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.     

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model’s ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.     

Conformational and thermodynamic properties of supercoiled DNA.

We used Monte Carlo simulations to investigate the conformational and thermodynamic properties of DNA molecules with physiological levels of supercoiling. Three parameters determine the properties of DNA in this model: Kuhn statistical length, torsional rigidity and effective double-helix diameter. The chains in the simulation resemble strongly those observed by electron microscopy and have the conformation of an interwound superhelix whose axis is often branched. We compared the geometry of simulated chains with that determined experimentally by electron microscopy and by topological methods. We found a very close agreement between the Monte Carlo and experimental values for writhe, superhelix axis length and the number of superhelical turns. The computed number of superhelix branches was found to be dependent on superhelix density, DNA chain length and double-helix diameter. We investigated the thermodynamics of supercoiling and found that at low superhelix density the entropic contribution to superhelix free energy is negligible, whereas at high superhelix density, the entropic and enthalpic contributions are nearly equal. We calculated the effect of supercoiling on the spatial distribution of DNA segments. The probability that a pair of DNA sites separated along the chain contour by at least 50 nm are juxtaposed is about two orders of magnitude greater in supercoiled DNA than in relaxed DNA. This increase in the effective local concentration of DNA is not strongly dependent on the contour separation between the sites. We discuss the implications of this enhancement of site juxtaposition by supercoiling in the context of protein-DNA interactions involving multiple DNA-binding sites.     

Effect of DNA supercoiling on the geometry of holliday junctions

Unusual DNA conformations including cruciforms play an important role in gene regulation and various DNA transactions. Cruciforms are also the models for Holliday junctions, the transient DNA conformations critically involved in DNA homologous and site-specific recombination, repair, and replication. Although the conformations of immobile Holliday junctions in linear DNA molecules have been analyzed with the use of various techniques, the role of DNA supercoiling has not been studied systematically. We utilized atomic force microscopy (AFM) to visualize cruciform geometry in plasmid DNA with different superhelical densities at various ionic conditions. Both folded and unfolded conformations of the cruciform were identified, and the data showed that DNA supercoiling shifts the equilibrium between folded and unfolded conformations of the cruciform toward the folded one. In topoisomers with low superhelical density, the population of the folded conformation is 50-80%, depending upon the ionic strength of the buffer and a type of cation added, whereas in the sample with high superhelical density, this population is as high as 98-100%. The time-lapse studies in aqueous solutions allowed us to observe the conformational transition of the cruciform directly. The time-dependent dynamics of the cruciform correlates with the structural changes revealed by the ensemble-averaged analysis of dry samples. Altogether, the data obtained show directly that DNA supercoiling is the major factor determining the Holliday junction conformation.     

Introduction of interrupted secondary structure in supercoiled DNA as a function of superhelix density: consideration of hairpin structures in superhelical DNA.

PM2 DNA was prepared with different superhelical densities (sigma) in order to examine the relationship betweenn supercoiling and the occurrence of a region(s) of unpaired bases in this DNA. A previous study showed that CH3HgOH reacts with native superhelical PM2 DNA more rapidly than the nicked form II. This evaluation of binding, monitored through the change of sedimentation velocity, was repeated on PM2 DNA I with different superhelical densities. Early binding is detected by an increase in sedimentation velocity and occurs with molecules with sigma' values betwee -0.025 and -0.037. The conversion of form I to form II with the single-strand-specific endonuclease from Neurospora crassa also occurs above a sigma value of -0.025. This data strongly supports the view that supercoiling produces interrupted secondary structure. The question whether the interrupted regions remain single stranded in character or form small intrastrand hairpin regions is considered by examining which model best fits the CH3HgOH- induced sedimentation velocity changes and the standard sedimentation velocity versus the superhelical density curve for the in vitro made DNAs. The hairpin model offers the most satisfactory explanations for all the results of this and previous studies.     

Control of bacterial DNA supercoiling

Two DNA topoisomerases control the level of negative supercoiling in bacterial cells. DNA gyrase introduces supercoils, and DNA topoisomerase I prevents supercoiling from reaching unacceptably high levels. Perturbations of supercoiling are corrected by the substrate preferences of these topoisomerases with respect to DNA topology and by changes in expression of the genes encoding the enzymes. However, supercoiling changes when the growth environment is altered in ways that also affect cellular energetics. The ratio of [ATP] to [ADP], to which gyrase is sensitive, may be involved in the response of supercoiling to growth conditions. Inside cells, supercoiling is partitioned into two components, superhelical tension and restrained supercoils. Shifts in superhelical tension elicited by nicking or by salt shock do not rapidly change the level of restrained supercoiling. However, a steady-state change in supercoiling caused by mutation of topA does alter both tension and restrained supercoils. This communication between the two compartments may play a role in the control of supercoiling.     

