Writhe of DNA induced by a terminal twist

This paper considers the three-dimensional structure of B-form DNA. The molecule may be open or covalently closed. For the former, its two ends are not allowed to move or rotate freely in space unless the molecule is under the influence of rigid body motions of the ambient space. Implied by the elastic rod model for DNA, the molecule writhes immediately when subject to a terminal twist as long as its axis is none of the following curves: lines, circular arcs, circular helices. This result is remarkably different from well-known results about DNA of other conformations. For example, if a DNA is regarded as an elastic rod whose axis is a circle, then it has no induced writhe when subject to a terminal twist until the latter meets a critical extent. To my mother for her 70th birthday An erratum to this article is available at .     

Intrinsic Bent DNA Sites in the Developmentally Amplified C3-22 Gene Promoter of Rhynchosciara americana (Diptera: Sciaridae)

The Rhynchosciara americana C3-22 gene is located in an amplified domain and is developmentally expressed. The aim of the present work was to identify intrinsically bent DNA sites in a segment containing the gene promoter and downstream sequence. The results indicated that this gene is flanked by intrinsically bent DNA sites. Three bent DNA sites (b^?3, b^?2, and b^?1) were localized in the promoter, and one was localized downstream of the gene (b⁺¹). These sites had helical parameters that confirmed the curved structure, as well as segments with left-handed superhelical writhe. In silico analysis of the promoters of four other insect genes, which encode secreted polypeptides, showed that they all had curved structures and similar helical parameters. Correlation with other results indicates that the detected intrinsically bent DNA sites that flank the C3-22 gene might be a consensus feature of the gene structure in the amplified domains.     

Structural changes in positively and negatively supercoiled DNA

The effect of superhelical constraint on the structure of covalently closed circular DNA (cccDNA; pBR322) with positive and negative writhe (superturn) has been investigated as a function of decreasing and increasing specific linking difference (mean superhelical density sigma). At low and moderate negative superhelical densities sigma, the overall average structure is maintained in an unwound B-form slightly modified. The overwound cccDNAs with positive writhe differ from those with negative writhe by an absence of cruciform structure. At high negative densities of supercoiling different changes involving the reversal of twist handedness are shown to lead to the formation of DNA segments in a conformation identical to the left-handed component of form V DNA.     

The Twist,Writhe, and Linking Number Distributions in Closed Circular DNA

Abstract

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.     

The twist, writhe, and linking number distributions in closed circular DNA

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.     

Link, twist, energy, and the stability of DNA minicircles

We describe how the stability properties of DNA minicircles can be directly read from plots of various biologically intuitive quantities along families of equilibrium configurations. Our conclusions follow from extensions of the mathematical theory of distinguished bifurcation diagrams that are applied within the specific context of an elastic rod model of minicircles. Families of equilibria arise as a twisting angle alpha is varied. This angle is intimately related to the continuously varying linking number Lk for nicked DNA configurations that is defined as the sum of Twist and Writhe. We present several examples of such distinguished bifurcation diagrams involving plots of the energy E, linking number Lk, and a twist moment m3, along families of cyclized equilibria of both intrinsically straight and intrinsically curved DNA fragments.     

Replication origins oriGNAI3 and oriB of the mammalian AMPD2 locus nested in a region of straight DNA flanked by intrinsically bent DNA sites

The aim of this work was to determine whether intrinsically bent DNA sites are present at, or close to, the mammalian replication origins oriGNAI3 and oriB in the Chinese hamster AMPD2 locus. Using an electrophoretic mobility shift assay and in silico analysis, we located four intrinsically bent DNA sites (b1 to b4) in a fragment that contains the oriGNAI3 and one site (b5) proximal to oriB. The helical parameters show that each bent DNA site is curved in a left-handed superhelical writhe. A 2D projection of 3D fragment trajectories revealed that oriGNAI3 is located in a relatively straight segment flanked by bent sites b1 and b2, which map in previously identified Scaffold/Matrix Attachment Region. Sites b3 and b4 are located approximately 2 kb downstream and force the fragment into a strong closed loop structure. The b5 site is also located in an S/MAR that is found just downstream of oriB.     

