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.     

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 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.     

Topological measurement of an A-tract bend angle: variation of duplex winding

The rotational variant method of Lutter et al. was developed to measure the bend angle induced when a protein binds to DNA. To measure the intrinsic bend conferred by a sequence of six adenine bases (an A6 tract), the method was modified by relaxing at high temperature to remove the bend. We describe here an alternative approach that involves unwinding the duplex DNA between adjacent bends in plasmids containing tandemly repeated blocks of A-tracts. This method measures the topological difference contributed by adjacent bends when they are in two different rotational settings, and therefore does not require reference to a straight state. The interbend DNA was unwound by use of the intercalator chloroquine, or, alternatively, by raising the temperature in the relaxation reaction. The effect of this unwinding is to change the pitch of the superhelix of the tandem repeats from which the bend angle is measured. The result is a bend angle value that is consistent with that measured using the bend-straightening version of the method. This version offers several advantages that complement the conventional bent versus straight approach.     

Bulge loops used to measure the helical twist of RNA in solution.

Bulge loops are commonly found in helical segments of cellular RNAs. When incorporated into long double-stranded RNAs, they may introduce points of flexibility or permanent bend that can be detected by the altered electrophoretic gel mobility of the RNA. We find that a single An or Un bulge loop near the middle of a long RNA helix significantly retards the RNA during polyacrylamide gel electrophoresis if n greater than or equal to 2. The mobility of an RNA containing two A2 bulges various periodically with the number of base pairs between the bulges. We interpret this to mean that A2 bulges varies periodically with the number of base pairs between the bulges. We interpret this to mean that Z2 bulges form torsionally stiff bends in the helix; the gel mobility reaches a minimum when the total helical twist between the bulges rotates the arms of the molecule into a cis conformation. The gel mobilities are proportional to the predicted end-to-end distance of the RNA if the average RNA helical repeat is 11.8 +/- 0.2 bp/turn and there is no helical twist (3 +/- 9 degrees) associated with the bulge (data obtained in 0.15 M Na+). Other sizes and sequences of bulges have very different effects on RNA helix conformation and flexibility. U2 bulges bend the helix to a much smaller degree than A2 bulges, while longer A or U bulge sequences probably allow bends of 90 degrees or more; all of these may be fairly flexible joints.(ABSTRACT TRUNCATED AT 250 WORDS)     

Supercoiled DNA is interwound in liquid crystalline solutions.

Two structures have been proposed for supercoiled DNA: it is idealized either as a toroidal ring or as a rod of two interwound duplex chains. The latter model is the most widely depicted but the evidence remains controversial. We have worked with monomers and dimers of two plasmids, pUC8 and pKS414, of similar size and natural superhelical density. pKS414 contains a bend promoting sequence whereas pUC8 does not. In concentrated solutions these plasmids form a partially ordered liquid crystalline phase which is found, using neutron diffraction, to consist of a hexagonally packed assembly of parallel rod-like particles. This shape strongly suggests an interwound conformation for which some structural parameters are deduced. The mass/unit length obtained by combining the area of the hexagonal lattice and the concentration is approximately 3.6 times that of linear DNA. This implies a shallow superhelical pitch angle approximately 36 degrees which, when combined with the known number of supercoil turns, yields the pitch approximately 360 A and radius approximately 80 A for the supercoil. Oriented X-ray fibre diffraction patterns at 92% relative humidity indicate a B type duplex structure. Nicked circular plasmids also form liquid crystals but their behaviour, as a function of concentration, differs from that of the superhelical plasmids.     

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.     

