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Allosteric communication mediated by protein contact clusters: A dynamical model 由蛋白质接触簇介导的异构通讯:动力学模型
arXiv - PHYS - Biological Physics Pub Date : 2024-08-27 DOI: arxiv-2408.15110
Ahmed A. A. I. Ali, Emanuel Dorbath, Gerhard Stock
{"title":"Allosteric communication mediated by protein contact clusters: A dynamical model","authors":"Ahmed A. A. I. Ali, Emanuel Dorbath, Gerhard Stock","doi":"arxiv-2408.15110","DOIUrl":"https://doi.org/arxiv-2408.15110","url":null,"abstract":"Allostery refers to the puzzling phenomenon of long-range communication\u0000between distant sites in proteins. Despite its importance in biomolecular\u0000regulation and signal transduction, the underlying dynamical process is not\u0000well understood. This study introduces a dynamical model of allosteric\u0000communication based on \"contact clusters\"-localized groups of highly correlated\u0000contacts that facilitate interactions between secondary structures. The model\u0000shows that allostery involves a multi-step process with cooperative contact\u0000changes within clusters and communication between distant clusters mediated by\u0000rigid secondary structures. Considering time-dependent experiments on a\u0000photoswitchable PDZ3 domain, extensive (in total $sim 500,mu$s) molecular\u0000dynamics simulations are conducted that directly monitor the photoinduced\u0000allosteric transition. The structural reorganization is illustrated by the time\u0000evolution of the contact clusters and the ligand, which affects the nonlocal\u0000coupling between distant clusters. A timescale analysis reveals dynamics from\u0000nano- to microseconds, which are in excellent agreement with the experimentally\u0000measured timescales.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Closed-loop control of active nematic flows 主动向列流动的闭环控制
arXiv - PHYS - Biological Physics Pub Date : 2024-08-26 DOI: arxiv-2408.14414
Katsu Nishiyama, John Berezney, Michael M. Norton, Akshit Aggarwal, Saptorshi Ghosh, Michael F. Hagan, Zvonimir Dogic, Seth Fraden
{"title":"Closed-loop control of active nematic flows","authors":"Katsu Nishiyama, John Berezney, Michael M. Norton, Akshit Aggarwal, Saptorshi Ghosh, Michael F. Hagan, Zvonimir Dogic, Seth Fraden","doi":"arxiv-2408.14414","DOIUrl":"https://doi.org/arxiv-2408.14414","url":null,"abstract":"Living things enact control of non-equilibrium, dynamical structures through\u0000complex biochemical networks, accomplishing spatiotemporally-orchestrated\u0000physiological tasks such as cell division, motility, and embryogenesis. While\u0000the exact minimal mechanisms needed to replicate these behaviors using\u0000synthetic active materials are unknown, controlling the complex, often chaotic,\u0000dynamics of active materials is essential to their implementation as engineered\u0000life-like materials. Here, we demonstrate the use of external feedback control\u0000to regulate and control the spatially-averaged speed of a model active material\u0000with time-varying actuation through applied light. We systematically vary the\u0000controller parameters to analyze the steady-state flow speed and temporal\u0000fluctuations, finding the experimental results in excellent agreement with\u0000predictions from both a minimal coarse-grained model and full\u0000nematohydrodynamic simulations. Our findings demonstrate that\u0000proportional-integral control can effectively regulate the dynamics of active\u0000nematics in light of challenges posed by the constituents, such as sample\u0000aging, protein aggregation, and sample-to-sample variability. As in living\u0000things, deviations of active materials from their steady-state behavior can\u0000arise from internal processes and we quantify the important consequences of\u0000this coupling on the controlled behavior of the active nematic. Finally, the\u0000interaction between the controller and the intrinsic timescales of the active\u0000material can induce oscillatory behaviors in a regime of parameter space that\u0000qualitatively matches predictions from our model. This work underscores the\u0000potential of feedback control in manipulating the complex dynamics of active\u0000matter, paving the way for more sophisticated control strategies in the design\u0000of responsive, life-like materials.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Peptide Classification from Statistical Analysis of Nanopore Translocation Experiments 通过对纳米孔转位实验的统计分析进行多肽分类
arXiv - PHYS - Biological Physics Pub Date : 2024-08-26 DOI: arxiv-2408.14275
Julian Hoßbach, Samuel Tovey, Tobias Ensslen, Jan C. Behrends, Christian Holm