The effect of intrinsic curvature on supercoiling: Predictions of elasticity theory

Elasticity theory of naturally curved rods is employed to study the effects of intrinsic curvature on the properties of the equilibrium conformations of supercoiled DNA. The results stand in sharp contrast to those obtained when the molecule is viewed as being straight in its relaxed form. Starting from very fundamental principles of the theory, we show that the torsion of an open segment with a curved duplex axis can vary when the temperature, and along with it, the intrinsic twist is changed. Conversely, an imposed helicity, such as might be associated with binding to a histone, can change the intrinsic twist. It is also shown that another consequence of the presence of naturally curved sequences is that the twist density will, in general, vary with position along the chain in all equilibrium states. Then portions of the molecule will be more or less susceptible to interaction with other agents sensitive to such a variation. Finally, some closed equilibrium global structures uniquely associated with intrinsic curvature are discussed. © 1993 John Wiley & Sons, Inc.     

DNA binding and nuclease protection by the HMf histones from the hyperthermophilic archaeon Methanothermus fervidus

The DNA-binding and nuclease-protection properties of the HMf histones from the hyperthermophilic archaeon Methanothermus fervidus have been shown to be consistent with the formation of nucleosome-like structures (NLS). These proteins bind to DNA molecules as short as 20 bp and form complexes that protect DNA fragments from micrococcal nuclease (MNase) digestion that are 30 bp, ∼ 60 bp and multiples of ∼ 60 bp in length. The sequences of 49 of the ∼ 60-bp DNA fragments protected from MNase digestion by HMfA have been determined and their intrinsic curvatures calculated. A circular permutation gel mobility-shift assay was used to determine directly the curvatures for five of these sequences. HMfA bound to intrinsically curved and noncurved DNAs, but exhibited a slight preference for the model curved DNA in binding competitions with a model noncurved DNA. The results obtained are consistent with the concept that the archaeal NLS is analogous, and possibly homologous, to the central core of the eukaryal nucleosome formed by a histone (H3 + H4)2 tetramer. Received: August 11, 1996 / Accepted: November 12, 1996     

Intrinsic bent DNA sites in the developmentally amplified C3-22 gene promoter of Rhynchosciara americana (Diptera: Sciaridae)

The Rhynchosciara americana C3-22 gene is located in an amplified domain and is developmentally expressed. The aim of the present work was to identify intrinsically bent DNA sites in a segment containing the gene promoter and downstream sequence. The results indicated that this gene is flanked by intrinsically bent DNA sites. Three bent DNA sites (b(-3), b(-2), and b(-1)) were localized in the promoter, and one was localized downstream of the gene (b(+1)). These sites had helical parameters that confirmed the curved structure, as well as segments with left-handed superhelical writhe. In silico analysis of the promoters of four other insect genes, which encode secreted polypeptides, showed that they all had curved structures and similar helical parameters. Correlation with other results indicates that the detected intrinsically bent DNA sites that flank the C3-22 gene might be a consensus feature of the gene structure in the amplified domains.     

Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles

Distributions of the linking number of circular DNA molecules, defined as the sum of twist and the writhing number, are obtained by Monte Carlo simulations of small, randomly closed DNA circles. We estimate the relative contributions of fluctuations in twist and writhe to the linking number distribution, as functions of DNA size. Published experimental data on topoisomer distributions in circular DNA molecules are interpreted to estimate the torsional rigidity of DNA in solution. We show that ignoring the writhe component of the linking number distribution, even for DNA circles as small as 250 base-pairs, leads to an underestimate for the torsional stiffness of the double helix. The value of the torsional modulus obtained from this analysis, C = 3.4 X 10(-19) erg cm, is from 10 to 40% larger than that estimated by others and more than twice as large as the values obtained from fluorescence depolarization or other time-resolved spectroscopic measurements. We also develop further the theoretical treatment of ring closure probabilities for DNA described in the previous article. It is shown that the torsional part of the ring closure probability, phi 0,1 (tau 0) is a periodic function of DNA length that contributes strongly to the ring closure probability for short chains but makes negligible contributions for chains over 1000 base-pairs in length.     

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.     

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 × 10⁻¹⁹ dyne cm², and persistence length, P = 500 Å. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (Δ1) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever Δ1 lies in the transition region. The free energies of the two minima are equal when Δ1_c = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be ΔG_bar = (0.20) k_BT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for Δ1 values in the transition region, and the two minimum mean potential energies are equal when Δ1 = 1.50. At the midpoint writhe, Δ1_c = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) k_BT, and the difference in their entropies is 1.3 k_B. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of Δ1 values from 0.85 to 1.85. The twist energy parameter (E_T), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition. © 1996 John Wiley & Sons, Inc.     

