Modulation of intramolecular interactions in superhelical DNA by curved sequences: a Monte Carlo simulation study

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

A quantitative model of a cooperative two-state equilibrium in DNA: experimental tests, insights, and predictions

Quantitative parameters for a two-state cooperative transition in duplex DNAs were finally obtained during the last 5 years. After a brief discussion of observations pertaining to the existence of the two-state equilibrium per se, the lengths, torsion, and bending elastic constants of the two states involved and the cooperativity parameter of the model are simply stated. Experimental tests of model predictions for the responses of DNA to small applied stretching, twisting, and bending stresses, and changes in temperature, ionic conditions, and sequence are described. The mechanism and significance of the large cooperativity, which enables significant DNA responses to such small perturbations, are also noted. The capacity of the model to resolve a number of long-standing and sometimes interconnected puzzles in the extant literature, including the origin of the broad pre-melting transition studied by numerous workers in the 1960s and 1970s, is demonstrated. Under certain conditions, the model predicts significant long-range attractive or repulsive interactions between hypothetical proteins with strong preferences for one or the other state that are bound to well-separated sites on the same DNA. A scenario is proposed for the activation of the ilvPG promoter on a supercoiled DNA by integration host factor.

Effect of sequence-dependent rigidity on plectoneme localization in dsDNA

We use Monte-Carlo simulations to study the effect of variable rigidity on plectoneme formation and localization in supercoiled double-stranded DNA. We show that the presence of soft sequences increases the number of plectoneme branches and that the edges of the branches tend to be localized at these sequences. We propose an experimental approach to test our results in vitro, and discuss the possible role played by plectoneme localization in the search process of transcription factors for their targets (promoter regions) on the bacterial genome.

Normal-Mode Analysis of Circular DNA at the Base-Pair Level. 2. Large-Scale Configurational Transformation of a Naturally Curved Molecule

Fine structural and energetic details embedded in the DNA base sequence, such as intrinsic curvature, are important to the packaging and processing of the genetic material. Here we investigate the internal dynamics of a 200 bp closed circular molecule with natural curvature using a newly developed normal-mode treatment of DNA in terms of neighboring base-pair "step" parameters. The intrinsic curvature of the DNA is described by a 10 bp repeating pattern of bending distortions at successive base-pair steps. We vary the degree of intrinsic curvature and the superhelical stress on the molecule and consider the normal-mode fluctuations of both the circle and the stable figure-8 configuration under conditions where the energies of the two states are similar. To extract the properties due solely to curvature, we ignore other important features of the double helix, such as the extensibility of the chain, the anisotropy of local bending, and the coupling of step parameters. We compare the computed normal modes of the curved DNA model with the corresponding dynamical features of a covalently closed duplex of the same chain length constructed from naturally straight DNA and with the theoretically predicted dynamical properties of a naturally circular, inextensible elastic rod, i.e., an O-ring. The cyclic molecules with intrinsic curvature are found to be more deformable under superhelical stress than rings formed from naturally straight DNA. As superhelical stress is accumulated in the DNA, the frequency, i.e., energy, of the dominant bending mode decreases in value, and if the imposed stress is sufficiently large, a global configurational rearrangement of the circle to the figure-8 form takes place. We combine energy minimization with normal-mode calculations of the two states to decipher the configurational pathway between the two states. We also describe and make use of a general analytical treatment of the thermal fluctuations of an elastic rod to characterize the motions of the minicircle as a whole from knowledge of the full set of normal modes. The remarkable agreement between computed and theoretically predicted values of the average deviation and dispersion of the writhe of the circular configuration adds to the reliability in the computational approach. Application of the new formalism to the computed modes of the figure-8 provides insights into macromolecular motions which are beyond the scope of current theoretical treatments.

Competition between curls and plectonemes near the buckling transition of stretched supercoiled DNA

Recent single-molecule experiments have observed that formation of a plectonemically supercoiled region in a stretched, twisted DNA proceeds via abrupt formation of a small plectonemic "bubble." A detailed mesoscopic model is presented for the formation of plectonemic domains, including their positional entropy, and the influence of small chiral loops or "curls" along the extended DNA. Curls begin to appear just before plectoneme formation, and are more numerous at low salt concentrations (<20 mM univalent ions) and at low forces (<0.5 pN). However, plectonemic domains quickly become far more stable slightly beyond the transition to supercoiling at moderate forces and physiological salt conditions. At the supercoiling transition, for shorter DNAs (2 kb) only one supercoiled domain appears, but for longer DNAs at lower forces (<0.5 pN) positional entropy favors formation of more than one plectonemic domain; a similar effect occurs for low salt. Although they are not the prevalent mode of supercoiling, curls are a natural transition state for binding of DNA-loop-trapping enzymes; we show how addition of loop-trapping enzymes can modify the supercoiling transition. The behavior of DNA torque is also discussed, including the effect of the measurement apparatus torque stiffness, which can play a role in determining how large the torque "overshoot" is at the buckling transition.