{"title":"Peptide Classification from Statistical Analysis of Nanopore Translocation Experiments","authors":"Julian Hoßbach, Samuel Tovey, Tobias Ensslen, Jan C. Behrends, Christian Holm","doi":"arxiv-2408.14275","DOIUrl":"https://doi.org/arxiv-2408.14275","url":null,"abstract":"Protein characterization using nanopore-based devices promises to be a\u0000breakthrough method in basic research, diagnostics, and analytics. Current\u0000research includes the use of machine learning to achieve this task. In this\u0000work, a comprehensive statistical analysis of nanopore current signals is\u0000performed and demonstrated to be sufficient for classifying up to 42 peptides\u0000with 70 % accuracy. Two sets of features, the statistical moments and the\u0000catch22 set, are compared both in their representations and after training\u0000small classifier neural networks. We demonstrate that complex features of the\u0000events, captured in both the catch22 set and the central moments, are key in\u0000classifying peptides with otherwise similar mean currents. These results\u0000highlight the efficacy of purely statistical analysis of nanopore data and\u0000suggest a path forward for more sophisticated classification techniques.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Easy-Plane Alignment of Anisotropic Biofluid Crystals in a Magnetic Field: Implications for Rod Orientation 磁场中各向异性生物流体晶体的易平面排列:磁棒定向的意义
arXiv - PHYS - Biological Physics Pub Date : 2024-08-25 DOI: arxiv-2408.13946
Robert J. Deissler, Robert Brown
{"title":"Easy-Plane Alignment of Anisotropic Biofluid Crystals in a Magnetic Field: Implications for Rod Orientation","authors":"Robert J. Deissler, Robert Brown","doi":"arxiv-2408.13946","DOIUrl":"https://doi.org/arxiv-2408.13946","url":null,"abstract":"We study the orientation in a uniform magnetic field of rod-like anisotropic\u0000biofluid crystals with an easy plane that makes an oblique angle with the\u0000crystal's c-axis. For a sufficiently strong field, these crystalline rods\u0000orient themselves such that the crystal's easy plane is parallel to the\u0000magnetic field, the rod's direction being defined as the direction of the\u0000crystal's c-axis. As the rod rotates about the crystal's hard axis there will\u0000therefore be a range of angles that the rod makes with the magnetic field. We\u0000detail this behavior by first providing illustrations of hemozoin crystals at\u0000various orientations. These illustrations clearly demonstrate that the\u0000orientation angle that the crystalline rod makes with respect to the magnetic\u0000field varies from about 30 deg to 150 deg. We also derive an analytical\u0000expression for the probability density function for the orientation angle. We\u0000find that the orientation angles are not uniformly distributed between the\u0000limits of 30 deg and 150 deg, but rather tend to cluster near these limits.\u0000This suggests experimental tests and addresses confusion about the rod\u0000orientation found in past literature. The relevance to other anisotropic\u0000biofluid crystals, such as those produced by gout, is also discussed.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thermodynamics for Reduced Models of Breakable Amyloid Filaments Based on Maximum Entropy Principle 基于最大熵原理的可断裂淀粉样蛋白丝还原模型热力学
arXiv - PHYS - Biological Physics Pub Date : 2024-08-25 DOI: arxiv-2409.05881
Xinyu Zhang, Haiyang Jia, Wuyue Yang, Liangrong Peng, Liu Hong
{"title":"Thermodynamics for Reduced Models of Breakable Amyloid Filaments Based on Maximum Entropy Principle","authors":"Xinyu Zhang, Haiyang Jia, Wuyue Yang, Liangrong Peng, Liu Hong","doi":"arxiv-2409.05881","DOIUrl":"https://doi.org/arxiv-2409.05881","url":null,"abstract":"Amyloid filaments are associated with neurodegenerative diseases such as\u0000Alzheimer's and Parkinson's. Simplified models of amyloid aggregation are\u0000crucial because the original mass-action equations involve numerous variables,\u0000complicating analysis and understanding. While dynamical aspects of simplified\u0000models have been widely studied, their thermodynamic properties are less\u0000understood. In this study, we explore the Maximum Entropy Principle\u0000(MEP)-reduced models, initially developed for dynamical analysis, from a\u0000brand-new thermodynamic perspective. Analytical expressions along with\u0000numerical simulations demonstrate that the discrete MEP-reduced model strictly\u0000retains laws of thermodynamics, which holds true even when filament lengths\u0000transit from discrete values to continuous real numbers. Our findings not only\u0000clarify the thermodynamic consistency between the MEP-reduced models and the\u0000original models of amyloid filaments for the first time, but also suggest\u0000avenues for future research into the model-reduction thermodynamics.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Giant enhancement of bacterial upstream swimming in macromolecular flows 细菌在大分子流中逆流而上的巨大增强效应
