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.     

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.     

Dimensions of plectonemically supercoiled DNA

With a view to determine the configuration and regularity of plectonemically supercoiled DNA, we have measured the small angle neutron scattering from pUC18 plasmid in saline solutions. Furthermore, we have derived the mathematical expression for the single chain scattering function (form factor) of a superhelical structure, including the longitudinal and transverse interference over the plectonemic pitch and radius, respectively. It was found that an interwound configuration describes the data well, provided interactions among supercoils are accounted for in the second virial approximation. The opening angle was observed to be relatively constant and close to 58 degrees, but it was necessary to include a significant distribution in radius and pitch. For diluted supercoils with vanishing mutual interaction, the derived structural results agree with independent measurements, including the distribution in linking number deficit as determined by gel electrophoresis. With increasing plasmid concentration, prior and covering the transition to the liquid-crystalline phase, the radius and pitch are seen to decrease significantly. The latter observation shows that compaction of negatively supercoiled DNA by confinement results in a decrease in writhing number at the cost of a positive twist exerted on the DNA duplex. It is our conjecture that the free energy associated with this excess twist is of paramount importance in controlling the critical boundaries pertaining to the transition to the anisotropic, liquid-crystalline phase.     

Structure of plectonemically supercoiled DNA

Using electron microscopy and topological methods, we have deduced an average structure for negatively supercoiled circular DNA in solution. Our data suggest that DNA has a branched plectonemic (interwound) form over the range of supercoiling tested. The length of the superhelix axis is constant at 41% of the DNA length, whereas the superhelix radius decreases essentially hyperbolically as supercoiling increases. The number of supercoils is 89% of the linking deficit. Both writhe and twist change with supercoiling, but the ratio of the change in writhe to the change in twist is fixed at 2.6:1. The extent of branching of the superhelix axis is proportional to the length of the plasmid, but is insensitive to superhelix density. The relationship between DNA flexibility constants for twisting and bending calculated using our structural data is similar to that deduced from previous studies. The extended thin form of plectonemically supercoiled DNA offers little compaction for cellular packaging, but promotes interaction between cis-acting sequence elements that may be distant in primary structure. We discuss additional biological implications of our structural data.     

Site-specific labeling of supercoiled DNA

Visualization of site-specific labels in long linear or circular DNA allows unambiguous identification of various local DNA structures. Here we describe a novel and efficient approach to site-specific DNA labeling. The restriction enzyme SfiI binds to DNA but leaves it intact in the presence of calcium and therefore may serve as a protein label of 13 bp recognition sites. Since SfiI requires simultaneous interaction with two DNA recognition sites for stable binding, this requirement is satisfied by providing an isolated recognition site in the DNA target and an additional short DNA duplex also containing the recognition site. The SfiI/DNA complexes were visualized with AFM and the specificity of the labeling was confirmed by the length measurements. Using this approach, two sites in plasmid DNA were labeled in the presence of a large excess of the helper duplex to compete with the formation of looped structures of the intramolecular synaptic complex. We show that the labeling procedure does not interfere with the superhelical tension-driven formation of alternative DNA structures such as cruciforms. The complex is relatively stable at low and high pH (pH 5 and 9) making the developed approach attractive for use at conditions requiring the pH change.     

Cruciform-resolvase interactions in supercoiled DNA

T4 endonuclease VII, which cleaves Holliday-like junctions in DNA, specifically cleaves short inverted repeats in supercoiled plasmids. These sequences are subject to site-specific cleavage by single-strand-specific nucleases, and cruciform formation has been suggested as an explanation for this observation. This proposal is greatly strengthened by the present data, since a formal analogy between cruciform structures and Holliday junctions exists. Resolution of a variety of unrelated cruciform sequences demonstrates that the cleavage process results in a linear molecule with hairpin ends and single ligatable nicks at positions corresponding to the stem-base of the cruciform. In two examples mapped in detail, the cleavages are exclusively introduced at two or three nucleotides from the end of the symmetric sequence at the 5' side on each strand. These studies demonstrate the potential of endonuclease VII as a probe of cruciform structure and the utility of short cruciform structures as Holliday junction models.     

