DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off.Comment: 8 pages, 1 figure. Accepted by Europhysics Letter

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

Treatments for chronic pruritus outside of the box

Patients with chronic pruritus are in desperate need of novel treatment options, as current therapeutic possibilities are often not effective, have a poor level of evidence and are mostly off-label. In recent years, much effort has been put into the identification of potential targets for the treatment of chronic pruritus. More importantly, a number of promising new drugs that are aimed at treating pruritus in different conditions are currently in advanced stages of clinical trials. Here, current pharmacological developments leading to potential new drugs for the treatment of chronic pruritus within various conditions are summarized. Hopefully, these new approaches will result in effective and safe therapies for our patients with chronic pruritus associated with dermatological or non-dermatological diseases in the near future

Phases of bosonic strings and two dimensional gauge theories

We suggest that the extrinsic curvature and torsion of a bosonic string can be employed as variables in a two dimensional Landau-Ginzburg gauge field theory. Their interpretation in terms of the abelian Higgs multiplet leads to two different phases. In the phase with unbroken gauge symmetry the ground state describes open strings while in the phase with broken gauge symmetry the ground state involves closed strings. When we allow for an additional abelian gauge structure along the string, we arrive at an interpretation in terms of the two dimensional SU(2) Yang-Mills theory.Comment: 8 page

How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity

Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existance of a deep connection between quantum gravity and knot theory at a dynamical level.Comment: 7p

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

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

Advanced Actuator Materials Powered by Biomimetic Helical Fiber Topologies

Helical constructs are ubiquitous in nature at all size domains, from molecular to macroscopic. The helical topology confers unique mechanical functions that activate certain phenomena, such as twining vines and vital cellular functions like the folding and packing of DNA into chromosomes. The understanding of active mechanical processes in plants, certain musculature in animals, and some biochemical processes in cells provides insight into the versatility of the helix. Most of these natural systems consist of helically oriented filaments embedded in a compliant matrix. In some cases, the matrix can change volume and in others the filaments can contract and the matrix is passive. In both cases, the helically arranged fibers determine the overall shape change with a great variety of responses involving length contraction/elongation, twisting, bending, and coiling. Synthetic actuator materials and systems that employ helical topologies have been described recently and demonstrate many fascinating and complex shape changes. However, significant new opportunities exist to mimic some of the most remarkable actions in nature, including the Vorticella\u27s coiling stalk and DNA\u27s supercoils, in the quest for superior artificial muscles