Active Brownian ring polymers

Abstract

The conformational and dynamical properties of semiflexible active Brownian ring polymers are investigated analytically. A ring is described by the Gaussian semiflexible polymer model accounting for the finite contour length. Activity is implemented by a Gaussian, non-Markovian stochastic process resembling either an external nonthermal force or a local self-propulsion velocity as for an active Ornstein-Uhlenbeck particle. Specifically, the fluctuation spectrum of normal-mode amplitudes is analyzed. At elevated activities, flexible (tension) modes dominate over bending modes even for semiflexible rings, corresponding to enhanced conformational fluctuations. The fluctuation spectrum exhibits a crossover from a quadratic to a quartic dependence on the mode number with increasing mode number, originating from intramolecular tension, but the relaxation behavior is either dominated by intra-polymer processes or the active stochastic process. A further increase in activity enhances fluctuations at large length scales at the expense of reduced fluctuations at small scales. Conformationally, the mean square ring diameter exhibits swelling qualitatively comparable to liner polymers. The ring's diffusive dynamics is enhanced, and the mean square displacement shows distinct activity-determined regimes, consecutively, a ballistic, a subdiffusive, and a diffusive regime. The subdiffusive regime disappears gradually with increasing activity.

Dynamics as a cause for the nanoscale organization of the genome

“…the time needed to recover to the initial conditions after applied stress, decreases with increasing activity 33 . In line with this observation, an active polymer also exhibits enhanced conformational fluctuations 37 and appears more flexible. In particular, the effective persistence length (the length over which a polymer is approximately stiff) of active polymers is decreased compared to their passive counterparts as a consequence of hairpin-formation 34 .…”

“…Considering structural elements of chromatin such as TADs, sub-TADs as well as chromatin loops such as those that can be extruded by SMC complexes 7,8 , one should take into account that chromatin blobs likely correspond to sub-regions of quasi-circular, not of linear polymers. However, the results for linear active polymers are qualitatively transferable to circular ones 37 , strengthening the hypothesis that blobs could correspond to loops or sub-TADs 21 .…”

“…Rather expectedly, simulations and analytical approaches of active semiflexible polymers reveal that the diffusion of active polymers is enhanced compared to their passive counterpart 33–37 . The scaling behavior of the mean square displacement transits from a ballistic motion at very short time scales due to the particle propulsion to a subdiffusive regime at intermediate times and a diffusive regime at long time scales 38 (Figure 5B).…”

Dynamics as a cause for the nanoscale organization of the genome

“…the time needed to recover to the initial conditions after applied stress, decreases with increasing activity [36]. In line with this observation, an active polymer also exhibits enhanced conformational fluctuations [40] and appears more flexible. In particular, the effective persistence length (the length over which a polymer is approximately stiff) of active polymers is decreased compared to their passive counterparts as a consequence of hairpin-formation [37].…”

“…However, it is also likely that such circular structures would form in a highly dynamic and transient manner, as largely demonstrated for TADs, for instance, using a variety of techniques [4,51]. The results for linear active polymers are qualitatively transferable to circular ones [40], strengthening the hypothesis that blobs could correspond to loops or sub-TADs [24].…”