Phase diagram of force-induced DNA unzipping in exactly solvable models

The mechanical separation of the double helical DNA structure induced by forces pulling apart the two DNA strands (``unzipping'') has been the subject of recent experiments. Analytical results are obtained within various models of interacting pairs of directed walks in the (1,1,...,1) direction on the hypercubic lattice, and the phase diagram in the force-temperature plane is studied for a variety of cases. The scaling behaviour is determined at both the unzipping and the melting transition. We confirm the existence of a cold denaturation transition recently observed in numerical simulations: for a finite range of forces the system gets unzipped by {\it decreasing} the temperature. The existence of this transition is rigorously established for generic lattice and continuum space models.Comment: 19 pages, 5 eps figures; revised version with minor changes, presentation simplified in the text with details in appendix. Accepted for publication in Phys. Rev.

Active interface growth and pattern formation in membrane-protein systems

Inspired by recent experimental observation of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particle-like inclusions which stimulate its growth. We find that the coupling between interfacial and inclusions dynam- ics yields microphase separation and the self-organisation of travelling waves. These patterns are strikingly similar to those detected in the aforementioned experiments on actin-protein systems. Our results further show that the active growth kinetics does not fall into the Kardar-Parisi-Zhang universality class for growing interfaces, displaying instead a novel superposition of equilibrium-like scaling and sustained oscillations.Comment: 5 pages, 5 figure

Facilitated diffusion on confined DNA

In living cells, proteins combine 3D bulk diffusion and 1D sliding along the DNA to reach a target faster. This process is known as facilitated diffusion, and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: we find that facilitated diffusion is most efficient inside an isotropic volume, and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin

Cytoplasmic streaming in plant cells: the role of wall slip

We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacuole viscosity and the slip layer close to the wall, we find that this simplified view, which does not rely on any coupling between motors, cytoplasm and vacuole other than that provided by viscous Stokes flow, is enough to account for the observed magnitude of streaming velocities in intracellular fluid in living plant cells.Comment: 18 pages (incl. appendix), 10 figures, accepted in J R Soc Interfac

Spontaneous symmetry breaking in active droplets provides a generic route to motility

We explore a generic mechanism whereby a droplet of active matter acquires motility by the spontaneous breakdown of a discrete symmetry. The model we study offers a simple representation of a "cell extract" comprising, e.g., a droplet of actomyosin solution. (Such extracts are used experimentally to model the cytoskeleton.) Actomyosin is an active gel whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes ('treadmilling'), the gel's dynamics arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. Adapting our model to wall-bound cells in two dimensions, we find that as wall friction is reduced, treadmilling-induced motility falls but SSB-mediated motility rises. The latter might therefore be crucial in three dimensions where frictional forces are likely to be modest. At a supra-cellular level, the same generic mechanism can impart motility to aggregates of non-motile but active bacteria; we show that SSB in this (extensile) case leads generically to rotational as well as translational motion.Comment: 13 pages, 8 figures, 1 tabl

Phase diagram for unzipping DNA with long-range interactions

We present a critique and extension of the mean-field approach to the mechanical pulling transition in bound polymer systems. Our model is motivated by the theoretically and experimentally important examples of adsorbed polymers and double-stranded DNA, and we focus on the case in which quenched disorder in the sequence of monomers is unimportant for the statistical mechanics. We show how including excluded volume interactions in the model affects the phase diagram for the critical pulling force, and we predict a re-entrancy phase at low temperatures which has not been previously discussed. We also consider the case of non-equilibrium pulling, in which the external force probes the local, rather than the global structure of the dsDNA or adsorbed polymer. The dynamics of the pulling transition in such experiments could illuminate the polymer's loop structure, which depends on the nature of excluded volume interactions.Comment: 4 pages, 2 figures; this version clarifies Eq. 8, and corrects errors in Fig.

Switching dynamics in cholesteric blue phases

Blue phases are networks of disclination lines, which occur in cholesteric liquid crystals near the transition to the isotropic phase. They have recently been used for the new generation of fast switching liquid crystal displays. Here we study numerically the steady states and switching hydrodynamics of blue phase I (BPI) and blue phase II (BPII) cells subjected to an electric field. When the field is on, there are three regimes: for very weak fields (and strong anchoring at the boundaries) the blue phases are almost unaffected, for intermediate fields the disclinations twist (for BPI) and unzip (for BPII), whereas for very large voltages the network dissolves in the bulk of the cell. Interestingly, we find that a BPII cell can recover its original structure when the field is switched off, whereas a BPI cell is found to be trapped more easily into metastable configurations. The kinetic pathways followed during switching on and off entails dramatic reorganisation of the disclination networks. We also discuss the effect of changing the director field anchoring at the boundary planes and of varying the direction of the applied field.Comment: 17 pages, 11 figure

Self-Assembly and Nonlinear Dynamics of Dimeric Colloidal Rotors in Cholesterics

We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-increasing phase lag between the dimer orientation and the local nematic director.Comment: 4 + 5 page