A new Euler's formula for DNA polyhedra

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components μ, of crossings c, and of Seifert circles s are related by a simple and elegant formula: s + μ = c + 2. This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus.     

Topological Analysis of Enzymatic Actions on DNA Polyhedral Links

Current synthetic biology has witnessed a revolution that natural DNA molecule steps onto a broad scientific area by assembling a large variety of three-dimensional structures with the connectivity of polyhedra. A mathematical model of these biomolecules is crucial to clarify the biological self-assembly principle, and unravel a first-step understanding of biological regulation and controlling mechanisms. In this paper, mechanisms of two different enzymatic actions on DNA polyhedra are elucidated through theoretical models of polyhedral links: (1) topoisomerase that untangles DNA polyhedral links produces separated single-stranded DNA circles through the crossing change operation; (2) recombinase generates a class of polyhedral circular paths or polyhedral knots by applying the crossing smoothing operation. Furthermore, we also discuss the possibility of applying two theoretical operations in molecular design of DNA polyhedra. Thus, our research provides a new sight of how geometry and topology of DNA polyhedra can be manipulated and controlled by enzymes, as well as has implications for molecular design and structural analysis of structural genome organization.     

The Propanediol Utilization (pdu) Operon of Salmonella enterica Serovar Typhimurium LT2 Includes Genes Necessary for Formation of Polyhedral Organelles Involved in Coenzyme B12-Dependent 1,2-Propanediol Degradation

The propanediol utilization (pdu) operon of Salmonella enterica serovar Typhimurium LT2 contains genes needed for the coenzyme B(12)-dependent catabolism of 1,2-propanediol. Here the completed DNA sequence of the pdu operon is presented. Analyses of previously unpublished pdu DNA sequence substantiated previous studies indicating that the pdu operon was acquired by horizontal gene transfer and allowed the identification of 16 hypothetical genes. This brings the total number of genes in the pdu operon to 21 and the total number of genes at the pdu locus to 23. Of these, six encode proteins of unknown function and are not closely related to sequences of known function found in GenBank. Two encode proteins involved in transport and regulation. Six probably encode enzymes needed for the pathway of 1,2-propanediol degradation. Two encode proteins related to those used for the reactivation of adenosylcobalamin (AdoCbl)-dependent diol dehydratase. Five encode proteins related to those involved in the formation of polyhedral organelles known as carboxysomes, and two encode proteins that appear distantly related to those involved in carboxysome formation. In addition, it is shown that S. enterica forms polyhedral bodies that are involved in the degradation of 1,2-propanediol. Polyhedra are formed during either aerobic or anaerobic growth on propanediol, but not during growth on other carbon sources. Genetic tests demonstrate that genes of the pdu operon are required for polyhedral body formation, and immunoelectron microscopy shows that AdoCbl-dependent diol dehydratase is associated with these polyhedra. This is the first evidence for a B(12)-dependent enzyme associated with a polyhedral body. It is proposed that the polyhedra consist of AdoCbl-dependent diol dehydratase (and perhaps other proteins) encased within a protein shell that is related to the shell of carboxysomes. The specific function of these unusual polyhedral bodies was not determined, but some possibilities are discussed.     

Dynamic polyhedral models of globular proteins

We have devised several mechanical models of globular proteins by approximating them to various polyhedra (dodecahedron, truncated octahedron, icosahedron, truncated icosahedron). The models comprise hollow blocks linked together in a flexible chain. Between blocks there is a set of several reversible, weak magnetic interactions such that when the chain is agitated, it will fold into a stable polyhedral structure about the size of a hand. Folding may be followed in real time with a video camera. Key to the success of the folding process is the lightness of the chain. Several side chains may also be added to the blocks such that they come together to create a polyhedral core when the chain folds. The models have a number of similarities to globular proteins: each chain folds into a unique, but dynamic, three-dimensional structure; the instructions that determine this structure are built into the configuration of blocks; and it is difficult to predict this structure given the unfolded block configuration. Furthermore, the chains fold quickly, generally in less than a minute, several pathways are involved, and these pathways progress through elements of "native" structure. In particular, the models emphasize the importance of restricted conformational mobility in assisting the chain to fold, and also in eliminating undesirable interactions. Because of these similarities to globular proteins, we believe that the polyhedral models will, with continued development, be helpful in understanding the protein folding process, while at the same time acting as valuable educational visual aids. They might also inspire the construction of new types of microscopic, self-assembling devices.     