Comparison of the computed structures for the phosphate-binding loop of the p21 protein containing the oncogenic site Gly 12 with the X-ray crystallographic structures for this region in the p21 protein and EFtu. A model for the structure of the p21 protein in its oncogenic form

The GTP-binding p21 protein encoded by the ras-oncogene can be activated to cause malignant transformation of cells by substitution of a single amino acid at critical positions along the polypeptide chain. Substitution of any non-cyclic L-amino acid for Gly 12 in the normal protein results in a transforming protein. This substitution occurs in a hydrophobic sequence (residues 6-15) which is known to be involved in binding the phosphate moities of GTP (and GDP). We find, using conformational energy calculations, that the 6-15 segment of the normal protein (with Gly 12) adopts structures that contain a bend at residues 11 and 12 with the Gly in the D* conformation, not allowed energetically for L-amino acids. Substitution of non-cyclic L-amino acids for Gly 12 results in shifting this bend to residues 12 and 13. We show that many computed structures for the Gly 12-containing phosphate binding loop, segment 9-15, are superimposable on the corresponding segment of the recently determined X-ray crystallographic structure for residues 1-171 of the p21 protein. All such structures contain bends at residues 11 and 12 and most of these contain Gly 12 in the C* or D* conformational state. Other computed conformations for the 9-15 segment were superimposable on the structure of the corresponding 18-23 segment of EFtu, the bacterial chain elongation factor having structural similarities to the p21 protein in the phosphate-binding regions. This segment contains a Val residue where a Gly occurs in the p21 protein. As previously predicted, all of these superimposable conformations contain a bend at positions 12 and 13, not 11 and 12. If these structures that are superimposable on EFtu are introduced into the p21 protein structure, bad contacts occur between the sidechain of the residue (here Val) at position 12 and another phosphate binding loop region around position 61. These bad contacts between the two segments can be removed by changing the conformation of the 61 region in the p21 protein to the corresponding position of the homologous region in EFtu. In this new conformation, a large site becomes available for the binding of phosphate residues. In addition, such phenomena as autophosphorylation of the p21 protein by GTP can be explained with this new model structure for the activated protein which cannot be explained by the structure for the non-activated protein.     

Superhelix dimensions of a 1868 base pair plasmid determined by scanning force microscopy in air and in aqueous solution.

We have used scanning force microscopy (SFM) to study the conformation of a 1868 base pair plasmid (p1868) in its open circular form and at a superhelical density of sigma= -0.034. The samples were deposited on a mica surface in the presence of MgCl2. DNA images were obtained both in air and in aqueous solutions, and the dimensions of the DNA superhelix were analysed. Evaluation of the whole plasmid yielded average superhelix dimensions of 27 +/- 9 nm (outer superhelix diameter D), 107 +/- 51 nm (superhelix pitch P), and 54 +/-8 degrees (superhelix pitch angle alpha). We also analysed compact superhelical regions within the plasmid separately, and determined values of D = 9.2 +/- 3.3 nm, P = 42 +/- 13 nm and alpha= 63 +/- 20 degrees for samples scanned in air or rehydrated in water. These results indicate relatively large conformation changes between superhelical and more open regions of the plasmid. In addition to the analysis of the DNA superhelix dimensions, we have followed the deposition process of open circular p1868 to mica in real time. These experiments show that it is possible to image DNA samples by SFM without prior drying, and that the surface bound DNA molecules retain some ability to change their position on the surface.     

Direct visualization of supercoiled DNA molecules in solution.

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

Helical phasing between DNA bends and the determination of bend direction.

The presence and location of bends in DNA can be inferred from the anomalous mobility of DNA fragments or protein-DNA complexes during electrophoresis in polyacrylamide gels. Direction of bending is not so easily determined. We show here that a protein-induced bend, when linked to a protein-independent DNA bend by a segment of variable length, exhibits an electrophoretic mobility that varies in a sinusoidal manner with the length of the linker. Mobility minima occur once for each addition to the linker of one helical turn of DNA. Since minima should occur when two bends reinforce one another, the direction of one bend relative to the other can be determined from the distances between the two centers of bending at which minima occur. Our results strongly support the idea that the A5-6 tracts in kinetoplast DNA bend towards the minor groove while the bend at the recombination site of the gamma delta resolvase (binding site I of the gamma delta res site) bends towards the major groove.     

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.     

