Coupling of actin hydrolysis and polymerization: Reduced description with two nucleotide states

The polymerization of actin filaments is coupled to the hydrolysis of adenosine triphosphate (ATP), which involves both the cleavage of ATP and the release of inorganic phosphate. We describe hydrolysis by a reduced two-state model with a cooperative cleavage mechanism, where the cleavage rate depends on the state of the neighboring actin protomer in a filament. We obtain theoretical predictions of experimentally accessible steady state quantities such as the size of the ATP-actin cap, the size distribution of ATP-actin islands, and the cleavage flux for cooperative cleavage mechanisms.Comment: 6 page

Dislocations and the critical endpoint of the melting line of vortex line lattices

We develop a theory for dislocation-mediated structural transitions in the vortex lattice which allows for a unified description of phase transitions between the three phases, the elastic vortex glass, the amorphous vortex glass, and the vortex liquid, in terms of a free energy functional for the dislocation density. The origin of a critical endpoint of the melting line at high magnetic fields, which has been recently observed experimentally, is explained.Comment: 4 pages, 1 figur

Large time off-equilibrium dynamics of a manifold in a random potential

We study the out of equilibrium dynamics of an elastic manifold in a random potential using mean-field theory. We find two asymptotic time regimes: (i) stationary dynamics, (ii) slow aging dynamics with violation of equilibrium theorems. We obtain an analytical solution valid for all large times with universal scalings of two-time quantities with space. A non-analytic scaling function crosses over to ultrametricity when the correlations become long-range. We propose procedures to test numerically or experimentally the extent to which this scenario holds for a given system.Comment: 12 page

Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints

The aim of the present paper is the study of the entropic elasticity of the dsDNA molecule, having a cristallographic length L of the order of 10 to 30 persistence lengths A, when it is subject to spatial obstructions. We have not tried to obtain the single molecule partition function by solving a Schodringer-like equation. We prefer to stay within a discretized version of the WLC model with an added one-monomer potential, simulating the spatial constraints. We derived directly from the discretized Boltzmann formula the transfer matrix connecting the partition functions relative to adjacent "effective monomers". We have plugged adequate Dirac delta-functions in the functional integral to ensure that the monomer coordinate and the tangent vector are independent variables. The partition function is, then, given by an iterative process which is both numerically efficient and physically transparent. As a test of our discretized approach, we have studied two configurations involving a dsDNA molecule confined between a pair of parallel plates.Comment: The most formal developments of Section I have been moved into an appendix and replaced by a direct derivation of the transfer matrix used in the applications. of Section II. Two paragraphs and two figures have been added to clarify the physical interpretation of the result

A Bragg glass phase in the vortex lattice of a type II superconductor

Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of the crystalline order. The resulting state of matter has been a longstanding puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into crystallites. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The lattice of vortices that can contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron diffraction data of the vortex lattice in type II superconductors provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transition and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and conductivity of electronic crystals.Comment: 9 pages, 4 figure

Effects of point defects on the phase diagram of vortex states in high-Tc superconductors in B//c axis

The phase diagram for the vortex states of high-$T_{\rm c}$ superconductors with point defects in $\vec{B} \parallel c$ axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.Comment: 4 pages, 9 eps figures (included in text), uses revtex.sty, overall changes with several additional data points, though conclusion is unchange

Effect of electron irradiation on vortex dynamics in YBa_2Cu_3O_{7-x} single crystals

We report on drastic change of vortex dynamics with increase of quenched disorder: for rather weak disorder we found a single vortex creep regime, which we attribute to a Bragg-glass phase, while for enhanced disorder we found an increase of both the depinning current and activation energy with magnetic field, which we attribute to entangled vortex phase. We also found that introduction of additional defects always increases the depinning current, but it increases activation energy only for elastic vortex creep, while it decreases activation energy for plastic vortex creep.Comment: 4 pages, 3 figures, submited to Phys. Rev.

Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $\nu\approx1.3$, $\beta\approx0.05$, $\gamma/\nu\approx2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.Comment: 4 pages, 3 eps-figures include

Instabilities and disorder-driven first-order transition of the vortex lattice

Transport studies in a Corbino disk geometry suggest that the Bragg glass phase undergoes a first-order transition into a disordered solid. This transition shows a sharp reentrant behavior at low fields. In contrast, in the conventional strip configuration, the phase transition is obscured by the injection of the disordered vortices through the sample edges, which results in the commonly observed vortex instabilities and smearing of the peak effect in NbSe2 crystals. These features are found to be absent in the Corbino geometry, in which the circulating vortices do not cross the sample edges.Comment: 12 pages 3 figures. Accepted for publication in Physical Review Letter

Mesoscopic models for DNA stretching under force: new results and comparison to experiments

Single molecule experiments on B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. It has been proposed that the first transition, at forces of 60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). We derive analytical formula using a coupled discrete worm like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connexion with previous fitting parameter values for denaturation profiles. We find that: (i) ssDNA is fitted, using an analytical formula, over a nanoNewton range with only three free parameters, the contour length, the bending modulus and the monomer size; (ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; (iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; (v) this formula fits perfectly well poly(dG-dC) and $\lambda$-DNA force-extension curves with consistent parameter values; (vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges.Comment: 14 pages, 9 figure