Analytical description of extension, torque, and supercoiling radius of a stretched twisted DNA

We study the mixture of extended and supercoiled DNA that occurs in a twisted DNA molecule under tension. Closed-form asymptotic solutions for the supercoiling radius, extension, and torque of the molecule are obtained in the high-force limit where electrostatic and elastic effects dominate. We demonstrate that experimental data obey the extension and torque scaling laws apparent in our formulas, in the regime where thermal fluctuation effects are quenched by applied force.     

Extracting DNA twist rigidity from experimental supercoiling data

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we obtain an estimate of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immersed.     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Physical Approaches to the Study of DNA

New micromanipulation techniques now enable physicists and biologists to study the behavior of single biomolecules such as DNA. In particular, it is possible to measure the elastic response of individual DNA molecules to changes in the double helix's supercoiling. The force versus extension diagram for torsionally relaxed DNA is continuous and allows one to evaluate the persistence length of the polymer. When the molecule is supercoiled, however, stretching leads to the buildup of torsional stress in the double helix's axis. When the twist energy thus generated increases beyond a critical value, the molecule is locally destabilized and changes conformation. This structural transition occurs at stretching forces which can be exerted in vivo by molecular motors and at degrees of supercoiling found in the cell, and may have implications for DNA structure and function within the nucleus.     

Supercoiling and denaturation of DNA loops

We study the statistical mechanics of small DNA loops emphasizing the competition between elasticity, supercoiling, and denaturation. Motivated by recent experiments and atomistic molecular dynamics simulation, we propose a new coarse-grained phenomenological model of DNA. We extend the classical elastic rod models to include the possibility of denaturation and nonlinear twist elasticity. Using this coarse-grained model, we obtain a phase diagram in terms of fractional overtwist and loop size that can be used to rationalize a number of experimental results which have also been confirmed by atomistic simulations.     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Elasticity theory of a twisted stack of plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch along and relative excess twist about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K₂₃ that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix. Received: 4 July 1997 / Received in final form: 16 October 1997 / Accepted: 21 October 1997     

Molecular elasticity and the geometric phase

We present a method for solving the wormlike-chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4pi. We develop an analogy between WLC elasticity and the geometric phase of a spin-1 / 2 system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers such as DNA.     

Supercoiling induces denaturation bubbles in circular DNA

We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in?vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.     

Fibril stability in solutions of twisted -sheet peptides: a new kind of micellization in chiral systems

The problem of fibril (fibre) formation in chiral systems is explored theoretically being supported by experiments on synthetic de novo 11-mer peptide forming self-assembled -sheet tapes. Experimental data unambiguously indicate that the tapes form fibrils of nearly monodisperse thickness ca . 8-10 nm. Fibril formation and stabilisation are attributed to inter-tape face-to-face attraction and their intrinsic twist, correspondingly. The proposed theory is capable of predicting the fibril aggregation number and its equilibrium twist in terms of molecular parameters of the primary tapes. The suggested novel mechanism of twist stabilisation of finite aggregates (fibrils) is different to the well-known stabilisation of micelles in amphiphilic systems, and it is likely to explain the formation and stability of fibrils in a wide variety of systems including proteinaceous amyloid fibres, sickle-cell hemoglobin fibres responsible for HbS anemia, corkscrew threads found in chromonics in the presence of chiral additives and native cellulose microfibrillar crystallites. The theory also makes it possible to extract the basic molecular parameters of primary tapes (inter-tape attraction energy, helical twist step, elastic moduli) from the experimental data. Received 7 May 1999 and Received in final form 15 February 2000