Unlinking of supercoiled DNA catenanes by type IIA topoisomerases

It was found recently that DNA catenanes, formed during replication of circular plasmids, become positively (+) supercoiled, and the unlinking of such catenanes by type IIA topoisomerases proceeds much more efficiently than the unlinking of negatively (-) supercoiled catenanes. In an attempt to explain this striking finding we studied, by computer simulation, conformational properties of supercoiled DNA catenanes. Although the simulation showed that conformational properties of (+) and (-) supercoiled replication catenanes are very different, these properties per se do not give any advantage to (+) supercoiled over (-) supercoiled DNA catenanes for unlinking. An advantage became evident, however, when we took into account the established features of the enzymatic reaction catalyzed by the topoisomerases. The enzymes create a sharp DNA bend in the first bound DNA segment and allow for the transport of the second segment only from inside the bend to its outside. We showed that in (-) supercoiled DNA catenanes this protein-bound bent segment becomes nearly inaccessible for segments of the other linked DNA molecule, inhibiting the unlinking.

Computational modeling of the chromatin fiber

The packing of the genomic DNA in the living cell is essential for its biological function. While individual aspects of the genome architecture, such as DNA and nucleosome structure or the arrangement of chromosome territories are well studied, much information is missing for a unified description of cellular DNA at all its structural levels. Computer modeling can contribute to such a description. We present here some typical approaches to models of the chromatin fiber, including different amounts of detail in the description of the local nucleosome structure. The main results from our simulations are that the physical properties of the chromatin fiber can be well described by a simplified model consisting of cylinder-like nucleosomes connected by flexible DNA segments, with a geometry determined by the bending and twisting angles between nucleosomes. Randomness in the local geometry - such as random absence of linker histone H1 - leads to a dramatic increase in the chromatin fiber flexibility. Furthermore, we show that chromatin is much more flexible to bending than to stretching, and that the structure of the chromatin fiber favors the formation of sharp bends.

Protein-induced local DNA bends regulate global topology of recombination products

The tyrosine family of recombinases produces two smaller DNA circles when acting on circular DNA harboring two recombination sites in head-to-tail orientation. If the substrate is supercoiled, these circles can be unlinked or form multiply linked catenanes. The topological complexity of the products varies strongly even for similar recombination systems. This dependence has been solved here. Our computer simulation of the synapsis showed that the bend angles, phi, created in isolated recombination sites by protein binding before assembly of the full complex, determine the product topology. To verify the validity of this theoretical finding we measured the values of phi for Cre/loxP and Flp/FRT systems. The measurement was based on cyclization of the protein-bound short DNA fragments in solution. Despite the striking similarity of the synapses for these recombinases, action of Cre on head-to-tail target sites produces mainly unlinked circles, while that of Flp yields multiply linked catenanes. In full agreement with theoretical expectations we found that the values of phi for these systems are very different, close to 35 degrees and 80 degrees, respectively. Our findings have general implications in how small protein machines acting locally on large DNA molecules exploit statistical properties of their substrates to bring about directed global changes in topology.

Effect of supercoiling on formation of protein-mediated DNA loops

DNA loop formation is one of several mechanisms used by organisms to regulate genes. The free energy of forming a loop is an important factor in determining whether the associated gene is switched on or off. In this paper we use an elastic rod model of DNA to determine the free energy of forming short (50-100 basepair), protein mediated DNA loops. Superhelical stress in the DNA of living cells is a critical factor determining the energetics of loop formation, and we explicitly account for it in our calculations. The repressor protein itself is regarded as a rigid coupler; its geometry enters the problem through the boundary conditions it applies on the DNA. We show that a theory with these ingredients is sufficient to explain certain features observed in modulation of in vivo gene activity as a function of the distance between operator sites for the lac repressor. We also use our theory to make quantitative predictions for the dependence of looping on superhelical stress, which may be testable both in vivo and in single-molecule experiments such as the tethered particle assay and the magnetic bead assay.

Two-angle model and phase diagram for chromatin

We have studied the phase diagram for chromatin within the framework of the two-angle model. Only a rough estimation of the forbidden surface of the phase diagram for chromatin was given in a previous work of Schiessel. We revealed the fine structure of this excluded-volume borderline numerically and analytically. Furthermore, we investigated the Coulomb repulsion of the DNA linkers to compare it with the previous results.

Polymer chain models of DNA and chromatin

Many properties of the genome in the cell nucleus can be understood by modeling DNA and chromatin as a flexible polymer chain. This article introduces into current models for such a coarse-grained description and reviews some recent results from our own group. Examples given are the unrolling of DNA from the histone core and the response of the 30 nm chromatin fiber to mechanical stretching.

DNA-loop formation on nucleosomes shown by in situ scanning force microscopy of supercoiled DNA

The flexibility of the chromatin structure, necessary for the processing of the genomic DNA, is controlled by a number of factors where flexibility and mobility of the nucleosomes is essential. Here, the influence of DNA supercoiling on the structure of single nucleosomes is investigated. Circular supercoiled plasmid DNA sub-saturated with histones was visualized by scanning force microscopy (SFM) in aqueous solution. SFM-imaging compared with topological analysis indicates instability of nucleosomes when the salt concentration is raised from 10 mM to 100 mM NaCl. Nucleosomes were observed after the deposition to the used scanning surface, i.e. mica coated with polylysine. On the images, the nucleosomes appear with a high probability in end-loops near the apices of the superhelices. In 100 mM NaCl but not in 10 mM NaCl, a significant number of complexes present the nucleosomes on superhelical crossings mainly located adjacent to an end-loop. The morphology of these structures and statistical analysis suggest that DNA loops were formed on the histone octamers, where the loop size distribution shows a pronounced peak at 50 nm. Recently, the formation and diffusion of loops on octamers has been discussed as a mechanism of translocations of nucleosomes along DNA. The presented data likely confirm the occurrence of loops, which may be stabilized by supercoiling. Analysis of the structure of regular nucleosomes not located on crossings indicates that reducing the salt concentration leads to more conformations, where DNA is partially unwrapped from the distal ends of the octamer.

