Simulations of knotting in confined circular DNA

The packing of DNA inside bacteriophages arguably yields the simplest example of genome organization in living organisms. As an assay of packing geometry, the DNA knot spectrum produced upon release of viral DNA from the P4 phage capsid has been analyzed, and compared to results of simulation of knots in confined volumes. We present new results from extensive stochastic sampling of confined self-avoiding and semiflexible circular chains with volume exclusion. The physical parameters of the chains (contour length, cross section, and bending rigidity) have been set to match those of P4 bacteriophage DNA. By using advanced sampling techniques, involving multiple Markov chain pressure-driven confinement combined with a thermodynamic reweighting technique, we establish the knot spectrum of the circular chains for increasing confinement up to the highest densities for which available algorithms can exactly classify the knots. Compactified configurations have an enclosing hull diameter ∼2.5 times larger than the P4 caliper size. The results are discussed in relation to the recent experiments on DNA knotting inside the capsid of a P4 tailless mutant. Our investigation indicates that confinement favors chiral knots over achiral ones, as found in the experiments. However, no significant bias of torus over twist knots is found, contrary to the P4 results. The result poses a crucial question for future studies of DNA packaging in P4: is the discrepancy due to the insufficient confinement of the equilibrium simulation or does it indicate that out-of-equilibrium mechanisms (such as rotation by packaging motors) affect the genome organization, hence its knot spectrum in P4?     

Transition between two regimes describing internal fluctuation of DNA in a nanochannel

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.     

Amplified stretch of bottlebrush-coated DNA in nanofluidic channels

The effect of a cationic-neutral diblock polypeptide on the conformation of single DNA molecules confined in rectangular nanochannels is investigated with fluorescence microscopy. An enhanced stretch along the channel is observed with increased binding of the cationic block of the polypeptide to DNA. A maximum stretch of 85% of the contour length can be achieved inside a channel with a cross-sectional diameter of 200 nm and at a 2-fold excess of polypeptide with respect to DNA charge. With site-specific fluorescence labelling, it is demonstrated that this maximum stretch is sufficient to map large-scale genomic organization. Monte Carlo computer simulation shows that the amplification of the stretch inside the nanochannels is owing to an increase in bending rigidity and thickness of bottlebrush-coated DNA. The persistence lengths and widths deduced from the nanochannel data agree with what has been estimated from the analysis of atomic force microscopy images of dried complexes on silica.     

Radius of gyration of plasmid DNA isoforms from static light scattering

Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square radius of gyration, R_G, of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open‐circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of R_G values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm‐like chain model, with the best‐fit value of the apparent persistence length for both the linear and open‐circular isoforms being statistically identical at 46 nm. A new expression was developed for the radius of gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano‐fluidic devices for DNA manipulation and size‐based separation processes for plasmid DNA purification. Biotechnol. Bioeng. 2010;107: 134–142. © 2010 Wiley Periodicals, Inc.     

On the molecular length of the replicative form DNA of bacteriophage phiX174

This paper describes an electron microscopic study of the circular replicative form DNA of bacteriophage φX174. The study has been carried out using a preparative technique in which the DNA molecules are adsorbed from solution on to the cleavage surface of mica and visualized in the electron microscope as a metal-shadowed replica (Gordon &; Kleinschmidt, 1969,1970). Contour lengths of open circular molecules were measured in samples obtained from preparations in which the following experimental parameters were varied: the ionic strength of the solution from which the DNA was adsorbed on the mica and the way in which the molecules were dried before shadowing. At the 0.05 significance level, varying these parameters had no effect on the mean length and variances of samples of molecules obtained from five experiments; the samples were therefore regarded as being drawn from the same molecular population with a mean length and variance of, respectively, 1.83 μm and 0.0117 μm².It was argued that the DNA molecules adsorbed on the mica are “frozen” into the molecular conformation present in solution at the time of adsorption and that, therefore, the experimentally determined contour lengths represent authentic molecular lengths in solution. Based on current estimates of the replicative form DNA molecular weight, the mean contour length obtained was slightly but significantly larger than the length predicted for molecules in an exact B configuration. The variance was larger than could be attributed solely to experimental error, indicating that the molecular population in aqueous solution is heterogeneous in contour length. These experimental results were shown to be consistent with a model for DNA structure in aqueous solution in which individual molecules are dynamic variants of a perturbed B form structure (von Hippel &; Wong, 1971).     

