Active dynamics and spatially coherent motion in chromosomes subject to enzymatic force dipoles.

Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motorlike enzymes. The enzymes can bind and unbind to specific sites of the polymer and produce a dipolar force on two neighboring monomers when bound. We study the resulting nonequilibrium dynamics of the polymer and find that the motion of the monomers has several properties that were observed experimentally for chromosomal loci: a subdiffusive mean-square displacement and the appearance of regions of correlated motion.

The influence of absorbing boundary conditions on the transition path time statistics.

We derive an analytical expression for the transition path time (TPT) distribution for a one-dimensional particle crossing a parabolic barrier. The solution is expressed in terms of the eigenfunctions and eigenvalues of the associated Fokker-Planck equation. The particle exhibits anomalous dynamics generated by a power-law memory kernel, which includes memoryless Markovian dynamics as a limiting case.

Motion of kinesin in a viscoelastic medium.

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution.

The effect of active fluctuations on the dynamics of particles, motors and DNA-hairpins.

Inspired by recent experiments on the dynamics of particles and polymers in artificial cytoskeletons and in cells, we introduce a modified Langevin equation for a particle in an environment that is a viscoelastic medium and that is brought out of equilibrium by the action of active fluctuations caused by molecular motors. We show that within such a model, the motion of a free particle crosses over from superdiffusive to subdiffusive as observed for tracer particles in an in vitro cytoskeleton or in a cell. We investigate the dynamics of a particle confined by a harmonic potential as a simple model for the motion of the tethered head of kinesin-1.

Dynamics of a polymer in an active and viscoelastic bath.

We study the dynamics of an ideal polymer chain in a viscoelastic medium and in the presence of active forces. The motion of the center of mass and of individual monomers is calculated. On time scales that are comparable to the persistence time of the active forces, monomers can move superdiffusively, while on larger time scales subdiffusive behavior occurs.

Role of trapping and crowding as sources of negative differential mobility.

Increasing the crowding in an environment does not necessarily trigger negative differential mobility of strongly pushed particles. Moreover, the choice of the model, in particular the kind of microscopic jump rates, may be very relevant in determining the mobility. We support these points via simple examples and we therefore address recent claims saying that crowding in an environment is likely to promote negative differential mobility.

Transient behaviour of a polymer dragged through a viscoelastic medium.

We study the dynamics of a polymer that is pulled by a constant force through a viscoelastic medium. This is a model for a polymer being pulled through a cell by an external force, or for an active biopolymer moving due to a self-generated force. Using the Rouse model with a memory dependent drag force, we find that the center of mass of the polymer follows a subballistic motion.

Exact current statistics of the asymmetric simple exclusion process with open boundaries.

Nonequilibrium systems are often characterized by the transport of some quantity at a macroscopic scale, such as, for instance, a current of particles through a wire. The asymmetric simple exclusion process (ASEP) is a paradigm for nonequilibrium transport that is amenable to exact analytical solution. In the present work, we determine the full statistics of the current in the finite size open ASEP for all values of the parameters.

Current fluctuations in the weakly asymmetric exclusion process with open boundaries.

The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. We apply this principle to the weakly asymmetric exclusion process (WASEP). We also calculate the cumulant generating function of the current and the density profiles associated with rare currents in finite systems using a numerical approach based on the density matrix renormalization group.

Geometry and topology of knotted ring polymers in an array of obstacles.

We study knotted polymers in equilibrium with an array of obstacles which models confinement in a gel or immersion in a melt. We find a crossover in both the geometrical and the topological behavior of the polymer. When the polymers' radius of gyration, RG, and that of the region containing the knot, R(G,k), are small compared to the distance b between the obstacles, the knot is weakly localized and RG scales as in a good solvent with an amplitude that depends on knot type.

The size of knots in polymers.

Circular DNA in viruses and bacteria is often knotted. While mathematically problematic, the determination of the knot size is crucial for the study of the physical and biological behaviour of long macromolecules. Here, we review work on the size distribution of these knots under equilibrium conditions.

Density-matrix renormalization-group study of current and activity fluctuations near nonequilibrium phase transitions.

Cumulants of a fluctuating current can be obtained from a free-energy-like generating function, which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the density-matrix renormalization group for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process.

Absorbing state phase transitions with quenched disorder.

Quenched disorder--in the sense of the Harris criterion--is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems.

Strong disorder fixed point in absorbing-state phase transitions.

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected.