Direct visualization of supercoiled DNA molecules in solution.

The shape of supercoiled DNA molecules in solution is directly visualized by cryo-electron microscopy of vitrified samples. We observe that: (i) supercoiled DNA molecules in solution adopt an interwound rather than a toroidal form, (ii) the diameter of the interwound superhelix changes from about 12 nm to 4 nm upon addition of magnesium salt to the solution and (iii) the partition of the linking deficit between twist and writhe can be quantitatively determined for individual molecules.     

A model for sedimentation in inhomogeneous media. I. Dynamic density gradients from sedimenting co-solutes

Macromolecular sedimentation in inhomogeneous media is of great practical importance. Dynamic density gradients have a long tradition in analytical ultracentrifugation, and are frequently used in preparative ultracentrifugation. In this paper, a new theoretical model for sedimentation in inhomogeneous media is presented, based on finite element solutions of the Lamm equation with spatial and temporal variation of the local solvent density and viscosity. It is applied to macromolecular sedimentation in the presence of a dynamic density gradient formed by the sedimentation of a co-solute at high concentration. It is implemented in the software SEDFIT for the analysis of experimental macromolecular concentration distributions. The model agrees well with the measured sedimentation profiles of a protein in a dynamic cesium chloride gradient, and may provide a measure for the effects of hydration or preferential solvation parameters. General features of protein sedimentation in dynamic density gradients are described.     

A quantitative test of Zimm's model for the rotor-speed-department sedimentation of linear DNA molecules

In 1974, Zimm described a theory which predicts that the sedimentation coefficient of high-molecular-weight DNA will decrease as the rotor speed of measurement increases. In 1979, this theory was revised, and the new formula predicts speed-dependence effects that are substantially smaller than the predictions of the original version. This report describes the results of subjecting both the original and the revised versions of the theory to quantitative tests using a well-defined sucrose-gradient system and a DNA of known molecular weight (T4c DNA). T4c bacteriophage is a mutant, whose DNA contains the unmodified base cytosine, instead of the glucosylated hydroxymethylcytosine characteristic of the T-even bacteriophages, and has a molecular weight of 115 ± 3 × 10⁶. The DNA of the wild-type phage (T4D⁺) was also used in some experiments. In addition to the quantitative tests, the experiments test for an effect first observed by Rubenstein and Leighton, which showed that the sedimentation coefficient measured for T2 DNA depended on the composition of the centrifuge tube used for the measurement (tube composition effect). It can be inferred from this observation that an interaction occurs between particle and tube wall during sedimentation, and this leads to a reduction in sedimentation velocity independent of the reduction in S described by Zimm's theory. The results show that in the range of 25,000–50,000 rpm, the original but theoretically incorrect form of the theory quite accurately describes the sedimentation behavior of both T4c and T4D⁺ DNA, although T4D⁺ was a special case in some respects. The revised (corrected) form of the theory predicts much less of a speed-dependence effect than that actually observed. The discrepancy between corrected theory and observation suggests that other factors (perhaps arising from the use of the swinging bucket rotor geometry) are causing the additional observed reduction in S_20,w. However, the experiments show that the tube composition effect does not seem to be one of these.     

Molecular mechanics model of supercoiled DNA

We describe a pseudo-atomic model of supercoiled DNA. Each base-pair of the DNA is represented in the model by three particles placed in a plane. The particle triplets are stacked to model stacked base-pairs in double-helical DNA, and closed circular conformations are generated to investigate supercoiling. This model is less detailed than all-atom models, which are too computationally demanding to be used to study supercoiling. On the other hand, this model contains details at the base-pair level and is therefore more elaborate than elastomechanical models. A potential energy function is written in terms of a set of internal co-ordinates defined to resemble a limited number of helical parameters. The modeled helical parameters, helical twist, base-roll, tilt and rise, are the most important parameters of the global shape of DNA. Experimentally measured mechanical properties of DNA are used to define the forces holding the particles together. We then use a procedure incorporating energy minimization and molecular dynamics to locate low energy conformations of the model DNA. The model was found to behave very much like rubber-tubing and elastomechanical models. The conformations and the effects of supercoiling pressure (a number proportional to the degree to which the total twist of the DNA has been altered from its natural value) on these conformations are all very similar to those observed in the latter two models. We also used this model to examine the effects of supercoiling pressure, base-sequence and mechanical properties on the conformations and energies of five sequences. The sequences studied include models of naturally straight DNA and DNA with static or natural bends.     