arXiv - PHYS - Biological Physics Pub Date : 2024-08-25 DOI: arxiv-2408.13694
Ding Cao, Ran Tao, Albane Théry, Song Liu, Arnold J. T. M. Mathijssen, Yilin Wu
{"title":"Giant enhancement of bacterial upstream swimming in macromolecular flows","authors":"Ding Cao, Ran Tao, Albane Théry, Song Liu, Arnold J. T. M. Mathijssen, Yilin Wu","doi":"arxiv-2408.13694","DOIUrl":"https://doi.org/arxiv-2408.13694","url":null,"abstract":"Many bacteria live in natural and clinical environments with abundant\u0000macromolecular polymers. Macromolecular fluids commonly display viscoelasticity\u0000and non-Newtonian rheological behavior; it is unclear how these complex-fluid\u0000properties affect bacterial transport in flows. Here we combine high-resolution\u0000microscopy and numerical simulations to study bacterial response to shear flows\u0000of various macromolecular fluids. In stark contrast to the case in Newtonian\u0000shear flows, we found that flagellated bacteria in macromolecular flows display\u0000a giant capacity of upstream swimming (a behavior resembling fish swimming\u0000against current) near solid surfaces: The cells can counteract flow washing at\u0000shear rates up to ~65 $s^{-1}$, one order of magnitude higher than the limit\u0000for cells swimming in Newtonian flows. The significant enhancement of upstream\u0000swimming depends on two characteristic complex-fluid properties, namely\u0000viscoelasticity and shear-thinning viscosity; meanwhile, increasing the\u0000viscosity with a Newtonian polymer can prevent upstream motion. By visualizing\u0000flagellar bundles and modeling bacterial swimming in complex fluids, we explain\u0000the phenomenon as primarily arising from the augmentation of a \"weathervane\u0000effect\" in macromolecular flows due to the presence of a viscoelastic lift\u0000force and a shear-thinning induced azimuthal torque promoting the alignment of\u0000bacteria against the flow direction. Our findings shed light on bacterial\u0000transport and surface colonization in macromolecular environments, and may\u0000inform the design of artificial helical microswimmers for biomedical\u0000applications in physiological conditions.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thermodynamic inference of correlations in nonequilibrium collective dynamics 非平衡集体动力学中相关性的热力学推断
arXiv - PHYS - Biological Physics Pub Date : 2024-08-23 DOI: arxiv-2408.13026
Michalis Chatzittofi, Ramin Golestanian, Jaime Agudo-Canalejo
{"title":"Thermodynamic inference of correlations in nonequilibrium collective dynamics","authors":"Michalis Chatzittofi, Ramin Golestanian, Jaime Agudo-Canalejo","doi":"arxiv-2408.13026","DOIUrl":"https://doi.org/arxiv-2408.13026","url":null,"abstract":"The theory of stochastic thermodynamics has revealed many useful fluctuation\u0000relations, with the thermodynamic uncertainty relation (TUR) being a theorem of\u0000major interest. When many nonequilibrium currents interact with each other, a\u0000naive application of the TUR to an individual current can result in an apparent\u0000violation of the TUR bound. Here, we explore how such an apparent violation can\u0000be used to put a lower bound on the strength of correlations as well as the\u0000number of interacting currents in collective dynamics. Our proposed protocol\u0000allows for the inference of hidden correlations in experiment, for example when\u0000a team of molecular motors pulls on the same cargo but only one or a subset of\u0000them is fluorescently tagged. By solving analytically and numerically several\u0000models of many-body nonequilibrium dynamics, we ascertain under which\u0000conditions this strategy can be applied and the inferred bound on correlations\u0000becomes tight.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Protein overabundance is driven by growth robustness 蛋白质过剩是生长稳健性的驱动因素
arXiv - PHYS - Biological Physics Pub Date : 2024-08-21 DOI: arxiv-2408.11952
H. James Choi, Teresa W. Lo, Kevin J. Cutler, Dean Huang, W. Ryan Will, Paul A. Wiggins
