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. The difference between this subdiffusion and that in the absence of active forces is quantified. We show that the polymer swells in response to active processes and determine how this swelling depends on the viscoelastic properties of the environment. Our results are compared to recent experiments on the motion of chromosomal loci in bacteria.

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. We find that the probability that the head is close to its binding site on the microtubule can be enhanced by a factor of two due to active forces. Finally, we study the dynamics of a particle in a double well potential as a model for the dynamics of DNA-hairpins. We show that the active forces effectively lower the potential barrier between the two minima and study the impact of this phenomenon on the zipping/unzipping rate.

We present the reduced dynamics of a bead in a Rouse chain which is submerged in a bath containing a driving agent that renders it out-of-equilibrium. We first review the generalized Langevin equation of the middle bead in an equilibrated bath. Thereafter, we introduce two driving forces. Firstly, we add a constant force that is applied to the first bead of the chain. We investigate how the generalized Langevin equation changes due to this perturbation for which the system evolves towards a new equilibrium state after some time. Secondly, we consider the case of stochastic active forces which will drive the system to a nonequilibrium state. Including these active forces results in a frenetic contribution to the second fluctuation-dissipation relation, in accord with a recent extension of the fluctuation-dissipation relation to nonequilibrium. The form of the frenetic term is analysed for the specific case of Gaussian, exponentially correlated active forces. We also discuss the resulting rich dynamics of the middle bead in which various regimes of normal diffusion, subdiffusion and superdiffusion can be present.

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. We determine the time evolution of the length and the shape of the polymer. Through an analysis of the velocity of the monomers, we investigate how the tension propagates through the polymer. We discuss how polymers can be used to probe the properties of a viscoelastic medium.

Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.