Heterocyst division in two blue-green algae

Bacteriophage 16-6-12 of Rhizobium lupini has a long, non-contractile tail and a head which is hexagonal in outline. The tail is 140 nm in length, 11 nm in diameter, and carries a short terminal fiber. Analysis of the tail structure by optical diffraction indicates that it is of the helical “stacked disc” type. After phenol-extraction from purified particles, the DNA of phage 16-6-12 can circularize in vitro. No significant difference in contour length was observed between the linear (14.34±0.28 μm) and circular (14.44±0.24 μm) forms of molecules. After partial denaturation with alkali an AT-GC-map was constructed, which shows an asymmetric distribution of AT- and GC-rich regions. It is concluded that this phage DNA can circularize due to the presence of cohesive ends and that it is not circularly permuted.     

Scaling theory of polymer translocation into confined regions

We examine the voltage-driven polymer translocation from a spacious region into a confined region imposed by two parallel planes, so that the entry is impeded by the entropic confinement but aided by the electric field inside the confined region. Two modes of entry are examined: linear translocation where a chain enters the confined region with chain ends, and hairpin translocation where a chain enters the confined region by forming a hairpin. Our calculation shows that translocation time increases with polymer length for linear entries but decreases with polymer length for hairpin entries. Applying to electrophoresis of DNA molecules through periodic spacious and confined regions, our theory shows that the dominance of hairpin translocations leads to the experimentally observed faster migration of longer DNA molecules. Our theory predicts experimental conditions for the validity of this law in terms of polymer length, size of the confined region, and solution conditions.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

Dynamics of long DNA confined by linear polymers

We studied the electrophoretic behavior of long DNA molecules in a linear polymer [polyacrylamide (PA)] solution through direct observation by means of fluorescence microscopy. DNA migrates in an I-shaped conformation in concentrated polymer solutions under steady electric fields, but it is not stretched up to its natural contour length in this I-shaped conformation under such fields. The stretching of DNA is induced under alternating current fields through the entanglement effect between DNA and host polymers. We experimentally investigated the conditions required for this stretching phenomenon and found that DNA can be stretched at a concentration of around 7% PA, under a field of around 10 Hz. These conditions do not depend on the length of the DNA chains. It is expected that DNA stretching will be useful in the optical mapping of specific sites along an individual DNA chain.     

Electron microscopic visualization of RecA-DNA filaments: Evidence for a cyclic extension of duplex DNA

As visualized by electron microscopy, RecA protein binds in a highly cooperative manner to single-stranded fd DNA in solutions of 0.01 M Tris (pH 7.5). The resulting nucleoprotein filament loops are 1.25 μm in length, have a fiber diameter of 12 nm and show an indication of a 4.5 nm repeat along the axis of the compact fibers. RecA binds to linear duplex fd DNA in solutions of 0.01 M Tris (pH 7.5) to yield chains of beads which, in the presence of Mg²⁺ and ATP, coalesce into smooth filaments with a length of 1.9 μm (the length of protein-free fd duplex DNA) and have a fiber diameter of 12 nm. In solutions containing Mg²⁺ and ATP-γ-S, however, RecA binds to duplex DNA in a highly cooperative manner to yield rigid filaments 3.0 μm in length. These filaments are 12 nm in diameter and show a very clear 7.5 nm axial repeat. This extension of DNA to 150% of its usual length in the apparent absence of any single-stranded components suggests that the DNA helix must also be highly unwound and provides new insights into the mode of RecA action.     

Synthesis of mitochondrial DNA in spermatocytes of Rhynchosciara hollaenderi

During the mid to late 4th instar period of larval development, the mitochondria of Rhynchosciara spermatocytes undergo highly characteristic morphological changes. In late meiosis the enlarged mitochondria fuse to form a single mitochondrial element which will ultimately extend the length of the spermatid tail. Our studies have shown that synthesis of a circular DNA occurs during this period of mitochondrial “differentiation.” This DNA has a density of 1.681 g/cm³; and its synthesis cannot be detected in somatic tissues such as salivary gland, fat body, or gastric cecum. From analysis of DNA extracted from mitochondrial pellets, we have shown that the circular DNA is associated with the mitochondria. The contour length of the mitochondrial DNA is 9 μm, equivalent to a molecular weight of 18 × 10⁶. Although most metazoan mitochondrial DNAs exhibit contour lengths of approximately 5 μm (10 × 10⁵ daltons), there is no extractable 5 μm circular DNA in these spermatocytes. Therefore, we conclude that either Rhynchosciara spermatocytes possess a distinct 9 μm mitochondrial DNA or that the spermatocyte mitochondrial DNA represents dimers of 5 μm monomers.     