Early melting of supercoiled DNA.

Denaturing gradient gel electrophoresis (formamide with urea) has been used to study the melting of supercoiled DNA. A linear gradient of denaturant concentration proportional to a 25 degrees C linear increase of temperature (Teff) from the left to the right edge of the gel was created perpendicular to DNA migration. The mobility of supercoiled DNA molecules was shown to drop to the level of relaxed molecules a long way (5-30 degrees C) before linear DNA began to melt. The further increase of Teff, including the melting range for linear molecules, caused no appreciable changes in the mobility of relaxed molecules. The transition curves are S-shaped for all the topoisomers, and an increase of superhelicity shifts the transition towards lower Teff values. The analysis of the results indicates that the observed relaxation of superhelical molecules is due to denatured region forming in them, their size increasing with the topoisomer number.     

Electrostatic-undulatory theory of plectonemically supercoiled DNA

We present an analytical calculation of the electrostatic interaction in a plectonemic supercoil within the Poisson-Boltzmann approximation. Undulations of the supercoil strands arising from thermal motion couple nonlinearly with the electrostatic interaction, giving rise to a strong enhancement of the bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution containing the bending and torsional energies and an electrostatic-undulatory free energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the usual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monovalent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In particular, we confirm the experimental observation that the writhe is a virtually constant fraction of the excess linking number over a wide range of superhelical densities. Another important prediction is the ionic strength dependence of the plectonemic parameters, which is in reasonable agreement with the results from computer simulations.     

Bidirectional sequencing of supercoiled plasmid DNA

In this paper we show that restriction DNA fragments can prime DNA synthesis of a homologous supercoiled plasmid DNA. Using the dideoxyribonucleotide chain terminator method, newly synthesized truncated chains can be detached from the primers by restriction enzyme digestion. Therefore, by choosing DNA fragments flanked by two different restriction enzymes sites, nucleotide sequence information can be simultaneously obtained on both regions of the DNA surrounding the restriction fragment. The advantage of this sequencing approach over current methods is that no prior knowledge of the primary sequence is needed to find the nucleotide sequence of a given DNA fragment. Thus, synthetic primers are not required and internal sequences of a given clone can be easily accessed without the need of fragmenting the original construct. The method has been used with rapid plasmid preparations, thus considerable time and effort can be saved in the gathering of nucleotide sequence information.     

Oversupercoiling and compactization of supercoiled DNA

Supercoiled DNA pGEMEX with length of 3993 nucleotides was immobilized on the different substrates (freshly cleaved mica, standard aminomica and modified aminomica) and visualized by atomic force microscopy. Plectonomically supercoiled DNA molecules as well as molecules with extremely high level of compactization (i.e. molecules with considerably higher supercoiled density values in comparing with experimentally measured and theoretically investigated ones) were visualized on modified aminomica. At the further increasing of the compactization level an axis length of oversupercoiled molecules was decreased from approximately 390 nm to approximately 140 nm and formation of minitoroids of approximately 50 nm diameter and molecules in sphere conformation were observed. Model of possible conformational transitions of supercoiled DNA was proposed basing on the analysis of captured AFM images at the increasing of supercoiling density.     

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.     

Nanomechanics of negatively supercoiled diaminopurine-substituted DNA

Single molecule experiments have demonstrated a progressive transition from a B- to an L-form helix as DNA is gently stretched and progressively unwound. The particular sequence of a DNA segment defines both base stacking and hydrogen bonding that affect the partitioning and conformations of the two phases. Naturally or artificially modified bases alter H-bonds and base stacking and DNA with diaminopurine (DAP) replacing adenine was synthesized to produce linear fragments with triply hydrogen-bonded DAP:T base pairs. Both unmodified and DAP-substituted DNA transitioned from a B- to an L-helix under physiological conditions of mild tension and unwinding. This transition avoids writhing and the ease of this transition may prevent cumbersome topological rearrangements in genomic DNA that would require topoisomerase activity to resolve. L-DNA displayed about tenfold lower persistence length than B-DNA. However, left-handed DAP-substituted DNA was twice as stiff as unmodified L-DNA. Unmodified DNA and DAP-substituted DNA have very distinct mechanical characteristics at physiological levels of negative supercoiling and tension.     

