Fundamental understanding of the effect of microscopic parameters on the dynamics of probe particles in different complex environments has wide implications. Examples include diffusion of proteins in the biological hydrogels, porous media, polymer matrix, etc. Here, we use extensive molecular dynamics simulations to investigate the dynamics of the probe particle in a polymer network on a diamond lattice which provides substantial crowding to mimic the cellular environment. Our simulations show that the dynamics of the probe increasingly becomes restricted, non-Gaussian and subdiffusive on increasing the network rigidity, binding affinity and the probe size.In addition, the velocity autocorrelation functions show negative dips owing to the viscoelasticity and caging due to surrounding network. These observations go with general experimental findings. Surprisingly for a probe particle of size comparable to the mesh size, unrestricted motion engulfing large length scales has been observed.This happens with the more flexible polymer network, which is easily pushed by the bigger probe. Our study gives a general qualitative picture of transport of probes in gel like medium, as encountered in different contexts.

A prime example of non-equilibrium or active environment is a biological cell. In order to understand in-vivo functioning of biomolecules such as proteins, chromatins, a description beyond equilibrium is absolutely necessary. In this context, biomolecules have been modeled as Rouse chains in Gaussian active bath. However, these non-equilibrium fluctuations in biological cells are non-Gaussian. This motivates us to take a Rouse chain subjected to a series of pulses of force with finite duration, mimicking run and tumble motion of a class of micro-organisms. Thus by construction, this active force is non-Gaussian. Our analytical calculations show that the mean square displacement (MSD) of center of mass (COM) grows faster and even shows superdiffusive behavior at higher activity, supporting recent experimental observation on active enzymes (A.-Y. Jee, Y.-K. Cho, S. Granick, and T. Tlusty, Proc. Natl. Acad. Sci. 115, 10812 (2018)), but chain reconfiguration is slower. The reconfiguration time of a chain with N monomers scales as N σ , where the exponent σ ≈ 2. In addition, the chain swells. We compare this activity-induced swelling with that of a Rouse chain in a Gaussian active bath. In principle, our predictions can be verified by future single molecule experiments.

A colloidal particle immersed in a bath of bacteria is a typical example of a passive particle in an active bath. To model this, we take an overdamped harmonically trapped particle subjected to a thermal and a non-equilibrium noise arising from the active bath.The harmonic well can be attributed to a laser trap or to the small amplitude motion of the sedimented colloid at the bottom of the capillary. In the long time, the system reaches a non-equilibrium steady state that can be described by an effective temperature. By adopting this notion of effective temperature, we investigate whether fluctuation relations for entropy hold. In addition, when subjected to a deterministic time dependent drag, we find that transient fluctuation theorem for work cannot be applied in conventional form. However, a steady state fluctuation relation for work emerges out with a renormalized temperature.

I. ABSTRACTWe consider a colloidal particle immersed in an active bath and derive a Smoluchowski equation that governs the dynamics of colloidal particle. We address this as active Smoluchowski equation. Our analysis based on this active Smoluchowski equation shows a short timesuperdiffusive behavior that strongly depends on the activity. Our model also predicts a non-monotonic dependence of mean energy dissipation against time, a signature of activityinduced dynamics. By introducing a frequency-dependent effective temperature, we show that the mean rate of entropy production is time dependent unlike a thermal system. The prime reason for these anomalies is the absence of any fluctuation-dissipation theorem for the active noise. We also comment on how microscopic details of activity can reverse the trends for mean energy dissipation and mean rate of entropy production.

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non- viscoelastic disconnected monomers. Our simulations...

Activity can also slow down the escape dynamics in dense environment by incorporating ruggedness in the energy landscape, as revealed in our analytical calculations.

In this topical review, we give an overview of the structure and dynamics of a single polymer chain in active baths, Gaussian or non-Gaussian. The review begins with the discussion of single flexible or semiflexible linear polymer chains subjected to two noises, thermal and active. The active noise has either Gaussian or non-Gaussian distribution but has a memory, accounting for the persistent motion of the active bath particles. This finite persistence makes the reconfiguration dynamics of the chain slow as compared to the purely thermal case and the chain swells. The active noise, also results superdiffusive or ballistic motion of the tagged monomer. We present all the calculations in details but mainly focus on the analytically exact or almost exact results on the topic, as obtained from our group in recent years. In addition, we briefly mention important works of other groups and include some of our new results. The review concludes with pointing out the implications of polymer chains in active bath in biologically relevant context and its future directions.

No abstract