Novel Myxobolus and Ellipsomyxa species (Cnidaria: Myxozoa) parasiting Brachyplatystoma rousseauxii (Siluriformes: Pimelodidae) in the Amazon basin,Brazil

We describe two novel myxosporean parasites from Brachyplatystoma rousseauxii, an economically important freshwater catfish from the Amazon basin, Brazil. Myxobolus tapajosi n. sp., was found in the gill filaments of 23.5% of 17 fish, with myxospores round to oval in frontal view and biconvex in lateral view: length 15 (13.5–17) μm and width 10.7 (9.6–11.4) μm; polar capsules equal, length 5.8 (4.6–7.1) μm and width 3 (2.3–3.8) μm containing polar tubules with 6–7 turns. Ellipsomyxa amazonensis n. sp. myxospores were found floating freely or inside plasmodia in the gall bladder of 23.5% of fish. The myxospores were ellipsoidal with rounded extremities: length 12.8 (12.3–13.6) μm and width 7.6 (6.7–8.7) μm; with two equal, slightly pyriform polar capsules, length 3.8 (3.8–4.0) μm and width 3.1 (2.5–3.4) μm, containing polar tubules with 2–3 turns. We combined spore morphometry, small-subunit ribosomal DNA data, specific host, and phylogenetic analyses, to identify both of these parasites as new myxozoan species. Maximum likelihood and Bayesian analyses showed that Myxobolus tapajosi n. sp. clustered in a basal branch in a subclade of parasites from exclusively South American pimelodid fishes. Ellipsomyxa amazonensis n. sp. clustered within the marine Ellipsomyxa lineage, but we suspect that although the parasite was collected in freshwater, its hosts perform a large migration throughout the Amazon basin and may have become infected from a brackish/marine polychaete host during the estuary phase of its life.     

DNA length and concentration dependencies of anisotropic phase transitions of DNA solutions

Critical concentrations for the isotropic to cholesteric phase transitions of double-stranded DNA fragments in simple buffered saline (0.1 M NaCl) solutions were determined as a function of DNA contour length ranging from approximately 50 nm to 2700 nm, by solid-state 31P NMR spectroscopy and polarized light microscopy. As expected for semirigid chains, the critical concentrations decrease sharply with increasing DNA length near the persistence length in the range from 50 to 110 nm, and approach a plateau when the contour length exceeds 190 nm. The biphasic region is substantially wider than observed for xanthan, another semirigid polyelectrolyte approximately twice as stiff as DNA, primarily because of low critical concentrations for first appearance of the anisotropic phase, C(i)*, in DNA samples > or =110 nm (320 base pairs) long. The limiting C(i)* for DNA > or =490 nm long is exceptionally low (only 13 mg/ml) and is substantially lower than the C(i)* of approximately 40 mg/ml reported for the stiffer xanthan polyelectrolyte. The much higher values of the critical concentrations, C(a)*, for the disappearance of the isotropic DNA phase (> or =67 mg/ml) are modestly higher than those observed for xanthan and are predicted reasonably well by a theory that has been applied to other semirigid polymers, if a DNA persistence length in the consensus range of 50-100 nm is assumed. By contrast, the broad biphasic region and low C(i)* values of DNA fragments > or =190 nm long could only be reconciled with theory by assuming persistence lengths of 200-400 nm. The latter discrepancies are presumed to reflect some combination of deficiencies in current theory as applied to chiral, strong polyelectrolytes such as DNA, and sequence-dependent variations in DNA properties such as flexibility, curvature, or interaction potential. The propensity of DNA to spontaneously self-order at low concentrations well in the physiological range may have biological significance.     

