Monte Carlo implementation of supercoiled double-stranded DNA

Metropolis Monte Carlo simulation is used to investigate the elasticity of torsionally stressed double-stranded DNA, in which twist and supercoiling are incorporated as a natural result of base-stacking interaction and backbone bending constrained by hydrogen bonds formed between DNA complementary nucleotide bases. Three evident regimes are found in extension versus torsion and/or force versus extension plots: a low-force regime in which over- and underwound molecules behave similarly under stretching; an intermediate-force regime in which chirality appears for negatively and positively supercoiled DNA and extension of underwound molecule is insensitive to the supercoiling degree of the polymer; and a large-force regime in which plectonemic DNA is fully converted to extended DNA and supercoiled DNA behaves quite like a torsionless molecule. The striking coincidence between theoretic calculations and recent experimental measurement of torsionally stretched DNA [Strick et al., Science {\bf 271}, 1835 (1996), Biophys. J. {\bf 74}, 2016 (1998)] strongly suggests that the interplay between base-stacking interaction and permanent hydrogen-bond constraint takes an important role in understanding the novel properties of elasticity of supercoiled DNA polymer.Comment: 21 pages, 6 PS figures. To appear at Biophys.

Theoretical models of DNA topology simplification by type IIA DNA topoisomerases

It was discovered 12 years ago that type IIA topoisomerases can simplify DNA topology—the steady-state fractions of knots and links created by the enzymes are many times lower than the corresponding equilibrium fractions. Though this property of the enzymes made clear biological sense, it was not clear how small enzymes could selectively change the topology of very large DNA molecules, since topology is a global property and cannot be determined by a local DNA–protein interaction. A few models, suggested to explain the phenomenon, are analyzed in this review. We also consider experimental data that both support and contravene these models

Non-equilibrium hydrodynamics of a rotating filament

The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The twirling-overwhirling transition is located and found to be strongly discontinuous. For finite bend and twist persistence length, thermal fluctuations lower the threshold rotational frequency, for infinite persistence length the threshold agrees with previous analytical predictions

Comment on "Elasticity Model of a Supercoiled DNA Molecule"

We perform simulations to numerically study the writhe distribution of a stiff polymer. We compare with analytic results of Bouchiat and Mezard (PRL 80 1556- (1998); cond-mat/9706050).Comment: 1 page, 1 figure revtex

Modeling Bacterial DNA: Simulation of Self-avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix

Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Like Chain (ssWLC) model, which is known to capture the folding properties of supercoiled DNA, and provide a detailed explanation of a standard MC simulation method. On the other hand, we explain how to extend this ssWLC model to include structural transitions of the helix.Comment: Book chapter to appear in The Bacterial Nucleoid, Methods and Protocols, Springer serie

Diffusion of a ring polymer in good solution via the Brownian dynamics

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.Comment: 11 pages, 4 figure

Elasticity and electrostatics of plectonemic DNA

We present a self-contained theory for the mechanical response of DNA in single molecule experiments. Our model is based on a 1D continuum description of the DNA molecule and accounts both for its elasticity and for DNA-DNA electrostatic interactions. We consider the classical loading geometry used in experiments where one end of the molecule is attached to a substrate and the other one is pulled by a tensile force and twisted by a given number of turns. We focus on configurations relevant to the limit of a large number of turns, which are made up of two phases, one with linear DNA and the other one with superhelical DNA. The model takes into account thermal fluctuations in the linear phase and electrostatic interactions in the superhelical phase. The values of the torsional stress, of the supercoiling radius and angle, and key features of the experimental extension-rotation curves, namely the slope of the linear region and thermal buckling threshold, are predicted. They are found in good agreement with experimental data.Comment: 19 pages and 6 figure

Torsional Directed Walks, Entropic Elasticity, and DNA Twist Stiffness

DNA and other biopolymers differ from classical polymers due to their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the `torsional directed walk'. Motivated by a recent experiment on single lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C=120nm and D=50nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.Comment: Plain TeX, harvmac, epsf; postscript available at http://dept.physics.upenn.edu/~nelson/index.shtm

Nonlinear Mechanical Response of DNA due to Anisotropic Bending Elasticity

The response of a short DNA segment to bending is studied, taking into account the anisotropy in the bending rigidities caused by the double-helical structure. It is shown that the anisotropy introduces an effective nonlinear twist-bend coupling that can lead to the formation of kinks and modulations in the curvature and/or in the twist, depending on the values of the elastic constants and the imposed deflection angle. The typical wavelength for the modulations, or the distance between the neighboring kinks is found to be set by half of the DNA pitch.Comment: 4 pages, 3 encapsulated EPS figure

Conformations of Linear DNA

We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition.Comment: 5 pages, RevTeX; 6 postscript figure