A stochastic analysis of first-order reaction networks

A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived. All authors contributed equally to this work.     

A Meta-Analysis of the Association between ESR1 Genetic Variants and the Risk of Breast Cancer

BackgroundSingle nucleotide polymorphisms (SNPs) in the estrogen receptor gene (ESR1) play critical roles in breast cancer (BC) susceptibility. Genome-wide association studies have reported that SNPs in ESR1 are associated with BC susceptibility; however, the results of recent studies have been inconsistent. Therefore, we performed this meta-analysis to obtain more accurate and credible results.MethodsWe pooled published literature from PubMed, EMBASE, and Web of Science and calculated odds ratios (ORs) with 95% confidence intervals (CIs) to assess the strength of associations using fixed effects models and random effects models. Twenty relevant case-control and cohort studies of the 3 related SNPs were identified.ResultsThree SNPs of the ESR1 gene, rs2077647:T>C, rs2228480:G>A and rs3798577:T>C, were not associated with increased BC risk in our overall meta-analysis. Stratified analysis by ethnicity showed that in Caucasians, the rs2228480 AA genotype was associated with a 26% decreased risk of BC compared with the GG genotype (OR = 0.740, 95% CI: 0.555–0.987). The C allele of the rs3798577:T>C variant was associated with decreased BC risk in Asians (OR = 0.828, 95% CI: 0.730–0.939), while Caucasians with this allele were found to experience significantly increased BC risk (OR = 1.551, 95% CI: 1.037–2.321). A non-significant association between rs2077647 and BC risk was identified in all of the evaluated ethnic populations.ConclusionRs3798577 was associated with an increased risk of BC in Caucasian populations but a decreased risk in Asians. Rs2228480 had a large protective effect in Caucasians, while rs2077647 was not associated with BC risk.     

低温处理对亚洲玉米螟幼虫抗寒性的诱导效应

室内条件下将亚洲玉米螟Ostrinia furnacalis (Guenée)幼虫放置在5℃(LT1处理组)和0℃(LT2处理组)下低温处理2 h后,分别测定了其低温诱导识别温度、存活率、抗寒性、过冷却点、体内水分和脂质含量百分率,并进行抗冻特异蛋白的诱导; 利用SDS-PAGE方法分析了低温诱导后亚洲玉米螟5 龄幼虫血清中抗冻特异蛋白。结果表明：亚洲玉米螟3、4和5龄幼虫的低温诱导识别温度分别为-13.5℃、-16.5℃和-18.5℃; 3、4和5龄幼虫存活率LT2组>LT1组>对照组(P<0.05);随虫龄增加,幼虫抗寒性逐步增强;对幼虫过冷却点无明显影响(P>0.05); 幼虫水分和脂质含量百分率为LT2组>LT1组>对照组,且随虫龄增加,虫体含水率和脂质含量百分率增高(P<0.05); 低温诱导产生了一种分子量约为29.0 kD的抗冻特异蛋白。研究结果表明低温诱导可以增强亚洲玉米螟幼虫的抗寒性。     

栗山天牛天敌花绒寄甲在栎林中的种群保持机制

花绒寄甲(Dastarcus helophoroides)(鞘翅目:寄甲科Bothrideridae)是寄生栗山天牛(Massicus raddei)中老龄幼虫和蛹的重要天敌,但其寄主栗山天牛世代周期长(3年1代)、发育比较整齐,不利于寄生性天敌种群数量的稳定.为了解利用花绒寄甲防治栗山天牛后,其种群能否在栎树林间长期保持较高的种群数量,达到持续控制栗山天牛的防治效果,调查研究了花绒寄甲在栎树林间的转主寄主和种群保持机制.结果表明,在东北辽东栎树干和树枝上除了栗山天牛外,还有其他8种天牛危害:双簇天牛(Moechotypa diphysis)、四点象天牛(Mesosa myops)、中华薄翅锯天牛(Megopis sinica)、锯天牛(Prionus insularis)、双带粒翅天牛(Lamiomimus gottschei)、八字绿虎天牛(Chlorophorus tohokensis)、日本绿虎天牛(C.japonicus)和拟蜡天牛(Stenygrinumquadrinotatum).其中以栗山天牛、双簇天牛、四点象天牛和拟蜡天牛数量较多,而花绒寄甲在辽东栎树干上的垂直分布与栗山天牛、双簇天牛和四点象天牛的垂直分布重叠较多.室内研究表明,花绒寄甲对四点象天牛老熟幼虫的寄生率达到26.67％,对蛹的寄生率达到了43.33％;对双簇天牛老熟幼虫的寄生率达到20.00％,对蛹的寄生率为6.67％.对双簇天牛和四点象天牛在林间的生活史调查和研究发现,花绒寄甲可寄生的这两种天牛的中老龄幼虫和蛹,在花绒寄甲不适宜寄生的栗山天牛幼龄幼虫期大量存在,表明双簇天牛和四点象天牛是花绒寄甲在栎树林中的主要转主寄主.由于这些转主寄主的存在,花绒寄甲在不利于其寄生的栗山天牛卵期、幼龄幼虫期可转移寄生这些寄主,从而在栗山天牛危害的栎树林间保持了较高的种群数量,达到对栗山天牛长期而有效的持续控制效果.     