Strand separation in negatively supercoiled DNA

We consider Benham’s model for strand separation in negatively supercoiled circular DNA, and study denaturation as function of the linking difference density κ<0. We propose a statistical version of this model, based on bayesian segmentation methods of current use in bioinformatics; this leads to new algorithms with priors adapted to supercoiled DNA, taking into account the random nature of the free energies needed to denature base pairs.     

Tungsten particle-induced nicking of supercoiled plasmid DNA

Small particles of metallic tungsten, known also as tungsten microprojectiles, are routinely used for biotechnological purposes. In such applications, tungsten was observed to affect the integrity of plasmid DNA. Here we present evidence that interaction between tungsten particles and intact circular plasmids pU19, pUC119, and ColE1 may result in generation of a limited number of single-strand DNA breaks. As a consequence, supercoiled DNA is converted into its open circular form and no fragmentation products can be detected. The rate of the tungsten-mediated reaction depends on pH but is not influenced by ascorbate, Tris, or EDTA. No DNA nicking can be observed when the tungsten particles are replaced by substances that can be leached out from these particles with water or incubation buffers. Likewise, commercial sodium tungstate, tungsten (VI) oxide, and tungsten (VI) chloride and products of its decomposition remain DNA undamaged. Native plasmid DNA molecules, upon adsorption on the surface of tungsten microparticles, may undergo some nicking without a need for participation of external catalysts.     

Monte Carlo implementation of supercoiled double-stranded DNA

Metropolis Monte Carlo simulation is used to investigate the elasticity of torsionally stressed double-stranded DNA, in which twist and supercoiling are incorporated as a natural result of base-stacking interaction and backbone bending constrained by hydrogen bonds formed between DNA complementary nucleotide bases. Three evident regimes are found in extension versus torsion and force versus extension plots: a low-force regime in which over- and underwound molecules behave similarly under stretching; an intermediate-force regime in which chirality appears for negatively and positively supercoiled DNA and extension of underwound molecule is insensitive to the supercoiling degree of the polymer; and a large-force regime in which plectonemic DNA is fully converted to extended DNA and supercoiled DNA behaves quite like a torsionless molecule. The striking coincidence between theoretic calculations and recent experimental measurement of torsionally stretched DNA (Strick et al., Science. 271:1835, 1996; Biophys. J. 74:2016, 1998) strongly suggests that the interplay between base-stacking interaction and permanent hydrogen-bond constraint takes an important role in understanding the novel properties of elasticity of supercoiled DNA polymer.     

DNA curvature influences the internal motions of supercoiled DNA.

We present evidence that short curved DNA segments can act as mediators for the ordering of large domains in superhelical DNA. Using a non-invasive solution method (dynamic light scattering), we investigated the effect of permanently curved inserts on the solution structure and on the internal motions of superhelical plasmid DNA. We find that the dynamics of superhelical DNA are strongly influenced by sequence- or protein-induced bending: in superhelical plasmids containing curved inserts the amplitude of the internal motion is lower than that of non-curved controls. Furthermore, the relative arrangement of curved sequences in the plasmids can influence the overall shape of the superhelical DNA. On linearized forms of the plasmids, these effects are not observed.     

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.     

Influencing the B-Z switch in supercoiled DNA

The effect of Z-binding ligands on the supercoiling threshold in the supercoil-induced B-Z transition has been examined from the point of view of a two-state model. Expressions have been derived for the determination of the shift in critical supercoil density in terms of the physical parameters of the DNA-ligand system. Representative calculations indicate that the stabilizing action of Z-binding ligands on the Z conformation in closed circular DNA depends largely on the binding characteristics of the ligand. Application of the theoretical data has been demonstrated using the experimental results reported by Lafer et al. (J. Biol. Chem. 261 (1986) 6438).