稻田节肢动物群落的营养联系

根据田间调查和室内饲养观察的资料,研究了稻田节肢动物群落的营养结构及类型。在稻田生态系统中,物种之间由于取食与被取食、寄生与被寄生、捕食与被捕食的营养联系,形成了复杂的食物链和食物网。依据物种在食物网中的位置和功能,可将福州市郊区稻田节肢动物群落的营养结构分为3种类型:1)食物网中尚未发现有重寄生环节;2)食物网中有重寄生环节;3)食物网中有兼寄生环节。为了探讨定量研究生物群落营养联系的可能性,本文运用图论的知识把食物网的结构描述为标向图、集合或邻接矩阵,同时用图论的运算法则解决了各种类型的食物网的合并问题,为研究复杂群落的营养关系提供了一种新方法。     

The Polyhedral Membrane does not Protect Polyhedra of AcMNPV Against Inactivation on Greenhouse Chrysanthemum

Polyhedral inactivation of wild-type AcMNPV and an AcMNPV mutant lacking the gene for the polyhedral membrane protein (AcMNPV-Delta pp34) was studied on greenhouse chrysanthemum. It was hypothesized that polyhedra without a polyhedral membrane might be more susceptible to inactivation on plants. The density of infectious polyhedra of both viruses on the leaf surface decreased in time in a near-exponential fashion. The inactivation curves suggested the presence of two distinct fractions of polyhedra with differences in persistence. One fraction of polyhedra is not inactivated at all, whereas the other fraction is inactivated in an exponential fashion. Relative inactivation rates of the inactivated polyhedra fraction for wild-type AcMNPV and AcMNPV-Delta pp34 were 0.16 and 0.13 per day, respectively, which is not significantly different. After 28 days on leaves in a greenhouse, both viruses still showed residual infectivity. The fraction of residual infectious polyhedra were not significantly different and amounted to approximately 20% of the original density for both wild-type AcMNPV and AcMNPV-Delta pp34. Therefore, the polyhedral membrane does not protect polyhedra against inactivation on greenhouse chrysanthemum.     

Abnormal formation of polyhedra resulting from a single mutation in the polyhedrin gene of Autographa californica multicapsid nucleopolyhedrovirus

A spontaneous mutant that produces a single abnormally large cubic polyhedron per infected cell was isolated from a polyhedra-positive recombinant Autographa californica multicapsid nucleopolyhedrovirus (AcMNPV). Both wild-type and mutant virus produce two forms of virus particles, budded virions and occluded virions. However, occluded virions are not found within the polyhedra of cells infected with mutant virus, as with the wild-type virus. These large cubic polyhedra do not have the typical lattice-like structure normally seen in wild-type polyhedra and are noninfectious. Spodoptera frugiperda 9 (SF9) cells which were infected with this virus had low infectivity to larvae. No significant alterations were found in the viral genome by restriction enzyme analysis, and no mutations were found in the 25K gene. A single point mutation resulting in an amino acid change of Gly25 to Asp was identified in the polyhedrin gene. A transfer vector containing the entire polyhedrin gene including the point mutation was constructed and used to cotransfect Sf9 cells with a polyhedron-negative recombinant virus. Large cubic polyhedra were once again observed, confirming that the Gly25 to Asp mutation is responsible for the formation of abnormal polyhedra.     

The chirality of ground DNA knots and links.

