A review of evolutionary graph theory with applications to game theory

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the “fixation probability” - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.     

肋骨接骨板的临床应用研究

目的:探讨肋骨接骨板治疗外伤性连枷胸的方法和疗效。方法:将我院2008年2月至2011年3月收治的47例外伤性连枷胸患者的临床资料进行回顾性分析。分为内固定组(肋骨接骨板内固定术)21例和保守组(呼吸机气体内固定、加压包扎固定)26例。对二组病例的恢复情况及并发症进行对照比较。结果:骨折全部骨性愈合,内固定组并发症发生率低于保守组(P<0.05),恢复优于保守组,差异有统计学意义(P<0.05)。结论:肋骨接骨板内固定术治疗外伤性连枷胸安全可行,且术后并发症少,值得推广。     

On different types of nerve endings in the frog median eminence after fixation with permanganate and glutaraldehyde-osmium

Summary In the frog median eminence, fixed with glutaraldehyde and osmium tetroxide, four types of nerve endings can be generally distinguished. These endings are in contact with the pericapillary spaces of primary portal vessels and can be identified by the internal structure and the size of their granules and vesicles. Type 1 contains large granules (1500–2400 Å in diameter) and small clear vesicles (300–500 Å in diameter), type 2 intermediate granules (about 1100–1700 Å in diameter) and small clear vesicles, type 3 small granules (about 600–1000 Å in diameter) and small clear vesicles, type 4 only numerous small clear vesicles. The mixed types containing the large, intermediate and small dense granules in the same ending are infrequently found.After KMnO₄ or LiMnO₄ fixation the granules and vesicles mentioned above are observed as follows. The large granules in the type 1 nerve ending appear mostly pale or less-dense. The intermediate granules in the type 2 also appear mostly pale or less-dense, but some frequently show granules of high density. The small granules in the type 3 consistently contain the dense substance and these endings can be subdivided into two different types according to the populations of different sizes of dense granules [type 3a (900–1000 Å) and type 3b (500–800 Å)]. Dense-cored and cleared-synaptic vesicles are frequently present with together in the type 3 endings. The small vesicles (300–400 Å), in the type 4, appear generally pale (type 4a), but some nerve endings contain small dense cored-vesicles (type 4b).The author wishes to thank Prof. H. Fujita for his advice and criticism.     

Imitation, internal absorption and the reversal of local drift in stochastic evolutionary games

Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the phenomenon of drift reversal in finite populations, taking into account that drift is a local quantity in strategy space. Secondly, we study a simple imitation dynamics, and show that it can lead to fixation at internal mixed-strategy fixed points even in finite populations. Imitation in infinite populations is adequately described by conventional replicator dynamics, and these equations are known to have internal fixed points. Internal absorption in finite populations on the other hand is a novel dynamic phenomenon. Due to an outward drift in finite populations this type of dynamic arrest is not found in other commonly studied microscopic dynamics, not even in those with the same deterministic replicator limit as imitation.     

单端固定式下颌骨修复体的应力分析

目的：针对包括一侧髁状突的下颌骨缺损,通过有限元应力分析,了解单端固定式下颌骨修复体在功能运动时的受力与变形规律,以期寻求更加合理的修复体的设计和固定方式。方法：建立下颌骨断端和修复体的简易三维模型,模拟咀嚼运动,施加垂直方向载荷,进行有限元法应力分析,计算出该模型各组成部分的应力分布和受力变形。结果：在该模型加载时,延伸板基部和近断端处上部的螺钉颈部是应力集中的部位,近断端处下部的螺钉颈部和修复体的远端舌侧为形变最大的部位。结论：单端固定式下颌骨修复体在加载时,延伸板的基部和靠近断端的固定螺钉是应力集中的部位,修复体远离固定的一侧是变形最大的部位,提示我们应将延伸板形态设计为尽可能加宽,并应增加下颌骨下缘处的固定,使修复体与下颌骨断端受力更加合理,变形也尽可能缩小。     

动力髋螺钉和股骨近端髓内钉两种内固定方式治疗老年股骨粗隆间骨折临床疗效

目的：比较动力髋螺钉（DHS）和股骨近端髓内钉（PFN）两种内固定方式治疗68例老年股骨粗隆间骨折临床疗效。方法：将68例股骨粗隆间骨折老年患者随机均分为两组,分别采取DHS和PFN不同内固定方式进行治疗,比较两组的术中出血量、手术时间、术后疗效及术后并发症发生率。结果：PFN组的优良率为91．18％,明显高于DHS组的70．59％（P=0．031〈0．05）;PFN组的术中出血量、手术时间及愈合时间均优于DHS组（P均〈0．05）。PFN组的并发症发生率为2．94％,低于DHS组的17．65％（P=0．046〈0．05）。结论：PFN较DHS固定方式治疗老年股骨粗隆间骨折更有效,并发症少,安全性大。     

The Structure of CcmP,a Tandem Bacterial Microcompartment Domain Protein from the β-Carboxysome,Forms a Subcompartment Within a Microcompartment

