Related papers: The evaluation of directionally writhing polymers
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…
The geometry of a smooth line is characterized locally by its curvature and torsion, or globally by its writhe. In many situations of physical interest the line is, however, not smooth so that the classical Frenet description of the…
Motivated by recent experiments on DNA torsion-force-extension characteristics we consider the writhing geometry of open stiff molecules. We exhibit a cyclic motion which allows arbitrarily large twisting of the end of a molecule via an…
We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to…
The winding of a single polymer in thermal equilibrium around a repulsive cylindrical obstacle is perhaps the simplest example of statistical mechanics in a multiply connected geometry. As shown by S.F. Edwards, this problem is closely…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here we ask if there exist local geometric features that may be used as a read-out of the underlying topology of generic polymers. We perform molecular…
The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As…
The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Studies of molecules that are intrinsically chiral, such as double-stranded DNA, is one example. Their properties…
The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the…
Motivated by experiments in which single DNA molecules are stretched and twisted we consider a perturbative approach around very high forces, where we determine the writhe distribution in a simple, analytically tractable model. Our results…
For a directed polymer in a random medium lying on an infinite cylinder, that is in 1+1 dimensions with finite width and periodic boundary conditions on the transverse direction, the winding number is simply the algebraic number of turns…
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
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…
Because of the double-helical structure of DNA, in which two strands of complementary nucleotides intertwine around each other, a covalently closed DNA molecule with no interruptions in either strand can be viewed as two interlocked…
Within a simple elastic theory, we study the elongation versus force characteristics of a supercoiled DNA molecule at thermal equilibrium in the regime of small supercoiling. The partition function is mapped to the path integral…
The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally-constrained single molecules give the first direct measurement of this…
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…
We study the geometry of a semiflexible polymer at finite temperatures. The writhe can be calculated from the properties of Gaussian random walks on the sphere. We calculate static and dynamic writhe correlation functions. The writhe of a…
We prove a central limit theorem for the winding number of a directed polymer on a cylinder, which is equivalent with proving the Gaussian fluctuations of the endpoint of the directed polymer in a spatial periodic environment.