Structural and Molecular Biology of the eye Lens Membrane

Abstract

The DNA double helix exhibits local sequence-dependent polymorphism at the level of the single base pair and dinucleotide step. Curvature of the DNA molecule occurs in DNA regions with a specific type of nucleotide sequence periodicities. Negative supercoiling induces in vitro local nucleotide sequence-dependent DNA structures such as cruciforms, left-handed DNA, multistranded structures, etc. Techniques based on chemical probes have been proposed that make it possible to study DNA local structures in cells. Recent results suggest that the local DNA structures observed in vitro exist in the cell, but their occurrence and structural details are dependent on the DNA superhelical density in the cell and can be related to some cellular processes.     

Effects of the pSC101 partition (par) locus on in vivo DNA supercoiling near the plasmid replication origin.

Previous work has shown that deletion of the partition (par) locus of plasmid pSC101 results in decreased overall superhelical density of plasmid DNA and concommitant inability of the plasmid to be stably inherited in populations of dividing cells. We report here that the biological effects of par correlate specifically with its ability to generate supercoils in vivo near the origin of pSC101 DNA replication. Using OsO4 reactivity of nucleotides adjoining 20 bp (G-C) tracts introduced into pSC101 DNA to measure local DNA supercoiling, we found that the wild type par locus generates supercoiling near the plasmid's replication origin adequate to convert a (G-C) tract in the region to Z form DNA. A 4 bp deletion that decreases par function, but produces no change in the overall superhelicity of pSC101 DNA as determined by chloroquine/agarose gel analysis, nevertheless reduced (G-C) tract supercoiling sufficiently to eliminate OsO4 reactivity. Mutation of the bacterial topA gene, which results in stabilized inheritance of par-deleted plasmids, restored supercoiling of (G-C) tracts in these plasmids and increased OsO4 reactivity in par+ replicons. Removal of par to a site more distant from the origin decreased supercoiling in a (G-C) tract adjacent to the origin and diminished par function. Collectively, these findings indicate that par activity is dependent on its ability to produce supercoiling at the replication origin rather than on the overall superhelical density of the plasmid DNA.     

The role of negative supercoiling in Hin-mediated site-specific recombination.

A series of biochemical assays were developed and performed to monitor the molecular events that occur during the Hin-mediated DNA inversion reaction. These events can be divided into five different stages: 1) binding of proteins (Hin, Fis, and HU) to DNA; 2) pairing of Hin-binding sites; 3) invertasome formation; 4) DNA strand cleavage; 5) strand rotation and religation. A series of topoisomers of the wild type DNA substrate plasmid (ranging from fully relaxed molecules to those with more than the physiological superhelical density (the physiological superhelical density of pKH336 from Escherichia coli DH10B is -0.072 in this study)) was generated, and the role of negative supercoiling in each step of the inversion reaction was investigated. We found differences in the dependence of the formation of paired Hin-binding sites and of the invertasome formation on the superhelical density of the substrate plasmid. Pairing of Hin-binding sites occurs independently from invertasome formation, and a relatively low degree of negative supercoiling is enough to promote maximal pairing. However, efficient invertasome formation requires higher levels of negative supercoiling.     

The expression of the Escherichia coli fis gene is strongly dependent on the superhelical density of DNA

The Escherichia coli DNA architectural protein FIS is a pleiotropic regulator, which couples the cellular physiology with transitions in the superhelical density of bacterial DNA. Recently, we have shown that this effect is in part mediated via DNA gyrase, the major cellular topoisomerase responsible for the elevation of negative supercoiling. Here, we demonstrate that, in turn, the expression of the fis gene strongly responds to alterations in the topology of DNA in vivo, being maximal at high levels of negative supercoiling. Any deviations from these optimal levels decrease fis promoter activity. This strict dependence of fis expression on the superhelical density suggests that fis may be involved in 'fine-tuning' the homeostatic control mechanism of DNA supercoiling in E. coli.     

Bacterial Nucleoid: Interplay of DNA Demixing and Supercoiling

This work addresses the question of the interplay of DNA demixing and supercoiling in bacterial cells. Demixing of DNA from other globular macromolecules results from the overall repulsion between all components of the system and leads to the formation of the nucleoid, which is the region of the cell that contains the genomic DNA in a rather compact form. Supercoiling describes the coiling of the axis of the DNA double helix to accommodate the torsional stress injected in the molecule by topoisomerases. Supercoiling is able to induce some compaction of the bacterial DNA, although to a lesser extent than demixing. In this work, we investigate the interplay of these two mechanisms with the goal of determining whether the total compaction ratio of the DNA is the mere sum or some more complex function of the compaction ratios due to each mechanism. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. This work reveals that there actually exist different regimes, depending on the crowder volume ratio and the DNA superhelical density. In particular, a regime in which the effects of DNA demixing and supercoiling on the compaction of the DNA coil simply add up is shown to exist up to moderate values of the superhelical density. In contrast, the mean radius of the DNA coil no longer decreases above this threshold and may even increase again for sufficiently large crowder concentrations. Finally, the model predicts that the DNA coil may depart from the spherical geometry very close to the jamming threshold as a trade-off between the need to minimize both the bending energy of the stiff plectonemes and the volume of the DNA coil to accommodate demixing.     

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.