Elastic model of highly supercoiled DNA

The equilibrium shapes of supercoiled DNA are investigated by employing an elastic model. First, a set of Euler equations is derived to determine the equilibrium shapes under ring-closure conditions. Two exact solutions that describe circular and figure-8 shapes are obtained. Using these and their topological properties, the configuration change from the circular to the figure-8 form is discussed. Second, more intricate structures of supercoiling DNA are studied by a numerical analysis. Among a class of configurations, the shape that has the minimum elastic energy is explicitly determined. Poisson's ratio, the ratio of the self-avoiding radius to the total length, and the deficit (or excess) of the linking number ΔLk are found to be the important parameters. We conclude that the topology and the elastic theory of looped DNA explain the essential features of the supercoiling phenomena.     

Compaction of single supercoiled DNA molecules adsorbed onto amino mica

A model of possible conformational transitions of supercoiled DNA in vitro in the absence of proteins under the conditions of increasing degree of compaction was developed. A 3993-bp pGEMEX supercoiled DNA immobilized on various substrates (freshly cleaved mica, standard amino mica, and modified amino mica with a hydrophobicity higher than that of standard amino mica) was visualized by atomic force microscopy in air. On the modified amino mica, which has an increased density of surface positive charges, single molecules with an extremely high degree of compaction were visualized in addition to plectonemic DNA molecules. As the degree of DNA supercoiling increased, the length of the first-order superhelical axis of molecules decreased from 570 to 370 nm, followed by the formation of second-and third-order superhelical axes about 280 and 140 nm long, respectively. The compaction of molecules ends with the formation of minitoroids about 50 nm in diameter and molecules of spherical shape. It was shown that the compaction of single supercoiled DNA molecules immobilized on amino mica to the level of minitoroids and spheroids is due to the shielding of mutually repulsing negatively charged phosphate groups of DNA by positively charged amino groups of the amino mica, which has a high charge density of its surface.     

No braiding of Holliday junctions in positively supercoiled DNA molecules

The Holliday junction is a prominent intermediate in genetic recombination that consists of four double helical arms of DNA flanking a branch point. Under many conditions, the Holliday junction arranges its arms into two stacked domains that can be oriented so that genetic markers are parallel or antiparallel. In this arrangement, two strands retain a helical conformation, and the other two strands effect the crossover between helical domains. The products of recombination are altered by a crossover isomerization event, which switches the strands fulfilling these two roles. It appears that effecting this switch from the parallel conformation by the simplest mechanism results in braiding the crossover strands at the branch point. In previous work we showed by topological means that a short, parallel, DNA double crossover molecule with closed ends did not braid its branch point; however, that molecule was too short to adopt the necessary positively supercoiled topology. Here, we have addressed the same problem using a larger molecule of the same type. We have constructed a parallel DNA double crossover molecule with closed ends, containing 14 double helical turns in each helix between its crossover points. We have prepared this molecule in a relaxed form by simple ligation and in a positively supercoiled form by ligation in the presence of netropsin. The positively supercoiled molecule is of the right topology to accommodate braiding. We have compared the relaxed and supercoiled versions for their responses to probes that include hydroxyl radicals, KMnO4, the junction resolvases endonuclease VII and RuvC, and RuvC activation of KMNO4 sensitivity. In no case did we find evidence for a braid at the crossover point. We conclude that Holliday junctions do not braid at their branch points, and that the topological problem created by crossover isomerization in the parallel conformation is likely to be solved by distributing the stress over the helices that flank the branch point.     

Compaction of single supercoiled DNA molecules adsorbed onto amino mica

A model of possible conformational transitions of supercoiled DNA in vitro in the absence of proteins under the conditions of increasing degree of compaction was developed. A 3993-bp pGEMEX supercoiled DNA immobilized on various substrates (freshly cleaved mica, standard amino mica, and modified amino mica with a hydrophobicity higher than that of standard amino mica) was visualized by atomic force microscopy in air. On the modified amino mica, which has an increased density of surface positive charges, single molecules with an extremely high degree of compaction were visualized in addition to plectonemic DNA molecules. As the degree of DNA supercoiling increased, the length of the first-order superhelical axis of molecules decreased from 570 to 370 nm, followed by the formation of second- and third-order superhelical axes about 280 and 140 nm long, respectively. The compaction of molecules ends with the formation of minitoroids about 50 nm in diameter and molecules of spherical shape. It was shown that the compaction of single supercoiled DNA molecules immobilized on amino mica to the level of minitoroids and spheroids is due to the shielding of mutually repulsing negatively charged phosphate groups of DNA by positively charged amino groups of the amino mica, which has a high charge density of its surface.     