The chirality of ground DNA knots and links is described and characterized in terms of color symmetry groups (CSG), i.e. color symmetry groups I and II, which correspond to topochirality (topological chirality) and topoachirality (topological achirality) which bear an uncanny resemblance to point groups I (proper) and point groups II (improper) used for testing geochirality (geometrical chirality) and geoachirality (geometrical achirality), respectively. By regarding these two crossing modes in mirror images as white and black vertices, DNA knots and links with minimal crossings can be mapped to vertex-bicolored graphs under a working hypothesis that DNA knots and links exist in ground states with minimal energy m0. The color symmetry group of a vertex-bicolored graph G is defined as the set of all permutations and permutation asymmetrizations of the vertices of G that preserve its topology (connectivity), where asymmetrization, denoted as (a), is the operation of changing vertices' colors, and a permutation followed by an (a) is a permutation asymmetrization. The color symmetry groups I contains only permutations, whereas color symmetry groups II comprise permutation asymmetrizations as well as permutations. Four DNA knots and links in nature are analyzed and tabulated consisely. In addition, the well-known figure-of-eight knot and Borromean rings are discussed in much the same way.     

DNA methylation in Drosophila melanogaster may depend on lineage heterogeneity

DNA methylation has been discovered in Drosophila only recently. Current evidence indicates that de novo methylation patterns in drosophila are maintained in a different way compared to vertebrates and plants. As the genomic role and determinants of DNA methylation are poorly understood in invertebrates, its link with several factors has been suggested. In this study, we tested for the putative link between DNA methylation patterns in Drosophila melanogaster and radiation or the activity of P transposon. Neither of the links was apparent from the results, however, we obtained some hints on a possible link between DNA methylation pattern and genomic heterogeneity of fly lineages.     

The flexibility of DNA double crossover molecules

Double crossover molecules are DNA structures containing two Holliday junctions connected by two double helical arms. There are several types of double crossover molecules, differentiated by the relative orientations of their helix axes, parallel or antiparallel, and by the number of double helical half-turns (even or odd) between the two crossovers. They are found as intermediates in meiosis and they have been used extensively in structural DNA nanotechnology for the construction of one-dimensional and two-dimensional arrays and in a DNA nanomechanical device. Whereas the parallel double helical molecules are usually not well behaved, we have focused on the antiparallel molecules; antiparallel molecules with an even number of half-turns between crossovers (termed DAE molecules) produce a reporter strand when ligated, facilitating their characterization in a ligation cyclization assay. Hence, we have estimated the flexibility of antiparallel DNA double crossover molecules by means of ligation-closure experiments. We are able to show that these molecules are approximately twice as rigid as linear duplex DNA.     

DNA methylation in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis> may depend on lineage heterogeneity

DNA methylation has been discovered in Drosophila only recently. Current evidence indicates that de novo methylation patterns in drosophila are maintained in a different way compared to vertebrates and plants. As the genomic role and determinants of DNA methylation are poorly understood in invertebrates, its link with several factors has been suggested. In this study, we tested for the putative link between DNA methylation patterns in Drosophila melanogaster and radiation or the activity of P transposon. Neither of the links were apparent from the results, however, we obtained some hints on a possible link between DNA methylation pattern and genomic heterogeneity of fly lineages.     

Chemotactic attraction of Crassostrea virginica hemolymph cells to Staphylococcus lactus.

The nuclear polyhedrosis virus (NPV) of Porthetria dispar was isolated and purified through a two-step zonal centrifugation procedure. The LD₅₀ of the purified NPV was determined by a dose-response assay. Quantitative analyses were made of whole polyhedra and of separated fractions of polyhedral protein, virus rods, and denatured material, i.e., the pellet obtained from low speed centrifugation of dissolved polyhedra, to determine the protein, DNA, and “RNA” (orcinol-positive material) present in this NPV. Approximately one-half the “RNA” was present in the denatured material. Trace elements were also determined, and four, Fe, Mg, Cu, and Zn, of the ten assayed were present in the polyhedral protein fraction, while only Mg and Zn were in the virus rod fraction.     

An Overview of Structural DNA Nanotechnology

Structural DNA Nanotechnology uses unusual DNA motifs to build target shapes and arrangements. These unusual motifs are generated by reciprocal exchange of DNA backbones, leading to branched systems with many strands and multiple helical domains. The motifs may be combined by sticky ended cohesion, involving hydrogen bonding or covalent interactions. Other forms of cohesion involve edge-sharing or paranemic interactions of double helices. A large number of individual species have been developed by this approach, including polyhedral catenanes, a variety of single-stranded knots, and Borromean rings. In addition to these static species, DNA-based nanomechanical devices have been produced that are ultimately targeted to lead to nanorobotics. Many of the key goals of structural DNA nanotechnology entail the use of periodic arrays. A variety of 2D DNA arrays have been produced with tunable features, such as patterns and cavities. DNA molecules have be used successfully in DNA-based computation as molecular representations of Wang tiles, whose self-assembly can be programmed to perform a calculation. About 4 years ago, on the fiftieth anniversary of the double helix, the area appeared to be at the cusp of a truly exciting explosion of applications; this was a correct assessment, and much progress has been made in the intervening period.     