Dynamics of DNA loop capture by the SfiI restriction endonuclease on supercoiled and relaxed DNA

The SfiI endonuclease is a prototype for DNA looping. It binds two copies of its recognition sequence and, if Mg(2+) is present, cuts both concertedly. Looping was examined here on supercoiled and relaxed forms of a 5.5 kb plasmid with three SfiI sites: sites 1 and 2 were separated by 0.4 kb, and sites 2 and 3 by 2.0 kb. SfiI converted this plasmid directly to the products cut at all three sites, though DNA species cleaved at one or two sites were formed transiently during a burst phase. The burst revealed three sets of doubly cut products, corresponding to the three possible pairings of sites. The equilibrium distribution between the different loops was evaluated from the burst phases of reactions initiated by adding MgCl(2) to SfiI bound to the plasmid. The short loop was favored over the longer loops, particularly on supercoiled DNA. The relative rates for loop capture were assessed after adding SfiI to solutions containing the plasmid and MgCl(2). On both supercoiled and relaxed DNA, the rate of loop capture across 0.4 kb was only marginally faster than over 2.0 kb or 2.4 kb. The relative strengths and rates of looping were compared to computer simulations of conformational fluctuations in DNA. The simulations concurred broadly with the experimental data, though they predicted that increasing site separations should cause a shallower decline in the equilibrium constants than was observed but a slightly steeper decline in the rates for loop capture. Possible reasons for these discrepancies are discussed.

Sequence-dependent nucleosome structural and dynamic polymorphism. Potential involvement of histone H2B N-terminal tail proximal domain

Relaxation of nucleosomes on an homologous series (pBR) of ca 350-370 bp DNA minicircles originating from plasmid pBR322 was recently used as a tool to study their structure and dynamics. These nucleosomes thermally fluctuated between three distinct DNA conformations within a histone N-terminal tail-modulated equilibrium: one conformation was canonical, with 1.75 turn wrapping and negatively crossed entering and exiting DNAs; another was also "closed", but with these DNAs positively crossed; and the third was "open", with a lower than 1.5 turn wrapping and uncrossed DNAs. In this work, a new minicircle series (5S) of similar size was used, which contained the 5S nucleosome positioning sequence. Results showed that DNA in pBR nucleosomes was untwisted by approximately 0.2 turn relative to 5S nucleosomes, which DNase I footprinting confirmed in revealing a approximately 1 bp untwisting at each of the two dyad-distal sites where H2B N-terminal tails pass between the two gyres. In contrast, both nucleosomes showed untwistings at the dyad-proximal sites, i.e. on the other gyre, which were also observed in the high-resolution crystal structure. 5S nucleosomes also differ with respect to their dynamics: they hardly accessed the positively crossed conformation, but had an easier access to the negatively crossed conformation. Simulation showed that such reverse effects on the conformational free energies could be simply achieved by slightly altering the trajectories of entering and exiting DNAs. We propose that this is accomplished by H2B tail untwisting at the distal sites through action at a distance ( approximately 20 bp) on H3-tail interactions with the small groove at the nucleosome entry-exit. These results may help to gain a first glimpse into the two perhaps most intriguing features of the high-resolution structure: the alignment of the grooves on the two gyres and the passage of H2B and H3 N-terminal tails between them.

Kinetics of Site–Site Interactions in Supercoiled DNA with Bent Sequences

A curved DNA segment is known to adopt a preferred end loop localization in superhelical (sc) DNA and thus may organize the overall conformation of the molecule. Through this process it influences the probability of site juxtaposition. We addressed the effect of a curvature on site-site interactions quantitatively by measuring the kinetics of cross-linking of two biotinylated positions in scDNA by streptavidin. The DNA was biotinylated at either symmetric or asymmetric positions with respect to a curved insert via triplex-forming oligonucleotides (TFOs) modified with biotin. We used a quench-flow device to mix the DNA with the protein and scanning force microscopy to quantify the reaction products. As a measure of the interaction probability, rate constants of cross-linking and local concentrations j(M) of one biotinylated site in the vicinity of the other were determined and compared to Monte Carlo simulations for corresponding DNAs. In good agreement with the simulations, a j(M) value of 1.74 microM between two sites 500bp apart was measured for an scDNA without curvature. When a curvature was centered between the sites, the interaction probability increased about twofold over the DNA without curvature, significantly less than expected from the simulations. However, the relative differences of the interaction probabilities due to varied biotin positions with respect to the curvature agreed quantitatively with the theory.