Electrophoretic mobility of supercoiled,catenated and knotted DNA molecules

We systematically varied conditions of two-dimensional (2D) agarose gel electrophoresis to optimize separation of DNA topoisomers that differ either by the extent of knotting, the extent of catenation or the extent of supercoiling. To this aim we compared electrophoretic behavior of three different families of DNA topoisomers: (i) supercoiled DNA molecules, where supercoiling covered the range extending from covalently closed relaxed up to naturally supercoiled DNA molecules; (ii) postreplicative catenanes with catenation number increasing from 1 to ∼15, where both catenated rings were nicked; (iii) knotted but nicked DNA molecules with a naturally arising spectrum of knots. For better comparison, we studied topoisomer families where each member had the same total molecular mass. For knotted and supercoiled molecules, we analyzed dimeric plasmids whereas catenanes were composed of monomeric forms of the same plasmid. We observed that catenated, knotted and supercoiled families of topoisomers showed different reactions to changes of agarose concentration and voltage during electrophoresis. These differences permitted us to optimize conditions for their separation and shed light on physical characteristics of these different types of DNA topoisomers during electrophoresis.     

Ising model forB-Z transition in supercoiled DNA

The possible existence of nucleic acids in right-handed and left-handed helical forms is considered. A statistical mechanical model is developed to obtain an expression for a change in twist during helical transformation in terms of corresponding free energies and linking for a supercoiled DNA. The theoretically predicted values are compared with those determined experimentally. The physico-chemical significance of the parameters is discussed.     

Modification of ColE1 DNA with osmium tetroxide generates positively supercoiled molecules

Covalent binding of osmium tetroxide to negatively supercoiled DNA in vitro initially induces its relaxation, accompanied by a formation of a single denaturation "bubble" per molecule. Binding of further osmium results in DNA overwinding and the appearance of positive supercoils as demonstrated by gel electrophoresis and electron microscopy.     

Helix stability and the mechanism of cruciform extrusion in supercoiled DNA molecules

The kinetic properties of cruciform extrusion in supercoiled DNA molecules fall into two main classes. C-type cruciforms extrude in the absence of added salt, at relatively low temperatures, with large activation energies, while S-type cruciforms exhibit no extrusion in the absence of salt, and maximal rates at 50 mM NaCl, with activation energies about one quarter those of the C-type. These diverse properties are believed to reflect two distinct pathways for the extrusion process, and are determined by the nature of the sequences which form the context of the inverted repeat. C-type kinetics are conferred by A + T rich sequences, implying a role of helix stability in the selection. In this study we have shown that: 1. Helix-destabilising solvents (dimethyl formamide and formamide) facilitate extrusion by normally S-type molecules at low temperatures in the absence of salt. 2. C-type extrusion is strongly suppressed by low concentrations (2-4 microM) distamycin, at which concentrations S-type extrusion is enhanced. 3. Some extrusion occurs in a C-type construct in the presence of 50 mM NaCl. This is increased by addition of 3 microM distamycin, under which conditions extrusion becomes effectively S-type. Thus S-type constructs can behave in a quasi-C-type manner in the presence of helix-destabilising solvents, and C-type extrusion is suppressed by binding a compound which stabilises A + T rich regions of DNA. Helix destabilisation leads to C-type behaviour, while helix stabilisation results in S-type properties. These studies demonstrate the influence of contextual helix stability on the selection of kinetic mechanism of cruciform extrusion.     

Behavior of supercoiled DNA.

