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

A Monte Carlo model for the generation of superhelical DNA structures at thermodynamic equilibrium (Klenin et al., 1991; Vologodskii et al., 1992) was modified to account for the presence of local curvature. Equilibrium ensembles of a 2700-bp DNA chain at linking number difference delta Lk = -15 were generated, with one or two permanent bends up to 120 degrees inserted at different positions. The computed structures were then analyzed with respect to the number and positions of the end loops of the interwound superhelix, and the intramolecular interaction probability of different segments of the DNA. We find that the superhelix structure is strongly organized by permanent bends. A DNA segment with a 30 degrees bend already has a significantly higher probability of being at the apex of a superhelix than the control, and for a 120 degrees bend the majority of DNAs have one end loop at the position of the bend. The entropy change due to the localization of a 120 permanent bend in the end loop is estimated to be -17 kJ mol-1 K-1. When two bends are inserted, the conformation of the superhelix is found to be strongly dependent on their relative positions: the straight interwound form dominates when the two bends are separated by 50% of the total DNA length, whereas the majority of the superhelices are in a branched conformation when the bends are separated by 33%. DNA segments in the vicinity of the permanent bend are strongly oriented with respect to each other.     

Energetics at the DNA Supercoiling Transition

Twisting a DNA molecule held under constant tension is accompanied by a transition from a linear to a plectonemic DNA configuration, in which part of the applied twist is absorbed in a superhelical structure. Recent experiments revealed the occurrence of an abrupt extension change at the onset of this transition. To elucidate its origin we study this abrupt DNA shortening using magnetic tweezers. We find that it strongly depends on the length of the DNA molecule and the ionic strength of the solution. This behavior can be well understood in the framework of a model in which the energy per writhe for the initial plectonemic loop is larger than for subsequent turns of the superhelix. By quantitative data analysis, relevant plectoneme energies and other parameters were extracted, providing good agreement with a simple theory. As a direct confirmation of the initial-loop model, we find that for a kinked DNA molecule the abrupt extension change occurs at significantly lower twist than the subsequent superhelix formation. This should allow pinning of the plectoneme position within supercoiled DNA if a kinked substrate is used, and enable the detection of enzymes and proteins which, themselves, bend or kink DNA.     

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.     

Supercoiling-induced DNA bending

Local DNA bending is a critical factor for numerous DNA functions including recognition of DNA by sequence-specific regulatory binding proteins. Negative DNA supercoiling increases both local and global DNA dynamics, and this dynamic flexibility can facilitate the formation of DNA-protein complexes. We have recently shown that apexes of supercoiled DNA molecules are sites that can promote the formation of an alternative DNA structure, a cruciform, suggesting that these positions in supercoiled DNA are under additional stress and perhaps have a distorted DNA geometry. To test this hypothesis, we used atomic force microscopy to directly measure the curvature of apical positions in supercoiled DNA. The measurements were performed for an inherently curved sequence formed by phased A tracts and a region of mixed sequence DNA. For this, we used plasmids in which an inverted repeat and A tract were placed at precise locations relative to each other. Under specific conditions, the inverted repeat formed a cruciform that was used as a marker for the unambiguous identification of the A tract location. When the A tract and cruciform were placed diametrically opposite, this yielded predominantly nonbranched plectonemic molecules with an extruded cruciform and A tract localized in the terminal loops. For both the curved A tract and mixed sequence nonbent DNA, their localization to an apex increased the angle of bending compared to that expected for DNA unconstrained in solution. This is consistent with increased helical distortion at an apical bend.     

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.     

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.     

Gene repression by minimal lac loops in vivo

The inflexibility of double-stranded DNA with respect to bending and twisting is well established in vitro. Understanding apparent DNA physical properties in vivo is a greater challenge. Here, we exploit repression looping with components of the Escherichia coli lac operon to monitor DNA flexibility in living cells. We create a minimal system for testing the shortest possible DNA repression loops that contain an E. coli promoter, and compare the results to prior experiments. Our data reveal that loop-independent repression occurs for certain tight operator/promoter spacings. When only loop-dependent repression is considered, fits to a thermodynamic model show that DNA twisting limits looping in vivo, although the apparent DNA twist flexibility is 2- to 4-fold higher than in vitro. In contrast, length-dependent resistance to DNA bending is not observed in these experiments, even for the shortest loops constraining <0.4 persistence lengths of DNA. As observed previously for other looping configurations, loss of the nucleoid protein heat unstable (HU) markedly disables DNA looping in vivo. Length-independent DNA bending energy may reflect the activities of architectural proteins and the structure of the DNA topological domain. We suggest that the shortest loops are formed in apical loops rather than along the DNA plectonemic superhelix.     

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.     

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.     

The influence of tertiary structural restraints on conformational transitions in superhelical DNA.