Computational analysis of the chiral action of type II DNA topoisomerases

It was found recently that bacterial type II DNA topoisomerase, topo IV, is much more efficient in relaxing (+) DNA supercoiling than (-) supercoiling. This means that the DNA-enzyme complex is chiral. This chirality can appear upon binding the first segment that participates in the strand passing reaction (G segment) or only after the second segment (T segment) joins the complex. The former possibility is analyzed here. We assume that upon binding the enzyme, the G segment forms a part of left-handed helical turn. This model is an extension of the hairpin model introduced earlier to explain simplification of DNA topology by these enzymes. Using statistical-mechanical simulation of DNA properties, we estimated different consequences of the model: (1) relative rates of relaxation of (+) and (-) supercoiling by the enzyme; (2) the distribution of positions of the G segment in supercoiled molecules; (3) steady-state distribution of knots in circular molecules created by the topoisomerase; (4) the variance of topoisomer distribution created by the enzyme; (5) the effect of (+) and (-) supercoiling on the binding topo II with G segment. The simulation results are capable of explaining nearly all available experimental data, at least semiquantitatively. A few predictions obtained in the model analysis can be tested experimentally.

Making contacts on a nucleic acid polymer

The interaction of proteins bound at distant sites on a nucleic acid chain plays an important role in many molecular biological processes. Contact between the proteins is established by looping of the intervening polymer, which can comprise either double- or single-stranded DNA or RNA, or interphase or metaphase chromatin. The effectiveness of this process, as well as the optimal separation distance, is highly dependent on the flexibility and conformation of the linker. This article reviews how the probability of looping-mediated interactions is calculated for different nucleic acid polymers. In addition, the application of the equations to the analysis of experimental data is illustrated.

Diffusion-controlled intrachain reactions of supercoiled DNA: Brownian Dynamics simulations

The Brownian Dynamics technique was used to model a diffusion-controlled intramolecular reaction of supercoiled DNA (2500 basepairs) in 0.1 M sodium chloride solution. The distance between the reactive groups along the DNA contour was 470 basepairs. The reaction radius was varied from 6 to 20 nm. The results are presented in terms of the probability distribution P(F)(t) of the first collision time. The general form of the function P(F)(t) could be correctly predicted by a simple analytical model of one-dimensional diffusion of the superhelix ends along the DNA contour. The distribution P(F)(t) is essentially non-exponential: within a large initial time interval, it scales as P(F)(t) approximately t(-1/2), which is typical for one-dimensional diffusion. However, the mean time of the first collision is inversely proportional to the reaction radius, as in three dimensions. A visual inspection of the simulated conformations showed that a considerable part of the collisions is caused by the bending of the superhelix axis in the regions of the end loops, where the axis is most flexible. This fact explains why the distribution P(F)(t) combines the features of one- and three-dimensional diffusion. The simulations were repeated for a DNA chain with a permanent bend of 100 degrees in the middle position between the reactive groups along the DNA contour. The permanent bend changes dramatically the form of the distribution P(F)(t) and reduces the mean time of the first collision by approximately one order of magnitude.

Computation of writhe in modeling of supercoiled DNA

We describe four previously unpublished methods allowing the computation of the writhe for a supercoiled DNA molecule modeled by a polymer chain consisting of straight segments. These methods are compared with each other in terms of computational efficiency and the scope of their applicability is discussed.

The effect of the DNA conformation on the rate of NtrC activated transcription of Escherichia coli RNA polymerase.sigma(54) holoenzyme

The transcription activator protein NtrC (nitrogen regulatory protein C) can catalyze the transition of Escherichia coli RNA polymerase complexed with the sigma 54 factor (RNAP.sigma(54)) from the closed complex (RNAP.sigma(54) bound at the promoter) to the open complex (melting of the promoter DNA). This process involves phosphorylation of NtrC (NtrC-P), assembly of an octameric NtrC-P complex at the enhancer sequence, interaction of this complex with promoter-bound RNAP.sigma(54) via DNA looping, and hydrolysis of ATP. We have used this system to study the influence of the DNA conformation on the transcription activation rate in single-round transcription experiments with superhelical plasmids as well as linearized templates. Most of the templates had an intrinsically curved DNA sequence between the enhancer and the promoter and differed with respect to the location of the curvature and the distance between the two DNA sites. The following results were obtained: (i) a ten- to 60-fold higher activation rate was observed with the superhelical templates as compared to the linearized conformation; (ii) the presence of an intrinsically curved DNA sequence increased the activation rate of linear templates about five times; (iii) no systematic effect for the presence and/or location of the inserted curved sequence was observed for the superhelical templates. However, the transcription activation rate varied up to a factor of 10 between some of the constructs. (iv) Differences in the distance between enhancer and promoter had little effect for the superhelical templates studied. The results were compared with theoretical calculations for the dependence of the contact probability between enhancer and promoter expressed as the molar local concentration j(M). A correlation of j(M) with the transcription activation rate was observed for values of 10(-8) M<j(M)<10(-6) M and a kinetic model for NtrC-P-catalyzed open complex formation was developed.

DNA rings with multiple energy minima

Within the context of DNA rings, we analyze the relationship between intrinsic shape and the existence of multiple stable equilibria, either nicked or cyclized with the same link. A simple test, based on a perturbation expansion of symmetry breaking within a continuum elastic rod model, provides good predictions of the occurrence of such multiple equilibria. The reliability of these predictions is verified by direct computation of nicked and cyclized equilibria for several thousand DNA minicircles with lengths of 200 and 900 bp. Furthermore, our computations of equilibria for nicked rings predict properties of the equilibrium distribution of link, as calculated by much more computationally intensive Monte Carlo simulations.