Dynamic bending rigidity of a 200-bp DNA in 4 mM ionic strength: a transient polarization grating study

DNA may exhibit three different kinds of bends: 1) permanent bends; 2) slowly relaxing bends due to fluctuations in a prevailing equilibrium between differently curved secondary conformations; and 3) rapidly relaxing dynamic bends within a single potential-of-mean-force basin. The dynamic bending rigidity (kappa(d)), or equivalently the dynamic persistence length, P(d) = kappa(d)/k(B)T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t < or = 10(-5) s. However, all three kinds of bends contribute to the total equilibrium persistence length, P(tot), according to 1/P(tot) congruent with 1/P(pb) + 1/P(sr) + 1/P(d), where P(pb) is the contribution of the permanent bends and P(sr) is the contribution of the slowly relaxing bends. Both P(d) and P(tot) are determined for the same 200-bp DNA in 4 mM ionic strength by measuring its optical anisotropy, r(t), from 0 to 10 micros. Time-resolved fluorescence polarization anisotropy (FPA) measurements yield r(t) for DNA/ethidium complexes (1 dye/200 bp) from 0 to 120 ns. A new transient polarization grating (TPG) experiment provides r(t) for DNA/methylene blue complexes (1 dye/100 bp) over a much longer time span, from 20 ns to 10 micros. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time (tau(R)) of the end-over-end tumbling motion, from which P(tot) = 500 A is estimated. The FPA data are used to obtain the best-fit pairs of P(d) and torsion elastic constant (alpha) values that fit those data equally well, and which are used to eliminate alpha as an independent variable. When the relevant theory is fitted to the entire TPG signal (S(t)), the end-over-end rotational diffusion coefficient is fixed at its measured value and alpha is eliminated in favor of P(d). Neither a true minimum in chi-squared nor a satisfactory fit could be obtained for P(d) anywhere in the range 500-5000 A, unless an adjustable amplitude of azimuthal wobble of the methylene blue was admitted. In that case, a well-defined global minimum and a reasonably good fit emerged at P(d) = 2000 A and (1/2) = 25 degrees. The discrimination against P(d) values <1600 A is very great. By combining the values, P(tot) = 500 A and P(d) = 2000 A with a literature estimate, P(pb) = 1370 A, a value P(sr) = 1300 A is estimated for the contribution of slowly relaxing bends. This value is analyzed in terms of a simple model in which the DNA is divided up into domains containing m bp, each of which experiences an all-or-none equilibrium between a straight and a uniformly curved conformation. With an appropriate estimate of the average bend angle per basepair of the curved conformation, a lower bound estimate, m = 55 bp, is obtained for the domain size of the coherently bent state. Previous measurements suggest that this coherent bend is not directional, or phase-locked, to the azimuthal orientation of the filament.     

Sequence-induced curvature of Tenebrio molitor satellite DNA

Single satellite DNA constitutes about 50% of the Tenebrio molitor genome. Electrophoresis of 142 base pair long satellite monomers on nondenaturating polyacrylamide gel shows retarded mobility, a characteristic of fragments with sequence-induced DNA curvature. Migrational analysis of circularly permuted satellite monomers revealed the existence of 2 bend centers in the monomer sequence. We calculated the trajectory of DNA helix axis according to the algorithm of De Santis et al. This model predicts that T molitor naked satellite DNA forms a solenoid structure with left-handed superhelix. One turn of the superhelix has approximately 310 base pairs and a 33 nm pitch. Point mutations found in the satellite DNA (1.8%) influence bending characteristics, but do not distort the general geometry of satellite superhelix.     

Saturation mutagenesis of a DNA region of bend. Base steps other than ApA influence the bend

A 60 base-pair region of a simian virus 40 DNA fragment was mutagenized to determine base-pairs that are critical for the fragment to bend. The site-directed mutagenesis saturated this region with all possible single base-pair substitutions. The mobility of each mutated fragment was measured by polyacrylamide electrophoresis at 4 degrees C and at 65 degrees C to assess the degree of bend. Four conclusions can be drawn. First, interruptions within the A tracts and changes in the phasing of the A tracts alter the degree of bend. Second, G tracts phased at a half-helical turn from an A tract are additive to the bend. Third, guanine residues in a nearest-neighbor contact with the A tracts modify the bend. Fourth, some mutations that do not obviously relate to the A tracts also alter the DNA bend and suggest clearly that base steps other than ApA are involved in sequence-directed DNA bends.