Effect of spontaneous twist on DNA minicircles

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.     

DNA Topological Context Affects Access to Eukaryotic DNA Topoisomerase I

Abstract

We have analyzed the reactivity of a 217 base pair segment of the intrinsically curved Crithidia fasciculata kinetoplast DNA towards eukaryotic DNA topoisomerase I. The substrates were open [linear fragment and nicked circle] and closed minidomains [closed relaxed circle and circles with linking differences of ?1 and ?2], We interpreted the results with the aid of a model that was used to predict the structures of the topoisomers. The modelling shows that the ΔLk(?l) form is unusually compact because of the curvature in the DNA. To determine the role of sequence-directed curvature in both the experimental and modeling studies, controls were examined in which the curved Crithidia sequence was replaced by an uncurved sequence obtained from the plasmid pBR322.

Reactivity of the Crithidia DNA [as analyzed both by the cleavage and the topoisomerization reactions] markedly varied among the DNA forms: (i) the hierarchy of overall reactivity observed is: linear fragment > nicked circular, closed circular [ΔLk(O)], interwound [ΔLk(?2)] > bent interwound [ΔLk(?l)]; (ii) the intensity of several cleavage positions differs among DNA forms.

The results show that eukaryotic DNA topoisomerase I is very sensitive to the conformation of the substrates and that its reactivity is modulated by the variation of the compactness of the DNA molecule. The C. fasciculata sequence contains a highly curved segment that determines the conformation of the closed circle in a complex way.     

Mapping the phase diagram of the writhe of DNA nanocircles using atomistic molecular dynamics simulations

We have investigated the effects of duplex length, sequence, salt concentration and superhelical density on the conformation of DNA nanocircles containing up to 178 base pairs using atomistic molecular dynamics simulation. These calculations reveal that the partitioning of twist and writhe is governed by a delicate balance of competing energetic terms. We have identified conditions which favour circular, positively or negatively writhed and denatured DNA conformations. Our simulations show that AT-rich DNA is more prone to denaturation when subjected to torsional stress than the corresponding GC containing circles. In contrast to the behaviour expected for a simple elastic rod, there is a distinct asymmetry in the behaviour of over and under-wound DNA nanocircles. The most biologically relevant negatively writhed state is more elusive than the corresponding positively writhed conformation, and is only observed for larger circles under conditions of high electrostatic screening. The simulation results have been summarised by plotting a phase diagram describing the various conformational states of nanocircles over the range of circle sizes and experimental conditions explored during the study. The changes in DNA structure that accompany supercoiling suggest a number of mechanisms whereby changes in DNA topology in vivo might be used to influence gene expression.     

Novel Polymorphism of RecA Fibrils Revealed by Atomic Force Microscopy

RecA fibrils in physiological conditions have been successfully imaged using Tapping Mode atomic force microscopy. This represents the first time images of recA have been obtained without drying, freezing and/or exposure to high vacuum conditions. While previously observed structures – the monomer, the hexamer, the short rod – were seen, a new type of fibril was also observed. This protofibril is narrower in diameter than the standard fibril, and occurs in three distinct morphologies: aperiodic, 100-nm periodic, and 150-nm periodic. In addition, much longer rods were observed, and appear curved and even circular.     

The trajectory of a stiff rod in a curved potential energy trough

The equilibrium trajectory of the axis of a rod subject to an externally imposed curved potential energy trough tends to conform to the shape of the curved trough, but also tends to be straight because of elastic resistance to bending. The actual path of the axis is a balance between the two extremes. We consider a potential energy trough centered along a circular arc of radiusR. For a rod of small length compared toR, we show that the axis at equilibrium forms an arc of a circle of radius greater thanR. The value of the radius of the axial path depends on the relative values of the Hooke’s Law bending constant for the rod and the depth and width of the trough. Motivation for the calculation is provided by nucleosomal DNA, which conforms to the surface of a roughtly cylindrical histone core at physiological ionic strength, but is observed to unwind into a partially extended conformation at very low ionic strength. We suggest that the rigidity to bending of short DNA segments becomes sufficiently great at low ionic strength to overcome attractive interactions with the histone surface. Alternately, of course, if during the cell cycle mutually attractive forces between DNA and histone core are weakened at constant ionic strength, the same type of unfolding would be expected to occur as the strength of the DNA-histone contacts drops below the level required to overcome elastic resistance to bending of the DNA rod.