Escaping speed of bacteria from confinement

Microswimmers such as bacteria exhibit large speed fluctuation when exploring their living environment. Here, we show that the bacterium Escherichia coli with a wide range of length speeds up beyond its free-swimming speed when passing through narrow and short confinement. The speedup is observed in two modes: for short bacteria with L <20 μm, the maximum speed occurs when the cell body leaves the confinement, but a flagellar bundle is still confined. For longer bacteria (L ≥ 20 μm), the maximum speed occurs when the middle of the cell, where the maximum number of flagellar bundles locate, is confined. The two speed-up modes are explained by a vanishing body drag and an increased flagella drag—a universal property of an “ideal swimmer.” The spatial variance of speed can be quantitatively explained by a simple model based on the resistance matrix of a partially confined bacterium. The speed change depends on the distribution of motors, and the latter is confirmed by fluorescent imaging of flagellar hooks. By measuring the duration of slowdown and speedup, we find that the effective chemotaxis is biased in filamentous bacteria, which might benefit their survival. The experimental setup can be useful to study the motion of microswimmers near surfaces with different surface chemistry.     

Small circular DNA in Drosophila melanogaster

Covalently closed small circular DNA isolated from Drosophila melanogaster is described. The small circular DNA is found in blastema stage eggs and in Schneider's cell culture line 2 and a cloned subline of line 2. It is heterogeneous in size, although the size distributions and mean sizes differ for each source. The small circular DNA from Schneider's line 2 cells ranges from 0.09-7.3 μm, with a mean contour length of 1.1 μm. This DNA has a buoyant density of 1.703 g/cc and appears to be present predominantly in the nuclear fraction of detergent-disrupted cells. The restriction enzyme EcoRI cleaves approximately 40% of the small circular DNA with a bias toward the larger size classes.Both logarithmic and stationary phase cells contain approximately 3–40 average sized small circular DNA molecules per cell, representing a maximum of 0.03% of the total cellular DNA. Exposure to cycloheximide or puromycin for 14 hr results in a 30 fold increase in the number of small circles per cell, but reduces the mean length of the circular DNA to 0.3 μm. The drug-amplified DNA has a buoyant density in the range of 1.698-1.703 g/cc. No amplification was seen in cells treated with either inhibitor for 3.5 hr. Ethidium bromide, cytosine arabinoside, β-ecdysone, and insulin all had no significant effect on the amount per cell of either small circular DNA or mitochondrial DNA.     

Confining annealed branched polymers inside spherical capsids

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R⁴ dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R² dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.     

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.     

Construction and electrophoretic migration of single-stranded DNA knots and catenanes

In recent years there has been growing interest in the question of how the particular topology of polymeric chains affects their overall dimensions and physical behavior. The majority of relevant studies are based on numerical simulation methods or analytical treatment; however, both these approaches depend on various assumptions and simplifications. Experimental verification is clearly needed but was hampered by practical difficulties in obtaining preparative amounts of knotted or catenated polymers with predefined topology and precisely set chain length. We introduce here an efficient method of production of various single-stranded DNA knots and catenanes that have the same global chain length. We also characterize electrophoretic migration of the produced single-stranded DNA knots and catenanes with increasing complexity.     

Kinetoplast DNA in Trypanosoma equinum1

Identification and characterization of kDNA is described in the naturally occurring totally dyskinetoplastic species Trypanosoma equinum. Fluorescence microscopy of live cells, using the highly sensitive and specific probe DAPI (4,6,-diamidino-2-phenyl-indole), showed the presence of a diversity of extranuclear fluorescent bodies scattered along the length of the organism. Transmission electron microscopic studies revealed a close similarity between the distribution of these DAPI-fluorescing particles and of dense aggregates of nonfibrillar material resembling the kDNA of dyskinetoplastic strains of other species. Variable sized remnants of kDNA, occurring singly or in clusters, were found scattered throughout the mitochondrion. Analytical cesium chloride ultracentrifugation of total cellular DNA extracts showed a kDNA banding profile at a buoyant density equal to 1.691 gm/cm³, representing approximately 11% of the total cellular DNA content. Molecular spreads of isolated kDNA revealed a population of open circular molecules ranging in contour length from 0.11–9.69 μm.     

Replicating circular DNA molecules in yeast

The yeast Saccharomyces cerevisiae contains a class of small circular DNA molecules, approximately 2 μm in contour length (Sinclair et al., 1967). In this report, it is shown that these molecules replicate as double-branched circles, similar to those observed during replication of the bacteriophage λ and Escherichia coli chromosomes. A normal rate of replication of these DNA circles requires the function of a nuclear gene, cdc 8.