Salt-dependent DNA superhelix diameter studied by small angle neutron scattering measurements and Monte Carlo simulations

Using small angle neutron scattering we have measured the static form factor of two different superhelical DNAs, p1868 (1868 bp) and pUC18 (2686 bp), in dilute aqueous solution at salt concentrations between 0 and 1.5 M Na+ in 10 mM Tris at 0% and 100% D2O. For both DNA molecules, the theoretical static form factor was also calculated from an ensemble of Monte Carlo configurations generated by a previously described model. Simulated and measured form factors of both DNAs showed the same behavior between 10 and 100 mM salt concentration: An undulation in the scattering curve at a momentum transfer q = 0.5 nm-1 present at lower concentration disappears above 100 mM. The position of the undulation corresponds to a distance of approximately 10-20 nm. This indicated a change in the DNA superhelix diameter, as the undulation is not present in the scattering curve of the relaxed DNA. From the measured scattering curves of superhelical DNA we estimated the superhelix diameter as a function of Na+ concentration by a quantitative comparison with the scattering curve of relaxed DNA. The ratio of the scattering curves of superhelical and relaxed DNA is very similar to the form factor of a pair of point scatterers. We concluded that the distance of this pair corresponds to the interstrand separation in the superhelix. The computed superhelix diameter of 16.0 +/- 0.9 nm at 10 mM decreased to 9.0 +/- 0.7 nm at 100 mM salt concentration. Measured and simulated scattering curves agreed almost quantitatively, therefore we also calculated the superhelix diameter from the simulated conformations. It decreased from 18.0 +/- 1.5 nm at 10 mM to 9.4 +/- 1.5 nm at 100 mM salt concentration. This value did not significantly change to lower values at higher Na+ concentration, in agreement with results obtained by electron microscopy, scanning force microscopy imaging in aqueous solution, and recent MC simulations, but in contrast to the observation of a lateral collapse of the DNA superhelix as indicated by cryo-electron microscopy studies.

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.

Measurement of the DNA bend angle induced by the catabolite activator protein using Monte Carlo simulation of cyclization kinetics

A Monte Carlo simulation method for studying DNA cyclization (or ring-closure) has been extended to the case of protein-induced bending, and its application to experimental data has been demonstrated. Estimates for the geometric parameters describing the DNA bend induced by the catabolite activator protein (CAP or CRP) were obtained which correctly predict experimental DNA cyclization probabilities (J factors), determined for a set of 11 150 to 166 bp DNA restriction fragments bearing A tracts phased against CAP binding sites. We find that simulation of out-of-phase molecules is difficult and time consuming, requiring the geometric parameters to be optimized individually rather than globally. A wedge angle model for DNA bending was found to make reasonable predictions for the free DNA. The bend angle in the CAP-DNA complex is estimated to be 85 to 90 degrees, in agreement with estimates from gel electrophoresis and X-ray co-crystal structures. Since the DNA is found to have a pre-existing bend of 15 degrees, the change in bend angle induced by CAP is 70 to 75 degrees, in a agreement with an estimate from topological measurements. We find evidence for slight (approximately 10 degrees) unwinding by CAP. The persistence length and helical repeat of the unbound portion of the DNA are in accord with literature-cited values, but the best-fit DNA torsional modulus C is found to be 1.7 (+/- 0.2) x 10(-19) erg. cm, versus literature estimates and best-fit values for the free DNA of 2.0 x 10(-19) to 3.4 x 10(-19) erg.com. Simulations using this low value of C predict that cyclization of molecules with out-of-phase bends proceeds via undertwisting or overtwisting of the DNA between the bends, so as to align the bends, rather than through conformations with substantial writhe. We present experiments on the topoisomers formed by cyclization with CAP which support this conclusion, and thereby rationalize the surprising result that cyclization can actually be enhanced by out-of-phase bends if the twist required to align the bends improves the torsional alignment of the ends. The relationship between the present work and previous studies on DNA bending by CAP is discussed, and recommendations are given for the efficient application of the cyclization/simulation approach to DNA bending.

A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes

For the interpretation of solution structural and dynamic data of linear and circular DNA molecules in the kb range, and for the prediction of the effect of local structural changes on the global conformation of such DNAs, we have developed an efficient and easy way to set up a program based on a second-order explicit Brownian dynamics algorithm. The DNA is modeled by a chain of rigid segments interacting through harmonic spring potentials for bending, torsion, and stretching. The electrostatics are handled using precalculated energy tables for the interactions between DNA segments as a function of relative orientation and distance. Hydrodynamic interactions are treated using the Rotne-Prager tensor. While maintaining acceptable precision, the simulation can be accelerated by recalculating this tensor only once in a certain number of steps.