Intact Flagellar Motor of Borrelia burgdorferi Revealed by Cryo-Electron Tomography: Evidence for Stator Ring Curvature and Rotor/C-Ring Assembly Flexion

The bacterial flagellar motor is a remarkable nanomachine that provides motility through flagellar rotation. Prior structural studies have revealed the stunning complexity of the purified rotor and C-ring assemblies from flagellar motors. In this study, we used high-throughput cryo-electron tomography and image analysis of intact Borrelia burgdorferi to produce a three-dimensional (3-D) model of the in situ flagellar motor without imposing rotational symmetry. Structural details of B. burgdorferi, including a layer of outer surface proteins, were clearly visible in the resulting 3-D reconstructions. By averaging the 3-D images of ∼1,280 flagellar motors, a ∼3.5-nm-resolution model of the stator and rotor structures was obtained. flgI transposon mutants lacked a torus-shaped structure attached to the flagellar rod, establishing the structural location of the spirochetal P ring. Treatment of intact organisms with the nonionic detergent NP-40 resulted in dissolution of the outermost portion of the motor structure and the C ring, providing insight into the in situ arrangement of the stator and rotor structures. Structural elements associated with the stator followed the curvature of the cytoplasmic membrane. The rotor and the C ring also exhibited angular flexion, resulting in a slight narrowing of both structures in the direction perpendicular to the cell axis. These results indicate an inherent flexibility in the rotor-stator interaction. The FliG switching and energizing component likely provides much of the flexibility needed to maintain the interaction between the curved stator and the relatively symmetrical rotor/C-ring assembly during flagellar rotation.Flagellum-based motility plays a critical role in the biology and pathogenesis of many bacteria (3, 6, 17, 31). The well-conserved flagellum is commonly divided into three physical parts: the flagellar motor, the helically shaped flagellar filament, and the hook which provides a universal joint between the motor and the filament. In most bacteria, counterclockwise rotation of the flagella results in bundling of the helical flagella and propulsion of the cell through liquid or viscous environments. Clockwise rotation of the flagellar motor results in random turning of the cell with little translational motion (“tumbling”). Bacterial motility is thus a zigzag pattern of runs and tumbles, in which chemotactic signals favor running toward attractants and away from repellents (3).Borrelia burgdorferi and other closely related spirochetes are the causative agents of Lyme disease, which is transmitted to humans via infected Ixodes ticks (40). Spirochetes have a distinctive morphology in that the flagella are enclosed within the outer membrane sheath and are thus called periplasmic flagella (6). The flagellar motors are located at both ends of the cell and are coordinated to rotate in opposite directions during translational motion and in the same direction (i.e., both clockwise or both counterclockwise) during the spirochete equivalent of tumbling, called “flexing” (6, 15). Spirochetes are also capable of reversing translational motion by coordinated reversal of the direction of motor rotation at both ends of the cell. Rotation of the flagella causes a serpentine movement of the entire cell body, allowing B. burgdorferi to efficiently bore its way through tissue and disseminate throughout the mammalian host, resulting in manifestations in the joints, nervous system, and heart (40).The flagellar motor is an extraordinary nanomachine powered by the electrochemical potential of specific ions across the cytoplasmic membrane (3). Current knowledge of the flagellar motor structure and rotational mechanisms is based primarily on studies of Escherichia coli and Salmonella enterica and is summarized in several recent comprehensive reviews (3, 22, 31, 39, 42). The flagellar motor is constructed from at least 20 different kinds of proteins. The approximate location of these flagellar proteins has been determined by a variety of approaches and appears to be relatively consistent in a wide variety of bacteria. It can be divided into several morphological domains: the MS ring (FliF, the base for the flagellar motor); the C ring (FliG, FliM, and FliN, the switch complex regulating motor rotation); the export apparatus (multiple-protein complex located at the cytoplasmic side of the MS ring); the rod (connecting the MS ring and the hook); the L and P rings on the rod (thought to serve as bushings at the outer membrane and at the peptidoglycan layer, respectively); and the stator, which is the motor force generator embedded in the cytoplasmic membrane. Electron microscopy studies of the purified flagellar motor have provided a detailed view of the rotor/C-ring assembly (11, 44). However, there is no structural information on the stator and the export apparatus in these reconstructions, because these membrane-associated structures are not retained following detergent extraction during the extensive basal body purification process. The stator and the export apparatus were visualized by using freeze fracture preparations of cytoplasmic membranes. It appears that 10 to 16 stator units form circular arrays in the membrane (9, 20). Part of the export apparatus is located in the central space of the C ring (18). Recently a 7-nm-resolution structure of the intact flagellar motor in situ was revealed by averaging 20 structures obtained using cryo-electron tomography (cryo-ET) of Treponema primitia cells (32). Further analysis of the intact flagellar motor structure would lead to a better understanding of the motor protein distribution, the rotor-stator interaction, and the mechanism of bacterial motility.Cryo-ET has emerged as a three-dimensional (3-D) imaging technique to bridge the information gap between X-ray crystallographic and optical microscopic methods (24, 30). This process involves rapidly freezing viable cells, collecting a series of electron micrographs at different angles, and computationally combining the resulting images into a 3-D density map. Cryo-ET allows investigation of the structure-function relationship of molecular complexes and supramolecular assemblies in their cellular environments without fixation, dehydration, embedding, or sectioning artifacts. Spirochetes are well suited for cryo-ET analysis because of their narrow cell diameter (typically 0.2 to 0.3 μm). Recently the cellular architecture of Treponema primitia, Treponema denticola, and B. burgdorferi, as well as the configuration of the B. burgdorferi periplasmic flagella, were revealed by cryo-ET (7, 16, 26, 33). In combination with advanced computational methods, cryo-ET is currently the most promising approach for determining the cellular architecture in situ at molecular resolution (30). We have developed novel strategies for capturing and averaging thousands of 3-D images of large macromolecular assemblies to obtain ∼2.0-nm-resolution structures (28, 29).In this study, we present the molecular structures of infectious wild-type (WT) and mutant B. burgdorferi organisms and their flagellar motors in situ using high-throughput cryo-ET and 3-D image analysis. By averaging subvolumes of 1,280 flagellar motors from 322 cells, we obtained a ∼3.5-nm-resolution model of the intact flagellar motor, providing a detailed view of rotor-stator interactions. In addition, detergent treatment of intact cells provided a preliminary identification of the rotor and stator structures. Through the comparison of WT and mutant cells, we have also determined the location of the flgI gene product in the B. burgdorferi flagellar motor.     