Spatial graphs as templates for habitat networks in boreal landscapes

Network topology serves as a useful model for biological systems at various scales. Contrary to many biological systems, spatial reference is crucial for habitat networks. Boreal forest landscapes provide a wide gradient of spatial patterns and, thus, unique network structures. Assuming forest-dwelling organisms in general aim to minimize travel distances during foraging, dispersal, etc., linear links across the landscape matrix constitute expected movement routes among forested areas in boreal landscapes. We quantified the number and length of links in a set of 57 boreal forest landscapes for four hierarchically nested graphs in order to compare the incremental changes in characteristics of resulting graph measures. The forest cover graphs consisted of the same set of forest patches, and hierarchical link types extracted from real landscapes: nearest neighbour graph (NN), minimum spanning tree (MST), Gabriel graph (GG) and minimum planar graph (MPG). Most of the links in graphs were NN and GG links. Commonly links were 100–200?m in length, but link lengths particularly in the GG and MPG shorten when the proportion of forest in landscapes increased. Most nodes had 3–5 links each, but the number of links per node depended on node size and the proportion of forest cover. GG and MPG graphs retain the topology of the underlying node layout. Changes in node pattern alter the NN and MST graphs more than GG and MPG. Variation in regional network topologies is likely to affect connectivity patterns in a landscape and, thus, many ecological processes that occur at a local scale. An appropriate network analysis enables the discovery and comparison of distinctive network patterns. Understanding network topologies provide practical tools for land use planning and biodiversity management of broader areas that target functional habitat networks.     

Supercoiled DNA-directed knotting by T4 topoisomerase.

The mechanism by which the type 2 topoisomerase from bacteriophage T4 mediates knotting of negatively supercoiled DNA was deduced from an analysis of product topology. The knotted products were nicked and then subjected to electrophoresis in order to separate species on the basis of the minimum number of crossings in the knotted form. Knots with defined numbers of crossings were purified and the configuration of these crossings determined in the electron microscope by the RecA coating method. The product knots were exclusively of the twist form, in which an interwound region is entrapped by a single interlock of two looped ends. The interwound region was of negative sign in greater than 98% of the molecules examined, whereas the single interlock was equally likely to be positive or negative. These results are interpreted in terms of a model for knot formation in which random strand passage mediated by the topoisomerase links bent or branched portions of a superhelix that has a specific interwound geometry. Superhelix interwinding and DNA contacts stabilized by excess enzyme molecules explain the very high frequency of knotting.     

Formation of unique structure in polypeptide chains. Theoretical investigation with the aid of a replica approach

A replica approach analogous to that used in spin glass systems is implemented to study the configurational space of a heteropolymeric model of protein with a quenched, disordered sequence of links in the limit of a large number of link types. It is shown that there exists a threshold value of chain heterogeneity which separates two qualitatively different types of behavior. For a low degree of heterogeneity the protein globule is like a homopolymer in a collapsed state without definite chain folds: an exponentially large number of folds make a significant contribution to the partition function in this regime. After the threshold heterogeneity has been overcome, the chain freezes drastically but without latent heat; few (approx. 1) frozen states with definite chain folds are thermodynamically dominant in this state. The relation of these results to thermodynamic aspects of protein folding is discussed.     