Looping dynamics of linear DNA molecules and the effect of DNA curvature: a study by Brownian dynamics simulation

A Brownian dynamics (BD) model described in the accompanying paper (Klenin, K., H. Merlitz, and J. Langowski. 1998. A Brownian dynamics program for the simulation of linear and circular DNA, and other wormlike chain polyelectrolytes. Biophys. J. 74:000-000) has been used for computing the end-to-end distance distribution function, the cyclization probability, and the cyclization kinetics of linear DNA fragments between 120 and 470 basepairs with optional insertion of DNA bends. Protein-mediated DNA loop formation was modeled by varying the reaction distance for cyclization between 0 and 10 nm. The low cyclization probability of DNA fragments shorter than the Kuhn length (300 bp) is enhanced by several orders of magnitude when the cyclization is mediated by a protein bridge of 10 nm diameter, and/or when the DNA is bent. From the BD trajectories, end-to-end collision frequencies were computed. Typical rates for loop formation of linear DNAs are 1.3 x 10(3) s(-1) (235 bp) and 4.8 x 10(2) s(-1) (470 bp), while the insertion of a 120 degree bend in the center increases this rate to 3.0 x 10(4) s(-1) (235 bp) and 5.5 x 10(3) s(-1) (470 bp), respectively. The duration of each encounter is between 0.05 and 0.5 micros for these DNAs. The results are discussed in the context of the interaction of transcription activator proteins.

Superhelix organization by DNA curvature as measured through site-specific labeling

For determining the position of a defined site in a superhelical DNA we have developed a method for introducing a covalent biotin label at a specific sequence while preserving the superhelicity. This is done by first introducing a specific nick, labeling the DNA by limited nick translation and sealing the nick with ligase. The superhelicity is controlled by including ethidium in the ligation reaction. Using scanning force of microscopy on DNAs labeled by this method, we have then compared the position of streptavidin markers at a specific site relative to the end loop of the superhelix. We found that in DNAs with permanently curved inserts the label is located preferentially at a defined distance from the end loop, while in controls without curved inserts the label position was random. This indicates that curves are located in or near the end loops in a superhelix.

Salt effects on the structure and internal dynamics of superhelical DNAs studied by light scattering and Brownian dynamics

Using laser light scattering, we have measured the static and dynamic structure factor of two different superhelical DNAs, p1868 (1868 bp) and simian virus 40 (SV40) (5243 bp), in dilute aqueous solution at salt concentrations between 1 mM and 3 M NaCl. For both DNA molecules, Brownian dynamics (BD) simulations were also performed, using a previously described model. A Fourier mode decomposition procedure was used to compute theoretical light scattering autocorrelation functions (ACFs) from the BD trajectories. Both measured and computed autocorrelation functions were then subjected to the same multiexponential decomposition procedure. Simulated and measured relaxation times as a function of scattering angle were in very good agreement. Similarly, computed and measured static structure factors and radii of gyration agreed within experimental error. One main result of this study is that the amplitudes of the fast-relaxing component in the ACF show a peak at 1 M salt concentration. This nonmonotonic behavior might be caused by an initial increase in the amplitudes of internal motions due to diminishing long-range electrostatic repulsions, followed by a decrease at higher salt concentration due to a compaction of the structure.

On the origin of the temperature dependence of the supercoiling free energy

Monte Carlo simulations using temperature-invariant torsional and bending rigidities fail to predict the rather steep decline of the experimental supercoiling free energy with increasing temperature, and consequently fail to predict the correct sign and magnitude of the supercoiling entropy. To illustrate this problem, values of the twist energy parameter (E(T)), which governs the supercoiling free energy, were simulated using temperature-invariant torsion and bending potentials and compared to experimental data on pBR322 over a range of temperatures. The slope, -dE(T)/dT, of the simulated values is also compared to the slope derived from previous calorimetric data. The possibility that the discrepancies arise from some hitherto undetected temperature dependence of the torsional rigidity was investigated. The torsion elastic constant of an 1876-bp restriction fragment of pBR322 was measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium over the range 278-323 K, and found to decline substantially over that interval. Simulations of a 4349-bp model DNA were performed using these measured temperature-dependent torsional rigidities. The slope, -dE(T)/dT, of the simulated data agrees satisfactorily with the slope derived from previous calorimetric measurements, but still lies substantially below that of Duguet's data. Models that involve an equilibrium between different secondary structure states with different intrinsic twists and torsion constants provide the most likely explanation for the variation of the torsion constant with T and other pertinent observations.

Configurational transitions in Fourier series-represented DNA supercoils

A new Fourier series representation of supercoiled DNA is employed in Langevin dynamics simulations to study large-scale configurational motions of intermediate-length chains. The polymer is modeled as an ideal elastic rod subject to long-range van der Waals' interactions. The van der Waals' term prevents the self-contact of distant chain segments and also mimics attractive forces thought to stabilize the association of closely spaced charged rods. The finite Fourier series-derived polymer formulation is an alternative to the piecewise B-spline curves used in past work to describe the motion of smoothly deformed supercoiled DNA in terms of a limited number of independent variables. This study focuses on two large-scale configurational events: the interconversion between circular and figure-8 forms at a relatively low level of supercoiling, and the transformation between branched and interwound structures at a higher superhelical density.

Nucleosomes as topological rheostats

Induction of transcription in eukaryotic promoters is accompanied by removal or remodeling of nucleosomes. Given that this process causes release of torsional stress, the question is asked relative to its fate and to its effects on local DNA conformation. Is it dispersed by free rotation through surrounding nucleosomes or does it stay locally to be used in the modulation or activation of the transcription machinery? The results of the calculations relative to the onset of writhing suggest that the free energy made available by removal of nucleosomes is in the range of values that corresponds to the transition linking difference, thus pointing to a possible regulatory mechanism for the local use of free energy in promoters.