Modularity in the evolution of yeast protein interaction network

Protein interaction networks are known to exhibit remarkable structures: scale-free and small-world and modular structures. To explain the evolutionary processes of protein interaction networks possessing scale-free and small-world structures, preferential attachment and duplication-divergence models have been proposed as mathematical models. Protein interaction networks are also known to exhibit another remarkable structural characteristic, modular structure. How the protein interaction networks became to exhibit modularity in their evolution? Here, we propose a hypothesis of modularity in the evolution of yeast protein interaction network based on molecular evolutionary evidence. We assigned yeast proteins into six evolutionary ages by constructing a phylogenetic profile. We found that all the almost half of hub proteins are evolutionarily new. Examining the evolutionary processes of protein complexes, functional modules and topological modules, we also found that member proteins of these modules tend to appear in one or two evolutionary ages. Moreover, proteins in protein complexes and topological modules show significantly low evolutionary rates than those not in these modules. Our results suggest a hypothesis of modularity in the evolution of yeast protein interaction network as systems evolution.     

Proteome analysis of sorbitol fermentation specific protein in Vibrio cholerae by 2-DE and MS

Vibrio cholerae can be differentiated into epidemic and non-epidemic strains by sorbitol fermentation speed, but little research has been done on its mechanisms. In this study, we investigated differential protein expression of the two strains in response to sorbitol metabolism. V. cholerae strains were cultured in media with and without sorbitol, respectively. Proteins were separated by 2-DE, and those that showed different expression in the two media were identified by MALDI-TOF MS. Fifteen proteins in epidemic strains and 11 proteins in non-epidemic strains showed a different expression in sorbitol medium. Among them, 4 proteins were common to epidemic and non-epidemic strains. Gene sequence analysis showed that some mutations occurred in these proteins between the two strains. Potential functions of these proteins included sugar uptake, amino acid uptake, electron transport, sulfate and thiosulfate transport.     

In Situ TEM Study of Volume Expansion in Porous Carbon Nanofiber/Sulfur Cathodes with Exceptional High‐Rate Performance

Although lithium sulfur batteries (LSBs) have attracted much interest owing to their high energy densities, synthesis of high‐rate cathodes and understanding their volume expansion behavior still remain challenging. Herein, electrospinning is used to prepare porous carbon nanofiber (PCNF) hosts, where both the pore volume and surface area are tailored by optimizing the sacrificial agent content and the activation temperature. Benefiting from the ameliorating functional features of high electrical conductivity, large pore volume, and Li ion permselective micropores, the PCNF/A550/S electrode activated at 550 °C exhibits a high sulfur loading of 71 wt%, a high capacity of 945 mA h g^?1 at 1 C, and excellent high‐rate capability. The in situ transmission electron microscope examination reveals that the lithiation product, Li₂S, is contained within the electrode with only ≈35% volume expansion and the carbon host remains intact without fracture. In contrast, the PCNF/A750/S electrode with damaged carbon spheres exhibits sulfur sublimation, a larger volume expansion of over 61%, and overflowing of Li₂S, a testament to its poor cyclic stability. These findings provide, for the first time, a new insight into the correlation between volume expansion and electrochemical performance of the electrode, offering a potential design strategy to synthesize high‐rate and stable LSB cathodes.