Stretching Instability of Helical Spring

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur, and propose experimental tests of our predictions.Comment: 5 pages, 4 figure

Statistical mechanics of triangulated ribbons

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from the angles between the normal vectors of adjacent triangles, the second where the edges are viewed as semiflexible polymers so that the bending energy is related to the angles between the tangent vectors of next-nearest neighbor triangles. The first model can be solved exactly whereas the second is more involved. It was recently introduced by Liverpool and Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a model for double-stranded biopolymers such as DNA. Comparing observables such as the autocorrelation functions of the tangent vectors and the bond-director field, the probability distribution functions of the end-to-end distance, and the mean squared twist we confirm the existence of local twist correlation, but find no indications for other predicted features such as twist-stretch coupling, kinks, or oscillations in the autocorrelation function of the bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio

The antiparallel loops in gal DNA

Interactions between proteins bound to distant sites along a DNA molecule require bending and twisting deformations in the intervening DNA. In certain systems, the sterically allowed protein–DNA and protein–protein interactions are hypothesized to produce loops with distinct geometries that may also be thermodynamically and biologically distinct. For example, theoretical models of Gal repressor/HU-mediated DNA-looping suggest that the antiparallel DNA loops, A1 and A2, are thermodynamically quite different. They are also biologically different, since in experiments using DNA molecules engineered to form only one of the two loops, the A2 loop failed to repress in vitro transcription. Surprisingly, single molecule measurements show that both loop trajectories form and that they appear to be quite similar energetically and kinetically

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

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure

Pulling a polymer out of a potential well and the mechanical unzipping of DNA

Motivated by the experiments on DNA under torsion, we consider the problem of pulling a polymer out of a potential well by a force applied to one of its ends. If the force is less than a critical value, then the process is activated and has an activation energy proportinal to the length of the chain. Above this critical value, the process is barrierless and will occur spontaneously. We use the Rouse model for the description of the dynamics of the peeling out and study the average behaviour of the chain, by replacing the random noise by its mean. The resultant mean-field equation is a nonlinear diffusion equation and hence rather difficult to analyze. We use physical arguments to convert this in to a moving boundary value problem, which can then be solved exactly. The result is that the time $t_{po}$ required to pull out a polymer of $N$ segments scales like $N^2$. For models other than the Rouse, we argue that $t_{po}\sim N^{1+\nu}$Comment: 11 pages, 6 figures. To appear in PhysicalReview

Single molecule experiments in biophysics: exploring the thermal behavior of nonequilibrium small systems

Biomolecules carry out very specialized tasks inside the cell where energies involved are few tens of k_BT, small enough for thermal fluctuations to be relevant in many biomolecular processes. In this paper I discuss a few concepts and present some experimental results that show how the study of fluctuation theorems applied to biomolecules contributes to our understanding of the nonequilibrium thermal behavior of small systems.Comment: Proceedings of the 22nd Statphys Conference 2004 (Bangalore,India). Invited contributio

Pulling self-interacting polymers in two-dimensions

We investigate a two-dimensional problem of an isolated self-interacting end-grafted polymer, pulled by one end. In the thermodynamic limit, we find that the model has only two different phases, namely a collapsed phase and a stretched phase. We show that the phase diagram obtained by Kumar {\it at al.\} [Phys. Rev. Lett. {\bf 98}, 128101 (2007)] for small systems, where differences between various statistical ensembles play an important role, differ from the phase diagram obtained here in the thermodynamic limit.Comment: 20 pages, 22 figure

Bending and Base-Stacking Interactions in Double-Stranded Semiflexible Polymer

Simple expressions for the bending and the base-stacking energy of double-stranded semiflexible biopolymers (such as DNA and actin) are derived. The distribution of the folding angle between the two strands is obtained by solving a Schr\"{o}dinger equation variationally. Theoretical results based on this model on the extension versus force and extension versus degree of supercoiling relations of DNA chain are in good agreement with the experimental observations of Cluzel {\it et al.} [Science {\bf 271}, 792 (1996)], Smith {\it et al.} [{\it ibid.} {\bf 271}, 795 (1996)], and Strick {\it et al.} [{\it ibid.} {\bf 271}, 1835 (1996)].Comment: 8 pages in Revtex format, with 4 EPS figure

Molecular elasticity and the geometric phase

We present a method for solving the Worm Like 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 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half 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 like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's comments, to appear in PR