Supercoiling-dependent flexibility of adenosine-tract-containing DNA detected by a topological method

Intrinsically bent DNA sequences have been implicated in the activation of transcription by promoting juxtaposition of DNA sequences near the terminal loop of a superhelical domain. We have developed a novel topological assay for DNA looping based on lambda integrative recombination to study the effects of intrinsically bent DNA sequences on the tertiary structure of negatively supercoiled DNA. Remarkably, the localization of adenosine-tract (A-tract) sequences in the terminal loop of a supercoiled plasmid is independent of the extent of intrinsic bending. The results suggest that A-tract-containing sequences have other properties that organize the structure of superhelical domains apart from intrinsic bending and may explain the lack of conservation in the degree of A-tract-dependent bending among DNA sequences located upstream of bacterial promoters.

The effect of ionic conditions on the conformations of supercoiled DNA. II. Equilibrium catenation

We studied the equilibrium formation of DNA catenanes to assess the conformational properties of supercoiled DNA as a function of ionic conditions and supercoiling density. Catenanes were formed by cyclizing linear DNA with long cohesive ends in the presence of supercoiled molecules. The efficiency of the catenation depends on the distance between opposing segments of DNA in the interwound superhelix. The fraction of cyclizing molecules that becomes topologically linked with the supercoiled DNA is the product of the concentration of the supercoiled DNA and a proportionality constant, B, that depends on conformations of supercoiled DNA. In parallel with these experimental studies, we calculated the values of B using Monte Carlo simulations of the equilibrium distribution of DNA conformations. There were no adjustable parameters in the calculations because all three parameters of the DNA model, bending and torsional elasticity of DNA and DNA effective diameter, specifying intersegment interactions, were known from independent studies. We found very good agreement between measured and simulated values of B for all the ionic conditions and DNA superhelix densities studied; the discrepancy was less than a factor of 2 over the 200-fold variation in B. The value of B decreases nearly exponentially with increasing superhelicity, this dependence being especially strong at low salt concentration. The dependence of B on the concentration of NaCl, MgCl(2), and spermidine can be described with good accuracy in terms of changes of the DNA effective diameter. We found no indication of superhelix collapse under any ionic conditions studied. We discuss, in light of these results, the biological importance of the effect of DNA supercoiling on the unlinking of the products of DNA replication.

The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis

We studied the conformations of supercoiled DNA as a function of superhelicity and ionic conditions by determining its sedimentation coefficient both experimentally and by calculation. To cancel out unknown parameters from both calculations and experiments, we determined the ratio of the sedimentation coefficient, s, to that of open circular DNA, s(oc). Calculations of the sedimentation coefficient were based on direct solution of the Burgers-Oseen problem for an equilibrium set of DNA conformations generated for each condition by the Metropolis Monte Carlo procedure. There were no adjustable parameters in the Monte Carlo simulations because all three parameters of the DNA model used, bending and torsional elasticity of DNA and DNA effective diameter specifying electrostatic interactions, were known from independent data. The good agreement between measured and calculated values of s/s(oc) allowed us to interpret the sedimentation results in terms of DNA conformations, with particular emphasis on the marked effect of ionic conditions. As NaCl concentration decreases, s/s(oc) increases because the superhelix becomes less regular and more compact. In the presence of just 10 mM MgCl(2), supercoiled DNA adopts essentially the same set of conformations as in moderate to high concentrations of NaCl. Our simulations showed that s is a strong function of the superhelix branching frequency. At near physiological ionic conditions, there are about four branches in the 7 kb DNA molecule used in this work. We found no indication of superhelix collapse in any ionic conditions even remotely approaching physiological ones. For all ionic conditions studied, we conclude that the electrostatic interaction of DNA segments specified by the DNA effective diameter is the primary determinant of supercoiled DNA conformations.

Brownian dynamics simulations of supercoiled DNA with bent sequences

The recently presented Brownian dynamics model for superhelical DNA is extended to include local curvature of the DNA helix axis. Here we analyze the effect of a permanent bend on the structure and dynamics of an 1870-bp superhelix with delta Lk = -10. Furthermore, we define quantitative expressions for computing structural parameters such as loop positions, superhelix diameter, and plectonemic content for trajectories of superhelical DNA, and assess the convergence toward global equilibrium. The structural fluctuations in an interwound superhelix, as reflected in the change in end loop positions, seem to occur by destruction/creation of loops rather than by a sliding motion of the DNA around its contour. Their time scale is on the order of 30-100 microseconds. A permanent bend changes the structure and the internal motions of the DNA drastically. The position of the end loop is fixed at the permanent bend, and the local motions of the chain are enhanced near the loops. A displacement of the bend from the end loop to a position inside the plectonemic part of the superhelix results in the formation of a new loop and the disappearance of the old one; we estimate the time involved in this process to be about 0.5 ms.