This paper examines theoretically the effects that restraints on the tertiary structure of a superhelical DNA domain exert on the energetics of linking and the onset of conformational transitions. The most important tertiary constraint arises from the nucleosomal winding of genomic DNA in vivo. Conformational transitions are shown to occur at equilibrium at less extreme superhelicities in DNA whose tertiary structure is restrained than in unrestrained molecules where the residual linking difference alpha res (that part of the superhelical deformation which is not absorbed by transitions) may be freely partitioned between twisting and bending. In the extreme case of a rigidly held tertiary structure, this analysis predicts that the B-Z transition will occur at roughly half the superhelix density needed to drive the same transition in solution, other factors remaining fixed. This suggests that superhelical transitions may occur at more moderate superhelical deformations in vivo than in solution. The influence on transition behavior of the tertiary structural restraints imposed by gel conditions also are discussed.     

DNA curvature influences the internal motions of supercoiled DNA.

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

The three-dimensional structure of supercoiled deoxyribonucleic acid in solution. Evidence obtained from the angular distribution of scattered light

1. The size and shape of superhelical double-stranded circular DNA from bacteriophage ØX174 were investigated by light-scattering. The molecular weight of the DNA is 3.17×10⁶ and the root-mean-square radius is 103.5nm. 2. The light-scattering envelopes of various theoretical three-dimensional models for such DNA molecules were calculated by repetitive computational techniques, and the results were compared with the experimental findings. 3. It is concluded that the structure of supercoiled DNA containing −12 superhelical turns in buffer of I0.2 corresponds best to one of the more compact models for superhelix structure such as the branched model, and the commonly employed straight interwound superhelix model is incompatible with the experimental results, at the superhelix density found.     

Structure and dynamics in DNA looped domains: CAG triplet repeat sequence dynamics probed by 2-aminopurine fluorescence

The triplet repeat sequence (CAG)n and related triplet repeats are associated with dynamic DNA mutations implicated in a number of debilitating human diseases. To gain insight into the dynamics of the (CAG)n repeat, we have substituted a single 2-aminopurine (2AP) fluorescent base for adenine at select positions within the 18 base looped domain of a (GC)3(CAG)6(GC)3 hairpin oligonucleotide. Using temperature-dependent steady-state fluorescence measurements in combination with time correlated photon counting spectroscopy, we show the conformation and dynamics of the C2APG domains to be strongly dependent on the position of the probe in the looped region. In other words, rather than being a uniform, single stranded loop, the (CAG)6 triplet repeat looped domain exhibits order and dynamics that are position dependent. The 2AP fluorescence dynamics within the C2APG repeat are well described by a 4 component exponential decay model, with lifetimes ranging from 5 ps to 4 ns. Differences in global DNA conformation (duplex, hairpin, single strand), as well as the local position of the probe within the loop of a given hairpin, predominantly are reflected in the relative amplitude rather than the lifetime of the probe. The time dependent 2AP anisotropy in the hairpin (CAG)n loops is sensitive to the position of the fluorescent base, with the fluorescence depolarization of a centrally located 2AP probe within the loop proceeding significantly more slowly than 2AP positioned at the 5'- or 3'-end of the repeat sequence near the loop-stem junction. These results are consistent with segmental motions of the CAG repeat, while also suggesting that the 2AP probe is significantly stacked, possibly even hydrogen bonded, within the partially structured CAG looped domain. Our results characterize the position-dependent and conformation-dependent dynamics and order within (CAG)n triplet repeat DNAs, properties of relevance to the biological mechanisms by which such domains can lead to disease states.     

Loop‐loop interactions govern multiple steps in indole‐3‐glycerol phosphate synthase catalysis

Substrate binding, product release, and likely chemical catalysis in the tryptophan biosynthetic enzyme indole‐3‐glycerol phosphate synthase (IGPS) are dependent on the structural dynamics of the β1α1 active‐site loop. Statistical coupling analysis and molecular dynamic simulations had previously indicated that covarying residues in the β1α1 and β2α2 loops, corresponding to Arg54 and Asn90, respectively, in the Sulfolobus sulfataricus enzyme (ssIGPS), are likely important for coordinating functional motions of these loops. To test this hypothesis, we characterized site mutants at these positions for changes in catalytic function, protein stability and structural dynamics for the thermophilic ssIGPS enzyme. Although there were only modest changes in the overall steady‐state kinetic parameters, solvent viscosity and solvent deuterium kinetic isotope effects indicated that these amino acid substitutions change the identity of the rate‐determining step across multiple temperatures. Surprisingly, the N90A substitution had a dramatic effect on the general acid/base catalysis of the dehydration step, as indicated by the loss of the descending limb in the pH rate profile, which we had previously assigned to Lys53 on the β1α1 loop. These changes in enzyme function are accompanied with a quenching of ps‐ns and µs‐ms timescale motions in the β1α1 loop as measured by nuclear magnetic resonance studies. Altogether, our studies provide structural, dynamic and functional rationales for the coevolution of residues on the β1α1 and β2α2 loops, and highlight the multiple roles that the β1α1 loop plays in IGPS catalysis. Thus, substitution of covarying residues in the active‐site β1α1 and β2α2 loops of indole‐3‐glycerol phosphate synthase results in functional, structural, and dynamic changes, highlighting the multiple roles that the β1α1 loop plays in enzyme catalysis and the importance of regulating the structural dynamics of this loop through noncovalent interactions with nearby structural elements.     

