Applications of the twist difference to DNA structural analysis

DNA superhelicity

Closing each strand of a DNA duplex upon itself fixes its linking number L. This topological condition couples together the secondary and tertiary structures of the resulting ccDNA topoisomer, a constraint that is not present in otherwise identical nicked or linear DNAs. Fixing L has a range of structural, energetic and functional consequences. Here we consider how L having different integer values (that is, different superhelicities) affects ccDNA molecules. The approaches used are primarily theoretical, and are developed from a historical perspective. In brief, processes that either relax or increase superhelicity, or repartition what is there, may either release or require free energy. The energies involved can be substantial, sufficient to influence many events, directly or indirectly. Here two examples are developed. The changes of unconstrained superhelicity that occur during nucleosome attachment and release are examined. And a simple theoretical model of superhelically driven DNA structural transitions is described that calculates equilibrium distributions for populations of identical topoisomers. This model is used to examine how these distributions change with superhelicity and other factors, and applied to analyze several situations of biological interest.

DNA topology in chromosomes: a quantitative survey and its physiological implications

Using a simple geometric model, we propose a general method for computing the linking number of the DNA embedded in chromatin fibers. The relevance of the method is reviewed through the single molecule experiments that have been performed in vitro with magnetic tweezers. We compute the linking number of the DNA in the manifold conformational states of the nucleosome which have been evidenced in these experiments and discuss the functional dynamics of chromosomes in the light of these manifold states.

Supercoiling and local denaturation of plasmids with a minimalist DNA model

We report molecular dynamics simulations of DNA nanocircles and submicrometer-sized plasmids with torsional stress. The multiple microseconds time scale is reached thanks to a new one-bead-per-nucleotide coarse-grained model that combines structural accuracy and predictive power, achieved by means of the accurate choice of the force field terms and their unbiased statistically based parametrization. The model is validated with experimental structural data and available all-atom simulations of DNA nanocircles. Besides reproducing the nanocircles' structures and behavior on the short time scale, our model is capable of exploring three orders of magnitude further in time and to sample more efficiently the configuration space, unraveling novel behaviors. We explored the microsecond dynamics of entire small plasmids and observed supercoiling and compaction in the overtwisted case. The stability of overtwisted nanocircles and plasmids is predicted up to macroscopic time scales. Conversely, in the undertwisted case, at physiological values of the superhelical density, after a metastable phase of supercoiling-compaction, we observe the formation and the complex dynamics of denaturation bubbles over a multiple microseconds time scale. Our results indicate that the torsional stress is involved in a delicate balance with the temperature to determine the denaturation equilibrium and regulate the transcription process.

Elastic property of single double-stranded DNA molecules: theoretical study and comparison with experiments

This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed, and a structural parameter called the folding angle straight phi is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide base pairs, the steric effects of base pairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using a path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from the right-handed B form to left-handed configurations similar to the Z-form configuration. Some formulas concerned with the application of path integral methods to polymeric systems are listed in the Appendixes.

Chirality and surface twist of DNA wrapped on protein surfaces

The surface twist, STw, is a measure of the component of duplex twist associated with the trajectory of the DNA axis wrapped on a protein surface. We calculate STw for various surfaces of revolution, including the cylinder and truncated paraboloid, ellipsoid, and hyperboloid of revolution. We show that the sign of STw cannot be stated unequivocally from knowledge of the chirality of the wrapping but depends also upon the nature of the wrapping (protein) surface. We define and discuss three geometric classes. Class (1) includes the cylinder, certain types of convex paraboloids, all concave paraboloids, the prolate ellipsoid, and the hyperboloid; here STw > 0 for right-handed wrapping and STw < 0 for left-handed wrapping. Class (2) is the sphere, for which STw = 0 for both types of handedness. Case (3) includes oblate ellipsoids and some regions of convex paraboloids; here STw < 0 for right handed wrapping and STw > 0 for left-handed wrapping.

Effects of DNA topology in the interaction with histone octamers and DNA topoisomerase I

Several simple proteins and complex protein systems exist which do not recognize a defined sequence but--rather--a specific DNA conformation. We describe experiments and principles for two of these systems: nucleosomes and eukaryotic DNA topoisomerase I. Evidences are summarized that describe the effects of negative DNA supercoiling on nucleosome formation and the influence of DNA intrinsic curvature on their localization. The function of the DNA rotational information in nucleosome positioning and in the selection of multiple alternative positions on the same helical phase are described. This function suggests a novel genetic regulatory mechanism, based on nucleosome mobility and on the correlation between in vitro and in vivo positions. We observe that the same rules that determine the in vitro localization apply to the in vivo nucleosome positioning, as determined by a technique that relies on the use of nystatin and on the import of active enzymes in living yeast cells. The sensitivity of DNA topoisomerase I to the topological condition of the DNA substrate is reviewed and discussed taking into account recent experiments that describe the effect of the DNA tridimensional context on the reaction. These topics are discussed in the following order: (i) Proteins that look for a consensus DNA conformation; (ii) Nucleosomes; (iii) Negative supercoiling and nucleosomes; (iv) DNA curvature/bending and nucleosomes; (v) Multiple positioning; (vi) Multiple nucleosomes offer a contribution to the solution of the linking number paradox; (vii) Rotational versus translational information; (viii) A regulatory mechanism; (ix) DNA topoisomerase I; (x) DNA topoisomerase I and DNA supercoiling: a regulation by topological feedback; (xi) DNA topoisomerase I and DNA curvature; (xii) The in-and-out problem in the accessibility of DNA information; (xiii) The integrating function of the free energy of supercoiling.

