Force spectroscopy experiments by optical tweezers and atomic force microscopy have m... Src SH3 protein domain is a typical two-state protein which has been confirmed by research of denaturant-induced unfolding dynamics.Force spectroscopy experiments by optical tweezers and atomic force microscopy have measured the force-dependent unfolding rates with different kinds of pulling geometry.However,the equilibrium folding and unfolding dynamics at constant forces has not been reported.Here,using stable magnetic tweezers,we performed equilibrium folding and unfolding dynamic measurement and force-jump measurement of src SH3 domain with tethering points at its N-and C-termini.From the obtained force-dependent transition rates,a detailed two-state free energy landscape of src SH3 protein is constructed with quantitative information of folding free energy,transition state barrier height and position,which exemplifies the capability of magnetic tweezers to study protein folding and unfolding dynamics. 展开更多
关键词 protein folding and unfolding magnetic tweezers free energy landscape transition state
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Role of unfolded protein response in lipogenesis 被引量:1
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作者 Ze Zheng, Chunbin Zhang, Kezhong Zhang, Center for Molecular Medicine and Genetics, Wayne State University School of Medicine, Detroit, MI 48201, United States , Department of Immunology and Mic robiology, Wayne State University School of Medicine, Detroit, MI 48201, United States 《World Journal of Hepatology》 CAS 2010年第6期203-207,共5页
The signal transduction network in regulating lipid metabolism is a hot topic of biomedical research. Recent research endeavors reveal that intracellular stress signaling from a cellular organelle called endoplasmic r... The signal transduction network in regulating lipid metabolism is a hot topic of biomedical research. Recent research endeavors reveal that intracellular stress signaling from a cellular organelle called endoplasmic reticulum (ER) is critically involved in lipid homeostasis and the development of metabolic disease. The ER is a site where newly-synthesized proteins are folded and assembled into their three-dimensional structures, modified and transported to their precise cellular destinations. A wide range of biochemical, physiological and pathological stimuli can interrupt the protein folding process in the ER and cause accumulation of unfolded or misfolded proteins in the ER lumen, a condition referred to as ER stress. To cope with this stress condition, the ER has evolved highly-specifi c signaling pathways collectively termed Unfolded Protein Response (UPR) or ER stress response. The UPR regulates transcriptionaland translational programs, affecting broad aspects of cellular metabolism and cell fate. Lipogenesis, the metabolic process of de novo lipid biosynthesis, occurs primarily in the liver where metabolic signals regulate expression of key enzymes in glycolytic and lipogenic pathways. Recent studies suggest that the UPR plays crucial roles in modulating lipogenesis under metabolic conditions. Here we address some of recent representative evidence regarding the role of the UPR in lipogenesis. 展开更多
关键词 Endoplasmic reticulum stress unfolded PROTEIN response LIPOGENESIS HEPATIC LIPID METABOLISM METABOLIC disease
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VERSAL UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS IN MORE GENERAL CASE UNDER TWO EQUIVALENT GROUPS 被引量:1
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作者 李养成 何伟 《Acta Mathematica Scientia》 SCIE CSCD 2008年第4期915-923,共9页
For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using th... For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established. 展开更多
关键词 Equivariant bifurcation problem unfoldING left-right equivalence contact equivalence
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(r, s)-STABILITY OF UNFOLDING OF г-EQUIVARIANT BIFURCATION PROBLEM 被引量:1
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作者 刘恒兴 张敦穆 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期408-418,共11页
In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally ... In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability. 展开更多
关键词 г-equivariant bifurcation problem unfoldING TRANSVERSALITY г-equivariant infinitesimally (r s)-stability г-equivariant (r s)-equivalence.
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Graded Stable Unfoldings in Bifurcation Problems 被引量:1
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作者 Zhang Guo-bin Zhang Dun-mu 《Wuhan University Journal of Natural Sciences》 EI CAS 2000年第3期257-264,共8页
We introduced stability of arbitrary degree number for unfordings of bifurcation problems and established the equivalence of three stabilities. Thom's transversality theory is used to character the new stability.
关键词 Thom-transversality unfoldING BIFURCATION
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