The carboxysome is a bacterial organelle found in all cyanobacteria; it encapsulates CO₂ fixation enzymes within a protein shell. The most abundant carboxysome shell protein contains a single bacterial microcompartment (BMC) domain. We present in vivo evidence that a hypothetical protein (dubbed CcmP) encoded in all β-cyanobacterial genomes is part of the carboxysome. We show that CcmP is a tandem BMC domain protein, the first to be structurally characterized from a β-carboxysome. CcmP forms a dimer of tightly stacked trimers, resulting in a nanocompartment-containing shell protein that may weakly bind 3-phosphoglycerate, the product of CO₂ fixation. The trimers have a large central pore through which metabolites presumably pass into the carboxysome. Conserved residues surrounding the pore have alternate side-chain conformations suggesting that it can be open or closed. Furthermore, CcmP and its orthologs in α-cyanobacterial genomes form a distinct clade of shell proteins. Members of this subgroup are also found in numerous heterotrophic BMC-associated gene clusters encoding functionally diverse bacterial organelles, suggesting that the potential to form a nanocompartment within a microcompartment shell is widespread. Given that carboxysomes and architecturally related bacterial organelles are the subject of intense interest for applications in synthetic biology/metabolic engineering, our results describe a new type of building block with which to functionalize BMC shells.     

A symmetry of fixation times in evoultionary dynamics

In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies.     

Copper Starvation-inducible Protein for Cytochrome Oxidase Biogenesis in Bradyrhizobium japonicum

Microarray analysis of Bradyrhizobium japonicum grown under copper limitation uncovered five genes named pcuABCDE, which are co-transcribed and co-regulated as an operon. The predicted gene products are periplasmic proteins (PcuA, PcuC, and PcuD), a TonB-dependent outer membrane receptor (PcuB), and a cytoplasmic membrane-integral protein (PcuE). Homologs of PcuC and PcuE had been discovered in other bacteria, namely PCu_AC and YcnJ, where they play a role in cytochrome oxidase biogenesis and copper transport, respectively. Deletion of the pcuABCDE operon led to a pleiotropic phenotype, including defects in the aa₃-type cytochrome oxidase, symbiotic nitrogen fixation, and anoxic nitrate respiration. Complementation analyses revealed that, under our assay conditions, the tested functions depended only on the pcuC gene and not on pcuA, pcuB, pcuD, or pcuE. The B. japonicum genome harbors a second pcuC-like gene (blr7088), which, however, did not functionally replace the mutated pcuC. The PcuC protein was overexpressed in Escherichia coli, purified to homogeneity, and shown to bind Cu(I) with high affinity in a 1:1 stoichiometry. The replacement of His⁷⁹, Met⁹⁰, His¹¹³, and Met¹¹⁵ by alanine perturbed copper binding. This corroborates the previously purported role of this protein as a periplasmic copper chaperone for the formation of the Cu_A center on the aa₃-type cytochrome oxidase. In addition, we provide evidence that PcuC and the copper chaperone ScoI are important for the symbiotically essential, Cu_A-free cbb₃-type cytochrome oxidase specifically in endosymbiotic bacteroids of soybean root nodules, which could explain the symbiosis-defective phenotype of the pcuC and scoI mutants.     

Characterization of galacturonosyl transferase genes rgtA, rgtB, rgtC, rgtD, and rgtE responsible for lipopolysaccharide synthesis in nitrogen-fixing endosymbiont Rhizobium leguminosarum: lipopolysaccharide core and lipid galacturonosyl residues confer membrane stability

Rhizobium lipopolysaccharide (LPS) contains four terminally linked galacturonic acid (GalA) residues; one attached to the lipid A and three attached to the core oligosaccharide moiety. Attachment of the GalA residues requires the lipid donor dodecaprenyl-phosphate GalA (Dod-P-GalA), which is synthesized by the GalA transferase RgtE reported here. The galacturonosyl transferases RgtA, -B, and -C utilize Dod-P-GalA to attach GalAs on the LPS core region, and RgtD attaches GalA to the lipid A 4' position. As reported here, the functions of the rgtD and rgtE genes were determined via insertion mutagenesis and structural characterization of the mutant lipid A. The rgtE(-) mutant lacked Dod-P-GalA as determined by mass spectrometry of total lipid extracts and the inability of rgtE(-) mutant membranes to provide the substrate for heterologously expressed RgtA activity. In addition, we created single mutations in each of the rgtA, -B, -C, -D, and -E genes to study the biological function of the GalA residues. The structures of the core oligosaccharide region from each of the rgt mutants were elucidated by glycosyl linkage analysis. Each mutant was assayed for its sensitivity to sodium deoxycholate and to the antimicrobial cationic peptide, polymyxin B (PmxB). The rgt mutants were more sensitive than the parent strain to deoxycholate by varying degrees. However, the rgtA, -B, and -C mutants were more resistant to PmxB, whereas the rgtD and E mutants were less resistant in comparison to the parent strain.