We study DNA supercoiling in a quantitative fashion by micromanipulating single linear DNA molecules with a magnetic field gradient. By anchoring one end of the DNA to multiple sites on a magnetic bead and the other end to multiple sites on a glass surface, we were able to exert torsional control on the DNA. A rotating magnetic field was used to induce rotation of the magnetic bead, and reversibly over- and underwind the molecule. The magnetic field was also used to increase or decrease the stretching force exerted by the magnetic bead on the DNA. The molecule's degree of supercoiling could therefore be quantitatively controlled and monitored, and tethered-particle motion analysis allowed us to measure the stretching force acting on the DNA. Experimental results indicate that this is a very powerful technique for measuring forces at the picoscale. We studied the effect of stretching forces ranging from 0.01 pN to 100 pN on supercoiled DNA (-0.1 < sigma < 0.2) in a variety of ionic conditions. Other effects, such as stretching-relaxing hysteresis and the braiding of two DNA molecules, are discussed.     

A computer-generated supercoiled model of the pUC19 plasmid

DNA models have become a powerful tool in the simulation of radiation-induced molecular damage. Here, a computer code was developed which calculates the coordinates of individual atoms in supercoiled plasmid DNA. In this prototype study, the known base-pair sequence of the pUC19 plasmid has been utilized. The model was built in a three-step process. Firstly, a Monte Carlo simulation was performed to shape a segment chain skeleton. Checks on elastic energy, distance and unknotting were applied. The temperature was considered in two different ways: (1) it was kept constant at 293 K and (2) it was gradually reduced from 350 K to less than 10 K. Secondly, a special smoothing procedure was introduced here to remove the edges from the segment chain without changing the total curve length while avoiding the production of overshooting arcs. Finally, the base pair sequence was placed along the smoothed segment chain and the positions of all the atoms were calculated. As a first result, a few examples of the supercoiled plasmid models will be presented, demonstrating the strong influence of appropriate control of the system temperature.     

Dynamic publication model for neurophysiology databases.

We have implemented a pair of database projects, one serving cortical electrophysiology and the other invertebrate neurones and recordings. The design for each combines aspects of two proven schemes for information interchange. The journal article metaphor determined the type, scope, organization and quantity of data to comprise each submission. Sequence databases encouraged intuitive tools for data viewing, capture, and direct submission by authors. Neurophysiology required transcending these models with new datatypes. Time-series, histogram and bivariate datatypes, including illustration-like wrappers, were selected by their utility to the community of investigators. As interpretation of neurophysiological recordings depends on context supplied by metadata attributes, searches are via visual interfaces to sets of controlled-vocabulary metadata trees. Neurones, for example, can be specified by metadata describing functional and anatomical characteristics. Permanence is advanced by data model and data formats largely independent of contemporary technology or implementation, including Java and the XML standard. All user tools, including dynamic data viewers that serve as a virtual oscilloscope, are Java-based, free, multiplatform, and distributed by our application servers to any contemporary networked computer. Copyright is retained by submitters; viewer displays are dynamic and do not violate copyright of related journal figures. Panels of neurophysiologists view and test schemas and tools, enhancing community support.     

Large-scale opening of A + T rich regions within supercoiled DNA molecules is suppressed by salt.

Large-scale cooperative helix opening has been previously observed in A + T rich sequences contained in supercoiled DNA molecules at elevated temperatures. Since it is well known that helix melting of linear DNA is suppressed by addition of salt, we have investigated the effects of added salts on opening transitions in negatively supercoiled DNA circles. We have found that localised large-scale stable melting in supercoiled DNA is strongly suppressed by modest elevation of salt concentration, in the range 10 to 30 mM sodium. This has been shown in a number of independent ways: 1. The temperature required to promote cruciform extrusion by the pathway that proceeds via the coordinate large-scale opening of an A + T rich region surrounding the inverted repeat (the C-type pathway, first observed in the extrusion of the ColE1 inverted repeat) is elevated by addition of salt. The temperature required for extrusion was increased by about 4 deg for an addition of 10 mM NaCl. 2. A + T rich regions in supercoiled DNA exhibit hyperreactivity towards osmium tetroxide as the temperature is raised; this reactivity is strongly suppressed by the addition of salt. At low salt concentrations of added NaCl (10 mM) we observe that there is an approximate equivalence between reducing the salt concentration, and the elevation of temperature. Above 30 mM NaCl the reactivity of the ColE1 sequences is completely supressed at normal temperatures. 3. Stable helix opening transitions in A + T rich sequences may be observed with elevated temperature, using two-dimensional gel electrophoresis; these transitions become progressively harder to demonstrate with the addition of salt. With the addition of low concentrations of salt, the onset of opening transitions shifts to higher superhelix density, and by 30 mM NaCl or more, no transitions are visible up to a temperature of 50 degrees C. Statistical mechanical simulation of the data indicate that the cooperativity free energy for the transition is unaltered by addition of salt, but that the free energy cost for opening each basepair is increased. These results demonstrate that addition of even relatively low concentrations of salt strongly suppress the large-scale helix opening of A + T rich regions, even at high levels of negative supercoiling. While the opening at low salt concentrations may reveal a propensity for such transitions, spontaneous opening is very unlikely under physiological conditions of salt, temperature and superhelicity, and we conclude that proteins will therefore be required to facilitate opening transitions in cellular DNA.     