Dynamic model for sedimentation of supercoiled molecules.

An experimental curve for the sedimentation of SV40 DNA has been fitted by using a three parameter theory. The chain stiffness parameter is evaluated at each point, and the general behavior as a function of the number of loops (superhelix density) has been described. The chain stiffness, like the sedimentation ratio, also depends on the superhelical density in a complicated way.     

Light-scattering studies on supercoil unwinding

It has been shown previously that supercoiled [unk]X174 bacteriophage intracellular DNA (mol.wt. 3.2x10(6)) with superhelix density, sigma=-0.025 (-12 superhelical turns) at 25 degrees C is best represented as a Y shape. In this work two techniques have been used to unwind the supercoil and study the changes in tertiary structure which result from changes in the secondary structure. The molecular weights from all experiments were in the range 3.2x10(6)+/-0.12x10(6). In experiments involving temperature change little change in the Y shape was observed between sigma=-0.027 (-13 superhelical turns, 14.9 degrees C) and sigma=-0.021 (-10 superhelical turns, 53.4 degrees C) as evidenced by the root-mean-square radius and the particle-scattering factor P(theta). However, at sigma=-0.0176 (-8 superhelical turns, 74.5 degrees C) the root-mean-square radius fell to between 60 and 70nm from 90nm indicating a large structural change, as did alterations in the P(theta) function. In experiments with the intercalating dye proflavine from values of bound proflavine of 0-0.06mol of dye/mol equiv. of nucleotide which correspond to values of sigma from -0.025 to -0.0004 (-12 to 0 superhelical turns) a similar transition was found when the superhelix density was changed by the same amount, and the molecule was shown to go through a further structural change as the unwinding of the duplex proceeded. At sigma=-0.018 (-9 superhelical turns) the structure was compatible with a toroid, and at sigma=-0.0004 it was compatible with a circle but at no point in the sequence of structure transitions was the structure compatible with the conventional straight interwound model normally visualized as the shape of supercoiled DNA.     

Theoretical model for the equilibrium behavior of DNA superhelices

A statistical-mechanical model for superhelical DNA is presented. The partition function for a DNA superhelix is written by using a combinatorial approach in order to allow for the known relation between the number of superhelical twists and the states of the base pairs in the double helix. While the theory allows any factors which might contribute to the free energy of superhelical twisting to be included in the statistical weights of the superhelical twists, only the reduction in configurational entropy is considered in this paper. Similarities between an imperfectly matched DNA double helix and a DNA superhelix are used in the derivation of expressions for the entropy of superhelical DNA. Although the partition function is presented in a general form, permitting many equilibrium properties of DNA superhelices to be treated, the application considered in this paper is the calculation of helix–coil transition curves. Several experimentally observed features of such transitions are predicted. For example, the curves are bimodal, with an early and a late transition relative to that of a nicked molecule. The results are very sensitive to the volume within which two parts of the double helix must meet when forming a superhelical twist. The free energy of superhelix formation is calculated, and the results are compared with those obtained from the data of Bauer and Vinograd for ethidium bromide intercalation. In the present model, the free energy increases less sharply with an increase in the number of superhelical twists than observed experimentally, indicating that factors other than configurational entropy probably make important contributions to the free energy of superhelix formation.     

Fluctuations in superhelical DNA.

The effect of superhelicity on the base-pair opening probability and on the probability of occurrence of cruciform states in palindromic regions is theoretically treated. The calculations show that below the superhelix density value of -sigma=0.05 superhelicity does not appreciably affect the characteristics of DNA secondary structure fluctuations. In the range of physiological superhelix densities sigma (-sigma=0.05-0.09) the base-pair opening probability markedly increases. However, within this range of sigma the base-pairs are opened only transiently and permanently open regions are not formed. Permanently opened regions appear at higher negative superhelix densities (-sigma greater than 0.10). At the values of -sigma higher than 0.06 a cruciform structure in the palindromic region centred in position 3965 proves to be the most probable fluctuational disturbance in the 0x174 duplex DNA. Different experimental approaches used for probing the fluctuations in superhelical DNA have been analysed. The results suggest that most direct quantitative information can be derived from data on the nicking of closed DNA by single strand-specific endonucleases. Such data (Wang, 1974) accord with the results of theoretical calculations. Calculations show that, due to base-pair opening, the total free energy of superhelical DNA should depend parabolically on sigma only up to some critical value of sigma=sigmac. If negative superhelicity exceeds this critical value, which under physiological conditions proves to be -sigma=0.085, the free energy should increase linearly with -sigma. The biological role of supercoiling is discussed in the light of obtained results.