蓖麻蚕核型多角体病毒DNA转染四种昆虫细胞系的研究

用蓖麻蚕核型多角体病毒(PcrNPV)DNA转染草地贪夜蛾(SF)、家蚕(Bm)、斜纹夜蛾(SL)和菜粉蝶(Pr)四种昆虫细胞系,结果表明,PcrNPV DNA能在SF细胞内复制增殖并形成多角体,Pr细胞系对PcrNPV DNA转染不敏感;Bm和SL细胞出现病变症状,但在电镜下未观察到病毒粒子或多角体。     

Network analysis of tree crowns distinguishes functional groups of Cerrado species

Deciduous, semideciduous and evergreen leaf phenological groups of Cerrado trees were studied using a representative network composed of nodes and links to uncover the structural traits of the crown. A node denotes the origin of a branch, and a link represents the branch emerging from a lateral bud. The network representation usually resulted in a graph with three links per node and twice as many links as nodes for each leaf phenological group. It was possible to identify four kinds of nodes according to the position and the number of links: initial, regular, emission and final nodes. The numbers of links and nodes and the distance between two kinds of nodes decreased from evergreen to deciduous species. A crown with a few nodes and links and a short distance between the kinds of nodes could facilitate the unfolding of foliage on leafless branches at the end of the dry season in deciduous trees. In contrast, foliage persistence in evergreens could facilitate the mass flow to new leaves produced during the entire year in a crown with a high number of links and nodes and with a large distance between nodes. There is a clear interdependence between the degree of leaf deciduousness and the crown structural traits in Cerrado tree species. Therefore, there are functional groups of trees in Cerrado vegetation that are characterized by a set of structural traits in the crown, which is associated with leaf deciduousness.     

Anatomy of Herpes Simplex Virus DNA. IX. Apparent Exclusion of Some Parental DNA Arrangements in the Generation of Intertypic (HSV-1 × HSV-2) Recombinants

We are reporting the physical location of parental DNA sequences in 28 recombinants produced by crossing herpes simplex viruses (HSV) 1 and 2. The parental crosses were of two kinds. In the first, temperature-sensitive mutants of HSV-1 and HSV-2 were crossed to produce wild-type recombinants. In the second, temperature-sensitive mutants of HSV-1 rendered resistant to phosphonoacetic acid were crossed with wild-type HSV-2, and recombinants that multiplied at nonpermissive temperature and were resistant to the drug were selected. The DNAs of the recombinants were mapped with XbaI, EcoRI, HpaI, HsuI, BglII, and, in some instances, KpnI restriction endonucleases. The results were as follows. (i) We established the colinear arrangements of HSV-1 and HSV-2 DNAs. (ii) There was extensive interchange of genomic regions, ranging from the exchange or the entire L of S component of HSV DNA to substitutions of regions within the same component. In some recombinants, the reiterated sequences ab and ac bracketing the L and S components of HSV DNA were heterotypic. Most recombinants grew well and showed no obvious defects. (iii) The number of crossover events ranged from one to as many as six. Although crossover events occurred throughout the DNA, some clustering of crossover events was observed. (iv) Analysis of recombinants permitted localization of several markers used in this study and appears to be a useful technique for marker mapping. (v) As previously reported, HSV DNA consists of four populations, differing in relative orientation of the L and S components. All recombinants could be displayed in one arrangement of L and S such that the number of crossover events was minimized. The data are consistent with the hypothesis that only one arrangement of the parental DNA participates in the generation of recombinants.     

Molecular Modelling of Helix Stability in Carrageenans

Molecular models of disaccharides, and single and double helices up to eight monomers in length have been constructed of the two types of glycosidic linkage in the carrageenan chain. These links are a galactose to anhydrogalactose link (GA link), and an anhydrogalactose to galactose link (AG link). These models are also based on 3-carrageenan, which contains a 4-sulphate galactose ring. The effects of the sulphate groups on the conformation of the helices may be seen by the angles of $ϕ$ϕ and N explored during the simulations by the AG and GA linkages. It has been observed that the molecule can explore a greater area of conformational space about the GA link than the AG link. This could be due to steric hindrance caused by the bulky sulphate group near the AG link. The sulphate group is further away from the GA link than from the AG link, and this may provide a possible explanation for the relatively unhindered movement about the GA link compared to the AG link. The results have also shown that the conformational space for the AG linkages, as well as the GA linkages vary between different lengths of the polysaccharide chain. Single helix models show little stability in molecular dynamics simulation, whereas the eight monomer double helix model is more stable than a six monomer double helix model.