{"title":"Protein overabundance is driven by growth robustness","authors":"H. James Choi, Teresa W. Lo, Kevin J. Cutler, Dean Huang, W. Ryan Will, Paul A. Wiggins","doi":"arxiv-2408.11952","DOIUrl":"https://doi.org/arxiv-2408.11952","url":null,"abstract":"Protein expression levels optimize cell fitness: Too low an expression level\u0000of essential proteins will slow growth by compromising essential processes;\u0000whereas overexpression slows growth by increasing the metabolic load. This\u0000trade-off naively predicts that cells maximize their fitness by sufficiency,\u0000expressing just enough of each essential protein for function. We test this\u0000prediction in the naturally-competent bacterium Acinetobacter baylyi by\u0000characterizing the proliferation dynamics of essential-gene knockouts at a\u0000single-cell scale (by imaging) as well as at a genome-wide scale (by TFNseq).\u0000In these experiments, cells proliferate for multiple generations as target\u0000protein levels are diluted from their endogenous levels. This approach\u0000facilitates a proteome-scale analysis of protein overabundance. As predicted by\u0000the Robustness-Load Trade-Off (RLTO) model, we find that roughly 70% of\u0000essential proteins are overabundant and that overabundance increases as the\u0000expression level decreases, the signature prediction of the model. These\u0000results reveal that robustness plays a fundamental role in determining the\u0000expression levels of essential genes and that overabundance is a key mechanism\u0000for ensuring robust growth.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of curvature on growing films of microorganisms 曲率对微生物生长膜的影响
arXiv - PHYS - Biological Physics Pub Date : 2024-08-21 DOI: arxiv-2408.11581
Yuta Kuroda, Takeshi Kawasaki, Andreas M. Menzel
{"title":"Effects of curvature on growing films of microorganisms","authors":"Yuta Kuroda, Takeshi Kawasaki, Andreas M. Menzel","doi":"arxiv-2408.11581","DOIUrl":"https://doi.org/arxiv-2408.11581","url":null,"abstract":"To provide insight into the basic properties of emerging structures when\u0000bacteria or other microorganisms conquer surfaces, it is crucial to analyze\u0000their growth behavior during the formation of thin films. In this regard, many\u0000theoretical studies focus on the behavior of elongating straight objects. They\u0000repel each other through volume exclusion and divide into two halves when\u0000reaching a certain threshold length. However, in reality, hardly any object of\u0000a certain elongation is perfectly straight. Therefore, we here study the\u0000consequences of curvature on the growth of colonies and thin active films. A\u0000given amount of curvature is prescribed to each growing individual.\u0000Particularly, we analyze how this individual curvature affects the size of\u0000orientationally ordered domains in the colony and find a significant decrease.\u0000Instead, strings of stacked curved cells emerge that show branched structures.\u0000Furthermore, we identify a significant spatio-orientational coupling that is\u0000not observed in colonies of straight cells. Our results are important for a\u0000fundamental understanding of the interaction and spreading of microorganisms on\u0000surfaces, with implications for medical applications and bioengineering.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Motor-driven microtubule diffusion in a photobleached dynamical coordinate system 光漂白动态坐标系中马达驱动的微管扩散
arXiv - PHYS - Biological Physics Pub Date : 2024-08-20 DOI: arxiv-2408.11216
Soichi Hirokawa, Heun Jin Lee, Rachel A Banks, Ana I Duarte, Bibi Najma, Matt Thomson, Rob Phillips
{"title":"Motor-driven microtubule diffusion in a photobleached dynamical coordinate system","authors":"Soichi Hirokawa, Heun Jin Lee, Rachel A Banks, Ana I Duarte, Bibi Najma, Matt Thomson, Rob Phillips","doi":"arxiv-2408.11216","DOIUrl":"https://doi.org/arxiv-2408.11216","url":null,"abstract":"Motor-driven cytoskeletal remodeling in cellular systems can often be\u0000accompanied by a diffusive-like effect at local scales, but distinguishing the\u0000contributions of the ordering process, such as active contraction of a network,\u0000from this active diffusion is difficult to achieve. Using light-dimerizable\u0000kinesin motors to spatially control the formation and contraction of a\u0000microtubule network, we deliberately photobleach a grid pattern onto the\u0000filament network serving as a transient and dynamic coordinate system to\u0000observe the deformation and translation of the remaining fluorescent squares of\u0000microtubules. We find that the network contracts at a rate set by motor speed\u0000but is accompanied by a diffusive-like spread throughout the bulk of the\u0000contracting network with effective diffusion constant two orders of magnitude\u0000lower than that for a freely-diffusing microtubule. We further find that on\u0000micron scales, the diffusive timescale is only a factor of approximately 3\u0000slower than that of advection regardless of conditions, showing that the global\u0000contraction and long-time relaxation from this diffusive behavior are both\u0000motor-driven but exhibit local competition within the network bulk.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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