Twist and writhe of a DNA loop containing intrinsic bends

The finite-element method of solid mechanics is applied to calculation of the three-dimensional structure of closed circular DNA, modeled as an elastic rod subject to large motions. The results predict the minimum elastic energy conformation of a closed loop of DNA as a function of relaxed equilibrium configuration and linking number (Lk). We apply the method to four different starting states: a straight rod, two rods containing either one or two 20 degrees bends, and a circular O-ring. The results, here at low superhelix density, show the changes in writhe (Wr) and in twist (Tw) as Lk is progressively lowered. The presence of even a single intrinsic bend reduces significantly the linking number change at which Wr first appears, compared to an initially straight, bend-free rod. The presence of two in-phase bends, situated at opposite ends of a diameter, leads to the formation of at least two distinct regions of different but relatively uniform Tw increment. The O-ring begins to writhe immediately upon reduction of Lk, and the Tw increment distribution is sinusoidal along the rod. The mechanics calculations, unlike other theoretical approaches, permit us to calculate Tw and Wr independent of the constraint of constant Lk.

Molecular modeling and energy refinement of supercoiled DNA

A method is presented for constructing the complete atomic structure of supercoiled DNA starting from a linear description of the double helical pathway. The folding pathway is defined by piecewise B-spline curves and the atoms are initially positioned with respect to the local Frenet trihedra determined by the equations of the curves. The resulting chemical structure is corrected and refined with an energy minimization procedure based on standard potential expressions. The refined molecular structure is then used to study the effects of supercoiling on the local secondary structure of DNA. The minimized structure is found to differ from an isotropic elastic rod model of the double helix, with the base pairs bending in an asymmetric fashion along the supercoiled trajectory. The starting trajectory is chosen so that the refined supercoiled structure is either underwound (10.37 base pairs per turn) or overwound (9.65 base pairs per turn) compared to the standard tenfold B-DNA fiber diffraction model. The underwound supercoil is also lower in energy than the overwound duplex. The variation of base pair sequence in poly(dA).poly(dT).poly(dAT).poly(dTA) and poly(dA5T5).poly(dT5A5) is additionally found to influence the secondary structural features along a given supercoiled pathway. Finally, the detailed features of the refined structures are found to be in agreement with known X-ray crystallographic structures of DNA oligomers.

Dependence of the linking deficiency of supercoiled minichromosomes upon nucleosome distortion

The contribution from each nucleosome to the linking number of minichrosome DNA depends on two factors. These are the wrapping number, omega, which is the number of times the DNA wraps about the axis of the nucleosome; and the winding number, phi, which is the number of base pairs on the nucleosome divided by the helical repeat of the DNA. If the nucleosome is distorted with DNA surface contacts being preserved, phi remains unchanged. The wrapping number may still change, however, depending on the extent of the distortion. For example, if the usual cylindrical shape of the nucleosome is deformed into an ellipsoid while preserving the equatorial radius, then the wrapping number will increase. We apply these concepts to minichromosomes torsionally stressed by supercoiling with, for example, DNA gyrase. We analyze the experimental result that the maximum amount of supercoiling obtained by gyrase treatment of minichromosomes is the same as that of naked DNA. In particular, we show that this phenomenon can be explained by a relatively slight distortion of the nucleosome core while maintaining the surface contacts of the DNA on the core.

Helical repeat and linking number of surface-wrapped DNA

The geometric properties of duplex DNA are systematically altered when the DNA is wrapped on a protein surface. The linking number of surface-wrapped closed circular DNA is the sum of two integers: the winding number, phi, a function of the helical repeat; and the surface linking number, SLk, a newly defined geometric constant that accounts for the effects of surface geometry on the twist and writhe of DNA. Changes in the helical repeat, h, and in the winding number can be deduced solely from surface geometry and superhelix density, sigma. This treatment relates the theoretically important properties twist and writhe to the more experimentally accessible quantities phi, h, SLk, and sigma. The analysis is applied to three biologically important cases: interwinding of DNA in a plectonemic superhelix, catenated DNA, and minichromosomes.