How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: An entropic stochastic resonance

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations

Scaling theory of driven polymer translocation

We present a theoretical argument to derive a scaling law between the mean translocation time $\tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between $\tau$ and $N$ is retained even in this case.Comment: 5 pages, 4 figure

Polymer Release out of a Spherical Vesicle through a Pore

Translocation of a polymer out of curved surface or membrane is studied via mean first passage time approach. Membrane curvature gives rise to a constraint on polymer conformation, which effectively drives the polymer to the outside of membrane where the available volume of polymer conformational fluctuation is larger. Considering a polymer release out of spherical vesicle, polymer translocation time $\tau$ is changed to the scaling behavior $\tau\sim L^2$ for $R<R_G$, from $\tau\sim L^3$ for $R\gg R_G$, where $L$ is the polymer contour length and $R$, $R_G$ are vesicle radius and polymer radius of gyration respectively. Also the polymer capture into a spherical budd is studied and possible apparatus for easy capture is suggested.Comment: 14 pages RevTeX, 6 postscript figures, published in Phys. Rev. E 57, 730 (1998

Effects of static and temporally fluctuating tensions on semiflexible polymer looping

Biopolymer looping is a dynamic process that occurs ubiquitously in cells for gene regulation, protein folding, etc. In cellular environments, biopolymers are often subject to tensions which are either static, or temporally fluctuating far away from equilibrium. We study the dynamics of semiflexible polymer looping in the presence of such tensions by using Brownian dynamics simulation combined with an analytical theory. We show a minute tension dramatically changes the looping time, especially for long chains. Considering a dichotomically flipping noise as a simple example of the nonequilibrium tension, we find the phenomenon of resonant activation, where the looping time can be the minimum at an optimal flipping time. We discuss our results in connection with recent experiments.Comment: 7 pages, 8 figures, accepted in the Journal of Chemical Physic

Stochastic Resonance of a Flexible Chain Crossing over a Barrier

We study the stochastic resonance (SR) of a flexible polymer surmounting a bistable-potential barrier. Due to the flexibility that can enhance crossing rate and change chain conformations at the barrier, the SR behaviors manifest many features of an entropic SR of a new kind, such as the power amplification peaks at optimal chain lengths and elastic constants as well as the optimal noise strengths. The pronounced peaks that emerge depending on the chain lengths and conformation states suggest novel means of manipulating biopolymers, such as efficient separation methods, within undulating channels.Comment: 13 pages, 9 figure