A model for sedimentation in inhomogeneous media. II. Compressibility of aqueous and organic solvents

The effects of solvent compressibility on the sedimentation behavior of macromolecules as observed in analytical ultracentrifugation are examined. Expressions for the density and pressure distributions in the solution column are derived and combined with the finite element solution of the Lamm equation in inhomogeneous media to predict the macromolecular concentration distributions under different conditions. Independently, analytical expressions are derived for the sedimentation of non-diffusing particles in the limit of low compressibility. Both models are quantitatively consistent and predict solvent compressibility to result in a reduction of the sedimentation rate along the solution column and a continuous accumulation of solutes in the plateau region. For both organic and aqueous solvents, the calculated deviations from the sedimentation in incompressible media can be very large and substantially above the measurement error. Assuming conventional configurations used for sedimentation velocity experiments in analytical ultracentrifugation, neglect of the compressibility of water leads to systematic errors underestimating sedimentation coefficients by approximately 1% at a rotor speeds of 45000 rpm, but increasing to 2-5% with increasing rotor speeds and decreasing macromolecular size. The proposed finite element solution of the Lamm equation can be used to take solvent compressibility quantitatively into account in direct boundary models for discrete species, sedimentation coefficient distributions or molar mass distributions. Using the analytical expressions for the sedimentation of non-diffusing particles, the ls-g*(s) distribution of apparent sedimentation coefficients is extended to the analysis of sedimentation in compressible solvents. The consideration of solvent compressibility is highly relevant not only when using organic solvents, but also in aqueous solvents when precise sedimentation coefficients are needed, for example, for hydrodynamic modeling.     

An explanation for rotor speed effects observed during sedimentation of large folded DNA molecules

A model is proposed to account for the changes in sedimentation coefficient (s) that are observed when isolated bacterial micleoids are sedimented at different rotor speeds. It is suggested that the terminal of DNA loops in the chromosome become analogous hydrodynamically to the ends of a linear DNA double-helix. The loops then become more extended at higher rotor speeds resulting in an increased fractional coefficient. Application of the Zimm (1974) equation to this model shows that the predicted changes in s values are consistent with those observed. Similar changes in s values occur when the chromosome is sedimented in rotors of different geometry including a zonal rotor. Thus, the changes are not due to wall interactions.     

A micelle model for the sedimentation behavior of bovine beta-casein

The monomer-single polymer model of G.A. Gilbert (Disc. Faraday Soc. 20 (1955) 68) for moving boundary sedimentation has been used by Payens and colleagues to explain the observed results for bovine caseins, and by Harrington and colleagues to explain the observed results for myosin fibrils. Electron microscope pictures of Buchheim and Schmidt have subsequently revealed micellar beta-casein in the form of slightly elongated or spherical particles having a bimodal size distribution, but with a broad range of particle sizes, at concentrations not too far above the critical micelle concentration. The equilibrium properties of a broadly distributed micellar system can be fitted by the shell model developed by one of us, and in the present article, the shell model is extended to predict the moving boundary sedimentation behavior of such a system. The observed sedimentation patterns, as well as the critical concentration predictions of the monomer-single polymer Gilbert sedimentation model, are satisfactorily described with the present model, based on a continuous distribution of intermediates between monomers and the largest possible spherical micelles. For one example considered, the predicted frequency distribution of molecular weight is in qualitative agreement with the frequency distribution of particle volume found by Buchheim and Schmidt.