Effect of supercoiling on the juxtaposition and relative orientation of DNA sites

There are many proteins that interact simultaneously with two or more DNA sites that are separated along the DNA contour. These sites must be brought close together to form productive complexes with the proteins. We used Monte Carlo simulation of supercoiled DNA conformations to study the effect of supercoiling and DNA length on the juxtaposition of DNA sites, the angle between them, and the branching of the interwound superhelix. Branching decreases the probability of juxtaposition of two DNA sites but increases the probability of juxtaposition of three sites at branch points. We found that the number of superhelix branches increases linearly with the length of DNA from 3 to 20 kb. The simulations showed that for all contour distances between two sites, the juxtaposition probability in supercoiled DNA is two orders of magnitude higher than in relaxed DNA. Supercoiling also results in a strong asymmetry of the angular distribution of juxtaposed sites. The effect of supercoiling on site-specific recombination and the introduction of supercoils by DNA gyrase is discussed in the context of the simulation results.

Calculations of nucleic acid conformations

The present computational power and sophistication of theoretical approaches to nucleic acid structural investigation are sufficient for the realization of static and dynamic models that correlate accurately with current crystallographic, NMR and solution-probing structural data, and consequently are able to provide valuable insights and predictions for a variety of nucleic acid conformational families. In molecular dynamics simulations, the year 1995 was marked by the foray of fast Ewald methods, an accomplishment resulting from several years' work in the search for an adequate treatment of the electrostatic long-range forces so primordial in nucleic acid behavior. In very large systems, and particularly in the RNA-folding field, techniques originating from artificial intelligence research, like constraint satisfaction programming or genetic algorithms, have established their utility and potential.

Sequence-specific labeling of superhelical DNA by triple helix formation and psoralen crosslinking

Site-specific labeling of covalently closed circular DNA was achieved by using triple helix-forming oligonucleotides 10, 11 and 27 nt in length. The sequences consisted exclusively of pyrimidines (C and T) with a reactive psoralen at the 5'-end and a biotin at the 3'-end. The probes were directed to different target sites on the plasmids pUC18 (2686 bp), pUC18/4A (2799 bp) and pUC1 8/4A-H 1 (2530 bp). After triple helix formation at acid pH the oligonucleotides were photocrosslinked to the target DNAs via the psoralen moiety, endowing the covalent adduct with unconditional stability, e.g. under conditions unfavorable for preservation of the triplex, such as neutral pH. Complex formation was monitored after polyacrylamide gel electrophoresis by streptavidin-alkaline phosphatase (SAP)-induced chemiluminescence. The yield of triple helix increased with the molar ratio of oligonucleotide to target and the length of the probe sequence (27mer > 11mer). The covalent adduct DNA were visualized by scanning force microscopy (SFM) using avidin or streptavidin as protein tags for the biotin group on the oligonucleotide probes. We discuss the versatility of triple helix DNA complexes for studying the conformation of superhelical DNA.

Simulating DNA at low resolution

The past year has witnessed the development of several new mathematical approaches to analyzing the structure of double-helical DNA and to incorporating the sequence-dependent features of the chain in computer simulations of long polymers. Of special interest in this respect are the local and global structural changes induced by the binding of various proteins to DNA, ranging from subtle bending, untwisting and sliding motions at the base-pair level to the apparent organization of supercoiled structure in chains that are thousands residues long. The computational effort has also included both new ways to incorporate the polyelectrolyte character of DNA and other environmental forces in simulations of long chains and new methods to keep track of the multitude of configurations so generated. The collective advances are pointing to ways that will soon connect the sequences of base pairs in large genomes to folded three-dimensional structures based on natural bending, twisting and translational tendencies and in response to deformations produced by the binding of different proteins.

Action at a distance in supercoiled DNA: effects of sequence on slither, branching, and intramolecular concentration

We report a computer modeling study of DNA supercoiling in model plasmids over the size range of 140-1260 bp. We used a computer model with basepair resolution. Molecular dynamics was used to produce ensembles at 300 K and to investigate intramolecular motions. The plasmid models varied by their sequence. The sequence types employed for comparison included a curve-bearing plasmid, a heterogenous sequence plasmid, and a homogenous sequence. Within the three sequence types tested at the 1260-bp plasmid size, we observed several sequence-dependent phenomena. Writhe, radius of gyration, slither motion, and branching probability were seen to be sequence dependent. Branching probability was the least in the homogenous plasmid and the greatest in the curve-bearing plasmid. The curve imposed a symmetry on the plasmid that was absent in the heterogenous sequence. Significant localizations and enhancements of intramolecular concentration were seen to a persistence length. Molecular dynamics allowed us to observe the mechanism of branch formation and reabsorption. We observed a size-dependent change in the types of motion observed in plasmids. Slither motion predominated in plasmids up to 600 bp in size, whereas global rearrangements were more important in the 1260 mer.

The elasticity of a single supercoiled DNA molecule

Single linear DNA molecules were bound at multiple sites at one extremity to a treated glass cover slip and at the other to a magnetic bead. The DNA was therefore torsionally constrained. A magnetic field was used to rotate the beads and thus to coil and pull the DNA. The stretching force was determined by analysis of the Brownian fluctuations of the bead. Here the elastic behavior of individual lambda DNA molecules over- and underwound by up to 500 turns was studied. A sharp transition was discovered from a low to a high extension state at a force of approximately 0.45 piconewtons for underwound molecules and at a force of approximately 3 piconewtons for overwound ones. These transitions, probably reflecting the formation of alternative structures in stretched coiled DNA molecules, might be relevant for DNA transcription and replication.